science problem and solution

• Science Notes Posts
• Contact Science Notes
• Todd Helmenstine Biography
• Anne Helmenstine Biography
• Free Printable Periodic Tables (PDF and PNG)
• Periodic Table Wallpapers
• Interactive Periodic Table
• Periodic Table Posters
• How to Grow Crystals
• Chemistry Projects
• Fire and Flames Projects
• Holiday Science

Chemistry Problems With Answers

• Physics Problems
• Unit Conversion Example Problems
• Chemistry Worksheets
• Biology Worksheets
• Periodic Table Worksheets
• Physical Science Worksheets
• Science Lab Worksheets
• My Amazon Books

Use chemistry problems as a tool for mastering chemistry concepts. Some of these examples show using formulas while others include lists of examples.

Acids, Bases, and pH Chemistry Problems

Learn about acids and bases. See how to calculate pH, pOH, K a , K b , pK a , and pK b .

• Practice calculating pH.
• Get example pH, pK a , pK b , K a , and K b calculations.
• Get examples of amphoterism.

Atomic Structure Problems

Learn about atomic mass, the Bohr model, and the part of the atom.

• Practice identifying atomic number, mass number, and atomic mass.
• Get examples showing ways to find atomic mass.
• Use Avogadro’s number and find the mass of a single atom .
• Review the Bohr model of the atom.
• Find the number of valence electrons of an element’s atom.

Chemical Bonds

Learn how to use electronegativity to determine whether atoms form ionic or covalent bonds. See chemistry problems drawing Lewis structures.

• Identify ionic and covalent bonds.
• Learn about ionic compounds and get examples.
• Practice identifying ionic compounds.
• Get examples of binary compounds.
• Learn about covalent compounds and their properties.
• See how to assign oxidation numbers.
• Practice drawing Lewis structures.
• Practice calculating bond energy.

Chemical Equations

Practice writing and balancing chemical equations.

• Learn the steps of balancing equations.
• Practice balancing chemical equations (practice quiz).
• Get examples finding theoretical yield.
• Practice calculating percent yield.
• Learn to recognize decomposition reactions.
• Practice recognizing synthesis reactions.
• Practice recognizing single replacement reactions.
• Recognize double replacement reactions.
• Find the mole ratio between chemical species in an equation.

Concentration and Solutions

Learn how to calculate concentration and explore chemistry problems that affect chemical concentration, including freezing point depression, boiling point elevation, and vapor pressure elevation.

• Get example concentration calculations in several units.
• Practice calculating normality (N).
• Practice calculating molality (m).
• Explore example molarity (M) calculations.
• Get examples of colligative properties of solutions.
• See the definition and examples of saturated solutions.
• See the definition and examples of unsaturated solutions.
• Get examples of miscible and immiscible liquids.

Error Calculations

Learn about the types of error and see worked chemistry example problems.

• See how to calculate percent.
• Practice absolute and relative error calculations.
• See how to calculate percent error.
• See how to find standard deviation.
• Calculate mean, median, and mode.
• Review the difference between accuracy and precision.

Equilibrium Chemistry Problems

Learn about Le Chatelier’s principle, reaction rates, and equilibrium.

• Solve activation energy chemistry problems.
• Review factors that affect reaction rate.
• Practice calculating the van’t Hoff factor.

Practice chemistry problems using the gas laws, including Raoult’s law, Graham’s law, Boyle’s law, Charles’ law, and Dalton’s law of partial pressures.

• Calculate vapor pressure.
• Solve Avogadro’s law problems.
• Practice Boyle’s law problems.
• See Charles’ law example problems.
• Solve combined gas law problems.
• Solve Gay-Lussac’s law problems.

Some chemistry problems ask you identify examples of states of matter and types of mixtures. While there are any chemical formulas to know, it’s still nice to have lists of examples.

• Practice density calculations.
• Identify intensive and extensive properties of matter.
• See examples of intrinsic and extrinsic properties of matter.
• Get the definition and examples of solids.
• Get the definition and examples of gases.
• See the definition and examples of liquids.
• Learn what melting point is and get a list of values for different substances.
• Get the azeotrope definition and see examples.
• See how to calculate specific volume of a gas.
• Get examples of physical properties of matter.
• Get examples of chemical properties of matter.
• Review the states of matter.

Molecular Structure Chemistry Problems

See chemistry problems writing chemical formulas. See examples of monatomic and diatomic elements.

• Practice empirical and molecular formula problems.
• Practice simplest formula problems.
• See how to calculate molecular mass.
• Get examples of the monatomic elements.
• See examples of binary compounds.
• Calculate the number of atoms and molecules in a drop of water.

Nomenclature

Practice chemistry problems naming ionic compounds, hydrocarbons, and covalent compounds.

• Practice naming covalent compounds.
• Learn hydrocarbon prefixes in organic chemistry.

Nuclear Chemistry

These chemistry problems involve isotopes, nuclear symbols, half-life, radioactive decay, fission, fusion.

• Review the types of radioactive decay.

Periodic Table

Learn how to use a periodic table and explore periodic table trends.

• Know the trends in the periodic table.
• Review how to use a periodic table.
• Explore the difference between atomic and ionic radius and see their trends on the periodic table.

Physical Chemistry

Explore thermochemistry and physical chemistry, including enthalpy, entropy, heat of fusion, and heat of vaporization.

• Practice heat of vaporization chemistry problems.
• Practice heat of fusion chemistry problems.
• Calculate heat required to turn ice into steam.
• Practice calculating specific heat.
• Get examples of potential energy.
• Get examples of kinetic energy.
• See example activation energy calculations.

Spectroscopy and Quantum Chemistry Problems

See chemistry problems involving the interaction between light and matter.

• Calculate wavelength from frequency or frequency from wavelength.

Stoichiometry Chemistry Problems

Practice chemistry problems balancing formulas for mass and charge. Learn about reactants and products.

• Get example mole ratio problems.
• Calculate percent yield.
• Learn how to assign oxidation numbers.
• Get the definition and examples of reactants in chemistry.
• Get the definition and examples of products in chemical reactions.

Unit Conversions

There are some many examples of unit conversions that they have their own separate page!

Physics Problems with Solutions

Physics problems with detailed solutions and explanations.

Physics problems with detailed solutions and thorough explanations are presented. Also physics formulas are included.

• Electrostatic Problems with Solutions and Explanations.
• Gravity Problems with Solutions and Explanations
• Projectile Problems with Solutions and Explanations
• Velocity and Speed: Problems
• Uniform Acceleration Motion: Problems
• Free Physics SAT and AP Practice Tests Questions .

Physics Formulas and Constants

• Physics Formulas Reference
• SI Prefixes Used with Units in Physics, Chemistry and Engineering
• Constants in Physics, Chemistry and Engineering

Popular Pages

• Privacy Policy

Filed under:

The 7 biggest problems facing science, according to 270 scientists

Share this story.

• Share this on Facebook
• Share this on Twitter
• Share this on Reddit
• Share All sharing options

Share All sharing options for: The 7 biggest problems facing science, according to 270 scientists

"Science, I had come to learn, is as political, competitive, and fierce a career as you can find, full of the temptation to find easy paths." — Paul Kalanithi, neurosurgeon and writer (1977–2015)

Science is in big trouble. Or so we’re told.

In the past several years, many scientists have become afflicted with a serious case of doubt — doubt in the very institution of science.

Explore the biggest challenges facing science, and how we can fix them:

• Academia has a huge money problem
• Too many studies are poorly designed
• Replicating results is crucial — and rare
• Peer review is broken
• Too much science is locked behind paywalls
• Science is poorly communicated
• Life as a young academic is incredibly stressful

Conclusion:

• Science is not doomed

As reporters covering medicine, psychology, climate change, and other areas of research, we wanted to understand this epidemic of doubt. So we sent scientists a survey asking this simple question: If you could change one thing about how science works today, what would it be and why?

We heard back from 270 scientists all over the world, including graduate students, senior professors, laboratory heads, and Fields Medalists . They told us that, in a variety of ways, their careers are being hijacked by perverse incentives. The result is bad science.

The scientific process, in its ideal form, is elegant: Ask a question, set up an objective test, and get an answer. Repeat. Science is rarely practiced to that ideal. But Copernicus believed in that ideal. So did the rocket scientists behind the moon landing.

But nowadays, our respondents told us, the process is riddled with conflict. Scientists say they’re forced to prioritize self-preservation over pursuing the best questions and uncovering meaningful truths.

"I feel torn between asking questions that I know will lead to statistical significance and asking questions that matter," says Kathryn Bradshaw, a 27-year-old graduate student of counseling at the University of North Dakota.

Today, scientists' success often isn't measured by the quality of their questions or the rigor of their methods. It's instead measured by how much grant money they win, the number of studies they publish, and how they spin their findings to appeal to the public.

Scientists often learn more from studies that fail. But failed studies can mean career death. So instead, they’re incentivized to generate positive results they can publish. And the phrase "publish or perish" hangs over nearly every decision. It’s a nagging whisper, like a Jedi’s path to the dark side.

"Over time the most successful people will be those who can best exploit the system," Paul Smaldino, a cognitive science professor at University of California Merced, says.

To Smaldino, the selection pressures in science have favored less-than-ideal research: "As long as things like publication quantity, and publishing flashy results in fancy journals are incentivized, and people who can do that are rewarded … they’ll be successful, and pass on their successful methods to others."

Many scientists have had enough.  They want to break this cycle of perverse incentives and rewards. They are going through a period of introspection, hopeful that the end result will yield stronger scientific institutions . In our survey and interviews, they offered a wide variety of ideas for improving the scientific process and bringing it closer to its ideal form.

Before we jump in, some caveats to keep in mind: Our survey was not a scientific poll. For one, the respondents disproportionately hailed from the biomedical and social sciences and English-speaking communities.

Many of the responses did, however, vividly illustrate the challenges and perverse incentives that scientists across fields face. And they are a valuable starting point for a deeper look at dysfunction in science today.

The place to begin is right where the perverse incentives first start to creep in: the money.

(1) Academia has a huge money problem

To do most any kind of research, scientists need money: to run studies, to subsidize lab equipment, to pay their assistants and even their own salaries. Our respondents told us that getting — and sustaining — that funding is a perennial obstacle.

Their gripe isn’t just with the quantity, which, in many fields, is shrinking. It’s the way money is handed out that puts pressure on labs to publish a lot of papers, breeds conflicts of interest, and encourages scientists to overhype their work.

In the United States, academic researchers in the sciences generally cannot rely on university funding alone to pay for their salaries, assistants, and lab costs. Instead, they have to seek outside grants. "In many cases the expectations were and often still are that faculty should cover at least 75 percent of the salary on grants," writes John Chatham, a professor of medicine studying cardiovascular disease at University of Alabama at Birmingham.

Grants also usually expire after three or so years, which pushes scientists away from long-term projects. Yet as John Pooley, a neurobiology postdoc at the University of Bristol, points out, the biggest discoveries usually take decades to uncover and are unlikely to occur under short-term funding schemes.

Outside grants are also in increasingly short supply. In the US, the largest source of funding is the federal government, and that pool of money has been plateauing for years, while young scientists enter the workforce at a faster rate than older scientists retire.

Take the National Institutes of Health, a major funding source. Its budget rose at a fast clip through the 1990s, stalled in the 2000s, and then dipped with sequestration budget cuts in 2013. All the while, rising costs for conducting science meant that each NIH dollar purchased less and less. Last year, Congress approved the biggest NIH spending hike in a decade . But it won’t erase the shortfall.

The consequences are striking: In 2000, more than 30 percent of NIH grant applications got approved. Today, it’s closer to 17 percent. "It's because of what's happened in the last 12 years that young scientists in particular are feeling such a squeeze," NIH Director Francis Collins said at the Milken Global Conference in May.

Truly novel research takes longer to produce, and it doesn’t always pay off. A National Bureau of Economic Research working paper found that, on the whole, truly unconventional papers tend to be less consistently cited in the literature. So scientists and funders increasingly shy away from them, preferring short-turnaround, safer papers. But everyone suffers from that: the NBER report found that novel papers also occasionally lead to big hits that inspire high-impact, follow-up studies.

"I think because you have to publish to keep your job and keep funding agencies happy, there are a lot of (mediocre) scientific papers out there ... with not much new science presented," writes Kaitlyn Suski, a chemistry and atmospheric science postdoc at Colorado State University.

Another worry: When independent, government, or university funding sources dry up, scientists may feel compelled to turn to industry or interest groups eager to generate studies to support their agendas.

Finally, all of this grant writing is a huge time suck, taking resources away from the actual scientific work. Tyler Josephson, an engineering graduate student at the University of Delaware, writes that many professors he knows spend 50 percent of their time writing grant proposals. "Imagine," he asks, "what they could do with more time to devote to teaching and research?"

It’s easy to see how these problems in funding kick off a vicious cycle. To be more competitive for grants, scientists have to have published work. To have published work, they need positive (i.e.,  statistically significant ) results. That puts pressure on scientists to pick "safe" topics that will yield a publishable conclusion — or, worse, may bias their research toward significant results.

"When funding and pay structures are stacked against academic scientists," writes Alison Bernstein, a neuroscience postdoc at Emory University, "these problems are all exacerbated."

Fixes for science's funding woes

Right now there are arguably too many researchers chasing too few grants. Or, as a 2014 piece in the Proceedings of the National Academy of Sciences put it: "The current system is in perpetual disequilibrium, because it will inevitably generate an ever-increasing supply of scientists vying for a finite set of research resources and employment opportunities."

"As it stands, too much of the research funding is going to too few of the researchers," writes Gordon Pennycook, a PhD candidate in cognitive psychology at the University of Waterloo. "This creates a culture that rewards fast, sexy (and probably wrong) results."

One straightforward way to ameliorate these problems would be for governments to simply increase the amount of money available for science. (Or, more controversially, decrease the number of PhDs, but we’ll get to that later.) If Congress boosted funding for the NIH and National Science Foundation, that would take some of the competitive pressure off researchers.

But that only goes so far. Funding will always be finite, and researchers will never get blank checks to fund the risky science projects of their dreams. So other reforms will also prove necessary.

One suggestion: Bring more stability and predictability into the funding process. "The NIH and NSF budgets are subject to changing congressional whims that make it impossible for agencies (and researchers) to make long term plans and commitments," M. Paul Murphy, a neurobiology professor at the University of Kentucky, writes. "The obvious solution is to simply make [scientific funding] a stable program, with an annual rate of increase tied in some manner to inflation."

Another idea would be to change how grants are awarded: Foundations and agencies could fund specific people and labs for a period of time rather than individual project proposals. (The Howard Hughes Medical Institute already does this.) A system like this would give scientists greater freedom to take risks with their work.

Alternatively, researchers in the journal mBio recently called for a lottery-style system. Proposals would be measured on their merits, but then a computer would randomly choose which get funded.

"Although we recognize that some scientists will cringe at the thought of allocating funds by lottery," the authors of the mBio piece write, "the available evidence suggests that the system is already in essence a lottery without the benefits of being random." Pure randomness would at least reduce some of the perverse incentives at play in jockeying for money.

There are also some ideas out there to minimize conflicts of interest from industry funding. Recently, in PLOS Medicine , Stanford epidemiologist John Ioannidis suggested that pharmaceutical companies ought to pool the money they use to fund drug research, to be allocated to scientists who then have no exchange with industry during study design and execution. This way, scientists could still get funding for work crucial for drug approvals — but without the pressures that can skew results.

These solutions are by no means complete, and they may not make sense for every scientific discipline. The daily incentives facing biomedical scientists to bring new drugs to market are different from the incentives facing geologists trying to map out new rock layers. But based on our survey, funding appears to be at the root of many of the problems facing scientists, and it’s one that deserves more careful discussion.

(2) Too many studies are poorly designed. Blame bad incentives.

Scientists are ultimately judged by the research they publish. And the pressure to publish pushes scientists to come up with splashy results, of the sort that get them into prestigious journals. "Exciting, novel results are more publishable than other kinds," says Brian Nosek , who co-founded the Center for Open Science at the University of Virginia.

The problem here is that truly groundbreaking findings simply don’t occur very often, which means scientists face pressure to game their studies so they turn out to be a little more "revolutionary." (Caveat: Many of the respondents who focused on this particular issue hailed from the biomedical and social sciences.)

Some of this bias can creep into decisions that are made early on: choosing whether or not to randomize participants, including a control group for comparison, or controlling for certain confounding factors but not others. (Read more on study design particulars  here .)

Many of our survey respondents noted that perverse incentives can also push scientists to cut corners in how they analyze their data.

"I have incredible amounts of stress that maybe once I finish analyzing the data, it will not look significant enough for me to defend," writes Jess Kautz, a PhD student at the University of Arizona. "And if I get back mediocre results, there's going to be incredible pressure to present it as a good result so they can get me out the door. At this moment, with all this in my mind, it is making me wonder whether I could give an intellectually honest assessment of my own work."

Increasingly, meta-researchers (who conduct research on research) are realizing that scientists often do find little ways to hype up their own results — and they’re not always doing it consciously. Among the most famous examples is a technique called "p-hacking," in which researchers test their data against many hypotheses and only report those that have statistically significant results.

In a recent study , which tracked the misuse of p-values in biomedical journals, meta-researchers found "an epidemic" of statistical significance: 96 percent of the papers that included a p-value in their abstracts boasted statistically significant results.

That seems awfully suspicious. It suggests the biomedical community has been chasing statistical significance, potentially giving dubious results the appearance of validity through techniques like p-hacking — or simply suppressing important results that don't look significant enough. Fewer studies share effect sizes (which arguably gives a better indication of how meaningful a result might be) or discuss measures of uncertainty.

"The current system has done too much to reward results," says Joseph Hilgard, a postdoctoral research fellow at the Annenberg Public Policy Center. "This causes a conflict of interest: The scientist is in charge of evaluating the hypothesis, but the scientist also desperately wants the hypothesis to be true."

The consequences are staggering. An estimated $200 billion — or the equivalent of 85 percent of global spending on research — is routinely wasted on poorly designed and redundant studies, according to meta-researchers who have analyzed inefficiencies in research. We know that as much as 30 percent of the most influential original medical research papers later turn out to be wrong or exaggerated.

Fixes for poor study design

Our respondents suggested that the two key ways to encourage stronger study design — and discourage positive results chasing — would involve rethinking the rewards system and building more transparency into the research process.

"I would make rewards based on the rigor of the research methods, rather than the outcome of the research," writes Simine Vazire, a journal editor and a social psychology professor at UC Davis. "Grants, publications, jobs, awards, and even media coverage should be based more on how good the study design and methods were, rather than whether the result was significant or surprising."

Likewise, Cambridge mathematician Tim Gowers argues that researchers should get recognition for advancing science broadly through informal idea sharing — rather than only getting credit for what they publish.

"We’ve gotten used to working away in private and then producing a sort of polished document in the form of a journal article," Gowers said. "This tends to hide a lot of the thought process that went into making the discoveries. I'd like attitudes to change so people focus less on the race to be first to prove a particular theorem, or in science to make a particular discovery, and more on other ways of contributing to the furthering of the subject."

When it comes to published results, meanwhile, many of our respondents wanted to see more journals put a greater emphasis on rigorous methods and processes rather than splashy results.

"I think the one thing that would have the biggest impact is removing publication bias: judging papers by the quality of questions, quality of method, and soundness of analyses, but not on the results themselves," writes Michael Inzlicht , a University of Toronto psychology and neuroscience professor.

Some journals are already embracing this sort of research. PLOS One , for example, makes a point of accepting negative studies (in which a scientist conducts a careful experiment and finds nothing) for publication, as does the aptly named Journal of Negative Results in Biomedicine .

More transparency would also help, writes Daniel Simons, a professor of psychology at the University of Illinois. Here’s one example: ClinicalTrials.gov , a site run by the NIH, allows researchers to register their study design and methods ahead of time and then publicly record their progress. That makes it more difficult for scientists to hide experiments that didn’t produce the results they wanted. (The site now holds information for more than 180,000 studies in 180 countries.)

Similarly, the AllTrials campaign is pushing for every clinical trial (past, present, and future) around the world to be registered, with the full methods and results reported. Some drug companies and universities have created portals that allow researchers to access raw data from their trials.

The key is for this sort of transparency to become the norm rather than a laudable outlier.

(3) Replicating results is crucial. But scientists rarely do it.

Replication is another foundational concept in science. Researchers take an older study that they want to test and then try to reproduce it to see if the findings hold up.

Testing, validating, retesting — it's all part of a slow and grinding process to arrive at some semblance of scientific truth. But this doesn't happen as often as it should, our respondents said. Scientists face few incentives to engage in the slog of replication. And even when they attempt to replicate a study, they often find they can’t do so . Increasingly it’s being called a "crisis of irreproducibility."

The stats bear this out: A 2015 study looked at 83 highly cited studies that claimed to feature effective psychiatric treatments. Only 16 had ever been successfully replicated. Another 16 were contradicted by follow-up attempts, and 11 were found to have substantially smaller effects the second time around. Meanwhile, nearly half of the studies (40) had never been subject to replication at all.

More recently, a landmark study published in the journal Science demonstrated that only a fraction of recent findings in top psychology journals could be replicated. This is happening in other fields too, says Ivan Oransky, one of the founders of the blog Retraction Watch , which tracks scientific retractions.

As for the underlying causes, our survey respondents pointed to a couple of problems. First, scientists have very few incentives to even try replication. Jon-Patrick Allem, a social scientist at the Keck School of Medicine of USC, noted that funding agencies prefer to support projects that find new information instead of confirming old results.

Journals are also reluctant to publish replication studies unless "they contradict earlier findings or conclusions," Allem writes. The result is to discourage scientists from checking each other's work. "Novel information trumps stronger evidence, which sets the parameters for working scientists."

The second problem is that many studies can be difficult to replicate. Sometimes their methods are too opaque. Sometimes the original studies had too few participants to produce a replicable answer. And sometimes, as we saw in the previous section, the study is simply poorly designed or outright wrong.

Again, this goes back to incentives: When researchers have to publish frequently and chase positive results, there’s less time to conduct high-quality studies with well-articulated methods.

Fixes for underreplication

Scientists need more carrots to entice them to pursue replication in the first place. As it stands, researchers are encouraged to publish new and positive results and to allow negative results to linger in their laptops or file drawers.

This has plagued science with a problem called "publication bias" — not all studies that are conducted actually get published in journals, and the ones that do tend to have positive and dramatic conclusions.

If institutions started to reward tenure positions or make hires based on the quality of a researcher’s body of work, instead of quantity, this might encourage more replication and discourage positive results chasing.

"The key that needs to change is performance review," writes Christopher Wynder, a former assistant professor at McMaster University. "It affects reproducibility because there is little value in confirming another lab's results and trying to publish the findings."

The next step would be to make replication of studies easier. This could include more robust sharing of methods in published research papers. "It would be great to have stronger norms about being more detailed with the methods," says University of Virginia’s Brian Nosek.

He also suggested more regularly adding supplements at the end of papers that get into the procedural nitty-gritty, to help anyone wanting to repeat an experiment.  "If I can rapidly get up to speed, I have a much better chance of approximating the results," he said.

Nosek has detailed other potential fixes that might help with replication — all part of his work at the Center for Open Science .

A greater degree of transparency and data sharing would enable replications, said Stanford’s John Ioannidis. Too often, anyone trying to replicate a study must chase down the original investigators for details about how the experiment was conducted.

"It is better to do this in an organized fashion with buy-in from all leading investigators in a scientific discipline," he explained, "rather than have to try to find the investigator in each case and ask him or her in detective-work fashion about details, data, and methods that are otherwise unavailable."

Researchers could also make use of new tools , such as open source software that tracks every version of a data set, so that they can share their data more easily and have transparency built into their workflow.

Some of our respondents suggested that scientists engage in replication prior to publication. "Before you put an exploratory idea out in the literature and have people take the time to read it, you owe it to the field to try to replicate your own findings," says John Sakaluk, a social psychologist at the University of Victoria.

For example, he has argued, psychologists could conduct small experiments with a handful of participants to form ideas and generate hypotheses. But they would then need to conduct bigger experiments, with more participants, to replicate and confirm those hypotheses before releasing them into the world. "In doing so,"  Sakaluk says, "the rest of us can have more confidence that this is something we might want to [incorporate] into our own research."

(4) Peer review is broken

Peer review is meant to weed out junk science before it reaches publication. Yet over and over again in our survey, respondents told us this process fails. It was one of the parts of the scientific machinery to elicit the most rage among the researchers we heard from.

Normally, peer review works like this: A researcher submits an article for publication in a journal. If the journal accepts the article for review, it's sent off to peers in the same field for constructive criticism and eventual publication — or rejection. (The level of anonymity varies; some journals have double-blind reviews, while others have moved to triple-blind review, where the authors, editors, and reviewers don’t know who one another are.)

It sounds like a reasonable system. But numerous studies and systematic reviews have shown that peer review doesn’t reliably prevent poor-quality science from being published.

The process frequently fails to detect fraud or other problems with manuscripts, which isn't all that surprising when you consider researchers aren't paid or otherwise rewarded for the time they spend reviewing manuscripts. They do it out of a sense of duty — to contribute to their area of research and help advance science.

But this means it's not always easy to find the best people to peer-review manuscripts in their field, that harried researchers delay doing the work (leading to publication delays of up to two years), and that when they finally do sit down to peer-review an article they might be rushed and miss errors in studies.

"The issue is that most referees simply don't review papers carefully enough, which results in the publishing of incorrect papers, papers with gaps, and simply unreadable papers," says Joel Fish, an assistant professor of mathematics at the University of Massachusetts Boston. "This ends up being a large problem for younger researchers to enter the field, since that means they have to ask around to figure out which papers are solid and which are not."

That's not to mention the problem of peer review bullying. Since the default in the process is that editors and peer reviewers know who the authors are (but authors don’t know who the reviews are), biases against researchers or institutions can creep in, opening the opportunity for rude, rushed, and otherwise unhelpful comments. (Just check out the popular #SixWordPeerReview hashtag on Twitter).

These issues were not lost on our survey respondents, who said peer review amounts to a broken system, which punishes scientists and diminishes the quality of publications. They want to not only overhaul the peer review process but also change how it's conceptualized.

Fixes for peer review

On the question of editorial bias and transparency, our respondents were surprisingly divided. Several suggested that all journals should move toward double-blinded peer review, whereby reviewers can't see the names or affiliations of the person they're reviewing and publication authors don't know who reviewed them. The main goal here was to reduce bias.

"We know that scientists make biased decisions based on unconscious stereotyping," writes Pacific Northwest National Lab postdoc Timothy Duignan. "So rather than judging a paper by the gender, ethnicity, country, or institutional status of an author — which I believe happens a lot at the moment — it should be judged by its quality independent of those things."

Yet others thought that more transparency, rather than less, was the answer: "While we correctly advocate for the highest level of transparency in publishing, we still have most reviews that are blinded, and I cannot know who is reviewing me," writes Lamberto Manzoli, a professor of epidemiology and public health at the University of Chieti, in Italy. "Too many times we see very low quality reviews, and we cannot understand whether it is a problem of scarce knowledge or conflict of interest."

Perhaps there is a middle ground. For example,  e Life , a new  open access journal that is rapidly rising in impact factor, runs a collaborative peer review process. Editors and peer reviewers work together on each submission to create a consolidated list of comments about a paper. The author can then reply to what the group saw as the most important issues, rather than facing the biases and whims of individual reviewers. (Oddly, this process is faster — eLife takes less time to accept papers than Nature or Cell.)

Still, those are mostly incremental fixes. Other respondents argued that we might need to radically rethink the entire process of peer review from the ground up.

"The current peer review process embraces a concept that a paper is final," says Nosek. "The review process is [a form of] certification, and that a paper is done." But science doesn't work that way. Science is an evolving process, and truth is provisional. So, Nosek said, science must "move away from the embrace of definitiveness of publication."

Some respondents wanted to think of peer review as more of a continuous process, in which studies are repeatedly and transparently updated and republished as new feedback changes them — much like Wikipedia entries. This would require some sort of expert crowdsourcing.

"The scientific publishing field — particularly in the biological sciences — acts like there is no internet," says Lakshmi Jayashankar, a senior scientific reviewer with the federal government. "The paper peer review takes forever, and this hurts the scientists who are trying to put their results quickly into the public domain."

One possible model already exists in mathematics and physics, where there is a long tradition of "pre-printing" articles. Studies are posted on an open website called  arXiv.org , often before being peer-reviewed and published in journals. There, the articles are sorted and commented on by a community of moderators, providing another chance to filter problems before they make it to peer review.

"Posting preprints would allow scientific crowdsourcing to increase the number of errors that are caught, since traditional peer-reviewers cannot be expected to be experts in every sub-discipline," writes Scott Hartman, a paleobiology PhD student at the University of Wisconsin.

And even after an article is published, researchers think the peer review process shouldn't stop. They want to see more "post-publication" peer review on the web, so that academics can critique and comment on articles after they've been published. Sites like PubPeer and F1000Research have already popped up to facilitate that kind of post-publication feedback.

"We do this a couple of times a year at conferences," writes Becky Clarkson, a geriatric medicine researcher at the University of Pittsburgh. "We could do this every day on the internet."

The bottom line is that traditional peer review has never worked as well as we imagine it to — and it’s ripe for serious disruption.

(5) Too much science is locked behind paywalls

After a study has been funded, conducted, and peer-reviewed, there's still the question of getting it out so that others can read and understand its results.

Over and over, our respondents expressed dissatisfaction with how scientific research gets disseminated. Too much is locked away in paywalled journals, difficult and costly to access, they said. Some respondents also criticized the publication process itself for being too slow, bogging down the pace of research.

On the access question, a number of scientists argued that academic research should be free for all to read. They chafed against the current model, in which for-profit publishers put journals behind pricey paywalls.

A single article in Science will set you back $30; a year-long subscription to Cell will cost $279. Elsevier publishes 2,000 journals that can cost up to $10,000 or $20,000 a year for a subscription.

Many US institutions pay those journal fees for their employees, but not all scientists (or other curious readers) are so lucky. In a recent issue of Science , journalist John Bohannon described the plight of a PhD candidate at a top university in Iran. He calculated that the student would have to spend $1,000 a week just to read the papers he needed.

As Michael Eisen, a biologist at UC Berkeley and co-founder of the Public Library of Science (or PLOS ) , put it , scientific journals are trying to hold on to the profits of the print era in the age of the internet.  Subscription prices have continued to climb, as a handful of big publishers (like Elsevier) have bought up more and more journals, creating mini knowledge fiefdoms.

"Large, publicly owned publishing companies make huge profits off of scientists by publishing our science and then selling it back to the university libraries at a massive profit (which primarily benefits stockholders)," Corina Logan, an animal behavior researcher at the University of Cambridge, noted. "It is not in the best interest of the society, the scientists, the public, or the research." (In 2014, Elsevier reported a profit margin of nearly 40 percent and revenues close to $3 billion.)

"It seems wrong to me that taxpayers pay for research at government labs and universities but do not usually have access to the results of these studies, since they are behind paywalls of peer-reviewed journals," added Melinda Simon, a postdoc microfluidics researcher at Lawrence Livermore National Lab.

Fixes for closed science

Many of our respondents urged their peers to publish in open access journals (along the lines of PeerJ or PLOS Biology ). But there’s an inherent tension here. Career advancement can often depend on publishing in the most prestigious journals, like Science or Nature , which still have paywalls.

There's also the question of how best to finance a wholesale transition to open access. After all, journals can never be entirely free. Someone has to pay for the editorial staff, maintaining the website, and so on. Right now, open access journals typically charge fees to those submitting papers, putting the burden on scientists who are already struggling for funding.

One radical step would be to abolish for-profit publishers altogether and move toward a nonprofit model. "For journals I could imagine that scientific associations run those themselves," suggested Johannes Breuer, a postdoctoral researcher in media psychology at the University of Cologne. "If they go for online only, the costs for web hosting, copy-editing, and advertising (if needed) can be easily paid out of membership fees."

As a model, Cambridge’s Tim Gowers has launched an online mathematics journal called Discrete Analysis . The nonprofit venture is owned and published by a team of scholars, it has no publisher middlemen, and access will be completely free for all.

Until wholesale reform happens, however, many scientists are going a much simpler route: illegally pirating papers.

Bohannon reported that millions of researchers around the world now use Sci-Hub , a site set up by Alexandra Elbakyan, a Russia-based neuroscientist, that illegally hosts more than 50 million academic papers. "As a devout pirate," Elbakyan told us, "I think that copyright should be abolished."

One respondent had an even more radical suggestion: that we abolish the existing peer-reviewed journal system altogether and simply publish everything online as soon as it’s done.

"Research should be made available online immediately, and be judged by peers online rather than having to go through the whole formatting, submitting, reviewing, rewriting, reformatting, resubmitting, etc etc etc that can takes years," writes Bruno Dagnino, formerly of the Netherlands Institute for Neuroscience. "One format, one platform. Judge by the whole community, with no delays."

A few scientists have been taking steps in this direction. Rachel Harding, a genetic researcher at the University of Toronto, has set up a website called Lab Scribbles , where she publishes her lab notes on the structure of huntingtin proteins in real time, posting data as well as summaries of her breakthroughs and failures. The idea is to help share information with other researchers working on similar issues, so that labs can avoid needless overlap and learn from each other's mistakes.

Not everyone might agree with approaches this radical; critics worry that too much sharing might encourage scientific free riding. Still, the common theme in our survey was transparency. Science is currently too opaque, research too difficult to share. That needs to change.

(6) Science is poorly communicated to the public

"If I could change one thing about science, I would change the way it is communicated to the public by scientists, by journalists, and by celebrities," writes Clare Malone, a postdoctoral researcher in a cancer genetics lab at Brigham and Women's Hospital.

She wasn't alone. Quite a few respondents in our survey expressed frustration at how science gets relayed to the public. They were distressed by the fact that so many laypeople hold on to completely unscientific ideas or have a crude view of how science works.

They have a point. Science journalism is often full of exaggerated, conflicting, or outright misleading claims. If you ever want to see a perfect example of this, check out "Kill or Cure," a site where Paul Battley meticulously documents all the times the Daily Mail reported that various items — from antacids to yogurt — either cause cancer, prevent cancer, or sometimes do both.

Sometimes bad stories are peddled by university press shops. In 2015, the University of Maryland issued a press release claiming that a single brand of chocolate milk could improve concussion recovery. It was an absurd case of science hype.

Indeed, one review in BMJ found that one-third of university press releases contained either exaggerated claims of causation (when the study itself only suggested correlation), unwarranted implications about animal studies for people, or unfounded health advice.

But not everyone blamed the media and publicists alone. Other respondents pointed out that scientists themselves often oversell their work, even if it's preliminary, because funding is competitive and everyone wants to portray their work as big and important and game-changing.

"You have this toxic dynamic where journalists and scientists enable each other in a way that massively inflates the certainty and generality of how scientific findings are communicated and the promises that are made to the public," writes Daniel Molden, an associate professor of psychology at Northwestern University. "When these findings prove to be less certain and the promises are not realized, this just further erodes the respect that scientists get and further fuels scientists desire for appreciation."

Fixes for better science communication

Opinions differed on how to improve this sorry state of affairs — some pointed to the media, some to press offices, others to scientists themselves.

Plenty of our respondents wished that more science journalists would move away from hyping single studies. Instead, they said, reporters ought to put new research findings in context, and pay more attention to the rigor of a study's methodology than to the splashiness of the end results.

"On a given subject, there are often dozens of studies that examine the issue," writes Brian Stacy of the US Department of Agriculture. "It is very rare for a single study to conclusively resolve an important research question, but many times the results of a study are reported as if they do."

But it’s not just reporters who will need to shape up. The "toxic dynamic" of journalists, academic press offices, and scientists enabling one another to hype research can be tough to change, and many of our respondents pointed out that there were no easy fixes — though recognition was an important first step.

Some suggested the creation of credible referees that could rigorously distill the strengths and weaknesses of research. (Some variations of this are starting to pop up: The Genetic Expert News Service solicits outside experts to weigh in on big new studies in genetics and biotechnology.) Other respondents suggested that making research free to all might help tamp down media misrepresentations.

Still other respondents noted that scientists themselves should spend more time learning how to communicate with the public — a skill that tends to be under-rewarded in the current system.

"Being able to explain your work to a non-scientific audience is just as important as publishing in a peer-reviewed journal, in my opinion, but currently the incentive structure has no place for engaging the public," writes Crystal Steltenpohl, a graduate assistant at DePaul University.

Reducing the perverse incentives around scientific research itself could also help reduce overhype.  "If we reward research based on how noteworthy the results are, this will create pressure to exaggerate the results (through exploiting flexibility in data analysis, misrepresenting results, or outright fraud)," writes UC Davis's Simine Vazire. "We should reward research based on how rigorous the methods and design are."

Or perhaps we should focus on improving science literacy. Jeremy Johnson, a project coordinator at the Broad Institute, argued that bolstering science education could help ameliorate a lot of these problems. "Science literacy should be a top priority for our educational policy," he said, "not an elective."

(7) Life as a young academic is incredibly stressful

When we asked researchers what they’d fix about science, many talked about the scientific process itself, about study design or peer review. These responses often came from tenured scientists who loved their jobs but wanted to make the broader scientific project even better.

But on the flip side, we heard from a number of researchers — many of them graduate students or postdocs — who were genuinely passionate about research but found the day-to-day experience of being a scientist grueling and unrewarding. Their comments deserve a section of their own.

Today, many tenured scientists and research labs depend on small armies of graduate students and postdoctoral researchers to perform their experiments and conduct data analysis.

These grad students and postdocs are often the primary authors on many studies. In a number of fields, such as the biomedical sciences, a postdoc position is a prerequisite before a researcher can get a faculty-level position at a university.

This entire system sits at the heart of modern-day science. (A new card game called Lab Wars pokes fun at these dynamics.)

But these low-level research jobs can be a grind. Postdocs typically work long hours and are relatively low-paid for their level of education — salaries are frequently pegged to stipends set by NIH National Research Service Award grants, which start at $43,692 and rise to $47,268 in year three.

Postdocs tend to be hired on for one to three years at a time, and in many institutions they are considered contractors, limiting their workplace protections. We heard repeatedly about extremely long hours and limited family leave benefits.

"Oftentimes this is problematic for individuals in their late 20s and early to mid-30s who have PhDs and who may be starting families while also balancing a demanding job that pays poorly," wrote one postdoc, who asked for anonymity.

This lack of flexibility tends to disproportionately affect women — especially women planning to have families — which helps contribute to gender inequalities in research. ( A 2012 paper found that female job applicants in academia are judged more harshly and are offered less money than males.) "There is very little support for female scientists and early-career scientists," noted another postdoc.

"There is very little long-term financial security in today's climate, very little assurance where the next paycheck will come from," wrote William Kenkel, a postdoctoral researcher in neuroendocrinology at Indiana University. "Since receiving my PhD in 2012, I left Chicago and moved to Boston for a post-doc, then in 2015 I left Boston for a second post-doc in Indiana. In a year or two, I will move again for a faculty job, and that's if I'm lucky. Imagine trying to build a life like that."

This strain can also adversely affect the research that young scientists do. "Contracts are too short term," noted another researcher. "It discourages rigorous research as it is difficult to obtain enough results for a paper (and hence progress) in two to three years. The constant stress drives otherwise talented and intelligent people out of science also."

Because universities produce so many PhDs but have way fewer faculty jobs available, many of these postdoc researchers have limited career prospects. Some of them end up staying stuck in postdoc positions for five or 10 years or more.

"In the biomedical sciences," wrote the first postdoc quoted above, "each available faculty position receives applications from hundreds or thousands of applicants, putting immense pressure on postdocs to publish frequently and in high impact journals to be competitive enough to attain those positions."

Many young researchers pointed out that PhD programs do fairly little to train people for careers outside of academia. "Too many [PhD] students are graduating for a limited number of professor positions with minimal training for careers outside of academic research," noted Don Gibson, a PhD candidate studying plant genetics at UC Davis.

Laura Weingartner, a graduate researcher in evolutionary ecology at Indiana University, agreed: "Few universities (specifically the faculty advisors) know how to train students for anything other than academia, which leaves many students hopeless when, inevitably, there are no jobs in academia for them."

Add it up and it's not surprising that we heard plenty of comments about anxiety and depression among both graduate students and postdocs. "There is a high level of depression among PhD students," writes Gibson. "Long hours, limited career prospects, and low wages contribute to this emotion."

A 2015 study at the University of California Berkeley found that 47 percent of PhD students surveyed could be considered depressed. The reasons for this are complex and can't be solved overnight. Pursuing academic research is already an arduous, anxiety-ridden task that's bound to take a toll on mental health.

But as Jennifer Walker explored recently at Quartz, many PhD students also feel isolated and unsupported, exacerbating those issues.

Fixes to keep young scientists in science

We heard plenty of concrete suggestions. Graduate schools could offer more generous family leave policies and child care for graduate students. They could also increase the number of female applicants they accept in order to balance out the gender disparity.

But some respondents also noted that workplace issues for grad students and postdocs were inseparable from some of the fundamental issues facing science that we discussed earlier. The fact that university faculty and research labs face immense pressure to publish — but have limited funding — makes it highly attractive to rely on low-paid postdocs.

"There is little incentive for universities to create jobs for their graduates or to cap the number of PhDs that are produced," writes Weingartner. "Young researchers are highly trained but relatively inexpensive sources of labor for faculty."

Some respondents also pointed to the mismatch between the number of PhDs produced each year and the number of academic jobs available.

A recent feature by Julie Gould in Nature explored a number of ideas for revamping the PhD system. One idea is to split the PhD into two programs: one for vocational careers and one for academic careers. The former would better train and equip graduates to find jobs outside academia.

This is hardly an exhaustive list. The core point underlying all these suggestions, however, was that universities and research labs need to do a better job of supporting the next generation of researchers. Indeed, that's arguably just as important as addressing problems with the scientific process itself. Young scientists, after all, are by definition the future of science.

Weingartner concluded with a sentiment we saw all too frequently: "Many creative, hard-working, and/or underrepresented scientists are edged out of science because of these issues. Not every student or university will have all of these unfortunate experiences, but they’re pretty common. There are a lot of young, disillusioned scientists out there now who are expecting to leave research."

Science needs to correct its greatest weaknesses

Science is not doomed.

For better or worse, it still works. Look no further than the novel vaccines to prevent Ebola, the discovery of gravitational waves , or new treatments for stubborn diseases. And it’s getting better in many ways. See the work of meta -researchers who study and evaluate research — a field that has gained prominence over the past 20 years.

More from this feature

We asked hundreds of scientists what they’d change about science. Here are 33 of our favorite responses.

But science is conducted by fallible humans, and it hasn’t been human-proofed to protect against all our foibles. The scientific revolution began just 500 years ago. Only over the past 100 has science become professionalized. There is still room to figure out how best to remove biases and align incentives.

To that end, here are some broad suggestions:

One: Science has to acknowledge and address its money problem. Science is enormously valuable and deserves ample funding. But the way incentives are set up can distort research.

Right now, small studies with bold results that can be quickly turned around and published in journals are disproportionately rewarded. By contrast, there are fewer incentives to conduct research that tackles important questions with robustly designed studies over long periods of time. Solving this won’t be easy, but it is at the root of many of the issues discussed above.

Two: Science needs to celebrate and reward failure. Accepting that we can learn more from dead ends in research and studies that failed would alleviate the "publish or perish" cycle. It would make scientists more confident in designing robust tests and not just convenient ones, in sharing their data and explaining their failed tests to peers, and in using those null results to form the basis of a career (instead of chasing those all-too-rare breakthroughs).

Three: Science has to be more transparent. Scientists need to publish the methods and findings more fully, and share their raw data in ways that are easily accessible and digestible for those who may want to reanalyze or replicate their findings.

There will always be waste and mediocre research, but as Stanford’s Ioannidis explains in a recent paper , a lack of transparency creates excess waste and diminishes the usefulness of too much research.

Again and again, we also heard from researchers, particularly in social sciences, who felt that their cognitive biases in their own work, influenced by pressures to publish and advance their careers, caused science to go off the rails. If more human-proofing and de-biasing were built into the process — through stronger peer review, cleaner and more consistent funding, and more transparency and data sharing — some of these biases could be mitigated.

These fixes will take time, grinding along incrementally — much like the scientific process itself. But the gains humans have made so far using even imperfect scientific methods would have been unimaginable 500 years ago. The gains from improving the process could prove just as staggering, if not more so.

Correction: An earlier version of this story misstated Noah Grand's title. At the time of the survey he was a lecturer in sociology at UCLA, not a professor.

Will you help keep Vox free for all?

At Vox, we believe that clarity is power, and that power shouldn’t only be available to those who can afford to pay. That’s why we keep our work free. Millions rely on Vox’s clear, high-quality journalism to understand the forces shaping today’s world. Support our mission and help keep Vox free for all by making a financial contribution to Vox today.

We accept credit card, Apple Pay, and Google Pay. You can also contribute via

The total solar eclipse is returning to the United States — better than before

Why did geologists reject the “anthropocene” epoch it’s not rock science., 17 astounding scientific mysteries that researchers can’t yet solve, sign up for the newsletter today, explained, thanks for signing up.

Check your inbox for a welcome email.

Oops. Something went wrong. Please enter a valid email and try again.

If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

To log in and use all the features of Khan Academy, please enable JavaScript in your browser.

Middle school biology - NGSS

Middle school earth and space science - ngss, middle school physics - ngss, high school biology, high school biology - ngss, high school chemistry, high school physics, high school physics - ngss, ap®︎/college biology, ap®︎/college chemistry, ap®︎/college environmental science, ap®︎/college physics 1, ap®︎/college physics 2, organic chemistry, health and medicine, cosmology and astronomy, electrical engineering, biology library, chemistry library, physics library, up class 11 chemistry, up class 12 chemistry, up class 11 physics, a brief introduction to biology, a brief introduction to physics, a brief introduction to chemistry.

An official website of the United States government

The .gov means it’s official. Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

The site is secure. The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

• Publications
• Account settings

Preview improvements coming to the PMC website in October 2024. Learn More or Try it out now .

• Advanced Search
• Journal List

Identifying problems and solutions in scientific text

Kevin heffernan.

Department of Computer Science and Technology, University of Cambridge, 15 JJ Thomson Avenue, Cambridge, CB3 0FD UK

Simone Teufel

Research is often described as a problem-solving activity, and as a result, descriptions of problems and solutions are an essential part of the scientific discourse used to describe research activity. We present an automatic classifier that, given a phrase that may or may not be a description of a scientific problem or a solution, makes a binary decision about problemhood and solutionhood of that phrase. We recast the problem as a supervised machine learning problem, define a set of 15 features correlated with the target categories and use several machine learning algorithms on this task. We also create our own corpus of 2000 positive and negative examples of problems and solutions. We find that we can distinguish problems from non-problems with an accuracy of 82.3%, and solutions from non-solutions with an accuracy of 79.7%. Our three most helpful features for the task are syntactic information (POS tags), document and word embeddings.

Introduction

Problem solving is generally regarded as the most important cognitive activity in everyday and professional contexts (Jonassen 2000 ). Many studies on formalising the cognitive process behind problem-solving exist, for instance (Chandrasekaran 1983 ). Jordan ( 1980 ) argues that we all share knowledge of the thought/action problem-solution process involved in real life, and so our writings will often reflect this order. There is general agreement amongst theorists that state that the nature of the research process can be viewed as a problem-solving activity (Strübing 2007 ; Van Dijk 1980 ; Hutchins 1977 ; Grimes 1975 ).

One of the best-documented problem-solving patterns was established by Winter ( 1968 ). Winter analysed thousands of examples of technical texts, and noted that these texts can largely be described in terms of a four-part pattern consisting of Situation, Problem, Solution and Evaluation. This is very similar to the pattern described by Van Dijk ( 1980 ), which consists of Introduction-Theory, Problem-Experiment-Comment and Conclusion. The difference is that in Winter’s view, a solution only becomes a solution after it has been evaluated positively. Hoey changes Winter’s pattern by introducing the concept of Response in place of Solution (Hoey 2001 ). This seems to describe the situation in science better, where evaluation is mandatory for research solutions to be accepted by the community. In Hoey’s pattern, the Situation (which is generally treated as optional) provides background information; the Problem describes an issue which requires attention; the Response provides a way to deal with the issue, and the Evaluation assesses how effective the response is.

An example of this pattern in the context of the Goldilocks story can be seen in Fig.  1 . In this text, there is a preamble providing the setting of the story (i.e. Goldilocks is lost in the woods), which is called the Situation in Hoey’s system. A Problem in encountered when Goldilocks becomes hungry. Her first Response is to try the porridge in big bear’s bowl, but she gives this a negative Evaluation (“too hot!”) and so the pattern returns to the Problem. This continues in a cyclic fashion until the Problem is finally resolved by Goldilocks giving a particular Response a positive Evaluation of baby bear’s porridge (“it’s just right”).

Example of problem-solving pattern when applied to the Goldilocks story.

Reproduced with permission from Hoey ( 2001 )

It would be attractive to detect problem and solution statements automatically in text. This holds true both from a theoretical and a practical viewpoint. Theoretically, we know that sentiment detection is related to problem-solving activity, because of the perception that “bad” situations are transformed into “better” ones via problem-solving. The exact mechanism of how this can be detected would advance the state of the art in text understanding. In terms of linguistic realisation, problem and solution statements come in many variants and reformulations, often in the form of positive or negated statements about the conditions, results and causes of problem–solution pairs. Detecting and interpreting those would give us a reasonably objective manner to test a system’s understanding capacity. Practically, being able to detect any mention of a problem is a first step towards detecting a paper’s specific research goal. Being able to do this has been a goal for scientific information retrieval for some time, and if successful, it would improve the effectiveness of scientific search immensely. Detecting problem and solution statements of papers would also enable us to compare similar papers and eventually even lead to automatic generation of review articles in a field.

There has been some computational effort on the task of identifying problem-solving patterns in text. However, most of the prior work has not gone beyond the usage of keyword analysis and some simple contextual examination of the pattern. Flowerdew ( 2008 ) presents a corpus-based analysis of lexio-grammatical patterns for problem and solution clauses using articles from professional and student reports. Problem and solution keywords were used to search their corpora, and each occurrence was analysed to determine grammatical usage of the keyword. More interestingly, the causal category associated with each keyword in their context was also analysed. For example, Reason–Result or Means-Purpose were common causal categories found to be associated with problem keywords.

The goal of the work by Scott ( 2001 ) was to determine words which are semantically similar to problem and solution, and to determine how these words are used to signal problem-solution patterns. However, their corpus-based analysis used articles from the Guardian newspaper. Since the domain of newspaper text is very different from that of scientific text, we decided not to consider those keywords associated with problem-solving patterns for use in our work.

Instead of a keyword-based approach, Charles ( 2011 ) used discourse markers to examine how the problem-solution pattern was signalled in text. In particular, they examined how adverbials associated with a result such as “thus, therefore, then, hence” are used to signal a problem-solving pattern.

Problem solving also has been studied in the framework of discourse theories such as Rhetorical Structure Theory (Mann and Thompson 1988 ) and Argumentative Zoning (Teufel et al. 2000 ). Problem- and solutionhood constitute two of the original 23 relations in RST (Mann and Thompson 1988 ). While we concentrate solely on this aspect, RST is a general theory of discourse structure which covers many intentional and informational relations. The relationship to Argumentative Zoning is more complicated. The status of certain statements as problem or solutions is one important dimension in the definitions of AZ categories. AZ additionally models dimensions other than problem-solution hood (such as who a scientific idea belongs to, or which intention the authors might have had in stating a particular negative or positive statement). When forming categories, AZ combines aspects of these dimensions, and “flattens” them out into only 7 categories. In AZ it is crucial who it is that experiences the problems or contributes a solution. For instance, the definition of category “CONTRAST” includes statements that some research runs into problems, but only if that research is previous work (i.e., not if it is the work contributed in the paper itself). Similarly, “BASIS” includes statements of successful problem-solving activities, but only if they are achieved by previous work that the current paper bases itself on. Our definition is simpler in that we are interested only in problem solution structure, not in the other dimensions covered in AZ. Our definition is also more far-reaching than AZ, in that we are interested in all problems mentioned in the text, no matter whose problems they are. Problem-solution recognition can therefore be seen as one aspect of AZ which can be independently modelled as a “service task”. This means that good problem solution structure recognition should theoretically improve AZ recognition.

In this work, we approach the task of identifying problem-solving patterns in scientific text. We choose to use the model of problem-solving described by Hoey ( 2001 ). This pattern comprises four parts: Situation, Problem, Response and Evaluation. The Situation element is considered optional to the pattern, and so our focus centres on the core pattern elements.

Goal statement and task

Many surface features in the text offer themselves up as potential signals for detecting problem-solving patterns in text. However, since Situation is an optional element, we decided to focus on either Problem or Response and Evaluation as signals of the pattern. Moreover, we decide to look for each type in isolation. Our reasons for this are as follows: It is quite rare for an author to introduce a problem without resolving it using some sort of response, and so this is a good starting point in identifying the pattern. There are exceptions to this, as authors will sometimes introduce a problem and then leave it to future work, but overall there should be enough signal in the Problem element to make our method of looking for it in isolation worthwhile. The second signal we look for is the use of Response and Evaluation within the same sentence. Similar to Problem elements, we hypothesise that this formulation is well enough signalled externally to help us in detecting the pattern. For example, consider the following Response and Evaluation: “One solution is to use smoothing”. In this statement, the author is explicitly stating that smoothing is a solution to a problem which must have been mentioned in a prior statement. In scientific text, we often observe that solutions implicitly contain both Response and Evaluation (positive) elements. Therefore, due to these reasons there should be sufficient external signals for the two pattern elements we concentrate on here.

When attempting to find Problem elements in text, we run into the issue that the word “problem” actually has at least two word senses that need to be distinguished. There is a word sense of “problem” that means something which must be undertaken (i.e. task), while another sense is the core sense of the word, something that is problematic and negative. Only the latter sense is aligned with our sense of problemhood. This is because the simple description of a task does not predispose problemhood, just a wish to perform some act. Consider the following examples, where the non-desired word sense is being used:

• “Das and Petrov (2011) also consider the problem of unsupervised bilingual POS induction”. (Chen et al. 2011 ).
• “In this paper, we describe advances on the problem of NER in Arabic Wikipedia”. (Mohit et al. 2012 ).

Here, the author explicitly states that the phrases in orange are problems, they align with our definition of research tasks and not with what we call here ‘problematic problems’. We will now give some examples from our corpus for the desired, core word sense:

• “The major limitation of supervised approaches is that they require annotations for example sentences.” (Poon and Domingos 2009 ).
• “To solve the problem of high dimensionality we use clustering to group the words present in the corpus into much smaller number of clusters”. (Saha et al. 2008 ).

When creating our corpus of positive and negative examples, we took care to select only problem strings that satisfy our definition of problemhood; “ Corpus creation ” section will explain how we did that.

Corpus creation

Our new corpus is a subset of the latest version of the ACL anthology released in March, 2016 1 which contains 22,878 articles in the form of PDFs and OCRed text. 2

The 2016 version was also parsed using ParsCit (Councill et al. 2008 ). ParsCit recognises not only document structure, but also bibliography lists as well as references within running text. A random subset of 2500 papers was collected covering the entire ACL timeline. In order to disregard non-article publications such as introductions to conference proceedings or letters to the editor, only documents containing abstracts were considered. The corpus was preprocessed using tokenisation, lemmatisation and dependency parsing with the Rasp Parser (Briscoe et al. 2006 ).

Definition of ground truth

Our goal was to define a ground truth for problem and solution strings, while covering as wide a range as possible of syntactic variations in which such strings naturally occur. We also want this ground truth to cover phenomena of problem and solution status which are applicable whether or not the problem or solution status is explicitly mentioned in the text.

To simplify the task, we only consider here problem and solution descriptions that are at most one sentence long. In reality, of course, many problem descriptions and solution descriptions go beyond single sentence, and require for instance an entire paragraph. However, we also know that short summaries of problems and solutions are very prevalent in science, and also that these tend to occur in the most prominent places in a paper. This is because scientists are trained to express their contribution and the obstacles possibly hindering their success, in an informative, succinct manner. That is the reason why we can afford to only look for shorter problem and solution descriptions, ignoring those that cross sentence boundaries.

To define our ground truth, we examined the parsed dependencies and looked for a target word (“problem/solution”) in subject position, and then chose its syntactic argument as our candidate problem or solution phrase. To increase the variation, i.e., to find as many different-worded problem and solution descriptions as possible, we additionally used semantically similar words (near-synonyms) of the target words “problem” or “solution” for the search. Semantic similarity was defined as cosine in a deep learning distributional vector space, trained using Word2Vec (Mikolov et al. 2013 ) on 18,753,472 sentences from a biomedical corpus based on all full-text Pubmed articles (McKeown et al. 2016 ). From the 200 words which were semantically closest to “problem”, we manually selected 28 clear synonyms. These are listed in Table  1 . From the 200 semantically closest words to “solution” we similarly chose 19 (Table  2 ). Of the sentences matching our dependency search, a subset of problem and solution candidate sentences were randomly selected.

Selected words for use in problem candidate phrase extraction

Selected words for use in solution candidate phrase extraction

An example of this is shown in Fig.  2 . Here, the target word “drawback” is in subject position (highlighted in red), and its clausal argument (ccomp) is “(that) it achieves low performance” (highlighted in purple). Examples of other arguments we searched for included copula constructions and direct/indirect objects.

Example of our extraction method for problems using dependencies. (Color figure online)

If more than one candidate was found in a sentence, one was chosen at random. Non-grammatical sentences were excluded; these might appear in the corpus as a result of its source being OCRed text.

800 candidates phrases expressing problems and solutions were automatically extracted (1600 total) and then independently checked for correctness by two annotators (the two authors of this paper). Both authors found the task simple and straightforward. Correctness was defined by two criteria:

• An unexplained phenomenon or a problematic state in science; or
• A research question; or
• An artifact that does not fulfil its stated specification.
• The phrase must not lexically give away its status as problem or solution phrase.

The second criterion saves us from machine learning cues that are too obvious. If for instance, the phrase itself contained the words “lack of” or “problematic” or “drawback”, our manual check rejected it, because it would be too easy for the machine learner to learn such cues, at the expense of many other, more generally occurring cues.

Sampling of negative examples

We next needed to find negative examples for both cases. We wanted them not to stand out on the surface as negative examples, so we chose them so as to mimic the obvious characteristics of the positive examples as closely as possible. We call the negative examples ‘non-problems’ and ‘non-solutions’ respectively. We wanted the only differences between problems and non-problems to be of a semantic nature, nothing that could be read off on the surface. We therefore sampled a population of phrases that obey the same statistical distribution as our problem and solution strings while making sure they really are negative examples. We started from sentences not containing any problem/solution words (i.e. those used as target words). From each such sentence, we at random selected one syntactic subtree contained in it. From these, we randomly selected a subset of negative examples of problems and solutions that satisfy the following conditions:

• The distribution of the head POS tags of the negative strings should perfectly match the head POS tags 3 of the positive strings. This has the purpose of achieving the same proportion of surface syntactic constructions as observed in the positive cases.
• The average lengths of the negative strings must be within a tolerance of the average length of their respective positive candidates e.g., non-solutions must have an average length very similar (i.e. + / -  small tolerance) to solutions. We chose a tolerance value of 3 characters.

Again, a human quality check was performed on non-problems and non-solutions. For each candidate non-problem statement, the candidate was accepted if it did not contain a phenomenon, a problematic state, a research question or a non-functioning artefact. If the string expressed a research task, without explicit statement that there was anything problematic about it (i.e., the ‘wrong’ sense of “problem”, as described above), it was allowed as a non-problem. A clause was confirmed as a non-solution if the string did not represent both a response and positive evaluation.

If the annotator found that the sentence had been slightly mis-parsed, but did contain a candidate, they were allowed to move the boundaries for the candidate clause. This resulted in cleaner text, e.g., in the frequent case of coordination, when non-relevant constituents could be removed.

From the set of sentences which passed the quality-test for both independent assessors, 500 instances of positive and negative problems/solutions were randomly chosen (i.e. 2000 instances in total). When checking for correctness we found that most of the automatically extracted phrases which did not pass the quality test for problem-/solution-hood were either due to obvious learning cues or instances where the sense of problem-hood used is relating to tasks (cf. “ Goal statement and task ” section).

Experimental design

In our experiments, we used three classifiers, namely Naïve Bayes, Logistic Regression and a Support Vector Machine. For all classifiers an implementation from the WEKA machine learning library (Hall et al. 2009 ) was chosen. Given that our dataset is small, tenfold cross-validation was used instead of a held out test set. All significance tests were conducted using the (two-tailed) Sign Test (Siegel 1956 ).

Linguistic correlates of problem- and solution-hood

We first define a set of features without taking the phrase’s context into account. This will tell us about the disambiguation ability of the problem/solution description’s semantics alone. In particular, we cut out the rest of the sentence other than the phrase and never use it for classification. This is done for similar reasons to excluding certain ‘give-away’ phrases inside the phrases themselves (as explained above). As the phrases were found using templates, we know that the machine learner would simply pick up on the semantics of the template, which always contains a synonym of “problem” or “solution”, thus drowning out the more hidden features hopefully inherent in the semantics of the phrases themselves. If we allowed the machine learner to use these stronger features, it would suffer in its ability to generalise to the real task.

ngrams Bags of words are traditionally successfully used for classification tasks in NLP, so we included bags of words (lemmas) within the candidate phrases as one of our features (and treat it as a baseline later on). We also include bigrams and trigrams as multi-word combinations can be indicative of problems and solutions e.g., “combinatorial explosion”.

Polarity Our second feature concerns the polarity of each word in the candidate strings. Consider the following example of a problem taken from our dataset: “very conservative approaches to exact and partial string matches overgenerate badly”. In this sentence, words such as “badly” will be associated with negative polarity, therefore being useful in determining problem-hood. Similarly, solutions will often be associated with a positive sentiment e.g. “smoothing is a good way to overcome data sparsity” . To do this, we perform word sense disambiguation of each word using the Lesk algorithm (Lesk 1986 ). The polarity of the resulting synset in SentiWordNet (Baccianella et al. 2010 ) was then looked up and used as a feature.

Syntax Next, a set of syntactic features were defined by using the presence of POS tags in each candidate. This feature could be helpful in finding syntactic patterns in problems and solutions. We were careful not to base the model directly on the head POS tag and the length of each candidate phrase, as these are defining characteristics used for determining the non-problem and non-solution candidate set.

Negation Negation is an important property that can often greatly affect the polarity of a phrase. For example, a phrase containing a keyword pertinent to solution-hood may be a good indicator but with the presence of negation may flip the polarity to problem-hood e.g., “this can’t work as a solution”. Therefore, presence of negation is determined.

Exemplification and contrast Problems and solutions are often found to be coupled with examples as they allow the author to elucidate their point. For instance, consider the following solution: “Once the translations are generated, an obvious solution is to pick the most fluent alternative, e.g., using an n-gram language model”. (Madnani et al. 2012 ). To acknowledge this, we check for presence of exemplification. In addition to examples, problems in particular are often found when contrast is signalled by the author (e.g. “however, “but”), therefore we also check for presence of contrast in the problem and non-problem candidates only.

Discourse Problems and solutions have also been found to have a correlation with discourse properties. For example, problem-solving patterns often occur in the background sections of a paper. The rationale behind this is that the author is conventionally asked to objectively criticise other work in the background (e.g. describing research gaps which motivate the current paper). To take this in account, we examine the context of each string and capture the section header under which it is contained (e.g. Introduction, Future work). In addition, problems and solutions are often found following the Situation element in the problem-solving pattern (cf. “ Introduction ” section). This preamble setting up the problem or solution means that these elements are likely not to be found occurring at the beginning of a section (i.e. it will usually take some sort of introduction to detail how something is problematic and why a solution is needed). Therefore we record the distance from the candidate string to the nearest section header.

Subcategorisation and adverbials Solutions often involve an activity (e.g. a task). We also model the subcategorisation properties of the verbs involved. Our intuition was that since problematic situations are often described as non-actions, then these are more likely to be intransitive. Conversely solutions are often actions and are likely to have at least one argument. This feature was calculated by running the C&C parser (Curran et al. 2007 ) on each sentence. C&C is a supertagger and parser that has access to subcategorisation information. Solutions are also associated with resultative adverbial modification (e.g. “thus, therefore, consequently”) as it expresses the solutionhood relation between the problem and the solution. It has been seen to occur frequently in problem-solving patterns, as studied by Charles ( 2011 ). Therefore, we check for presence of resultative adverbial modification in the solution and non-solution candidate only.

Embeddings We also wanted to add more information using word embeddings. This was done in two different ways. Firstly, we created a Doc2Vec model (Le and Mikolov 2014 ), which was trained on  ∼  19  million sentences from scientific text (no overlap with our data set). An embedding was created for each candidate sentence. Secondly, word embeddings were calculated using the Word2Vec model (cf. “ Corpus creation ” section). For each candidate head, the full word embedding was included as a feature. Lastly, when creating our polarity feature we query SentiWordNet using synsets assigned by the Lesk algorithm. However, not all words are assigned a sense by Lesk, so we need to take care when that happens. In those cases, the distributional semantic similarity of the word is compared to two words with a known polarity, namely “poor” and “excellent”. These particular words have traditionally been consistently good indicators of polarity status in many studies (Turney 2002 ; Mullen and Collier 2004 ). Semantic similarity was defined as cosine similarity on the embeddings of the Word2Vec model (cf. “ Corpus creation ” section).

Modality Responses to problems in scientific writing often express possibility and necessity, and so have a close connection with modality. Modality can be broken into three main categories, as described by Kratzer ( 1991 ), namely epistemic (possibility), deontic (permission / request / wish) and dynamic (expressing ability).

Problems have a strong relationship to modality within scientific writing. Often, this is due to a tactic called “hedging” (Medlock and Briscoe 2007 ) where the author uses speculative language, often using Epistemic modality, in an attempt to make either noncommital or vague statements. This has the effect of allowing the author to distance themselves from the statement, and is often employed when discussing negative or problematic topics. Consider the following example of Epistemic modality from Nakov and Hearst ( 2008 ): “A potential drawback is that it might not work well for low-frequency words”.

To take this linguistic correlate into account as a feature, we replicated a modality classifier as described by (Ruppenhofer and Rehbein 2012 ). More sophisticated modality classifiers have been recently introduced, for instance using a wide range of features and convolutional neural networks, e.g, (Zhou et al. 2015 ; Marasović and Frank 2016 ). However, we wanted to check the effect of a simpler method of modality classification on the final outcome first before investing heavily into their implementation. We trained three classifiers using the subset of features which Ruppenhofer et al. reported as performing best, and evaluated them on the gold standard dataset provided by the authors 4 . The results of the are shown in Table  3 . The dataset contains annotations of English modal verbs on the 535 documents of the first MPQA corpus release (Wiebe et al. 2005 ).

Modality classifier results (precision/recall/f-measure) using Naïve Bayes (NB), logistic regression, and a support vector machine (SVM)

Italicized results reflect highest f-measure reported per modal category

Logistic Regression performed best overall and so this model was chosen for our upcoming experiments. With regards to the optative and concessive modal categories, they can be seen to perform extremely poorly, with the optative category receiving a null score across all three classifiers. This is due to a limitation in the dataset, which is unbalanced and contains very few instances of these two categories. This unbalanced data also is the reason behind our decision of reporting results in terms of recall, precision and f-measure in Table  3 .

The modality classifier was then retrained on the entirety of the dataset used by Ruppenhofer and Rehbein ( 2012 ) using the best performing model from training (Logistic Regression). This new model was then used in the upcoming experiment to predict modality labels for each instance in our dataset.

As can be seen from Table  4 , we are able to achieve good results for distinguishing a problematic statement from non-problematic one. The bag-of-words baseline achieves a very good performance of 71.0% for the Logistic Regression classifier, showing that there is enough signal in the candidate phrases alone to distinguish them much better than random chance.

Results distinguishing problems from non-problems using Naïve Bayes (NB), logistic regression (LR) and a support vector machine (SVM)

Each feature set’s performance is shown in isolation followed by combinations with other features. Tenfold stratified cross-validation was used across all experiments. Statistical significance with respect to the baseline at the p  < 0.05 , 0.01, 0.001 levels is denoted by *, ** and *** respectively

Taking a look at Table  5 , which shows the information gain for the top lemmas,

Information gain (IG) in bits of top lemmas from the bag-of-words baseline in Table  4

we can see that the top lemmas are indeed indicative of problemhood (e.g. “limit”,“explosion”). Bigrams achieved good performance on their own (as did negation and discourse) but unfortunately performance deteriorated when using trigrams, particularly with the SVM and LR. The subcategorisation feature was the worst performing feature in isolation. Upon taking a closer look at our data, we saw that our hypothesis that intransitive verbs are commonly used in problematic statements was true, with over 30% of our problems (153) using them. However, due to our sampling method for the negative cases we also picked up many intransitive verbs (163). This explains the almost random chance performance (i.e.  50%) given that the distribution of intransitive verbs amongst the positive and negative candidates was almost even.

The modality feature was the most expensive to produce, but also didn’t perform very well is isolation. This surprising result may be partly due to a data sparsity issue

where only a small portion (169) of our instances contained modal verbs. The breakdown of how many types of modal senses which occurred is displayed in Table  6 . The most dominant modal sense was epistemic. This is a good indicator of problemhood (e.g. hedging, cf. “ Linguistic correlates of problem- and solution-hood ” section) but if the accumulation of additional data was possible, we think that this feature may have the potential to be much more valuable in determining problemhood. Another reason for the performance may be domain dependence of the classifier since it was trained on text from different domains (e.g. news). Additionally, modality has also shown to be helpful in determining contextual polarity (Wilson et al. 2005 ) and argumentation (Becker et al. 2016 ), so using the output from this modality classifier may also prove useful for further feature engineering taking this into account in future work.

Number of instances of modal senses

Polarity managed to perform well but not as good as we hoped. However, this feature also suffers from a sparsity issue resulting from cases where the Lesk algorithm (Lesk 1986 ) is not able to resolve the synset of the syntactic head.

Knowledge of syntax provides a big improvement with a significant increase over the baseline results from two of the classifiers.

Examining this in greater detail, POS tags with high information gain mostly included tags from open classes (i.e. VB-, JJ-, NN- and RB-). These tags are often more associated with determining polarity status than tags such as prepositions and conjunctions (i.e. adverbs and adjectives are more likely to be describing something with a non-neutral viewpoint).

The embeddings from Doc2Vec allowed us to obtain another significant increase in performance (72.9% with Naïve Bayes) over the baseline and polarity using Word2Vec provided the best individual feature result (77.2% with SVM).

Combining all features together, each classifier managed to achieve a significant result over the baseline with the best result coming from the SVM (81.8%). Problems were also better classified than non-problems as shown in the confusion matrix in Table  7 . The addition of the Word2Vec vectors may be seen as a form of smoothing in cases where previous linguistic features had a sparsity issue i.e., instead of a NULL entry, the embeddings provide some sort of value for each candidate. Particularly wrt. the polarity feature, cases where Lesk was unable to resolve a synset meant that a ZERO entry was added to the vector supplied to the machine learner. Amongst the possible combinations, the best subset of features was found by combining all features with the exception of bigrams, trigrams, subcategorisation and modality. This subset of features managed to improve results in both the Naïve Bayes and SVM classifiers with the highest overall result coming from the SVM (82.3%).

Confusion matrix for problems

The results for disambiguation of solutions from non-solutions can be seen in Table  8 . The bag-of-words baseline performs much better than random, with the performance being quite high with regard to the SVM (this result was also higher than any of the baseline performances from the problem classifiers). As shown in Table  9 , the top ranked lemmas from the best performing model (using information gain) included “use” and “method”. These lemmas are very indicative of solutionhood and so give some insight into the high baseline returned from the machine learners. Subcategorisation and the result adverbials were the two worst performing features. However, the low performance for subcategorisation is due to the sampling of the non-solutions (the same reason for the low performance of the problem transitivity feature). When fitting the POS-tag distribution for the negative samples, we noticed that over 80% of the head POS-tags were verbs (much higher than the problem heads). The most frequent verb type being the infinite form.

Results distinguishing solutions from non-solutions using Naïve Bayes (NB), logistic regression (LR) and a support vector machine (SVM)

Each feature set’s performance is shown in isolation followed by combinations with other features. Tenfold stratified cross-validation was used across all experiments

Information gain (IG) in bits of top lemmas from the bag-of-words baseline in Table  8

This is not surprising given that a very common formulation to describe a solution is to use the infinitive “TO” since it often describes a task e.g., “One solution is to find the singletons and remove them”. Therefore, since the head POS tags of the non-solutions had to match this high distribution of infinitive verbs present in the solution, the subcategorisation feature is not particularly discriminatory. Polarity, negation, exemplification and syntactic features were slightly more discriminate and provided comparable results. However, similar to the problem experiment, the embeddings from Word2Vec and Doc2Vec proved to be the best features, with polarity using Word2Vec providing the best individual result (73.4% with SVM).

Combining all features together managed to improve over each feature in isolation and beat the baseline using all three classifiers. Furthermore, when looking at the confusion matrix in Table  10 the solutions were classified more accurately than the non-solutions. The best subset of features was found by combining all features without adverbial of result, bigrams, exemplification, negation, polarity and subcategorisation. The best result using this subset of features was achieved by the SVM with 79.7%. It managed to greatly improve upon the baseline but was just shy of achieving statistical significance ( p = 0.057 ).

Confusion matrix for solutions

In this work, we have presented new supervised classifiers for the task of identifying problem and solution statements in scientific text. We have also introduced a new corpus for this task and used it for evaluating our classifiers. Great care was taken in constructing the corpus by ensuring that the negative and positive samples were closely matched in terms of syntactic shape. If we had simply selected random subtrees for negative samples without regard for any syntactic similarity with our positive samples, the machine learner may have found easy signals such as sentence length. Additionally, since we did not allow the machine learner to see the surroundings of the candidate string within the sentence, this made our task even harder. Our performance on the corpus shows promise for this task, and proves that there are strong signals for determining both the problem and solution parts of the problem-solving pattern independently.

With regard to classifying problems from non-problems, features such as the POS tag, document and word embeddings provide the best features, with polarity using the Word2Vec embeddings achieving the highest feature performance. The best overall result was achieved using an SVM with a subset of features (82.3%). Classifying solutions from non-solutions also performs well using the embedding features, with the best feature also being polarity using the Word2Vec embeddings, and the highest result also coming from the SVM with a feature subset (79.7%).

In future work, we plan to link problem and solution statements which were found independently during our corpus creation. Given that our classifiers were trained on data solely from the ACL anthology, we also hope to investigate the domain specificity of our classifiers and see how well they can generalise to domains other than ACL (e.g. bioinformatics). Since we took great care at removing the knowledge our classifiers have of the explicit statements of problem and solution (i.e. the classifiers were trained only on the syntactic argument of the explicit statement of problem-/solution-hood), our classifiers should in principle be in a good position to generalise, i.e., find implicit statements too. In future work, we will measure to which degree this is the case.

To facilitate further research on this topic, all code and data used in our experiments can be found here: www.cl.cam.ac.uk/~kh562/identifying-problems-and-solutions.html

Acknowledgements

The first author has been supported by an EPSRC studentship (Award Ref: 1641528). We thank the reviewers for their helpful comments.

1 http://acl-arc.comp.nus.edu.sg/ .

2 The corpus comprises 3,391,198 sentences, 71,149,169 words and 451,996,332 characters.

3 The head POS tags were found using a modification of the Collins’ Head Finder. This modified algorithm addresses some of the limitations of the head finding heuristics described by Collins ( 2003 ) and can be found here: http://nlp.stanford.edu/nlp/javadoc/javanlp/edu/stanford/nlp/trees/ModCollinsHeadFinder.html .

4 https://www.uni-hildesheim.de/ruppenhofer/data/modalia_release1.0.tgz.

Contributor Information

Kevin Heffernan, Email: [email protected] .

Simone Teufel, Email: [email protected] .

• Baccianella S, Esuli A, Sebastiani F. Sentiwordnet 3.0: An enhanced lexical resource for sentiment analysis and opinion mining. LREC. 2010; 10 :2200–2204. [ Google Scholar ]
• Becker, M., Palmer, A., & Frank, A. (2016). Clause types and modality in argumentative microtexts. In Workshop on foundations of the language of argumentation (in conjunction with COMMA) .
• Briscoe, T., Carroll, J., & Watson, R. (2006). The second release of the rasp system. In Proceedings of the COLING/ACL on interactive presentation sessions, association for computational linguistics pp. 77–80.
• Chandrasekaran B. Towards a taxonomy of problem solving types. AI Magazine. 1983; 4 (1):9. [ Google Scholar ]
• Charles M. Adverbials of result: Phraseology and functions in the problem-solution pattern. Journal of English for Academic Purposes. 2011; 10 (1):47–60. doi: 10.1016/j.jeap.2011.01.002. [ CrossRef ] [ Google Scholar ]
• Chen, D., Dyer, C., Cohen, S. B., & Smith, N. A. (2011). Unsupervised bilingual pos tagging with markov random fields. In Proceedings of the first workshop on unsupervised learning in NLP, association for computational linguistics pp. 64–71.
• Collins M. Head-driven statistical models for natural language parsing. Computational Linguistics. 2003; 29 (4):589–637. doi: 10.1162/089120103322753356. [ CrossRef ] [ Google Scholar ]
• Councill, I. G., Giles, C. L., & Kan, M. Y. (2008). Parscit: An open-source CRF reference string parsing package. In LREC .
• Curran, J. R., Clark, S., & Bos, J. (2007). Linguistically motivated large-scale NLP with C&C and boxer. In Proceedings of the 45th annual meeting of the ACL on interactive poster and demonstration sessions, association for computational linguistics pp. 33–36.
• Flowerdew L. Corpus-based analyses of the problem-solution pattern: A phraseological approach. Amsterdam: John Benjamins Publishing; 2008. [ Google Scholar ]
• Grimes JE. The thread of discourse. Berlin: Walter de Gruyter; 1975. [ Google Scholar ]
• Hall M, Frank E, Holmes G, Pfahringer B, Reutemann P, Witten IH. The weka data mining software: An update. ACM SIGKDD Explorations Newsletter. 2009; 11 (1):10–18. doi: 10.1145/1656274.1656278. [ CrossRef ] [ Google Scholar ]
• Hoey M. Textual interaction: An introduction to written discourse analysis. Portland: Psychology Press; 2001. [ Google Scholar ]
• Hutchins J. On the structure of scientific texts. UEA Papers in Linguistics. 1977; 5 (3):18–39. [ Google Scholar ]
• Jonassen DH. Toward a design theory of problem solving. Educational Technology Research and Development. 2000; 48 (4):63–85. doi: 10.1007/BF02300500. [ CrossRef ] [ Google Scholar ]
• Jordan MP. Short texts to explain problem-solution structures-and vice versa. Instructional Science. 1980; 9 (3):221–252. doi: 10.1007/BF00177328. [ CrossRef ] [ Google Scholar ]
• Kratzer, A. (1991). Modality. In von Stechow & Wunderlich (Eds.), Semantics: An international handbook of contemporary research .
• Le QV, Mikolov T. Distributed representations of sentences and documents. ICML. 2014; 14 :1188–1196. [ Google Scholar ]
• Lesk, M. (1986). Automatic sense disambiguation using machine readable dictionaries: How to tell a pine cone from an ice cream cone. In Proceedings of the 5th annual international conference on Systems documentation, ACM (pp. 24–26).
• Madnani, N., Tetreault, J., & Chodorow, M. (2012). Exploring grammatical error correction with not-so-crummy machine translation. In Proceedings of the seventh workshop on building educational applications using NLP, association for computational linguistics pp. 44–53.
• Mann WC, Thompson SA. Rhetorical structure theory: Toward a functional theory of text organization. Text-Interdisciplinary Journal for the Study of Discourse. 1988; 8 (3):243–281. doi: 10.1515/text.1.1988.8.3.243. [ CrossRef ] [ Google Scholar ]
• Marasović, A., & Frank, A. (2016). Multilingual modal sense classification using a convolutional neural network. In Proceedings of the 1st Workshop on Representation Learning for NLP .
• McKeown K, Daume H, Chaturvedi S, Paparrizos J, Thadani K, Barrio P, Biran O, Bothe S, Collins M, Fleischmann KR, et al. Predicting the impact of scientific concepts using full-text features. Journal of the Association for Information Science and Technology. 2016; 67 :2684–2696. doi: 10.1002/asi.23612. [ CrossRef ] [ Google Scholar ]
• Medlock B, Briscoe T. Weakly supervised learning for hedge classification in scientific literature. ACL, Citeseer. 2007; 2007 :992–999. [ Google Scholar ]
• Mikolov, T., Sutskever, I., Chen, K., Corrado, G. S., & Dean, J. (2013). Distributed representations of words and phrases and their compositionality. In Advances in neural information processing systems (pp. 3111–3119).
• Mohit, B., Schneider, N., Bhowmick, R., Oflazer, K., & Smith, N. A. (2012). Recall-oriented learning of named entities in arabic wikipedia. In Proceedings of the 13th conference of the European chapter of the association for computational linguistics, association for computational linguistics (pp. 162–173).
• Mullen T, Collier N. Sentiment analysis using support vector machines with diverse information sources. EMNLP. 2004; 4 :412–418. [ Google Scholar ]
• Nakov, P., Hearst, M. A. (2008). Solving relational similarity problems using the web as a corpus. In: ACL (pp. 452–460).
• Poon, H., & Domingos, P. (2009). Unsupervised semantic parsing. In Proceedings of the 2009 conference on empirical methods in natural language processing: Volume 1-association for computational linguistics (pp. 1–10).
• Ruppenhofer, J., & Rehbein, I. (2012). Yes we can!? Annotating the senses of English modal verbs. In Proceedings of the 8th international conference on language resources and evaluation (LREC), Citeseer (pp. 24–26).
• Saha, S. K., Mitra, P., & Sarkar, S. (2008). Word clustering and word selection based feature reduction for maxent based hindi ner. In ACL (pp. 488–495).
• Scott, M. (2001). Mapping key words to problem and solution. In Patterns of text: In honour of Michael Hoey Benjamins, Amsterdam (pp. 109–127).
• Siegel S. Nonparametric statistics for the behavioral sciences. New York: McGraw-hill; 1956. [ Google Scholar ]
• Strübing, J. (2007). Research as pragmatic problem-solving: The pragmatist roots of empirically-grounded theorizing. In The Sage handbook of grounded theory (pp. 580–602).
• Teufel, S., et al. (2000). Argumentative zoning: Information extraction from scientific text. PhD Thesis, Citeseer .
• Turney, P. D. (2002). Thumbs up or thumbs down?: Semantic orientation applied to unsupervised classification of reviews. In Proceedings of the 40th annual meeting on association for computational linguistics, association for computational linguistics (pp. 417–424).
• Van Dijk TA. Text and context explorations in the semantics and pragmatics of discourse. London: Longman; 1980. [ Google Scholar ]
• Wiebe J, Wilson T, Cardie C. Annotating expressions of opinions and emotions in language. Language Resources and Evaluation. 2005; 39 (2):165–210. doi: 10.1007/s10579-005-7880-9. [ CrossRef ] [ Google Scholar ]
• Wilson, T., Wiebe, J., & Hoffmann, P. (2005). Recognizing contextual polarity in phrase-level sentiment analysis. In Proceedings of the conference on human language technology and empirical methods in natural language processing, association for computational linguistics (pp. 347–354).
• Winter, E. O. (1968). Some aspects of cohesion. In Sentence and clause in scientific English . University College London.
• Zhou, M., Frank, A., Friedrich, A., & Palmer, A. (2015). Semantically enriched models for modal sense classification. In Workshop on linking models of lexical, sentential and discourse-level semantics (LSDSem) (p. 44).

• school Campus Bookshelves
• menu_book Bookshelves
• perm_media Learning Objects
• login Login
• how_to_reg Request Instructor Account
• hub Instructor Commons
• Download Page (PDF)
• Download Full Book (PDF)
• Periodic Table
• Physics Constants
• Scientific Calculator
• Reference & Cite
• Tools expand_more
• Readability

selected template will load here

This action is not available.

1.8: Solving Problems in Physics

• Last updated
• Save as PDF
• Page ID 4304

Learning Objectives

• Describe the process for developing a problem-solving strategy.
• Explain how to find the numerical solution to a problem.
• Summarize the process for assessing the significance of the numerical solution to a problem.

Problem-solving skills are clearly essential to success in a quantitative course in physics. More important, the ability to apply broad physical principles—usually represented by equations—to specific situations is a very powerful form of knowledge. It is much more powerful than memorizing a list of facts. Analytical skills and problem-solving abilities can be applied to new situations whereas a list of facts cannot be made long enough to contain every possible circumstance. Such analytical skills are useful both for solving problems in this text and for applying physics in everyday life.

As you are probably well aware, a certain amount of creativity and insight is required to solve problems. No rigid procedure works every time. Creativity and insight grow with experience. With practice, the basics of problem solving become almost automatic. One way to get practice is to work out the text’s examples for yourself as you read. Another is to work as many end-of-section problems as possible, starting with the easiest to build confidence and then progressing to the more difficult. After you become involved in physics, you will see it all around you, and you can begin to apply it to situations you encounter outside the classroom, just as is done in many of the applications in this text.

Although there is no simple step-by-step method that works for every problem, the following three-stage process facilitates problem solving and makes it more meaningful. The three stages are strategy, solution, and significance. This process is used in examples throughout the book. Here, we look at each stage of the process in turn.

Strategy is the beginning stage of solving a problem. The idea is to figure out exactly what the problem is and then develop a strategy for solving it. Some general advice for this stage is as follows:

• Examine the situation to determine which physical principles are involved . It often helps to draw a simple sketch at the outset. You often need to decide which direction is positive and note that on your sketch. When you have identified the physical principles, it is much easier to find and apply the equations representing those principles. Although finding the correct equation is essential, keep in mind that equations represent physical principles, laws of nature, and relationships among physical quantities. Without a conceptual understanding of a problem, a numerical solution is meaningless.
• Make a list of what is given or can be inferred from the problem as stated (identify the “knowns”) . Many problems are stated very succinctly and require some inspection to determine what is known. Drawing a sketch be very useful at this point as well. Formally identifying the knowns is of particular importance in applying physics to real-world situations. For example, the word stopped means the velocity is zero at that instant. Also, we can often take initial time and position as zero by the appropriate choice of coordinate system.
• Identify exactly what needs to be determined in the problem (identify the unknowns). In complex problems, especially, it is not always obvious what needs to be found or in what sequence. Making a list can help identify the unknowns.
• Determine which physical principles can help you solve the problem . Since physical principles tend to be expressed in the form of mathematical equations, a list of knowns and unknowns can help here. It is easiest if you can find equations that contain only one unknown—that is, all the other variables are known—so you can solve for the unknown easily. If the equation contains more than one unknown, then additional equations are needed to solve the problem. In some problems, several unknowns must be determined to get at the one needed most. In such problems it is especially important to keep physical principles in mind to avoid going astray in a sea of equations. You may have to use two (or more) different equations to get the final answer.

The solution stage is when you do the math. Substitute the knowns (along with their units) into the appropriate equation and obtain numerical solutions complete with units . That is, do the algebra, calculus, geometry, or arithmetic necessary to find the unknown from the knowns, being sure to carry the units through the calculations. This step is clearly important because it produces the numerical answer, along with its units. Notice, however, that this stage is only one-third of the overall problem-solving process.

Significance

After having done the math in the solution stage of problem solving, it is tempting to think you are done. But, always remember that physics is not math. Rather, in doing physics, we use mathematics as a tool to help us understand nature. So, after you obtain a numerical answer, you should always assess its significance:

• Check your units . If the units of the answer are incorrect, then an error has been made and you should go back over your previous steps to find it. One way to find the mistake is to check all the equations you derived for dimensional consistency. However, be warned that correct units do not guarantee the numerical part of the answer is also correct.
• Check the answer to see whether it is reasonable. Does it make sense? This step is extremely important: –the goal of physics is to describe nature accurately. To determine whether the answer is reasonable, check both its magnitude and its sign, in addition to its units. The magnitude should be consistent with a rough estimate of what it should be. It should also compare reasonably with magnitudes of other quantities of the same type. The sign usually tells you about direction and should be consistent with your prior expectations. Your judgment will improve as you solve more physics problems, and it will become possible for you to make finer judgments regarding whether nature is described adequately by the answer to a problem. This step brings the problem back to its conceptual meaning. If you can judge whether the answer is reasonable, you have a deeper understanding of physics than just being able to solve a problem mechanically.
• Check to see whether the answer tells you something interesting. What does it mean? This is the flip side of the question: Does it make sense? Ultimately, physics is about understanding nature, and we solve physics problems to learn a little something about how nature operates. Therefore, assuming the answer does make sense, you should always take a moment to see if it tells you something about the world that you find interesting. Even if the answer to this particular problem is not very interesting to you, what about the method you used to solve it? Could the method be adapted to answer a question that you do find interesting? In many ways, it is in answering questions such as these science that progresses.

Identifying problems and solutions in scientific text

• Open access
• Published: 06 April 2018
• Volume 116 , pages 1367–1382, ( 2018 )

Cite this article

You have full access to this open access article

• Kevin Heffernan 1 &
• Simone Teufel 1  

10k Accesses

34 Citations

2 Altmetric

Explore all metrics

Research is often described as a problem-solving activity, and as a result, descriptions of problems and solutions are an essential part of the scientific discourse used to describe research activity. We present an automatic classifier that, given a phrase that may or may not be a description of a scientific problem or a solution, makes a binary decision about problemhood and solutionhood of that phrase. We recast the problem as a supervised machine learning problem, define a set of 15 features correlated with the target categories and use several machine learning algorithms on this task. We also create our own corpus of 2000 positive and negative examples of problems and solutions. We find that we can distinguish problems from non-problems with an accuracy of 82.3%, and solutions from non-solutions with an accuracy of 79.7%. Our three most helpful features for the task are syntactic information (POS tags), document and word embeddings.

Similar content being viewed by others

Pattern-Based Acquisition of Scientific Entities from Scholarly Article Titles

Towards Computation of Novel Ideas from Corpora of Scientific Text

Philosophical reasoning about science: a quantitative, digital study

Moti Mizrahi & Michael Adam Dickinson

Avoid common mistakes on your manuscript.

Introduction

Problem solving is generally regarded as the most important cognitive activity in everyday and professional contexts (Jonassen 2000 ). Many studies on formalising the cognitive process behind problem-solving exist, for instance (Chandrasekaran 1983 ). Jordan ( 1980 ) argues that we all share knowledge of the thought/action problem-solution process involved in real life, and so our writings will often reflect this order. There is general agreement amongst theorists that state that the nature of the research process can be viewed as a problem-solving activity (Strübing 2007 ; Van Dijk 1980 ; Hutchins 1977 ; Grimes 1975 ).

One of the best-documented problem-solving patterns was established by Winter ( 1968 ). Winter analysed thousands of examples of technical texts, and noted that these texts can largely be described in terms of a four-part pattern consisting of Situation, Problem, Solution and Evaluation. This is very similar to the pattern described by Van Dijk ( 1980 ), which consists of Introduction-Theory, Problem-Experiment-Comment and Conclusion. The difference is that in Winter’s view, a solution only becomes a solution after it has been evaluated positively. Hoey changes Winter’s pattern by introducing the concept of Response in place of Solution (Hoey 2001 ). This seems to describe the situation in science better, where evaluation is mandatory for research solutions to be accepted by the community. In Hoey’s pattern, the Situation (which is generally treated as optional) provides background information; the Problem describes an issue which requires attention; the Response provides a way to deal with the issue, and the Evaluation assesses how effective the response is.

An example of this pattern in the context of the Goldilocks story can be seen in Fig.  1 . In this text, there is a preamble providing the setting of the story (i.e. Goldilocks is lost in the woods), which is called the Situation in Hoey’s system. A Problem in encountered when Goldilocks becomes hungry. Her first Response is to try the porridge in big bear’s bowl, but she gives this a negative Evaluation (“too hot!”) and so the pattern returns to the Problem. This continues in a cyclic fashion until the Problem is finally resolved by Goldilocks giving a particular Response a positive Evaluation of baby bear’s porridge (“it’s just right”).

Reproduced with permission from Hoey ( 2001 )

Example of problem-solving pattern when applied to the Goldilocks story.

It would be attractive to detect problem and solution statements automatically in text. This holds true both from a theoretical and a practical viewpoint. Theoretically, we know that sentiment detection is related to problem-solving activity, because of the perception that “bad” situations are transformed into “better” ones via problem-solving. The exact mechanism of how this can be detected would advance the state of the art in text understanding. In terms of linguistic realisation, problem and solution statements come in many variants and reformulations, often in the form of positive or negated statements about the conditions, results and causes of problem–solution pairs. Detecting and interpreting those would give us a reasonably objective manner to test a system’s understanding capacity. Practically, being able to detect any mention of a problem is a first step towards detecting a paper’s specific research goal. Being able to do this has been a goal for scientific information retrieval for some time, and if successful, it would improve the effectiveness of scientific search immensely. Detecting problem and solution statements of papers would also enable us to compare similar papers and eventually even lead to automatic generation of review articles in a field.

There has been some computational effort on the task of identifying problem-solving patterns in text. However, most of the prior work has not gone beyond the usage of keyword analysis and some simple contextual examination of the pattern. Flowerdew ( 2008 ) presents a corpus-based analysis of lexio-grammatical patterns for problem and solution clauses using articles from professional and student reports. Problem and solution keywords were used to search their corpora, and each occurrence was analysed to determine grammatical usage of the keyword. More interestingly, the causal category associated with each keyword in their context was also analysed. For example, Reason–Result or Means-Purpose were common causal categories found to be associated with problem keywords.

The goal of the work by Scott ( 2001 ) was to determine words which are semantically similar to problem and solution, and to determine how these words are used to signal problem-solution patterns. However, their corpus-based analysis used articles from the Guardian newspaper. Since the domain of newspaper text is very different from that of scientific text, we decided not to consider those keywords associated with problem-solving patterns for use in our work.

Instead of a keyword-based approach, Charles ( 2011 ) used discourse markers to examine how the problem-solution pattern was signalled in text. In particular, they examined how adverbials associated with a result such as “thus, therefore, then, hence” are used to signal a problem-solving pattern.

Problem solving also has been studied in the framework of discourse theories such as Rhetorical Structure Theory (Mann and Thompson 1988 ) and Argumentative Zoning (Teufel et al. 2000 ). Problem- and solutionhood constitute two of the original 23 relations in RST (Mann and Thompson 1988 ). While we concentrate solely on this aspect, RST is a general theory of discourse structure which covers many intentional and informational relations. The relationship to Argumentative Zoning is more complicated. The status of certain statements as problem or solutions is one important dimension in the definitions of AZ categories. AZ additionally models dimensions other than problem-solution hood (such as who a scientific idea belongs to, or which intention the authors might have had in stating a particular negative or positive statement). When forming categories, AZ combines aspects of these dimensions, and “flattens” them out into only 7 categories. In AZ it is crucial who it is that experiences the problems or contributes a solution. For instance, the definition of category “CONTRAST” includes statements that some research runs into problems, but only if that research is previous work (i.e., not if it is the work contributed in the paper itself). Similarly, “BASIS” includes statements of successful problem-solving activities, but only if they are achieved by previous work that the current paper bases itself on. Our definition is simpler in that we are interested only in problem solution structure, not in the other dimensions covered in AZ. Our definition is also more far-reaching than AZ, in that we are interested in all problems mentioned in the text, no matter whose problems they are. Problem-solution recognition can therefore be seen as one aspect of AZ which can be independently modelled as a “service task”. This means that good problem solution structure recognition should theoretically improve AZ recognition.

In this work, we approach the task of identifying problem-solving patterns in scientific text. We choose to use the model of problem-solving described by Hoey ( 2001 ). This pattern comprises four parts: Situation, Problem, Response and Evaluation. The Situation element is considered optional to the pattern, and so our focus centres on the core pattern elements.

Goal statement and task

Many surface features in the text offer themselves up as potential signals for detecting problem-solving patterns in text. However, since Situation is an optional element, we decided to focus on either Problem or Response and Evaluation as signals of the pattern. Moreover, we decide to look for each type in isolation. Our reasons for this are as follows: It is quite rare for an author to introduce a problem without resolving it using some sort of response, and so this is a good starting point in identifying the pattern. There are exceptions to this, as authors will sometimes introduce a problem and then leave it to future work, but overall there should be enough signal in the Problem element to make our method of looking for it in isolation worthwhile. The second signal we look for is the use of Response and Evaluation within the same sentence. Similar to Problem elements, we hypothesise that this formulation is well enough signalled externally to help us in detecting the pattern. For example, consider the following Response and Evaluation: “One solution is to use smoothing”. In this statement, the author is explicitly stating that smoothing is a solution to a problem which must have been mentioned in a prior statement. In scientific text, we often observe that solutions implicitly contain both Response and Evaluation (positive) elements. Therefore, due to these reasons there should be sufficient external signals for the two pattern elements we concentrate on here.

When attempting to find Problem elements in text, we run into the issue that the word “problem” actually has at least two word senses that need to be distinguished. There is a word sense of “problem” that means something which must be undertaken (i.e. task), while another sense is the core sense of the word, something that is problematic and negative. Only the latter sense is aligned with our sense of problemhood. This is because the simple description of a task does not predispose problemhood, just a wish to perform some act. Consider the following examples, where the non-desired word sense is being used:

“Das and Petrov (2011) also consider the problem of unsupervised bilingual POS induction”. (Chen et al. 2011 ).

“In this paper, we describe advances on the problem of NER in Arabic Wikipedia”. (Mohit et al. 2012 ).

Here, the author explicitly states that the phrases in orange are problems, they align with our definition of research tasks and not with what we call here ‘problematic problems’. We will now give some examples from our corpus for the desired, core word sense:

“The major limitation of supervised approaches is that they require annotations for example sentences.” (Poon and Domingos 2009 ).

“To solve the problem of high dimensionality we use clustering to group the words present in the corpus into much smaller number of clusters”. (Saha et al. 2008 ).

When creating our corpus of positive and negative examples, we took care to select only problem strings that satisfy our definition of problemhood; “ Corpus creation ” section will explain how we did that.

Corpus creation

Our new corpus is a subset of the latest version of the ACL anthology released in March, 2016 Footnote 1 which contains 22,878 articles in the form of PDFs and OCRed text. Footnote 2

The 2016 version was also parsed using ParsCit (Councill et al. 2008 ). ParsCit recognises not only document structure, but also bibliography lists as well as references within running text. A random subset of 2500 papers was collected covering the entire ACL timeline. In order to disregard non-article publications such as introductions to conference proceedings or letters to the editor, only documents containing abstracts were considered. The corpus was preprocessed using tokenisation, lemmatisation and dependency parsing with the Rasp Parser (Briscoe et al. 2006 ).

Definition of ground truth

Our goal was to define a ground truth for problem and solution strings, while covering as wide a range as possible of syntactic variations in which such strings naturally occur. We also want this ground truth to cover phenomena of problem and solution status which are applicable whether or not the problem or solution status is explicitly mentioned in the text.

To simplify the task, we only consider here problem and solution descriptions that are at most one sentence long. In reality, of course, many problem descriptions and solution descriptions go beyond single sentence, and require for instance an entire paragraph. However, we also know that short summaries of problems and solutions are very prevalent in science, and also that these tend to occur in the most prominent places in a paper. This is because scientists are trained to express their contribution and the obstacles possibly hindering their success, in an informative, succinct manner. That is the reason why we can afford to only look for shorter problem and solution descriptions, ignoring those that cross sentence boundaries.

Example of our extraction method for problems using dependencies. (Color figure online)

To define our ground truth, we examined the parsed dependencies and looked for a target word (“problem/solution”) in subject position, and then chose its syntactic argument as our candidate problem or solution phrase. To increase the variation, i.e., to find as many different-worded problem and solution descriptions as possible, we additionally used semantically similar words (near-synonyms) of the target words “problem” or “solution” for the search. Semantic similarity was defined as cosine in a deep learning distributional vector space, trained using Word2Vec (Mikolov et al. 2013 ) on 18,753,472 sentences from a biomedical corpus based on all full-text Pubmed articles (McKeown et al. 2016 ). From the 200 words which were semantically closest to “problem”, we manually selected 28 clear synonyms. These are listed in Table  1 . From the 200 semantically closest words to “solution” we similarly chose 19 (Table  2 ). Of the sentences matching our dependency search, a subset of problem and solution candidate sentences were randomly selected.

An example of this is shown in Fig.  2 . Here, the target word “drawback” is in subject position (highlighted in red), and its clausal argument (ccomp) is “(that) it achieves low performance” (highlighted in purple). Examples of other arguments we searched for included copula constructions and direct/indirect objects.

If more than one candidate was found in a sentence, one was chosen at random. Non-grammatical sentences were excluded; these might appear in the corpus as a result of its source being OCRed text.

800 candidates phrases expressing problems and solutions were automatically extracted (1600 total) and then independently checked for correctness by two annotators (the two authors of this paper). Both authors found the task simple and straightforward. Correctness was defined by two criteria:

The sentence must unambiguously and clearly state the phrase’s status as either a problem or a solution. For problems, the guidelines state that the phrase has to represent one of the following:

An unexplained phenomenon or a problematic state in science; or

A research question; or

An artifact that does not fulfil its stated specification.

For solutions, the phrase had to represent a response to a problem with a positive evaluation. Implicit solutions were also allowed.

The phrase must not lexically give away its status as problem or solution phrase.

The second criterion saves us from machine learning cues that are too obvious. If for instance, the phrase itself contained the words “lack of” or “problematic” or “drawback”, our manual check rejected it, because it would be too easy for the machine learner to learn such cues, at the expense of many other, more generally occurring cues.

Sampling of negative examples

We next needed to find negative examples for both cases. We wanted them not to stand out on the surface as negative examples, so we chose them so as to mimic the obvious characteristics of the positive examples as closely as possible. We call the negative examples ‘non-problems’ and ‘non-solutions’ respectively. We wanted the only differences between problems and non-problems to be of a semantic nature, nothing that could be read off on the surface. We therefore sampled a population of phrases that obey the same statistical distribution as our problem and solution strings while making sure they really are negative examples. We started from sentences not containing any problem/solution words (i.e. those used as target words). From each such sentence, we at random selected one syntactic subtree contained in it. From these, we randomly selected a subset of negative examples of problems and solutions that satisfy the following conditions:

The distribution of the head POS tags of the negative strings should perfectly match the head POS tags Footnote 3 of the positive strings. This has the purpose of achieving the same proportion of surface syntactic constructions as observed in the positive cases.

The average lengths of the negative strings must be within a tolerance of the average length of their respective positive candidates e.g., non-solutions must have an average length very similar (i.e. \(+/-\) small tolerance) to solutions. We chose a tolerance value of 3 characters.

Again, a human quality check was performed on non-problems and non-solutions. For each candidate non-problem statement, the candidate was accepted if it did not contain a phenomenon, a problematic state, a research question or a non-functioning artefact. If the string expressed a research task, without explicit statement that there was anything problematic about it (i.e., the ‘wrong’ sense of “problem”, as described above), it was allowed as a non-problem. A clause was confirmed as a non-solution if the string did not represent both a response and positive evaluation.

If the annotator found that the sentence had been slightly mis-parsed, but did contain a candidate, they were allowed to move the boundaries for the candidate clause. This resulted in cleaner text, e.g., in the frequent case of coordination, when non-relevant constituents could be removed.

From the set of sentences which passed the quality-test for both independent assessors, 500 instances of positive and negative problems/solutions were randomly chosen (i.e. 2000 instances in total). When checking for correctness we found that most of the automatically extracted phrases which did not pass the quality test for problem-/solution-hood were either due to obvious learning cues or instances where the sense of problem-hood used is relating to tasks (cf. “ Goal statement and task ” section).

Experimental design

In our experiments, we used three classifiers, namely Naïve Bayes, Logistic Regression and a Support Vector Machine. For all classifiers an implementation from the WEKA machine learning library (Hall et al. 2009 ) was chosen. Given that our dataset is small, tenfold cross-validation was used instead of a held out test set. All significance tests were conducted using the (two-tailed) Sign Test (Siegel 1956 ).

Linguistic correlates of problem- and solution-hood

We first define a set of features without taking the phrase’s context into account. This will tell us about the disambiguation ability of the problem/solution description’s semantics alone. In particular, we cut out the rest of the sentence other than the phrase and never use it for classification. This is done for similar reasons to excluding certain ‘give-away’ phrases inside the phrases themselves (as explained above). As the phrases were found using templates, we know that the machine learner would simply pick up on the semantics of the template, which always contains a synonym of “problem” or “solution”, thus drowning out the more hidden features hopefully inherent in the semantics of the phrases themselves. If we allowed the machine learner to use these stronger features, it would suffer in its ability to generalise to the real task.

ngrams Bags of words are traditionally successfully used for classification tasks in NLP, so we included bags of words (lemmas) within the candidate phrases as one of our features (and treat it as a baseline later on). We also include bigrams and trigrams as multi-word combinations can be indicative of problems and solutions e.g., “combinatorial explosion”.

Polarity Our second feature concerns the polarity of each word in the candidate strings. Consider the following example of a problem taken from our dataset: “very conservative approaches to exact and partial string matches overgenerate badly”. In this sentence, words such as “badly” will be associated with negative polarity, therefore being useful in determining problem-hood. Similarly, solutions will often be associated with a positive sentiment e.g. “smoothing is a good way to overcome data sparsity” . To do this, we perform word sense disambiguation of each word using the Lesk algorithm (Lesk 1986 ). The polarity of the resulting synset in SentiWordNet (Baccianella et al. 2010 ) was then looked up and used as a feature.

Syntax Next, a set of syntactic features were defined by using the presence of POS tags in each candidate. This feature could be helpful in finding syntactic patterns in problems and solutions. We were careful not to base the model directly on the head POS tag and the length of each candidate phrase, as these are defining characteristics used for determining the non-problem and non-solution candidate set.

Negation Negation is an important property that can often greatly affect the polarity of a phrase. For example, a phrase containing a keyword pertinent to solution-hood may be a good indicator but with the presence of negation may flip the polarity to problem-hood e.g., “this can’t work as a solution”. Therefore, presence of negation is determined.

Exemplification and contrast Problems and solutions are often found to be coupled with examples as they allow the author to elucidate their point. For instance, consider the following solution: “Once the translations are generated, an obvious solution is to pick the most fluent alternative, e.g., using an n-gram language model”. (Madnani et al. 2012 ). To acknowledge this, we check for presence of exemplification. In addition to examples, problems in particular are often found when contrast is signalled by the author (e.g. “however, “but”), therefore we also check for presence of contrast in the problem and non-problem candidates only.

Discourse Problems and solutions have also been found to have a correlation with discourse properties. For example, problem-solving patterns often occur in the background sections of a paper. The rationale behind this is that the author is conventionally asked to objectively criticise other work in the background (e.g. describing research gaps which motivate the current paper). To take this in account, we examine the context of each string and capture the section header under which it is contained (e.g. Introduction, Future work). In addition, problems and solutions are often found following the Situation element in the problem-solving pattern (cf. “ Introduction ” section). This preamble setting up the problem or solution means that these elements are likely not to be found occurring at the beginning of a section (i.e. it will usually take some sort of introduction to detail how something is problematic and why a solution is needed). Therefore we record the distance from the candidate string to the nearest section header.

Subcategorisation and adverbials Solutions often involve an activity (e.g. a task). We also model the subcategorisation properties of the verbs involved. Our intuition was that since problematic situations are often described as non-actions, then these are more likely to be intransitive. Conversely solutions are often actions and are likely to have at least one argument. This feature was calculated by running the C&C parser (Curran et al. 2007 ) on each sentence. C&C is a supertagger and parser that has access to subcategorisation information. Solutions are also associated with resultative adverbial modification (e.g. “thus, therefore, consequently”) as it expresses the solutionhood relation between the problem and the solution. It has been seen to occur frequently in problem-solving patterns, as studied by Charles ( 2011 ). Therefore, we check for presence of resultative adverbial modification in the solution and non-solution candidate only.

Embeddings We also wanted to add more information using word embeddings. This was done in two different ways. Firstly, we created a Doc2Vec model (Le and Mikolov 2014 ), which was trained on \(\sim \,19\)  million sentences from scientific text (no overlap with our data set). An embedding was created for each candidate sentence. Secondly, word embeddings were calculated using the Word2Vec model (cf. “ Corpus creation ” section). For each candidate head, the full word embedding was included as a feature. Lastly, when creating our polarity feature we query SentiWordNet using synsets assigned by the Lesk algorithm. However, not all words are assigned a sense by Lesk, so we need to take care when that happens. In those cases, the distributional semantic similarity of the word is compared to two words with a known polarity, namely “poor” and “excellent”. These particular words have traditionally been consistently good indicators of polarity status in many studies (Turney 2002 ; Mullen and Collier 2004 ). Semantic similarity was defined as cosine similarity on the embeddings of the Word2Vec model (cf. “ Corpus creation ” section).

Modality Responses to problems in scientific writing often express possibility and necessity, and so have a close connection with modality. Modality can be broken into three main categories, as described by Kratzer ( 1991 ), namely epistemic (possibility), deontic (permission / request / wish) and dynamic (expressing ability).

Problems have a strong relationship to modality within scientific writing. Often, this is due to a tactic called “hedging” (Medlock and Briscoe 2007 ) where the author uses speculative language, often using Epistemic modality, in an attempt to make either noncommital or vague statements. This has the effect of allowing the author to distance themselves from the statement, and is often employed when discussing negative or problematic topics. Consider the following example of Epistemic modality from Nakov and Hearst ( 2008 ): “A potential drawback is that it might not work well for low-frequency words”.

To take this linguistic correlate into account as a feature, we replicated a modality classifier as described by (Ruppenhofer and Rehbein 2012 ). More sophisticated modality classifiers have been recently introduced, for instance using a wide range of features and convolutional neural networks, e.g, (Zhou et al. 2015 ; Marasović and Frank 2016 ). However, we wanted to check the effect of a simpler method of modality classification on the final outcome first before investing heavily into their implementation. We trained three classifiers using the subset of features which Ruppenhofer et al. reported as performing best, and evaluated them on the gold standard dataset provided by the authors Footnote 4 . The results of the are shown in Table  3 . The dataset contains annotations of English modal verbs on the 535 documents of the first MPQA corpus release (Wiebe et al. 2005 ).

Logistic Regression performed best overall and so this model was chosen for our upcoming experiments. With regards to the optative and concessive modal categories, they can be seen to perform extremely poorly, with the optative category receiving a null score across all three classifiers. This is due to a limitation in the dataset, which is unbalanced and contains very few instances of these two categories. This unbalanced data also is the reason behind our decision of reporting results in terms of recall, precision and f-measure in Table  3 .

The modality classifier was then retrained on the entirety of the dataset used by Ruppenhofer and Rehbein ( 2012 ) using the best performing model from training (Logistic Regression). This new model was then used in the upcoming experiment to predict modality labels for each instance in our dataset.

As can be seen from Table  4 , we are able to achieve good results for distinguishing a problematic statement from non-problematic one. The bag-of-words baseline achieves a very good performance of 71.0% for the Logistic Regression classifier, showing that there is enough signal in the candidate phrases alone to distinguish them much better than random chance.

Taking a look at Table  5 , which shows the information gain for the top lemmas,

we can see that the top lemmas are indeed indicative of problemhood (e.g. “limit”,“explosion”). Bigrams achieved good performance on their own (as did negation and discourse) but unfortunately performance deteriorated when using trigrams, particularly with the SVM and LR. The subcategorisation feature was the worst performing feature in isolation. Upon taking a closer look at our data, we saw that our hypothesis that intransitive verbs are commonly used in problematic statements was true, with over 30% of our problems (153) using them. However, due to our sampling method for the negative cases we also picked up many intransitive verbs (163). This explains the almost random chance performance (i.e.  50%) given that the distribution of intransitive verbs amongst the positive and negative candidates was almost even.

The modality feature was the most expensive to produce, but also didn’t perform very well is isolation. This surprising result may be partly due to a data sparsity issue

where only a small portion (169) of our instances contained modal verbs. The breakdown of how many types of modal senses which occurred is displayed in Table  6 . The most dominant modal sense was epistemic. This is a good indicator of problemhood (e.g. hedging, cf. “ Linguistic correlates of problem- and solution-hood ” section) but if the accumulation of additional data was possible, we think that this feature may have the potential to be much more valuable in determining problemhood. Another reason for the performance may be domain dependence of the classifier since it was trained on text from different domains (e.g. news). Additionally, modality has also shown to be helpful in determining contextual polarity (Wilson et al. 2005 ) and argumentation (Becker et al. 2016 ), so using the output from this modality classifier may also prove useful for further feature engineering taking this into account in future work.

Polarity managed to perform well but not as good as we hoped. However, this feature also suffers from a sparsity issue resulting from cases where the Lesk algorithm (Lesk 1986 ) is not able to resolve the synset of the syntactic head.

Knowledge of syntax provides a big improvement with a significant increase over the baseline results from two of the classifiers.

Examining this in greater detail, POS tags with high information gain mostly included tags from open classes (i.e. VB-, JJ-, NN- and RB-). These tags are often more associated with determining polarity status than tags such as prepositions and conjunctions (i.e. adverbs and adjectives are more likely to be describing something with a non-neutral viewpoint).

The embeddings from Doc2Vec allowed us to obtain another significant increase in performance (72.9% with Naïve Bayes) over the baseline and polarity using Word2Vec provided the best individual feature result (77.2% with SVM).

Combining all features together, each classifier managed to achieve a significant result over the baseline with the best result coming from the SVM (81.8%). Problems were also better classified than non-problems as shown in the confusion matrix in Table  7 . The addition of the Word2Vec vectors may be seen as a form of smoothing in cases where previous linguistic features had a sparsity issue i.e., instead of a NULL entry, the embeddings provide some sort of value for each candidate. Particularly wrt. the polarity feature, cases where Lesk was unable to resolve a synset meant that a ZERO entry was added to the vector supplied to the machine learner. Amongst the possible combinations, the best subset of features was found by combining all features with the exception of bigrams, trigrams, subcategorisation and modality. This subset of features managed to improve results in both the Naïve Bayes and SVM classifiers with the highest overall result coming from the SVM (82.3%).

The results for disambiguation of solutions from non-solutions can be seen in Table  8 . The bag-of-words baseline performs much better than random, with the performance being quite high with regard to the SVM (this result was also higher than any of the baseline performances from the problem classifiers). As shown in Table  9 , the top ranked lemmas from the best performing model (using information gain) included “use” and “method”. These lemmas are very indicative of solutionhood and so give some insight into the high baseline returned from the machine learners. Subcategorisation and the result adverbials were the two worst performing features. However, the low performance for subcategorisation is due to the sampling of the non-solutions (the same reason for the low performance of the problem transitivity feature). When fitting the POS-tag distribution for the negative samples, we noticed that over 80% of the head POS-tags were verbs (much higher than the problem heads). The most frequent verb type being the infinite form.

This is not surprising given that a very common formulation to describe a solution is to use the infinitive “TO” since it often describes a task e.g., “One solution is to find the singletons and remove them”. Therefore, since the head POS tags of the non-solutions had to match this high distribution of infinitive verbs present in the solution, the subcategorisation feature is not particularly discriminatory. Polarity, negation, exemplification and syntactic features were slightly more discriminate and provided comparable results. However, similar to the problem experiment, the embeddings from Word2Vec and Doc2Vec proved to be the best features, with polarity using Word2Vec providing the best individual result (73.4% with SVM).

Combining all features together managed to improve over each feature in isolation and beat the baseline using all three classifiers. Furthermore, when looking at the confusion matrix in Table  10 the solutions were classified more accurately than the non-solutions. The best subset of features was found by combining all features without adverbial of result, bigrams, exemplification, negation, polarity and subcategorisation. The best result using this subset of features was achieved by the SVM with 79.7%. It managed to greatly improve upon the baseline but was just shy of achieving statistical significance ( \(p=0.057\) ).

In this work, we have presented new supervised classifiers for the task of identifying problem and solution statements in scientific text. We have also introduced a new corpus for this task and used it for evaluating our classifiers. Great care was taken in constructing the corpus by ensuring that the negative and positive samples were closely matched in terms of syntactic shape. If we had simply selected random subtrees for negative samples without regard for any syntactic similarity with our positive samples, the machine learner may have found easy signals such as sentence length. Additionally, since we did not allow the machine learner to see the surroundings of the candidate string within the sentence, this made our task even harder. Our performance on the corpus shows promise for this task, and proves that there are strong signals for determining both the problem and solution parts of the problem-solving pattern independently.

With regard to classifying problems from non-problems, features such as the POS tag, document and word embeddings provide the best features, with polarity using the Word2Vec embeddings achieving the highest feature performance. The best overall result was achieved using an SVM with a subset of features (82.3%). Classifying solutions from non-solutions also performs well using the embedding features, with the best feature also being polarity using the Word2Vec embeddings, and the highest result also coming from the SVM with a feature subset (79.7%).

In future work, we plan to link problem and solution statements which were found independently during our corpus creation. Given that our classifiers were trained on data solely from the ACL anthology, we also hope to investigate the domain specificity of our classifiers and see how well they can generalise to domains other than ACL (e.g. bioinformatics). Since we took great care at removing the knowledge our classifiers have of the explicit statements of problem and solution (i.e. the classifiers were trained only on the syntactic argument of the explicit statement of problem-/solution-hood), our classifiers should in principle be in a good position to generalise, i.e., find implicit statements too. In future work, we will measure to which degree this is the case.

To facilitate further research on this topic, all code and data used in our experiments can be found here: www.cl.cam.ac.uk/~kh562/identifying-problems-and-solutions.html

http://acl-arc.comp.nus.edu.sg/ .

The corpus comprises 3,391,198 sentences, 71,149,169 words and 451,996,332 characters.

The head POS tags were found using a modification of the Collins’ Head Finder. This modified algorithm addresses some of the limitations of the head finding heuristics described by Collins ( 2003 ) and can be found here: http://nlp.stanford.edu/nlp/javadoc/javanlp/edu/stanford/nlp/trees/ModCollinsHeadFinder.html .

https://www.uni-hildesheim.de/ruppenhofer/data/modalia_release1.0.tgz.

Baccianella, S., Esuli, A., & Sebastiani, F. (2010). Sentiwordnet 3.0: An enhanced lexical resource for sentiment analysis and opinion mining. LREC , 10 , 2200–2204.

Google Scholar  

Becker, M., Palmer, A., & Frank, A. (2016). Clause types and modality in argumentative microtexts. In Workshop on foundations of the language of argumentation (in conjunction with COMMA) .

Briscoe, T., Carroll, J., & Watson, R. (2006). The second release of the rasp system. In Proceedings of the COLING/ACL on interactive presentation sessions, association for computational linguistics pp. 77–80.

Chandrasekaran, B. (1983). Towards a taxonomy of problem solving types. AI Magazine , 4 (1), 9.

Charles, M. (2011). Adverbials of result: Phraseology and functions in the problem-solution pattern. Journal of English for Academic Purposes , 10 (1), 47–60.

Article   Google Scholar  

Chen, D., Dyer, C., Cohen, S. B., & Smith, N. A. (2011). Unsupervised bilingual pos tagging with markov random fields. In Proceedings of the first workshop on unsupervised learning in NLP, association for computational linguistics pp. 64–71.

Collins, M. (2003). Head-driven statistical models for natural language parsing. Computational Linguistics , 29 (4), 589–637.

Article   MathSciNet   MATH   Google Scholar  

Councill, I. G., Giles, C. L., & Kan, M. Y. (2008). Parscit: An open-source CRF reference string parsing package. In LREC .

Curran, J. R., Clark, S., & Bos, J. (2007). Linguistically motivated large-scale NLP with C&C and boxer. In Proceedings of the 45th annual meeting of the ACL on interactive poster and demonstration sessions, association for computational linguistics pp. 33–36.

Flowerdew, L. (2008). Corpus-based analyses of the problem-solution pattern: A phraseological approach (Vol. 29). Amsterdam: John Benjamins Publishing.

Book   Google Scholar  

Grimes, J. E. (1975). The thread of discourse (Vol. 207). Berlin: Walter de Gruyter.

Hall, M., Frank, E., Holmes, G., Pfahringer, B., Reutemann, P., & Witten, I. H. (2009). The weka data mining software: An update. ACM SIGKDD Explorations Newsletter , 11 (1), 10–18.

Hoey, M. (2001). Textual interaction: An introduction to written discourse analysis . Portland: Psychology Press.

Hutchins, J. (1977). On the structure of scientific texts. UEA Papers in Linguistics , 5 (3), 18–39.

Jonassen, D. H. (2000). Toward a design theory of problem solving. Educational Technology Research and Development , 48 (4), 63–85.

Jordan, M. P. (1980). Short texts to explain problem-solution structures-and vice versa. Instructional Science , 9 (3), 221–252.

Kratzer, A. (1991). Modality. In von Stechow & Wunderlich (Eds.), Semantics: An international handbook of contemporary research .

Le, Q. V., & Mikolov, T. (2014). Distributed representations of sentences and documents. ICML , 14 , 1188–1196.

Lesk, M. (1986). Automatic sense disambiguation using machine readable dictionaries: How to tell a pine cone from an ice cream cone. In Proceedings of the 5th annual international conference on Systems documentation, ACM (pp. 24–26).

Madnani, N., Tetreault, J., & Chodorow, M. (2012). Exploring grammatical error correction with not-so-crummy machine translation. In Proceedings of the seventh workshop on building educational applications using NLP, association for computational linguistics pp. 44–53.

Mann, W. C., & Thompson, S. A. (1988). Rhetorical structure theory: Toward a functional theory of text organization. Text-Interdisciplinary Journal for the Study of Discourse , 8 (3), 243–281.

Marasović, A., & Frank, A. (2016). Multilingual modal sense classification using a convolutional neural network. In Proceedings of the 1st Workshop on Representation Learning for NLP .

McKeown, K., Daume, H., Chaturvedi, S., Paparrizos, J., Thadani, K., Barrio, P., et al. (2016). Predicting the impact of scientific concepts using full-text features. Journal of the Association for Information Science and Technology , 67 , 2684–2696.

Medlock, B., & Briscoe, T. (2007). Weakly supervised learning for hedge classification in scientific literature. ACL, Citeseer , 2007 , 992–999.

Mikolov, T., Sutskever, I., Chen, K., Corrado, G. S., & Dean, J. (2013). Distributed representations of words and phrases and their compositionality. In Advances in neural information processing systems (pp. 3111–3119).

Mohit, B., Schneider, N., Bhowmick, R., Oflazer, K., & Smith, N. A. (2012). Recall-oriented learning of named entities in arabic wikipedia. In Proceedings of the 13th conference of the European chapter of the association for computational linguistics, association for computational linguistics (pp. 162–173).

Mullen, T., & Collier, N. (2004). Sentiment analysis using support vector machines with diverse information sources. EMNLP , 4 , 412–418.

Nakov, P., Hearst, M. A. (2008). Solving relational similarity problems using the web as a corpus. In: ACL (pp. 452–460).

Poon, H., & Domingos, P. (2009). Unsupervised semantic parsing. In Proceedings of the 2009 conference on empirical methods in natural language processing: Volume 1-association for computational linguistics (pp. 1–10).

Ruppenhofer, J., & Rehbein, I. (2012). Yes we can!? Annotating the senses of English modal verbs. In Proceedings of the 8th international conference on language resources and evaluation (LREC), Citeseer (pp. 24–26).

Saha, S. K., Mitra, P., & Sarkar, S. (2008). Word clustering and word selection based feature reduction for maxent based hindi ner. In ACL (pp. 488–495).

Scott, M. (2001). Mapping key words to problem and solution. In Patterns of text: In honour of Michael Hoey Benjamins, Amsterdam (pp. 109–127).

Siegel, S. (1956). Nonparametric statistics for the behavioral sciences . New York: McGraw-hill.

MATH   Google Scholar  

Strübing, J. (2007). Research as pragmatic problem-solving: The pragmatist roots of empirically-grounded theorizing. In The Sage handbook of grounded theory (pp. 580–602).

Teufel, S., et al. (2000). Argumentative zoning: Information extraction from scientific text. PhD Thesis, Citeseer .

Turney, P. D. (2002). Thumbs up or thumbs down?: Semantic orientation applied to unsupervised classification of reviews. In Proceedings of the 40th annual meeting on association for computational linguistics, association for computational linguistics (pp. 417–424).

Van Dijk, T. A. (1980). Text and context explorations in the semantics and pragmatics of discourse . London: Longman.

Wiebe, J., Wilson, T., & Cardie, C. (2005). Annotating expressions of opinions and emotions in language. Language Resources and Evaluation , 39 (2), 165–210.

Wilson, T., Wiebe, J., & Hoffmann, P. (2005). Recognizing contextual polarity in phrase-level sentiment analysis. In Proceedings of the conference on human language technology and empirical methods in natural language processing, association for computational linguistics (pp. 347–354).

Winter, E. O. (1968). Some aspects of cohesion. In Sentence and clause in scientific English . University College London.

Zhou, M., Frank, A., Friedrich, A., & Palmer, A. (2015). Semantically enriched models for modal sense classification. In Workshop on linking models of lexical, sentential and discourse-level semantics (LSDSem) (p. 44).

Download references

Acknowledgements

The first author has been supported by an EPSRC studentship (Award Ref: 1641528). We thank the reviewers for their helpful comments.

Author information

Authors and affiliations.

Department of Computer Science and Technology, University of Cambridge, 15 JJ Thomson Avenue, Cambridge, CB3 0FD, UK

Kevin Heffernan & Simone Teufel

You can also search for this author in PubMed   Google Scholar

Corresponding author

Correspondence to Kevin Heffernan .

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License ( http://creativecommons.org/licenses/by/4.0/ ), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Reprints and permissions

About this article

Heffernan, K., Teufel, S. Identifying problems and solutions in scientific text. Scientometrics 116 , 1367–1382 (2018). https://doi.org/10.1007/s11192-018-2718-6

Download citation

Received : 08 October 2017

Published : 06 April 2018

Issue Date : August 2018

DOI : https://doi.org/10.1007/s11192-018-2718-6

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

• Problem-solving patterns
• Machine learning
• Find a journal
• Publish with us
• Track your research

January 6, 2020

The Most Important Scientific Problems Have Yet to Be Solved

If certain areas of science appear to be quite mature, others are in the process of development, and yet others remain to be born

By Santiago Ramón y Cajal

Santiago Ramón y Cajal in the 1880s.

This article was published in Scientific American’s former blog network and reflects the views of the author, not necessarily those of Scientific American

Santiago Ramón y Cajal (1852-1934) was a neuroscientist and pathologist, and Spain’s first Nobel laureate. This excerpt from his book Advice for a Young Investigator was first posted on the MIT Press Reader on January 6, 2020. An essay on his remarkable scientific drawings appeared in Scientific American in 2015.

Here is a false concept often heard from the lips of the newly graduated: “Everything of major importance in the various areas of science has already been clarified. What difference does it make if I add some minor detail or gather up what is left in some field where more diligent observers have already collected the abundant, ripe grain. Science won’t change its perspective because of my work, and my name will never emerge from obscurity.”

This is often indolence masquerading as modesty. However, it is also expressed by worthy young men reflecting on the first pangs of dismay experienced when undertaking some major project. This superficial concept of science must be eradicated by the young investigator who does not wish to fail, hopelessly overcome by the struggle developing in his mind between the utilitarian suggestions that are part and parcel of his ethical environment (which may soon convert him to an ordinary and financially successful general practitioner), and those nobler impulses of duty and loyalty urging him on to achievement and honor.

On supporting science journalism

If you're enjoying this article, consider supporting our award-winning journalism by subscribing . By purchasing a subscription you are helping to ensure the future of impactful stories about the discoveries and ideas shaping our world today.

Wanting to earn the trust placed in him by his mentors, the inexperienced observer hopes to discover a new lode at the earth’s surface, where easy exploration will build his reputation quickly. Unfortunately, with his first excursions into the literature hardly begun, he is shocked to find that the metal lies deep within the ground—surface deposits have been virtually exhausted by observers fortunate enough to arrive earlier and exercise their simple right of eminent domain.

It is nevertheless true that if we arrived on the scene too late for certain problems, we were also born too early to help solve others. Within a century we shall come, by the natural course of events, to monopolize science, plunder its major assets, and harvest its vast fields of data.

Yet we must recognize that there are times when, on the heels of a chance discovery or the development of an important new technique, magnificent scientific discoveries occur one after another as if by spontaneous generation. This happened during the Renaissance when Descartes, Pascal, Galileo, Bacon, Boyle, Newton, our own Sanchez, and others revealed clearly the errors of the ancients and spread the belief that the Greeks, far from exhausting the field of science, had scarcely taken the first steps in understanding the universe. It is a wonderful and fortunate thing for a scientist to be born during one of these great decisive moments in the history of ideas, when much of what has been done in the past is invalidated. Under these circumstances, it could not be easier to choose a fertile area of investigation.

However, let us not exaggerate the importance of such events. Instead, bear in mind that even in our own time science is often built on the ruins of theories once thought to be indestructible. It is important to realize that if certain areas of science appear to be quite mature, others are in the process of development, and yet others remain to be born. Especially in biology, where immense amounts of work have been carried out during the last century, the most essential problems remain unsolved—the origin of life, the problems of heredity and development, the structure and chemical composition of the cell, and so on.

It is fair to say that, in general, no problems have been exhausted; instead, men have been exhausted by the problems. Soil that appears impoverished to one researcher reveals its fertility to another. Fresh talent approaching the analysis of a problem without prejudice will always see new possibilities—some aspect not considered by those who believe that a subject is fully understood. Our knowledge is so fragmentary that unexpected findings appear in even the most fully explored topics. Who, a few short years ago, would have suspected that light and heat still held scientific secrets in reserve? Nevertheless, we now have  argon  in the atmosphere, the  x-rays  of Roentgen, and the  radium  of the Curies, all of which illustrate the inadequacy of our former methods, and the prematurity of our former syntheses.

The best application of the following beautiful dictum of Geoffroy Saint-Hilaire is in biology: “The infinite is always before us.” And the same applies to Carnoy’s no less graphic thought: “Science is a perpetual creative process.” Not everyone is destined to venture into the forest and by sheer determination carve out a serviceable road. However, even the most humble among us can take advantage of the path opened by genius and by traveling along it extract one or another secret from the unknown.

If the beginner is willing to accept the role of gathering details that escaped the wise discoverer, he can be assured that those searching for minutiae eventually acquire an analytical sense so discriminating, and powers of observation so keen, that they are able to solve important problems successfully.

So many apparently trivial observations have led investigators with a thorough knowledge of methods to great scientific conquests! Furthermore, we must bear in mind that because science relentlessly differentiates, the minutiae of today often become important principles tomorrow.

It is also essential to remember that our appreciation of what is important and what is minor, what is great and what is small, is based on false wisdom, on a true anthropomorphic error. Superior and inferior do not exist in nature, nor do primary and secondary relationships. The hierarchies that our minds take pleasure in assigning to natural phenomena arise from the fact that instead of considering things individually, and how they are interrelated, we view them strictly from the perspective of their usefulness or the pleasure they give us. In the chain of life all links are equally valuable because all prove equally necessary.

Things that we see from a distance or do not know how to evaluate are considered small. Even assuming the perspective of human egotism, think how many issues of profound importance to humanity lie within the protoplasm of the simplest microbe! Nothing seems more important in bacteriology than a knowledge of infectious bacteria, and nothing more secondary than the inoffensive microbes that grow abundantly in decomposing organic material. Nevertheless, if these humble fungi—whose mission is to return to the general circulation of matter those substances incorporated by the higher plants and animals—were to disappear, humans could not inhabit the planet.

The far-reaching importance of attention to detail in technical methodology is perhaps demonstrated more clearly in biology than in any other sphere. To cite but one example, recall that Koch, the great German bacteriologist, thought of adding a little alkali to a basic aniline dye, and this allowed him to stain and thus discover the tubercle bacillus—revealing the etiology of a disease that had until then remained uncontrolled by the wisdom of the most illustrious pathologists.

Even the most prominent of the great geniuses have demonstrated a lack of intellectual perspective in the appraisal of scientific insights. Today, we can find many seeds of great discoveries that were mentioned as curiosities of little importance in the writings of the ancients, and even in those of the wise men of the Renaissance. Lost in the pages of a confused theological treatise ( Christianismi restitutio ) are three apparently disdainful lines written by Servetus referring to the pulmonary circulation, which now constitute his major claim to fame. The Aragonese philosopher would be surprised indeed if he were to rise from the dead today. He would find his laborious metaphysical disquisitions totally forgotten, whereas the observation he used simply to argue for the residence of the soul in the blood is widely praised! Or again, it has been inferred from a passage of Seneca’s that the ancients knew the magnifying powers of a crystal sphere filled with water. Who would have suspected that in this phenomenon of magnification, disregarded for centuries, slumbered the embryo of two powerful analytical instruments, the microscope and telescope—and two equally great sciences, biology and astronomy!

In summary, there are no small problems. Problems that appear small are large problems that are not understood. Instead of tiny details unworthy of the intellectual, we have men whose tiny intellects cannot rise to penetrate the infinitesimal. Nature is a harmonious mechanism where all parts, including those appearing to play a secondary role, cooperate in the functional whole. In contemplating this mechanism, shallow men arbitrarily divide its parts into essential and secondary, whereas the insightful thinker is content with classifying them as understood and poorly understood, ignoring for the moment their size and immediately useful properties. No one can predict their importance in the future.

7 Science Fair Projects that Solve Problems

• August 5, 2023

Share this post:

Science fair projects that solve problems are a great way for students to test their interest and aptitude for a career in STEM (science-technology-engineering-math). But they shouldn’t choose just any old topic. To make the most of the opportunity, try to focus on projects with real-world applications. This will give them hands-on experience directly related to a good-paying job field, like  engineering .

With planning and hard work, the right science fair project might bump up a student’s chances for a scholarship or a trip to one of the science competitions sponsored by the Society for Science .

Do your students need help sketching the experimental set-up for a science fair presentation? Check out these resources:

• No-Prep Worksheets – How to Draw like an Engineer and Isometric Drawing
• 3D Isometric Drawing and Design for Middle School
• My Engineering Draw & Write Journal for Kids : 48 Fun Drawing and Writing Prompts to Learn about the Engineering Design Process.

Don’t get me wrong — creating foaming volcanoes or diagramming the human circulatory system are fun and classic ideas for a science fair project. But unless your student plans to go to med school or major in geology, these typical projects won’t do much to advance his or her future career. Far more practical engineering jobs will be available in the 21st century.

In this post you’ll find seven problem-solving science fair projects gleaned from the Education.com website. They provide simple, but realistic, introductions to real-world careers in electronics, robotics & automation, and construction engineering.

For more help with choosing a science fair topic, setting up your experiment, collecting and analyzing the data, and presenting your results, visit NASA’s video page on How to do a Science Fair Project .

Solving problems in Smart Technology

Consider the hottest topic in industry today – Smart Manufacturing, or Industry 4.0, sometimes called the Industrial Internet of Things (IIOT). Industry 4.0 is just one facet of the global push towards Smart Cities, Smart Homes, and Smart Agriculture.

All these concepts center on wireless connectivity between machines using cellular networks. So, for Smart Homes, this means your utilities, fridge, lights, security, HVAC, and other systems would be connected through an app on your smartphone. From there you can track and control these systems to keep your home safe and comfortable, while reducing water and energy use.

[Click here to join the STEM-Inspirations mailing list ]

For Industry 4.0, companies are connecting the machines used in their manufacturing and power generation plants at different locations around the world. On top of that, they are creating “digital twins” of each machine, which are 3D animated computer models of the machines.

The idea is to collect real-time data from each machine and then use that data, along with artificial intelligence (AI), machine vision, and even virtual reality simulations, to:

• Design new products
• Predict when a machine will need maintenance BEFORE something goes wrong
• Optimize the output of the machines and harmonize them to work together

Solving problems in Robotics

Another major topic in industry is  robotics and automation . Automation means that machines are programmed to perform tasks without human help. Some robots are standalone, “service” robots, like the Roomba. Others, like robotic arms in factories and warehouses, pick and place items to be processed.

The more human-friendly “collaborative” robots can improve human capacity and are safe to work around. Put together, these technologies allow some manufacturing plants to run “lights out,” without any human input for days.

Robots are boosting agriculture, both in planting and harvesting fields and in packaging food. With Smart Agriculture technology, farmers collect data in their fields with mobile apps applying artificial intelligence (AI) software to reduce fertilizer needs and optimize water use.

Help students sketch their experimental set-up for science fair presentations with these resources: No-Prep Worksheets – How to Draw like an Engineer and Isometric Drawing 3D Isometric Drawing and Design for Middle School My Engineering Draw & Write Journal for Kids : 48 Fun Drawing and Writing Prompts to Learn about the Engineering Design Process.

Solving Engineering Problems

Most science fair projects on the internet seem to focus on the basic sciences, like biology and chemistry. But in light of the skills gap we are now experiencing between the available job force and manufacturing industry requirements, I believe engineering-focused science fair projects that solve problems in Industry 4.0, robotics, automation, and construction may be better choices for building up tomorrow’s workforce.

Here are 7 science fair project ideas that focus on solving problems:

1. cell phone dead zones science fair project.

https://www.education.com/science-fair/article/cell-phone-dead-zones/

Students learn how wireless networks work, find dead zones where wireless signals are lost, and determine ways to reduce these zones – important preparation for students who hope to work on Smart Homes, Smart Factories, Smart Cities, or Smart Agriculture.

2. App development science fair project

https://www.education.com/science-fair/article/iphone-application-design/

An app on a phone or tablet can be an interactive game, a navigational device, a business software package, or just about anything else you can imagine. This project allows you to get a head start in the growing app design field by designing your own app for popular smartphones.

3. Smoke detector science fair project

https://www.education.com/science-fair/article/smoke-detectors-working/?source=related_materials&order=2

Sensors of all kinds solve problems for smart technologies and robotics engineering. Sensors can detect motion, gases, light, heat, and other changes in the environment to allow robots to avoid collisions or Smart Homes to detect a fire, for example. This project compares the effectiveness of two types of sensors in a smoke detector.

4. Faraday’s experiment science fair project

https://www.education.com/science-fair/article/faraday-experiment-current-generated-magnet/

Electric currents create their own magnetic fields, and the movement of magnets induces , or creates, current in a wire. Motors and generators use magnetic movement to create current and send electricity to do useful work to power machines. In this lab, you will recreate Michael Faraday’s famous experiment by building a solenoid  (a coil of wire) and experiment with moving magnets to produce current.

5 & 6. EMFs science fair projects

https://www.education.com/science-fair/article/smart-card-electromagnetic-fields/

https://www.education.com/science-fair/article/EMF-affect-us/

Radio Frequency Identification (RFID) is an electronic technology used in credit cards, ID Cards, and theft prevention systems, as well as in manufacturing, warehousing and shipping products. The first project measures the electromagnetic fields (EMFs) given off by various RFID transmitters, which may have harmful effects on people. The second project looks directly at how EMFs can affect us physically.

7. Rust prevention science fair project

https://www.education.com/science-fair/article/bust-that-rust/

Metals rust, and that can be a big problem when it comes to bridges, buildings, cars, and any object exposed to air and water. This project examines the process of oxidation (not just rust) that ultimately breaks down every physical object and looks at ways to prevent that from happening.

For more problem-solving science fair project ideas, follow the STEM-Inspirations Science Fair Projects board on Pinterest.

Copyright © 2017-2021 by Holly B. Martin

Click here to join the STEM-Inspirations mailing list .

Hi, I'm Holly!

I help you educate and inspire students to pursue careers in STEM/STEAM!

Click here to learn more about me and how I can help you .

ChatGPT for Teachers

Trauma-informed practices in schools, teacher well-being, cultivating diversity, equity, & inclusion, integrating technology in the classroom, social-emotional development, covid-19 resources, invest in resilience: summer toolkit, civics & resilience, all toolkits, degree programs, trauma-informed professional development, teacher licensure & certification, how to become - career information, classroom management, instructional design, lifestyle & self-care, online higher ed teaching, current events, stem projects that tackle real-world problems.

STEM learning is largely about designing creative solutions for real-world problems. When students learn within the context of authentic, problem-based STEM design, they can more clearly see the genuine impact of their learning. That kind of authenticity builds engagement, taking students from groans of “When will I ever use this?” to a genuine connection between skills and application.

Using STEM to promote critical thinking and innovation

“Educational outcomes in traditional settings focus on how many answers a student knows. We want students to learn how to develop a critical stance with their work: inquiring, editing, thinking flexibly, and learning from another person’s perspective,” says Arthur L. Costa in his book Learning and Leading with Habits of Mind . “The critical attribute of intelligent human beings is not only having information but also knowing how to act on it.”

Invention and problem-solving aren’t just for laboratory thinkers hunkered down away from the classroom. Students from elementary to high school can wonder, design, and invent a real product that solves real problems. “ Problem-solving involves finding answers to questions and solutions for undesired effects. STEM lessons revolve around the engineering design process (EDP) — an organized, open-ended approach to investigation that promotes creativity, invention, and prototype design, along with testing and analysis,” says Ann Jolly in her book STEM by Design . “These iterative steps will involve your students in asking critical questions about the problem, and guide them through creating and testing actual prototypes to solve that problem.”

STEM projects that use real-world problems

Here are some engaging projects that get your students thinking about how to solve real-world problems.

Preventing soil erosion

In this project, meant for sixth – 12th grade, students learn to build a seawall to protest a coastline from erosion, calculating wave energy to determine the best materials for the job.  See the project.

Growing food during a flood

A natural disaster that often devastates communities, floods can make it difficult to grow food. In this project, students explore “a problem faced by farmers in Bangladesh and how to grow food even when the land floods.”  See the project .

Solving a city’s design needs

Get your middle or high school students involved in some urban planning. Students can identify a city’s issues, relating to things like transportation, the environment, or overcrowding — and design solutions. See the project here or this Lego version for younger learners.

Creating clean water

Too many areas of the world — including cities in our own country — do not have access to clean water. In this STEM project, teens will learn how to build and test their own water filtration systems.  See the project here .

Improving the lives of those with disabilities

How can someone with crutches or a wheelchair carry what they need? Through some crafty designs! This project encourages middle school students to think creatively  and  to participate in civic engagement.   See the project here .

Cleaning up an oil spill

We’ve all seen images of beaches and wildlife covered in oil after a disastrous spill. This project gets elementary to middle school students designing and testing oil spill clean-up kits. See the project here .

Building earthquake-resistant structures

With the ever-increasing amount of devastating earthquakes around the world, this project solves some major problems. Elementary students can learn to create earthquake resistant structures in their classroom. See the project here .

Constructing solar ovens

In remote places or impoverished areas, it’s possible to make solar ovens to safely cook food. In this project, elementary students construct solar ovens to learn all about how they work and their environmental and societal impact.  See the project here .

Stopping apple oxidization

Stop those apples from turning brown with this oxidation-based project. Perfect for younger learners, students can predict, label, count, and experiment! See the project here .

Advancing as a STEAM educator

The push for STEM has evolved into the STEAM movement, adding the arts for further enrichment and engagement. There are so many ways to embed STEM or STEAM lessons in your curriculum, but doing it well requires foundational knowledge and professional development. Imagine what type of impact you could have on your students and your community if you were supported by a theoretical framework, a variety of strategies, and a wealth of ideas and resources.

You may also like to read

• Teaching STEM: Challenging Students to Think Through Tough Problems
• Professional Development Resources for STEM Teachers
• What is the Washington State STEM Lighthouse Program?
• Characteristics of a Great STEAM Program
• Building a Partnership Between Your School and a STEAM Organization
• The Art of Inquiry in STEAM Education

Categorized as: Tips for Teachers and Classroom Resources

Tagged as: Art ,  Educational Technology ,  Engaging Activities ,  Math and Science ,  Science ,  STEAM

• Online & Campus Master's in Elementary Educat...
• 2020 Civics Engagement & Resilience: Tools fo...
• Online & Campus Master's in Curriculum Develo...

• Publications
• Conferences & Events
• Professional Learning
• Science Standards
• Awards & Competitions
• Daily Do Lesson Plans
• Free Resources
• American Rescue Plan
• For Preservice Teachers
• NCCSTS Case Collection
• Partner Jobs in Education
• Interactive eBooks+
• Digital Catalog
• Regional Product Representatives
• e-Newsletters
• Bestselling Books
• Latest Books
• Popular Book Series
• Prospective Authors
• Web Seminars
• Exhibits & Sponsorship
• Conference Reviewers
• National Conference • Denver 24
• Leaders Institute 2024
• National Conference • New Orleans 24
• Submit a Proposal
• Latest Resources
• Professional Learning Units & Courses
• For Districts
• Online Course Providers
• Schools & Districts
• College Professors & Students
• The Standards
• Teachers and Admin
• eCYBERMISSION
• Toshiba/NSTA ExploraVision
• Junior Science & Humanities Symposium
• Teaching Awards
• Climate Change
• Earth & Space Science
• New Science Teachers
• Early Childhood
• Middle School
• High School
• Postsecondary
• Informal Education
• Journal Articles
• Lesson Plans
• e-newsletters
• Science & Children
• Science Scope
• The Science Teacher
• Journal of College Sci. Teaching
• Connected Science Learning
• NSTA Reports
• Next-Gen Navigator
• Science Update
• Teacher Tip Tuesday
• Trans. Sci. Learning

MyNSTA Community

• My Collections

A Problem-Solving Experiment

Using Beer’s Law to Find the Concentration of Tartrazine

The Science Teacher—January/February 2022 (Volume 89, Issue 3)

By Kevin Mason, Steve Schieffer, Tara Rose, and Greg Matthias

Share Start a Discussion

A problem-solving experiment is a learning activity that uses experimental design to solve an authentic problem. It combines two evidence-based teaching strategies: problem-based learning and inquiry-based learning. The use of problem-based learning and scientific inquiry as an effective pedagogical tool in the science classroom has been well established and strongly supported by research ( Akinoglu and Tandogan 2007 ; Areepattamannil 2012 ; Furtak, Seidel, and Iverson 2012 ; Inel and Balim 2010 ; Merritt et al. 2017 ; Panasan and Nuangchalerm 2010 ; Wilson, Taylor, and Kowalski 2010 ).

Floyd James Rutherford, the founder of the American Association for the Advancement of Science (AAAS) Project 2061 once stated, “To separate conceptually scientific content from scientific inquiry,” he underscored, “is to make it highly probable that the student will properly understand neither” (1964, p. 84). A more recent study using randomized control trials showed that teachers that used an inquiry and problem-based pedagogy for seven months improved student performance in math and science ( Bando, Nashlund-Hadley, and Gertler 2019 ). A problem-solving experiment uses problem-based learning by posing an authentic or meaningful problem for students to solve and inquiry-based learning by requiring students to design an experiment to collect and analyze data to solve the problem.

In the problem-solving experiment described in this article, students used Beer’s Law to collect and analyze data to determine if a person consumed a hazardous amount of tartrazine (Yellow Dye #5) for their body weight. The students used their knowledge of solutions, molarity, dilutions, and Beer’s Law to design their own experiment and calculate the amount of tartrazine in a yellow sports drink (or citrus-flavored soda).

According to the Next Generation Science Standards, energy is defined as “a quantitative property of a system that depends on the motion and interactions of matter and radiation with that system” ( NGSS Lead States 2013 ). Interactions of matter and radiation can be some of the most challenging for students to observe, investigate, and conceptually understand. As a result, students need opportunities to observe and investigate the interactions of matter and radiation. Light is one example of radiation that interacts with matter.

Light is electromagnetic radiation that is detectable to the human eye and exhibits properties of both a wave and a particle. When light interacts with matter, light can be reflected at the surface, absorbed by the matter, or transmitted through the matter ( Figure 1 ). When a single beam of light enters a substance at a perpendicularly (at a 90 ° angle to the surface), the amount of reflection is minimal. Therefore, the light will either be absorbed by the substance or be transmitted through the substance. When a given wavelength of light shines into a solution, the amount of light that is absorbed will depend on the identity of the substance, the thickness of the container, and the concentration of the solution.

Light interacting with matter.

(Retrieved from https://etorgerson.files.wordpress.com/2011/05/light-reflect-refract-absorb-label.jpg ).

Beer’s Law states the amount of light absorbed is directly proportional to the thickness and concentration of a solution. Beer’s Law is also sometimes known as the Beer-Lambert Law. A solution of a higher concentration will absorb more light and transmit less light ( Figure 2 ). Similarly, if the solution is placed in a thicker container that requires the light to pass through a greater distance, then the solution will absorb more light and transmit less light.

Light transmitted through a solution.

(Retrieved from https://media.springernature.com/original/springer-static/image/chp%3A10.1007%2F978-3-319-57330-4_13/MediaObjects/432946_1_En_13_Fig4_HTML.jpg ).

Definitions of key terms.

Absorbance (A) – the process of light energy being captured by a substance

Beer’s Law (Beer-Lambert Law) – the absorbance (A) of light is directly proportional to the molar absorptivity (ε), thickness (b), and concentration (C) of the solution (A = εbC)

Concentration (C) – the amount of solute dissolved per amount of solution

Cuvette – a container used to hold a sample to be tested in a spectrophotometer

Energy (E) – a quantitative property of a system that depends on motion and interactions of matter and radiation with that system (NGSS Lead States 2013).

Intensity (I) – the amount or brightness of light

Light – electromagnetic radiation that is detectable to the human eye and exhibits properties of both a wave and a particle

Molar Absorptivity (ε) – a property that represents the amount of light absorbed by a given substance per molarity of the solution and per centimeter of thickness (M-1 cm-1)

Molarity (M) – the number of moles of solute per liters of solution (Mol/L)

Reflection – the process of light energy bouncing off the surface of a substance

Spectrophotometer – a device used to measure the absorbance of light by a substance

Tartrazine – widely used food and liquid dye

Transmittance (T) – the process of light energy passing through a substance

The amount of light absorbed by a solution can be measured using a spectrophotometer. The solution of a given concentration is placed in a small container called a cuvette. The cuvette has a known thickness that can be held constant during the experiment. It is also possible to obtain cuvettes of different thicknesses to study the effect of thickness on the absorption of light. The key definitions of the terms related to Beer’s Law and the learning activity presented in this article are provided in Figure 3 .

Overview of the problem-solving experiment

In the problem presented to students, a 140-pound athlete drinks two bottles of yellow sports drink every day ( Figure 4 ; see Online Connections). When she starts to notice a rash on her skin, she reads the label of the sports drink and notices that it contains a yellow dye known as tartrazine. While tartrazine is safe to drink, it may produce some potential side effects in large amounts, including rashes, hives, or swelling. The students must design an experiment to determine the concentration of tartrazine in the yellow sports drink and the number of milligrams of tartrazine in two bottles of the sports drink.

While a sports drink may have many ingredients, the vast majority of ingredients—such as sugar or electrolytes—are colorless when dissolved in water solution. The dyes added to the sports drink are responsible for the color of the sports drink. Food manufacturers may use different dyes to color sports drinks to the desired color. Red dye #40 (allura red), blue dye #1 (brilliant blue), yellow dye #5 (tartrazine), and yellow dye #6 (sunset yellow) are the four most common dyes or colorants in sports drinks and many other commercial food products ( Stevens et al. 2015 ). The concentration of the dye in the sports drink affects the amount of light absorbed.

In this problem-solving experiment, the students used the previously studied concept of Beer’s Law—using serial dilutions and absorbance—to find the concentration (molarity) of tartrazine in the sports drink. Based on the evidence, the students then determined if the person had exceeded the maximum recommended daily allowance of tartrazine, given in mg/kg of body mass. The learning targets for this problem-solving experiment are shown in Figure 5 (see Online Connections).

Pre-laboratory experiences

A problem-solving experiment is a form of guided inquiry, which will generally require some prerequisite knowledge and experience. In this activity, the students needed prior knowledge and experience with Beer’s Law and the techniques in using Beer’s Law to determine an unknown concentration. Prior to the activity, students learned how Beer’s Law is used to relate absorbance to concentration as well as how to use the equation M 1 V 1 = M 2 V 2 to determine concentrations of dilutions. The students had a general understanding of molarity and using dimensional analysis to change units in measurements.

The techniques for using Beer’s Law were introduced in part through a laboratory experiment using various concentrations of copper sulfate. A known concentration of copper sulfate was provided and the students followed a procedure to prepare dilutions. Students learned the technique for choosing the wavelength that provided the maximum absorbance for the solution to be tested ( λ max ), which is important for Beer’s Law to create a linear relationship between absorbance and solution concentration. Students graphed the absorbance of each concentration in a spreadsheet as a scatterplot and added a linear trend line. Through class discussion, the teacher checked for understanding in using the equation of the line to determine the concentration of an unknown copper sulfate solution.

After the students graphed the data, they discussed how the R2 value related to the data set used to construct the graph. After completing this experiment, the students were comfortable making dilutions from a stock solution, calculating concentrations, and using the spectrophotometer to use Beer’s Law to determine an unknown concentration.

Introducing the problem

After the initial experiment on Beer’s Law, the problem-solving experiment was introduced. The problem presented to students is shown in Figure 4 (see Online Connections). A problem-solving experiment provides students with a valuable opportunity to collaborate with other students in designing an experiment and solving a problem. For this activity, the students were assigned to heterogeneous or mixed-ability laboratory groups. Groups should be diversified based on gender; research has shown that gender diversity among groups improves academic performance, while racial diversity has no significant effect ( Hansen, Owan, and Pan 2015 ). It is also important to support students with special needs when assigning groups. The mixed-ability groups were assigned intentionally to place students with special needs with a peer who has the academic ability and disposition to provide support. In addition, some students may need additional accommodations or modifications for this learning activity, such as an outlined lab report, a shortened lab report format, or extended time to complete the analysis. All students were required to wear chemical-splash goggles and gloves, and use caution when handling solutions and glass apparatuses.

Designing the experiment

During this activity, students worked in lab groups to design their own experiment to solve a problem. The teacher used small-group and whole-class discussions to help students understand the problem. Students discussed what information was provided and what they need to know and do to solve the problem. In planning the experiment, the teacher did not provide a procedure and intentionally provided only minimal support to the students as needed. The students designed their own experimental procedure, which encouraged critical thinking and problem solving. The students needed to be allowed to struggle to some extent. The teacher provided some direction and guidance by posing questions for students to consider and answer for themselves. Students were also frequently reminded to review their notes and the previous experiment on Beer’s Law to help them better use their resources to solve the problem. The use of heterogeneous or mixed-ability groups also helped each group be more self-sufficient and successful in designing and conducting the experiment.

Students created a procedure for their experiment with the teacher providing suggestions or posing questions to enhance the experimental design, if needed. Safety was addressed during this consultation to correct safety concerns in the experimental design or provide safety precautions for the experiment. Students needed to wear splash-proof goggles and gloves throughout the experiment. In a few cases, students realized some opportunities to improve their experimental design during the experiment. This was allowed with the teacher’s approval, and the changes to the procedure were documented for the final lab report.

Conducting the experiment

A sample of the sports drink and a stock solution of 0.01 M stock solution of tartrazine were provided to the students. There are many choices of sports drinks available, but it is recommended that the ingredients are checked to verify that tartrazine (yellow dye #5) is the only colorant added. This will prevent other colorants from affecting the spectroscopy results in the experiment. A citrus-flavored soda could also be used as an alternative because many sodas have tartrazine added as well. It is important to note that tartrazine is considered safe to drink, but it may produce some potential side effects in large amounts, including rashes, hives, or swelling. A list of the materials needed for this problem-solving experiment is shown in Figure 6 (see Online Connections).

This problem-solving experiment required students to create dilutions of known concentrations of tartrazine as a reference to determine the unknown concentration of tartrazine in a sports drink. To create the dilutions, the students were provided with a 0.01 M stock solution of tartrazine. The teacher purchased powdered tartrazine, available from numerous vendors, to create the stock solution. The 0.01 M stock solution was prepared by weighing 0.534 g of tartrazine and dissolving it in enough distilled water to make a 100 ml solution. Yellow food coloring could be used as an alternative, but it would take some research to determine its concentration. Since students have previously explored the experimental techniques, they should know to prepare dilutions that are somewhat darker and somewhat lighter in color than the yellow sports drink sample. Students should use five dilutions for best results.

Typically, a good range for the yellow sports drink is standard dilutions ranging from 1 × 10-3 M to 1 × 10-5 M. The teacher may need to caution the students that if a dilution is too dark, it will not yield good results and lower the R2 value. Students that used very dark dilutions often realized that eliminating that data point created a better linear trendline, as long as it didn’t reduce the number of data points to fewer than four data points. Some students even tried to use the 0.01 M stock solution without any dilution. This was much too dark. The students needed to do substantial dilutions to get the solutions in the range of the sports drink.

After the dilutions are created, the absorbance of each dilution was measured using a spectrophotometer. A Vernier SpectroVis (~$400) spectrophotometer was used to measure the absorbance of the prepared dilutions with known concentrations. The students adjusted the spectrophotometer to use different wavelengths of light and selected the wavelength with the highest absorbance reading. The same wavelength was then used for each measurement of absorbance. A wavelength of 650 nanometers (nm) provided an accurate measurement and good linear relationship. After measuring the absorbance of the dilutions of known concentrations, the students measured the absorbance of the sports drink with an unknown concentration of tartrazine using the spectrophotometer at the same wavelength. If a spectrophotometer is not available, a color comparison can be used as a low-cost alternative for completing this problem-solving experiment ( Figure 7 ; see Online Connections).

Analyzing the results

After completing the experiment, the students graphed the absorbance and known tartrazine concentrations of the dilutions on a scatter-plot to create a linear trendline. In this experiment, absorbance was the dependent variable, which should be graphed on the y -axis. Some students mistakenly reversed the axes on the scatter-plot. Next, the students used the graph to find the equation for the line. Then, the students solve for the unknown concentration (molarity) of tartrazine in the sports drink given the linear equation and the absorbance of the sports drink measured experimentally.

To answer the question posed in the problem, the students also calculated the maximum amount of tartrazine that could be safely consumed by a 140 lb. person, using the information given in the problem. A common error in solving the problem was not converting the units of volume given in the problem from ounces to liters. With the molarity and volume in liters, the students then calculated the mass of tartrazine consumed per day in milligrams. A sample of the graph and calculations from one student group are shown in Figure 8 . Finally, based on their calculations, the students answered the question posed in the original problem and determined if the person’s daily consumption of tartrazine exceeded the threshold for safe consumption. In this case, the students concluded that the person did NOT consume more than the allowable daily limit of tartrazine.

Sample graph and calculations from a student group.

Communicating the results

After conducting the experiment, students reported their results in a written laboratory report that included the following sections: title, purpose, introduction, hypothesis, materials and methods, data and calculations, conclusion, and discussion. The laboratory report was assessed using the scoring rubric shown in Figure 9 (see Online Connections). In general, the students did very well on this problem-solving experiment. Students typically scored a three or higher on each criteria of the rubric. Throughout the activity, the students successfully demonstrated their ability to design an experiment, collect data, perform calculations, solve a problem, and effectively communicate those results.

This activity is authentic problem-based learning in science as the true concentration of tartrazine in the sports drink was not provided by the teacher or known by the students. The students were generally somewhat biased as they assumed the experiment would result in exceeding the recommended maximum consumption of tartrazine. Some students struggled with reporting that the recommended limit was far higher than the two sports drinks consumed by the person each day. This allows for a great discussion about the use of scientific methods and evidence to provide unbiased answers to meaningful questions and problems.

The most common errors in this problem-solving experiment were calculation errors, with the most common being calculating the concentrations of the dilutions (perhaps due to the use of very small concentrations). There were also several common errors in communicating the results in the laboratory report. In some cases, students did not provide enough background information in the introduction of the report. When the students communicated the results, some students also failed to reference specific data from the experiment. Finally, in the discussion section, some students expressed concern or doubts in the results, not because there was an obvious error, but because they did not believe the level consumed could be so much less than the recommended consumption limit of tartrazine.

The scientific study and investigation of energy and matter are salient topics addressed in the Next Generation Science Standards ( Figure 10 ; see Online Connections). In a chemistry classroom, students should have multiple opportunities to observe and investigate the interaction of energy and matter. In this problem-solving experiment students used Beer’s Law to collect and analyze data to determine if a person consumed an amount of tartrazine that exceeded the maximum recommended daily allowance. The students correctly concluded that the person in the problem did not consume more than the recommended daily amount of tartrazine for their body weight.

In this activity students learned to work collaboratively to design an experiment, collect and analyze data, and solve a problem. These skills extend beyond any one science subject or class. Through this activity, students had the opportunity to do real-world science to solve a problem without a previously known result. The process of designing an experiment may be difficult for some students that are often accustomed to being given an experimental procedure in their previous science classroom experiences. However, because students sometimes struggled to design their own experiment and perform the calculations, students also learned to persevere in collecting and analyzing data to solve a problem, which is a valuable life lesson for all students. ■

Online Connections

The Beer-Lambert Law at Chemistry LibreTexts: https://bit.ly/3lNpPEi

Beer’s Law – Theoretical Principles: https://teaching.shu.ac.uk/hwb/chemistry/tutorials/molspec/beers1.htm

Beer’s Law at Illustrated Glossary of Organic Chemistry: http://www.chem.ucla.edu/~harding/IGOC/B/beers_law.html

Beer Lambert Law at Edinburgh Instruments: https://www.edinst.com/blog/the-beer-lambert-law/

Beer’s Law Lab at PhET Interactive Simulations: https://phet.colorado.edu/en/simulation/beers-law-lab

Figure 4. Problem-solving experiment problem statement: https://bit.ly/3pAYHtj

Figure 5. Learning targets: https://bit.ly/307BHtb

Figure 6. Materials list: https://bit.ly/308a57h

Figure 7. The use of color comparison as a low-cost alternative: https://bit.ly/3du1uyO

Figure 9. Summative performance-based assessment rubric: https://bit.ly/31KoZRj

Figure 10. Connecting to the Next Generation Science Standards : https://bit.ly/3GlJnY0

Kevin Mason ( [email protected] ) is Professor of Education at the University of Wisconsin–Stout, Menomonie, WI; Steve Schieffer is a chemistry teacher at Amery High School, Amery, WI; Tara Rose is a chemistry teacher at Amery High School, Amery, WI; and Greg Matthias is Assistant Professor of Education at the University of Wisconsin–Stout, Menomonie, WI.

Akinoglu, O., and R. Tandogan. 2007. The effects of problem-based active learning in science education on students’ academic achievement, attitude and concept learning. Eurasia Journal of Mathematics, Science, and Technology Education 3 (1): 77–81.

Areepattamannil, S. 2012. Effects of inquiry-based science instruction on science achievement and interest in science: Evidence from Qatar. The Journal of Educational Research 105 (2): 134–146.

Bando R., E. Nashlund-Hadley, and P. Gertler. 2019. Effect of inquiry and problem-based pedagogy on learning: Evidence from 10 field experiments in four countries. The National Bureau of Economic Research 26280.

Furtak, E., T. Seidel, and H. Iverson. 2012. Experimental and quasi-experimental studies of inquiry-based science teaching: A meta-analysis. Review of Educational Research 82 (3): 300–329.

Hansen, Z., H. Owan, and J. Pan. 2015. The impact of group diversity on class performance. Education Economics 23 (2): 238–258.

Inel, D., and A. Balim. 2010. The effects of using problem-based learning in science and technology teaching upon students’ academic achievement and levels of structuring concepts. Pacific Forum on Science Learning and Teaching 11 (2): 1–23.

Merritt, J., M. Lee, P. Rillero, and B. Kinach. 2017. Problem-based learning in K–8 mathematics and science education: A literature review. The Interdisciplinary Journal of Problem-based Learning 11 (2).

NGSS Lead States. 2013. Next Generation Science Standards: For states, by states. Washington, DC: National Academies Press.

Panasan, M., and P. Nuangchalerm. 2010. Learning outcomes of project-based and inquiry-based learning activities. Journal of Social Sciences 6 (2): 252–255.

Rutherford, F.J. 1964. The role of inquiry in science teaching. Journal of Research in Science Teaching 2 (2): 80–84.

Stevens, L.J., J.R. Burgess, M.A. Stochelski, and T. Kuczek. 2015. Amounts of artificial food dyes and added sugars in foods and sweets commonly consumed by children. Clinical Pediatrics 54 (4): 309–321.

Wilson, C., J. Taylor, and S. Kowalski. 2010. The relative effects and equity of inquiry-based and commonplace science teaching on students’ knowledge, reasoning, and argumentation. Journal of Research in Science Teaching 47 (3): 276–301.

Chemistry Crosscutting Concepts Curriculum Disciplinary Core Ideas General Science Inquiry Instructional Materials Labs Lesson Plans Mathematics NGSS Pedagogy Science and Engineering Practices STEM Teaching Strategies Technology Three-Dimensional Learning High School

You may also like

Reports Article

• school Campus Bookshelves
• menu_book Bookshelves
• perm_media Learning Objects
• login Login
• how_to_reg Request Instructor Account
• hub Instructor Commons
• Download Page (PDF)
• Download Full Book (PDF)
• Periodic Table
• Physics Constants
• Scientific Calculator
• Reference & Cite
• Tools expand_more
• Readability

selected template will load here

This action is not available.

6.1.1: Practice Problems- Solution Concentration

• Last updated
• Save as PDF
• Page ID 217282

PROBLEM \(\PageIndex{1}\)

Explain what changes and what stays the same when 1.00 L of a solution of NaCl is diluted to 1.80 L.

The number of moles always stays the same in a dilution.

The concentration and the volumes change in a dilution.

PROBLEM \(\PageIndex{2}\)

What does it mean when we say that a 200-mL sample and a 400-mL sample of a solution of salt have the same molarity? In what ways are the two samples identical? In what ways are these two samples different?

The two samples contain the same proportion of moles of salt to liters of solution, but have different numbers of actual moles.

PROBLEM \(\PageIndex{3}\)

Determine the molarity for each of the following solutions:

• 0.444 mol of CoCl 2 in 0.654 L of solution
• 98.0 g of phosphoric acid, H 3 PO 4 , in 1.00 L of solution
• 0.2074 g of calcium hydroxide, Ca(OH) 2 , in 40.00 mL of solution
• 10.5 kg of Na 2 SO 4 ·10H 2 O in 18.60 L of solution
• 7.0 × 10 −3 mol of I 2 in 100.0 mL of solution
• 1.8 × 10 4 mg of HCl in 0.075 L of solution

PROBLEM \(\PageIndex{4}\)

Determine the molarity of each of the following solutions:

• 1.457 mol KCl in 1.500 L of solution
• 0.515 g of H 2 SO 4 in 1.00 L of solution
• 20.54 g of Al(NO 3 ) 3 in 1575 mL of solution
• 2.76 kg of CuSO 4 ·5H 2 O in 1.45 L of solution
• 0.005653 mol of Br 2 in 10.00 mL of solution
• 0.000889 g of glycine, C 2 H 5 NO 2 , in 1.05 mL of solution

5.25 × 10 -3 M

6.122 × 10 -2 M

1.13 × 10 -2 M

PROBLEM \(\PageIndex{5}\)

Calculate the number of moles and the mass of the solute in each of the following solutions:

(a) 2.00 L of 18.5 M H 2 SO 4 , concentrated sulfuric acid (b) 100.0 mL of 3.8 × 10 −5 M NaCN, the minimum lethal concentration of sodium cyanide in blood serum (c) 5.50 L of 13.3 M H 2 CO, the formaldehyde used to “fix” tissue samples (d) 325 mL of 1.8 × 10 −6 M FeSO 4 , the minimum concentration of iron sulfate detectable by taste in drinking water

37.0 mol H 2 SO 4

3.63 × 10 3 g H 2 SO 4

3.8 × 10 −6 mol NaCN

1.9 × 10 −4 g NaCN

73.2 mol H 2 CO

2.20 kg H 2 CO

5.9 × 10 −7 mol FeSO 4

8.9 × 10 −5 g FeSO 4

PROBLEM \(\PageIndex{6}\)

Calculate the molarity of each of the following solutions:

(a) 0.195 g of cholesterol, C 27 H 46 O, in 0.100 L of serum, the average concentration of cholesterol in human serum (b) 4.25 g of NH 3 in 0.500 L of solution, the concentration of NH 3 in household ammonia (c) 1.49 kg of isopropyl alcohol, C 3 H 7 OH, in 2.50 L of solution, the concentration of isopropyl alcohol in rubbing alcohol (d) 0.029 g of I 2 in 0.100 L of solution, the solubility of I 2 in water at 20 °C

5.04 × 10 −3 M

1.1 × 10 −3 M

PROBLEM \(\PageIndex{7}\)

There is about 1.0 g of calcium, as Ca 2+ , in 1.0 L of milk. What is the molarity of Ca 2+ in milk?

PROBLEM \(\PageIndex{8}\)

What volume of a 1.00- M Fe(NO 3 ) 3 solution can be diluted to prepare 1.00 L of a solution with a concentration of 0.250 M ?

PROBLEM \(\PageIndex{9}\)

If 0.1718 L of a 0.3556- M C 3 H 7 OH solution is diluted to a concentration of 0.1222 M , what is the volume of the resulting solution?

PROBLEM \(\PageIndex{10}\)

What volume of a 0.33- M C 12 H 22 O 11 solution can be diluted to prepare 25 mL of a solution with a concentration of 0.025 M ?

PROBLEM \(\PageIndex{11}\)

What is the concentration of the NaCl solution that results when 0.150 L of a 0.556- M solution is allowed to evaporate until the volume is reduced to 0.105 L?

PROBLEM \(\PageIndex{12}\)

What is the molarity of the diluted solution when each of the following solutions is diluted to the given final volume?

• 1.00 L of a 0.250- M solution of Fe(NO 3 ) 3 is diluted to a final volume of 2.00 L
• 0.5000 L of a 0.1222- M solution of C 3 H 7 OH is diluted to a final volume of 1.250 L
• 2.35 L of a 0.350- M solution of H 3 PO 4 is diluted to a final volume of 4.00 L
• 22.50 mL of a 0.025- M solution of C 12 H 22 O 11 is diluted to 100.0 mL

PROBLEM \(\PageIndex{13}\)

What is the final concentration of the solution produced when 225.5 mL of a 0.09988- M solution of Na 2 CO 3 is allowed to evaporate until the solution volume is reduced to 45.00 mL?

PROBLEM \(\PageIndex{14}\)

A 2.00-L bottle of a solution of concentrated HCl was purchased for the general chemistry laboratory. The solution contained 868.8 g of HCl. What is the molarity of the solution?

PROBLEM \(\PageIndex{15}\)

An experiment in a general chemistry laboratory calls for a 2.00- M solution of HCl. How many mL of 11.9 M HCl would be required to make 250 mL of 2.00 M HCl?

PROBLEM \(\PageIndex{16}\)

What volume of a 0.20- M K 2 SO 4 solution contains 57 g of K 2 SO 4 ?

PROBLEM \(\PageIndex{17}\)

The US Environmental Protection Agency (EPA) places limits on the quantities of toxic substances that may be discharged into the sewer system. Limits have been established for a variety of substances, including hexavalent chromium , which is limited to 0.50 mg/L. If an industry is discharging hexavalent chromium as potassium dichromate (K 2 Cr 2 O 7 ), what is the maximum permissible molarity of that substance?

4.8 × 10 −6 M

Contributors

Paul Flowers (University of North Carolina - Pembroke), Klaus Theopold (University of Delaware) and Richard Langley (Stephen F. Austin State University) with contributing authors.  Textbook content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at http://cnx.org/contents/[email protected] ).

• Adelaide Clark, Oregon Institute of Technology

• Bipolar Disorder
• Therapy Center
• When To See a Therapist
• Types of Therapy
• Best Online Therapy
• Best Couples Therapy
• Best Family Therapy
• Managing Stress
• Sleep and Dreaming
• Understanding Emotions
• Self-Improvement
• Healthy Relationships
• Student Resources
• Personality Types
• Verywell Mind Insights
• 2023 Verywell Mind 25
• Mental Health in the Classroom
• Editorial Process
• Meet Our Review Board
• Crisis Support

Overview of the Problem-Solving Mental Process

Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

Rachel Goldman, PhD FTOS, is a licensed psychologist, clinical assistant professor, speaker, wellness expert specializing in eating behaviors, stress management, and health behavior change.

• Identify the Problem
• Define the Problem
• Form a Strategy
• Organize Information
• Allocate Resources
• Monitor Progress
• Evaluate the Results

Frequently Asked Questions

Problem-solving is a mental process that involves discovering, analyzing, and solving problems. The ultimate goal of problem-solving is to overcome obstacles and find a solution that best resolves the issue.

The best strategy for solving a problem depends largely on the unique situation. In some cases, people are better off learning everything they can about the issue and then using factual knowledge to come up with a solution. In other instances, creativity and insight are the best options.

It is not necessary to follow problem-solving steps sequentially, It is common to skip steps or even go back through steps multiple times until the desired solution is reached.

In order to correctly solve a problem, it is often important to follow a series of steps. Researchers sometimes refer to this as the problem-solving cycle. While this cycle is portrayed sequentially, people rarely follow a rigid series of steps to find a solution.

The following steps include developing strategies and organizing knowledge.

1. Identifying the Problem

While it may seem like an obvious step, identifying the problem is not always as simple as it sounds. In some cases, people might mistakenly identify the wrong source of a problem, which will make attempts to solve it inefficient or even useless.

Some strategies that you might use to figure out the source of a problem include :

• Asking questions about the problem
• Breaking the problem down into smaller pieces
• Looking at the problem from different perspectives
• Conducting research to figure out what relationships exist between different variables

2. Defining the Problem

After the problem has been identified, it is important to fully define the problem so that it can be solved. You can define a problem by operationally defining each aspect of the problem and setting goals for what aspects of the problem you will address

At this point, you should focus on figuring out which aspects of the problems are facts and which are opinions. State the problem clearly and identify the scope of the solution.

3. Forming a Strategy

After the problem has been identified, it is time to start brainstorming potential solutions. This step usually involves generating as many ideas as possible without judging their quality. Once several possibilities have been generated, they can be evaluated and narrowed down.

The next step is to develop a strategy to solve the problem. The approach used will vary depending upon the situation and the individual's unique preferences. Common problem-solving strategies include heuristics and algorithms.

• Heuristics are mental shortcuts that are often based on solutions that have worked in the past. They can work well if the problem is similar to something you have encountered before and are often the best choice if you need a fast solution.
• Algorithms are step-by-step strategies that are guaranteed to produce a correct result. While this approach is great for accuracy, it can also consume time and resources.

Heuristics are often best used when time is of the essence, while algorithms are a better choice when a decision needs to be as accurate as possible.

4. Organizing Information

Before coming up with a solution, you need to first organize the available information. What do you know about the problem? What do you not know? The more information that is available the better prepared you will be to come up with an accurate solution.

When approaching a problem, it is important to make sure that you have all the data you need. Making a decision without adequate information can lead to biased or inaccurate results.

5. Allocating Resources

Of course, we don't always have unlimited money, time, and other resources to solve a problem. Before you begin to solve a problem, you need to determine how high priority it is.

If it is an important problem, it is probably worth allocating more resources to solving it. If, however, it is a fairly unimportant problem, then you do not want to spend too much of your available resources on coming up with a solution.

At this stage, it is important to consider all of the factors that might affect the problem at hand. This includes looking at the available resources, deadlines that need to be met, and any possible risks involved in each solution. After careful evaluation, a decision can be made about which solution to pursue.

6. Monitoring Progress

After selecting a problem-solving strategy, it is time to put the plan into action and see if it works. This step might involve trying out different solutions to see which one is the most effective.

It is also important to monitor the situation after implementing a solution to ensure that the problem has been solved and that no new problems have arisen as a result of the proposed solution.

Effective problem-solvers tend to monitor their progress as they work towards a solution. If they are not making good progress toward reaching their goal, they will reevaluate their approach or look for new strategies .

7. Evaluating the Results

After a solution has been reached, it is important to evaluate the results to determine if it is the best possible solution to the problem. This evaluation might be immediate, such as checking the results of a math problem to ensure the answer is correct, or it can be delayed, such as evaluating the success of a therapy program after several months of treatment.

Once a problem has been solved, it is important to take some time to reflect on the process that was used and evaluate the results. This will help you to improve your problem-solving skills and become more efficient at solving future problems.

A Word From Verywell​

It is important to remember that there are many different problem-solving processes with different steps, and this is just one example. Problem-solving in real-world situations requires a great deal of resourcefulness, flexibility, resilience, and continuous interaction with the environment.

Get Advice From The Verywell Mind Podcast

Hosted by therapist Amy Morin, LCSW, this episode of The Verywell Mind Podcast shares how you can stop dwelling in a negative mindset.

Follow Now : Apple Podcasts / Spotify / Google Podcasts

You can become a better problem solving by:

• Practicing brainstorming and coming up with multiple potential solutions to problems
• Being open-minded and considering all possible options before making a decision
• Breaking down problems into smaller, more manageable pieces
• Asking for help when needed
• Researching different problem-solving techniques and trying out new ones
• Learning from mistakes and using them as opportunities to grow

It's important to communicate openly and honestly with your partner about what's going on. Try to see things from their perspective as well as your own. Work together to find a resolution that works for both of you. Be willing to compromise and accept that there may not be a perfect solution.

Take breaks if things are getting too heated, and come back to the problem when you feel calm and collected. Don't try to fix every problem on your own—consider asking a therapist or counselor for help and insight.

If you've tried everything and there doesn't seem to be a way to fix the problem, you may have to learn to accept it. This can be difficult, but try to focus on the positive aspects of your life and remember that every situation is temporary. Don't dwell on what's going wrong—instead, think about what's going right. Find support by talking to friends or family. Seek professional help if you're having trouble coping.

Davidson JE, Sternberg RJ, editors.  The Psychology of Problem Solving .  Cambridge University Press; 2003. doi:10.1017/CBO9780511615771

Sarathy V. Real world problem-solving .  Front Hum Neurosci . 2018;12:261. Published 2018 Jun 26. doi:10.3389/fnhum.2018.00261

By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

Responding to Climate Change

NASA is a world leader in climate studies and Earth science. While its role is not to set climate policy or prescribe particular responses or solutions to climate change, its purview does include providing the robust scientific data needed to understand climate change. NASA then makes this information available to the global community – the public, policy- and decision-makers and scientific and planning agencies around the world.

Climate change is one of the most complex issues facing us today. It involves many dimensions – science, economics, society, politics, and moral and ethical questions – and is a global problem, felt on local scales, that will be around for thousands of years. Carbon dioxide, the heat-trapping greenhouse gas that is the primary driver of recent global warming, lingers in the atmosphere for many thousands of years, and the planet (especially the ocean) takes a while to respond to warming. So even if we stopped emitting all greenhouse gases today, global warming and climate change will continue to affect future generations. In this way, humanity is “committed” to some level of climate change.

How much climate change? That will be determined by how our emissions continue and exactly how our climate responds to those emissions. Despite increasing awareness of climate change, our emissions of greenhouse gases continue on a relentless rise . In 2013, the daily level of carbon dioxide in the atmosphere surpassed 400 parts per million for the first time in human history . The last time levels were that high was about three to five million years ago, during the Pliocene Epoch.

Because we are already committed to some level of climate change, responding to climate change involves a two-pronged approach:

• Reducing emissions of and stabilizing the levels of heat-trapping greenhouse gases in the atmosphere (“mitigation”) ;
• Adapting to the climate change already in the pipeline (“adaptation”) .

Mitigation and Adaptation

Mitigation – reducing climate change – involves reducing the flow of heat-trapping greenhouse gases into the atmosphere , either by reducing sources of these gases (for example, the burning of fossil fuels for electricity, heat, or transport) or enhancing the “sinks” that accumulate and store these gases (such as the oceans, forests, and soil). The goal of mitigation is to avoid significant human interference with Earth's climate , “stabilize greenhouse gas levels in a timeframe sufficient to allow ecosystems to adapt naturally to climate change, ensure that food production is not threatened, and to enable economic development to proceed in a sustainable manner” (from the 2014 report on Mitigation of Climate Change from the United Nations Intergovernmental Panel on Climate Change, page 4).

Adaptation – adapting to life in a changing climate – involves adjusting to actual or expected future climate. The goal is to reduce our risks from the harmful effects of climate change (like sea-level rise, more intense extreme weather events, or food insecurity). It also includes making the most of any potential beneficial opportunities associated with climate change (for example, longer growing seasons or increased yields in some regions).

Throughout history, people and societies have adjusted to and coped with changes in climate and extremes with varying degrees of success. Climate change (drought in particular) has been at least partly responsible for the rise and fall of civilizations . Earth’s climate has been relatively stable for the past 10,000 years, and this stability has allowed for the development of our modern civilization and agriculture. Our modern life is tailored to that stable climate and not the much warmer climate of the next thousand-plus years. As our climate changes, we will need to adapt. The faster the climate changes, the more difficult it will be.

While climate change is a global issue, it is felt on a local scale. Local governments are therefore at the frontline of adaptation. Cities and local communities around the world have been focusing on solving their own climate problems . They are working to build flood defenses, plan for heat waves and higher temperatures, install better-draining pavements to deal with floods and stormwater, and improve water storage and use.

According to the 2014 report on Climate Change Impacts, Adaptation and Vulnerability (page 8) from the United Nations Intergovernmental Panel on Climate Change, governments at various levels are also getting better at adaptation. Climate change is being included into development plans: how to manage the increasingly extreme disasters we are seeing, how to protect coastlines and deal with sea-level rise, how to best manage land and forests, how to deal with and plan for drought, how to develop new crop varieties, and how to protect energy and public infrastructure.

How NASA Is Involved

NASA, with its Eyes on the Earth and wealth of knowledge on Earth’s climate, is one of the world’s experts in climate science . NASA’s role is to provide the robust scientific data needed to understand climate change. For example, data from the agency’s Gravity Recovery and Climate Experiment (GRACE) , its follow-on mission ( GRACE-FO ), the Ice, Cloud and land Elevation Satellite (ICESat), and the ICESat-2 missions have shown rapid changes in the Earth's great ice sheets. The Sentinel-6 Michael Freilich and the Jason series of missions have documented rising global sea level since 1992.

NASA makes detailed climate data available to the global community – the public, policy-, and decision-makers and scientific and planning agencies around the world. It is not NASA’s role to set climate policy or recommend solutions to climate change. NASA is one of 13 U.S. government agencies that form part of the U.S. Global Change Research Program, which has a legal mandate to help the nation and the world understand, assess, predict, and respond to global change. These U.S. partner agencies include the Department of Agriculture , the Environmental Protection Agency , and the Department of Energy , each of which has a different role depending on their area of expertise.

Although NASA’s main focus is not on energy-technology research and development, work is being done around the agency and by/with various partners and collaborators to find other sources of energy to power our needs.

Related Articles

For further reading on NASA’s work on mitigation and adaptation, take a look at these pages:

Earth Science in Action

• Sustainability and Government Resources
• NASA's Electric Airplane
• NASA Aeronautics
• NASA Spinoff (Technology Transfer Program)

Discover More Topics From NASA

Explore Earth Science

Earth Science Data

Facts About Earth

Follow Polygon online:

• Follow Polygon on Facebook
• Follow Polygon on Youtube
• Follow Polygon on Instagram

Site search

• What to Watch
• What to Play
• PlayStation
• All Entertainment
• Dragon’s Dogma 2
• FF7 Rebirth
• Zelda: Tears of the Kingdom
• Baldur’s Gate 3
• Buyer’s Guides
• Galaxy Brains
• All Podcasts

Filed under:

• Entertainment

The 3-body problem is real, and it’s really unsolvable

Oh god don’t make me explain math

Share this story

• Share this on Facebook
• Share this on Reddit
• Share All sharing options

Share All sharing options for: The 3-body problem is real, and it’s really unsolvable

Everybody seems to be talking about 3 Body Problem , the new Netflix series based on Cixin Liu’s Remembrance of Earth’s Past book trilogy . Fewer people are talking about the two series’ namesake: The unsolvable physics problem of the same name.

This makes sense, because it’s confusing . In physics, the three-body problem attempts to find a way to predict the movements of three objects whose gravity interacts with each of the others — like three stars that are close together in space. Sounds simple enough, right? Yet I myself recently pulled up the Wikipedia article on the three-body problem and closed the tab in the same manner that a person might stagger away from a bright light. Apparently the Earth, sun, and moon are a three-body system? Are you telling me we don’t know how the moon moves ? Scientists have published multiple solutions for the three-body problem? Are you telling me Cixin Liu’s books are out of date?

All I’d wanted to know was why the problem was considered unsolvable, and now memories of my one semester of high school physics were swimming before my eyes like so many glowing doom numbers. However, despite my pains, I have readied several ways that we non-physicists can be confident that the three-body problem is, in fact, unsolvable.

Reason 1: This is a special definition of ‘unsolvable’

The three-body problem is extra confusing, because scientists are seemingly constantly finding new solutions to the three-body problem! They just don’t mean a one-solution-for-all solution. Such a formula does exist for a two-body system, and apparently Isaac Newton figured it out in 1687 . But systems with more than two bodies are, according to physicists, too chaotic (i.e., not in the sense of a child’s messy bedroom, but in the sense of “chaos theory”) to be corralled by a single solution.

When physicists say they have a new solution to the three-body problem, they mean that they’ve found a specific solution for three-body systems that have certain theoretical parameters. Don’t ask me to explain those parameters, because they’re all things like “the three masses are collinear at each instant” or “a zero angular momentum solution with three equal masses moving around a figure-eight shape.” But basically: By narrowing the focus of the problem to certain arrangements of three-body systems, physicists have been able to derive formulas that predict the movements of some of them, like in our solar system. The mass of the Earth and the sun create a “ restricted three-body problem ,” where a less-big body (in this case, the moon) moves under the influence of two massive ones (the Earth and the sun).

What physicists mean when they say the three-body problem has no solution is simply that there isn’t a one-formula-fits-all solution to every way that the gravity of three objects might cause those objects to move — which is exactly what Three-Body Problem bases its whole premise on.

Reason 2: 3 Body Problem picked an unsolved three-body system on purpose

Henri Poincaré’s research into a general solution to the three-body problem formed the basis of what would become known as chaos theory (you might know it from its co-starring role in Jurassic Park ). And 3 Body Problem itself isn’t about any old three-body system. It’s specifically about an extremely chaotic three-body system, the exact kind of arrangement of bodies that Poincaré was focused on when he showed that the problem is “unsolvable.”

[ Ed. note: The rest of this section includes some spoilers for 3 Body Problem .]

In both Liu’s books and Netflix’s 3 Body Problem , humanity faces an invasion by aliens (called Trisolarans in the English translation of the books, and San-Ti in the TV series) whose home solar system features three suns in a chaotic three-body relationship. It is a world where, unlike ours, the heavens are fundamentally unpredictable. Periods of icy cold give way to searing heat that give way to swings in gravity that turn into temporary reprieves that can never be trusted. The unpredictable nature of the San-Ti environment is the source of every detail of their physicality, their philosophy, and their desire to claim Earth for their own.

In other words, 3 Body Problem ’s three-body problem is unsolvable because Liu wanted to write a story with an unsolvable three-body system, so he chose one of the three-body systems for which we have not discovered a solution, and might never.

Reason 3: Scientists are still working on the three-body problem

Perhaps the best reason I can give you to believe that the three-body problem is real, and is really unsolvable, is that some scientists published a whole set of new solutions for specific three-body systems very recently .

If physicists are still working on the three-body problem, we can safely assume that it has not been solved. Scientists, after all, are the real experts. And I am definitely not.

The next level of puzzles.

Take a break from your day by playing a puzzle or two! We’ve got SpellTower, Typeshift, crosswords, and more.

Sign up for the newsletter Patch Notes

A weekly roundup of the best things from Polygon

Just one more thing!

Please check your email to find a confirmation email, and follow the steps to confirm your humanity.

Oops. Something went wrong. Please enter a valid email and try again.

Loading comments...

FFXIV housing lottery schedule for April 2024

Glam up your Warhammer 40K minis with everyday products from the beauty aisle

Don’t have the time to read (or watch) Shōgun? Get the audiobooks for just $10

Cloud’s unreliable narration only makes Final Fantasy 7 Rebirth’s ending more confusing

Imaginary, Lisa Frankenstein, Netflix’s The Beautiful Game, and every new movie to watch at home this weekend

• Dragon’s Dogma 2 guides, walkthroughs, and explainers

Should you give the grimoires to Myrddin or Trysha in Dragon’s Dogma 2?

Here's the science refresher you need before diving into Netflix's '3 Body Problem'

• Netflix's " 3 Body Problem " is based on a science-fiction trilogy and follows a group of physicists.
• We asked an astronomer and an aerospace engineer to explain some of the show's scientific concepts.
• It might help to have a bit of background on the Fermi paradox and the Wow! signal before you watch.

The upcoming Netflix show "3 Body Problem" is a sci-fi story about a group of physicists grappling with the discovery of an alien civilization .

Taking its name from a tricky bit of orbital mechanics — three celestial bodies moving around each other — the show is based on the science-fiction trilogy " Remembrance of Earth's Past " by Liu Cixin.

In the show, several of the main characters studied physics at Oxford University . Luckily, you don't need to have the same background to enjoy the show.

However, there are a few scientific concepts that might be helpful to know before you tune in on March 21.

The three-body problem is unsolvable and chaotic

Some of the show's action takes place in a virtual world that's orbited by three suns. The celestial mechanics of such a planet have long perplexed scientists in the real world.

"This is a centuries-old problem," Shane Ross, an aerospace and ocean engineering professor at Virginia Tech, told Business Insider.

Isaac Newton was able to figure out the two-body problem, how a pair of massive objects like stars or planets move when affected by each other's gravity.

"The two-body problem is sort of the paradigm of stability," Ross said. Adding in a third body, though, makes everything topsy-turvy.

From a mathematical perspective , "it's unsolvable," Ross said of the three-body problem. "You can't write out the solution for all time as some algebraic formula."

It's a bit like the butterfly effect: a small change can vastly alter the outcome. "Any uncertainty we have in the initial conditions grows exponentially, to the point where the future state of the system is essentially unpredictable."

Alpha Centauri is the closest star system to Earth

The three-body system in the story is based on a real neighboring star system called Alpha Centauri.

At about 4 light-years from Earth, it's the closest star system to our own and contains three stars: Alpha Centauri A, Alpha Centauri B, and Proxima Centauri, which has two planets orbiting around it.

"We're talking about something super close to us," Franck Marchis, a senior planetary astronomer with the SETI Institute, said. "It's like looking at the backyard of neighbors, basically."

However, it would take special conditions for life, at least as we know it, to survive, on either planet around Proxima Centauri. "The conditions for life are extremely rare," Ross said. "I think the Earth is a very special planet," adding that "there could be life that takes some other form that we don't know about."

If a civilization from Alpha Centauri evolved at a similar pace to our own, then "they're probably more advanced than us," Marchis said because the system is estimated to be between 5 and 7 billion years old whereas Earth's solar system formed 4.5 billion years ago.

The Fermi paradox poses the question, where are all the aliens?

If there are highly evolved beings on other planets, why haven't they gotten in touch? That's the question astrophysicist Ye Wenjie is asking when she brings up the Fermi paradox in the show.

In 1950, Nobel prize-winning physicist Enrico Fermi wondered where all the extraterrestrials were. Decades later, other scientists picked up the question. If other civilizations existed, they must have left some evidence.

To Marchis, what became known as the Fermi paradox is an outdated way of thinking. "The idea is that because we are a civilization that's become technologically advanced, the first thing that we do is to travel through the galaxy, 'Star Trek'-like," he said.

Instead, he prefers the "zoo hypothesis."

Related stories

If they are truly advanced, he said, "they probably reached a certain level of sentientness or consciousness that makes them more respectful of other civilizations which are progressing."

In short, they're purposefully avoiding contact with our planet .

Aliens could have communicated through the Wow! signal

One of the most mysterious potential alien communications is known as the Wow! signal. In the show, Clarence (Benedict Wong) describes how the strange signal was picked up in Ohio and China.

During the 1970s, researchers at Ohio State University really were involved in the Search for Extraterrestrial Intelligence, or SETI . They used a radio observatory nicknamed "Big Ear" to try and pick up extraterrestrial communications.

In 1977, volunteer Jerry Ehman was looking at a computer printout of a signal Big Ear had picked up three days earlier. He circled the numbers and wrote "Wow!" alongside them. The 72-second signal was strong and located at a frequency known as the hydrogen line.

At the time, researchers thought aliens would communicate via that frequency "because it's the easiest way to send signals through the galaxy," Marchis said.

The signal has never repeated or been detected again Marchis said. (And no other observatories reported picking up the signal, in China or anywhere else.)

Since the signal itself wasn't saved, there's no way of knowing if it contained a message, Marchis said. Some more mundane explanations for the signal have been suggested, like the radio transmission reflecting off a passing comet.

SETI has come a long way since the '70s, with many researchers using newer technology and a broader range of signals, Marchis said. "We assume that if aliens will communicate with us," he said, "they're slightly more advanced than the people from the 1970s."

Occam's razor suggests simple explanations are often better

Like many other sci-fi movies and shows before it, including "Contact" and "Fringe," "3 Body Problem" makes a reference to Occam's razor.

In 1852, philosopher Sir William Hamilton coined the term "Occam's razor," attributing the idea to 14th-century theologian William of Ockham.

William of Ockham had written, "Numquam ponenda est pluralitas sine necessitate," or "Plurality must never be posited without necessity." It's an idea that Aristotle and Ptolemy also stated.

Today, the well-known concept is usually stated as "the simplest solution is usually correct." The often-cited example is, if you hear the sound of hoofbeats, think horses, not zebras (provided you're not on the savanna).

Neutrino detectors are built deep underground

The trailer for the show includes a dramatic shot of one of the characters stepping into what looks like a neutrino detector and falling, presumably to her death.

Neutrinos, also known as ghost particles, are subatomic particles that the sun and  supernovae  create. Billions pass through your body at any given time.

Much like particle accelerators, the devices may help unlock some of the universe's secrets. They're often built underground to shield them from cosmic rays that can interfere with the data.

Three celestial bodies lined up is known as syzygy

During the show's third episode, the three suns in the virtual world all line up in a triple eclipse.

Ross pointed out that the show debuts around a "cosmically significant day," the vernal equinox . "That's the day when all across the world it's equal daylight and nighttime," he said.

It's also close to the upcoming solar eclipse that has a path of totality through a large portion of North America.

"That's the sun, moon, and Earth all in a line," Ross said. "It's called syzygy, when three celestial bodies are exactly in a line."

• Main content

• Skip to main content
• Keyboard shortcuts for audio player

Aliens attack science in '3 Body Problem,' a new adaptation of a Chinese sci-fi novel

Eric Deggans

The new Netflix series brings to life a sprawling, successful Chinese novel outlining a new kind of alien invasion. Above, Zine Tseng in 3 Body Problem. Maria Heras/Netflix hide caption

The new Netflix series brings to life a sprawling, successful Chinese novel outlining a new kind of alien invasion. Above, Zine Tseng in 3 Body Problem.

My favorite kind of science fiction involves stories rooted in real science — much as I love a good lightsaber or phaser fight, there is something special about seeing characters wrestle with concepts closer to our current understanding of how the universe works.

That's why I enjoy so much of what happens in Netflix's 3 Body Problem , the TV series which brings to life a sprawling, successful Chinese novel rooted in science, outlining a new kind of alien invasion.

Book Reviews

'three-body problem' asks a classic sci-fi question, in chinese.

3 Body Problem actually starts with two problems. First, we meet investigators tackling a string of unexplained suicides by scientists, including one who had a bizarre countdown written on the walls of his home in blood with his eyes gouged out. (Fortunately, viewers only see the horrific aftermath.) Benedict Wong plays one of those investigators, continually lightening the show's ominous vibe with his spot-on portrayal of a world-weary gumshoe tracking the world's biggest mystery with a healthy dose of gallows humor.

Benedict Wong plays Da Shi in 3 Body Problem. Ed Miller/Netflix hide caption

Benedict Wong plays Da Shi in 3 Body Problem.

"One of the betting sites had him picked as a favorite for the next Nobel Prize in physics," Wong's assistant tells him of the scientist who died.

"You can bet on that?" Wong's character replies, looking over the gruesome scene.

Tracking why science is broken

The other problem which surfaces immediately is that science seems to have stopped working. Researchers are reporting results from experiments in supercolliders that make no sense, putting the lie to all our accepted theories of physics. Saul Durand — played by Jovan Adepo, Durand is one among a group of brilliant, young scientist friends at the center of the story — notes simply, "science is broken."

Jovan Adepo and Jin Cheng in 3 Body Problem. Ed Miller/Netflix hide caption

Jovan Adepo and Jin Cheng in 3 Body Problem.

This all adds up to a unique attack on humanity's scientific progress. But who – or what – is behind these bizarre occurrences, involving events which don't seem possible in the modern world?

Netflix's show takes its time unveiling the full scope of the story and answering these questions, which leads to the third problem here. It takes a while for the series' narrative to really gain momentum – my advice is to hang on through the first three episodes (yes, I also hate streaming shows which ask this of beleaguered viewers; but in this case, it's worth it).

The pacing may not be a surprise, given that two of the series' three creators are David Benioff and D.B. Weiss, former showrunners of HBO's Game of Thrones , which had its own problems with narrative flow at times (the third creator is former True Blood writer/executive producer Alexander Woo). Once the show does find its groove, the series builds into an epic science fiction tale with eye-popping special effects – the tragic destruction of a huge ship packed with people is one that stuck with me long after viewing — and a timeline stretching from China's 1960s-era cultural revolution to the present day.

Bringing a Chinese sci fi-literary triumph to TV

Netflix's 3 Body Problem is based on a 2008 novel from Chinese engineer and science fiction writer Liu Cixin; the original novel became a book series touted by big names like Barack Obama. It managed the neat trick of popularizing Chinese science fiction internationally while delivering compelling observations on the nature of humanity's societal and technological progress, some of which actually find their way into the TV show.

Cultural Revolution-Meets-Aliens: Chinese Writer Takes On Sci-Fi

It makes sense that a story like this — which crosses between Western and Chinese culture to tell the story of a planet under threat – would be cracked by Netflix. The streaming service has educated a generation of American customers to appreciate smart, entertaining TV from South Korea, Latin America, Europe and elsewhere across the globe.

So kicking off 3 Body Problem with a scene showing a young Chinese scientist watching an angry mob murder her father – who is also a scientist – during the purges of China's cultural revolution feels daring and entirely on brand. Later on, that younger scientist, fueled by hate and loss, will make a decision that puts the entire planet at risk, showing how disappointment in humanity's missteps can lead to desperate, misguided solutions.

Fans of the books will find some tweaks here to make for better television, amping up the thriller elements of the story to ask a compelling question: How to fight an alien enemy targeting the world's scientific progress?

As the characters in 3 Body Problem lurch toward answers, we all get to bask in an ambitious narrative fueling an ultimately impressive tale. Just remember to be patient as the series sets the stage early on.

• Trending Now
• Foundational Courses
• Data Science
• Practice Problem
• Machine Learning
• System Design
• DevOps Tutorial

Welcome to the daily solving of our PROBLEM OF THE DAY with Yash Dwivedi . We will discuss the entire problem step-by-step and work towards developing an optimized solution. This will not only help you brush up on your concepts of BST but also build up problem-solving skills. In this problem, we are given the root of a Binary Search Tree. The task is to find the minimum valued element in this given BST.

Example : Input:           5         /    \        4      6       /        \      3          7     /    1 Output: 1 Give the problem a try before going through the video. All the best!!! Problem Link: https://www.geeksforgeeks.org/problems/minimum-element-in-bst/1 Solution IDE Link: https://ide.geeksforgeeks.org/online-cpp14-compiler/2b60f0af-83ee-4d7f-b088-0ac5b6d5e505