Research does solve real-world problems: experts must work together to make it happen

how can you solve real world problems

Deputy Vice Chancellor Research & Innovation, University of South Australia

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Tanya Monro receives funding from the Australian Research Council. She is Deputy Vice Chancellor of the University of South Australia, a member of the Commonwealth Science Council, the CSIRO board, the SA Economic Development Board and Defence SA.

University of South Australia provides funding as a member of The Conversation AU.

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how can you solve real world problems

Generating knowledge is one of the most exciting aspects of being human. The inventiveness required to apply this knowledge to solve practical problems is perhaps our most distinctive attribute.

But right now we have before us some hairy challenges – whether that be figuring our how to save our coral reefs from warmer water , landing a human on Mars , eliminating the gap in life expectancy between the “haves” and “have-nots” or delivering reliable carbon-free energy .

It’s commonly said that an interdisciplinary approach is vital if we are to tackle such real world challenges. But what does this really mean?

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Listen and read with care and you’ll start to notice that the words crossdisciplinary, multidisciplinary, interdisciplinary and transdisciplinary are used interchangeably. These words describe distinctly different ways of harnessing the power of disciplinary expertise to chart a course into the unknown.

In navigation, the tools and methods matter – choose differently and you’ll end up in a different spot. How we go about creating knowledge and solving problems really matters – it changes not only what questions can be asked and answered but fundamentally shapes what’s possible.

What is a discipline?

For centuries we have organised research within disciplines, and this has delivered extraordinary depths of knowledge.

But what is a discipline? It’s a shared language, an environment in which there’s no need to explain the motivation for one’s work, and in which people have a shared sense of what’s valuable.

For example, my background discipline is optical physics. I know what it’s like to be able to skip down the corridor and say,

“I’ve figured out how we can get broadband flat dispersion - we just need to tailor the radial profile!”

…and have people instantly not just know what I mean, but be able to add their own ideas and drive the work forward.

In long-established disciplines it’s often necessary to focus in a narrow area to be able to extend the limits of knowledge within the time-frame of a PhD. And while it’s rarely obvious at the time what benefits will flow from digging a little deeper, our way of life has been transformed over and over as result.

how can you solve real world problems

Disciplines focus talent and so can be amazingly efficient ways of generating knowledge. But they can also be extraordinarily difficult to penetrate from the outside without understanding that discipline’s particular language and shared values.

The current emphasis on real-world impact has sharpened awareness on the need to translate knowledge into outcomes. It has also brought attention to the critical role partnerships with industry and other end-users of research play in this process.

Creating impact across disciplines

Try to solve a problem with the tools of a single discipline alone, and it’s as if you have a hammer - everything starts to look like a nail. It’s usually obvious when expertise from more than one discipline is needed.

Consider a panel of experts drawn from different fields to each apply the tools of their field to a problem that’s been externally framed. This has traditionally been how expertise from the social sciences is brought to bear on challenges in public health or the environment.

This is a crossdisciplinary approach , which can produce powerful outcomes provided that those who posed the question are positioned to make decisions based on the knowledge generated. But the research fields themselves are rarely influenced by this glancing encounter with different approaches to knowledge generation.

Multidisciplinary research involves the application of tools from one discipline to questions from other fields. An example is the application of crystallography, discovered by the Braggs, to unravel the structure of proteins . This requires concepts to transfer across domains, sometimes in real time but usually with a lag of years or decades.

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Interdisciplinary research happens when researchers from different fields come together to pose a challenge that wouldn’t be possible in isolation. One example is the highly transparent optical fibres that underpin intercontinental telecommunication networks.

The knowledge creation that made this possible involved glass chemists, optical physicists and communication engineers coming together to articulate the possible, and develop the shared language required to make it a reality. When fields go on this journey together over decades, new fields are born.

In this example the question itself was clear – how can we harness the transparency of silica glass to create optical transmission systems that can transport large volumes of data over long distances?

But what about the questions we don’t know how to pose because without knowledge of another field we don’t know what’s possible? This line of reasoning leads us into the domain of transdisciplinary research .

Transdisciplinary research requires a willingness to craft new questions – whether because they were considered intractable or because without the inspiration from left field they simply didn’t arise. An example of this is applying photonics to IVF incubators - the idea that it could be possible to “listen” to how embryos experience their environment is unlikely to have arisen without bringing these fields together.

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In my own field, physics, I discovered that when talking to people from other areas the simple question “what would you like to measure?” quickly led to uncharted territory.

Before long we were usually, together, posing fundamentally new questions and establishing teams to tackle them. This can be scary territory but it’s tremendously rewarding and creates space for creativity and the emergence of disruptive technologies.

Excellence, communication, co-location, funding

One of the best ways of getting out of a disciplinary silo is to take every opportunity to talk to others outside your field. Disciplinary excellence is the starting point to get to the table.

And while disciplinary collaborations can flourish over large distances because they share a language and values, it’s usually true that once you mix disciplines co-location becomes a real asset. Then of course there are the questions of how we fund and organise research concentrations to allow inter- and transdisciplinary research to flourish.

With the increased emphasis on impact, these questions are becoming ever more pressing. Organisations that get this right will thrive.

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how can you solve real world problems

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Ideas Made to Matter

How to use algorithms to solve everyday problems

Kara Baskin

May 8, 2017

How can I navigate the grocery store quickly? Why doesn’t anyone like my Facebook status? How can I alphabetize my bookshelves in a hurry? Apple data visualizer and MIT System Design and Management graduate Ali Almossawi solves these common dilemmas and more in his new book, “ Bad Choices: How Algorithms Can Help You Think Smarter and Live Happier ,” a quirky, illustrated guide to algorithmic thinking. 

For the uninitiated: What is an algorithm? And how can algorithms help us to think smarter?

An algorithm is a process with unambiguous steps that has a beginning and an end, and does something useful.

Algorithmic thinking is taking a step back and asking, “If it’s the case that algorithms are so useful in computing to achieve predictability, might they also be useful in everyday life, when it comes to, say, deciding between alternative ways of solving a problem or completing a task?” In all cases, we optimize for efficiency: We care about time or space.

Note the mention of “deciding between.” Computer scientists do that all the time, and I was convinced that the tools they use to evaluate competing algorithms would be of interest to a broad audience.

Why did you write this book, and who can benefit from it?

All the books I came across that tried to introduce computer science involved coding. My approach to making algorithms compelling was focusing on comparisons. I take algorithms and put them in a scene from everyday life, such as matching socks from a pile, putting books on a shelf, remembering things, driving from one point to another, or cutting an onion. These activities can be mapped to one or more fundamental algorithms, which form the basis for the field of computing and have far-reaching applications and uses.

I wrote the book with two audiences in mind. One, anyone, be it a learner or an educator, who is interested in computer science and wants an engaging and lighthearted, but not a dumbed-down, introduction to the field. Two, anyone who is already familiar with the field and wants to experience a way of explaining some of the fundamental concepts in computer science differently than how they’re taught.

I’m going to the grocery store and only have 15 minutes. What do I do?

Do you know what the grocery store looks like ahead of time? If you know what it looks like, it determines your list. How do you prioritize things on your list? Order the items in a way that allows you to avoid walking down the same aisles twice.

For me, the intriguing thing is that the grocery store is a scene from everyday life that I can use as a launch pad to talk about various related topics, like priority queues and graphs and hashing. For instance, what is the most efficient way for a machine to store a prioritized list, and what happens when the equivalent of you scratching an item from a list happens in the machine’s list? How is a store analogous to a graph (an abstraction in computer science and mathematics that defines how things are connected), and how is navigating the aisles in a store analogous to traversing a graph?

Nobody follows me on Instagram. How do I get more followers?

The concept of links and networks, which I cover in Chapter 6, is relevant here. It’s much easier to get to people whom you might be interested in and who might be interested in you if you can start within the ball of links that connects those people, rather than starting at a random spot.

You mention Instagram: There, the hashtag is one way to enter that ball of links. Tag your photos, engage with users who tag their photos with the same hashtags, and you should be on your way to stardom.

What are the secret ingredients of a successful Facebook post?

I’ve posted things on social media that have died a sad death and then posted the same thing at a later date that somehow did great. Again, if we think of it in terms that are relevant to algorithms, we’d say that the challenge with making something go viral is really getting that first spark. And to get that first spark, a person who is connected to the largest number of people who are likely to engage with that post, needs to share it.

With [my first book], “Bad Arguments,” I spent a month pouring close to $5,000 into advertising for that project with moderate results. And then one science journalist with a large audience wrote about it, and the project took off and hasn’t stopped since.

What problems do you wish you could solve via algorithm but can’t?

When we care about efficiency, thinking in terms of algorithms is useful. There are cases when that’s not the quality we want to optimize for — for instance, learning or love. I walk for several miles every day, all throughout the city, as I find it relaxing. I’ve never asked myself, “What’s the most efficient way I can traverse the streets of San Francisco?” It’s not relevant to my objective.

Algorithms are a great way of thinking about efficiency, but the question has to be, “What approach can you optimize for that objective?” That’s what worries me about self-help: Books give you a silver bullet for doing everything “right” but leave out all the nuances that make us different. What works for you might not work for me.

Which companies use algorithms well?

When you read that the overwhelming majority of the shows that users of, say, Netflix, watch are due to Netflix’s recommendation engine, you know they’re doing something right.

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To Solve Real-World Problems, We Need Interdisciplinary Science

Solving today’s complex, global problems will take interdisciplinary science

By Graham A. J. Worthy & Cherie L. Yestrebsky

how can you solve real world problems

T he Indian River Lagoon, a shallow estuary that stretches for 156 miles along Florida's eastern coast, is suffering from the activities of human society. Poor water quality and toxic algal blooms have resulted in fish kills, manatee and dolphin die-offs and takeovers by invasive species. But the humans who live here have needs, too: the eastern side of the lagoon is buffered by a stretch of barrier islands that are critical to Florida's economy, tourism and agriculture, as well as for launching NASA missions into space.

As in Florida, many of the world's coastlines are in serious trouble as a result of population growth and the pollution it produces. Moreover, the effects of climate change are accelerating both environmental and economic decline. Given what is at risk, scientists like us—a biologist and a chemist at the University of Central Florida—feel an urgent need to do research that can inform policy that will increase the resiliency and sustainability of coastal communities. How can our research best help balance environmental and social needs within the confines of our political and economic systems? This is the level of complexity that scientists must enter into instead of shying away from.

Although new technologies will surely play a role in tackling issues such as climate change, rising seas and coastal flooding, we cannot rely on innovation alone. Technology generally does not take into consideration the complex interactions between people and the environment. That is why coming up with solutions will require scientists to engage in an interdisciplinary team approach—something that is common in the business world but is relatively rare in universities.

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Universities are a tremendous source of intellectual power, of course. But students and faculty are typically organized within departments, or academic silos. Scientists are trained in the tools and language of their respective disciplines and learn to communicate their findings to one another using specific jargon.

When the goal of research is a fundamental understanding of a physical or biological system within a niche community, this setup makes a lot of sense. But when the problem the research is trying to solve extends beyond a closed system and includes its effects on society, silos create a variety of barriers. They can limit creativity, flexibility and nimbleness and actually discourage scientists from working across disciplines. As professors, we tend to train our students in our own image, inadvertently producing specialists who have difficulty communicating with the scientist in the next building—let alone with the broader public. This makes research silos ineffective at responding to developing issues in policy and planning, such as how coastal communities and ecosystems worldwide will adapt to rising seas.

Science for the Bigger Picture

As scientists who live and work in Florida, we realized that we needed to play a bigger role in helping our state—and country—make evidence-based choices when it comes to vulnerable coastlines. We wanted to make a more comprehensive assessment of both natural and human-related impacts to the health, restoration and sustainability of our coastal systems and to conduct long-term, integrated research.

At first, we focused on expanding research capacity in our biology, chemistry and engineering programs because each already had a strong coastal research presence. Then, our university announced a Faculty Cluster Initiative, with a goal of developing interdisciplinary academic teams focused on solving tomorrow's most challenging societal problems. While putting together our proposal, we discovered that there were already 35 faculty members on the Orlando campus who studied coastal issues. They belonged to 12 departments in seven colleges, and many of them had never even met. It became clear that simply working on the same campus was insufficient for collaboration.

So we set out to build a team of people from a wide mix of backgrounds who would work in close proximity to one another on a daily basis. These core members would also serve as a link to the disciplinary strengths of their tenure home departments. Initially, finding experts who truly wanted to embrace the team aspect was more difficult than we thought. Although the notion of interdisciplinary research is not new, it has not always been encouraged in academia. Some faculty who go in that direction still worry about whether it will threaten their recognition when applying for grants, seeking promotions or submitting papers to high-impact journals. We are not suggesting that traditional academic departments should be disbanded. On the contrary, they give the required depth to the research, whereas the interdisciplinary team gives breadth to the overall effort.

Our cluster proposal was a success, and in 2019 the National Center for Integrated Coastal Research (UCF Coastal) was born. Our goal is to guide more effective economic development, environmental stewardship, hazard-mitigation planning and public policy for coastal communities. To better integrate science with societal needs, we have brought together biologists, chemists, engineers and biomedical researchers with anthropologists, sociologists, political scientists, planners, emergency managers and economists. It seems that the most creative perspectives on old problems have arisen when people with different training and life experiences are talking through issues over cups of coffee. After all, “interdisciplinary” must mean more than just different flavors of STEM. In academia, tackling the effects of climate change demands more rigorous inclusion of the social sciences—an area that has been frequently overlooked.

The National Science Foundation, as well as other groups, has recently required that all research proposals incorporate a social sciences component, as an attempt to assess the broader implications of projects. Unfortunately, in many cases, simply adding a social scientist to a proposal is done only to check a box rather than to make a true commitment to allowing the discipline to inform a project. Instead social, economic and policy needs must be considered at the outset of research design, not as an afterthought. Otherwise our work might fail at the implementation stage, which means we are not being as effective as we could be in solving real-world problems. As a result, the public might become skeptical of how much scientists can contribute toward solutions.

Connecting with the Public

The reality is that communicating research findings to the public is an increasingly critical responsibility of scientists. Doing so has a measurable effect on how politicians prioritize policy, funding and regulations. UCF Coastal was brought into a world where science is not always respected—sometimes it is even portrayed as the enemy. There has been a significant erosion of trust in science over recent years, and we must work more deliberately to regain it. The public, we have found, wants to see quality academic research that is grounded in the societal challenges we are facing. That is why we are melding pure academic research with applied research to focus on issues that are immediate—helping a town or business recovering from Hurricane Irma, for example—as well as long term, such as directly advising a community how to build resiliency as flooding becomes more frequent.

As scientists, we cannot expect to explain the implications of our research to the wider public if we cannot first understand one another. A benefit of regularly working side by side is that we are crafting a common language, reconciling the radically different meanings that the same words can have to a variety of specialists. Finally, we are learning to speak to one another with more clarity and understand more explicitly how our niches fit into the bigger picture. We are also more aware of culture and industry as driving forces in shaping consensus and policy. Rather than handing city planners a stack of research papers and walking away, UCF Coastal sees itself as a collaborator that listens instead of just lecturing.

This style of academic mission is not only relevant to issues around climate change. It relates to every aspect of modern society, including genetic engineering, automation, artificial intelligence, and so on. The launch of UCF Coastal has garnered positive attention from industry, government agencies, local communities and academics. We think that is because people do want to come together to solve problems, but they need a better mechanism for doing so. We hope to be that conduit while inspiring other academic institutions to do the same.

After all, we have heard for years to “think globally, act locally,” and that “all politics is local.” Florida's Indian River Lagoon will be restored only if there is engagement among residents, local industries, academics, government agencies and nonprofit organizations. As scientists, it is our responsibility to help everyone involved understand that problems that took decades to create will take decades to fix. We need to present the most helpful solutions while explaining the intricacies of the trade-offs for each one. Doing so is only possible if we see ourselves as part of an interdisciplinary, whole-community approach. By listening and responding to fears and concerns, we can make a stronger case for why scientifically driven decisions will be more effective in the long run.

Scientific American Magazine Vol 319 Issue 4

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Real World Problem-Solving

Real world problem-solving (RWPS) is what we do every day. It requires flexibility, resilience, resourcefulness, and a certain degree of creativity. A crucial feature of RWPS is that it involves continuous interaction with the environment during the problem-solving process. In this process, the environment can be seen as not only a source of inspiration for new ideas but also as a tool to facilitate creative thinking. The cognitive neuroscience literature in creativity and problem-solving is extensive, but it has largely focused on neural networks that are active when subjects are not focused on the outside world, i.e., not using their environment. In this paper, I attempt to combine the relevant literature on creativity and problem-solving with the scattered and nascent work in perceptually-driven learning from the environment. I present my synthesis as a potential new theory for real world problem-solving and map out its hypothesized neural basis. I outline some testable predictions made by the model and provide some considerations and ideas for experimental paradigms that could be used to evaluate the model more thoroughly.

1. Introduction

In the Apollo 13 space mission, astronauts together with ground control had to overcome several challenges to bring the team safely back to Earth (Lovell and Kluger, 2006 ). One of these challenges was controlling carbon dioxide levels onboard the space craft: “For 2 days straight [they] had worked on how to jury-rig the Odysseys canisters to the Aquarius's life support system. Now, using materials known to be available onboard the spacecraft—a sock, a plastic bag, the cover of a flight manual, lots of duct tape, and so on—the crew assembled a strange contraption and taped it into place. Carbon dioxide levels immediately began to fall into the safe range” (Team, 1970 ; Cass, 2005 ).

The success of Apollo 13's recovery from failure is often cited as a glowing example of human resourcefulness and inventiveness alongside more well-known inventions and innovations over the course of human history. However, this sort of inventive capability is not restricted to a few creative geniuses, but an ability present in all of us, and exemplified in the following mundane example. Consider a situation when your only suit is covered in lint and you do not own a lint remover. You see a roll of duct tape, and being resourceful you reason that it might be a good substitute. You then solve the problem of lint removal by peeling a full turn's worth of tape and re-attaching it backwards onto the roll to expose the sticky side all around the roll. By rolling it over your suit, you can now pick up all the lint.

In both these examples (historic as well as everyday), we see evidence for our innate ability to problem-solve in the real world. Solving real world problems in real time given constraints posed by one's environment are crucial for survival. At the core of this skill is our mental capability to get out of “sticky situations” or impasses, i.e., difficulties that appear unexpectedly as impassable roadblocks to solving the problem at hand. But, what are the cognitive processes that enable a problem solver to overcome such impasses and arrive at a solution, or at least a set of promising next steps?

A central aspect of this type of real world problem solving, is the role played by the solver's surrounding environment during the problem-solving process. Is it possible that interaction with one's environment can facilitate creative thinking? The answer to this question seems somewhat obvious when one considers the most famous anecdotal account of creative problem solving, namely that of Archimedes of Syracuse. During a bath, he found a novel way to check if the King's crown contained non-gold impurities. The story has traditionally been associated with the so-called “Eureka moment,” the sudden affective experience when a solution to a particularly thorny problem emerges. In this paper, I want to temporarily turn our attention away from the specific “aha!” experience itself and take particular note that Archimedes made this discovery, not with his eyes closed at a desk, but in a real-world context of a bath 1 . The bath was not only a passive, relaxing environment for Archimedes, but also a specific source of inspiration. Indeed it was his noticing the displacement of water that gave him a specific methodology for measuring the purity of the crown; by comparing how much water a solid gold bar of the same weight would displace as compared with the crown. This sort of continuous environmental interaction was present when the Apollo 13 engineers discovered their life-saving solution, and when you solved the suit-lint-removal problem with duct tape.

The neural mechanisms underlying problem-solving have been extensively studied in the literature, and there is general agreement about the key functional networks and nodes involved in various stages of problem-solving. In addition, there has been a great deal of work in studying the neural basis for creativity and insight problem solving, which is associated with the sudden emergence of solutions. However, in the context of problem-solving, creativity, and insight have been researched as largely an internal process without much interaction with and influence from the external environment (Wegbreit et al., 2012 ; Abraham, 2013 ; Kounios and Beeman, 2014 ) 2 . Thus, there are open questions of what role the environment plays during real world problem-solving (RWPS) and how the brain enables the assimilation of novel items during these external interactions.

In this paper, I synthesize the literature on problem-solving, creativity and insight, and particularly focus on how the environment can inform RWPS. I explore three environmentally-informed mechanisms that could play a critical role: (1) partial-cue driven context-shifting, (2) heuristic prototyping and learning novel associations, and (3) learning novel physical inferences. I begin first with some intuitions about real world problem solving, that might help ground this discussion and providing some key distinctions from more traditional problem solving research. Then, I turn to a review of the relevant literature on problem-solving, creativity, and insight first, before discussing the three above-mentioned environmentally-driven mechanisms. I conclude with a potential new model and map out its hypothesized neural basis.

2. Problem solving, creativity, and insight

2.1. what is real world problem-solving.

Archimedes was embodied in the real world when he found his solution. In fact, the real world helped him solve the problem. Whether or not these sorts of historic accounts of creative inspiration are accurate 3 , they do correlate with some of our own key intuitions about how problem solving occurs “in the wild.” Real world problem solving (RWPS) is different from those that occur in a classroom or in a laboratory during an experiment. They are often dynamic and discontinuous, accompanied by many starts and stops. Solvers are never working on just one problem. Instead, they are simultaneously juggling several problems of varying difficulties and alternating their attention between them. Real world problems are typically ill-defined, and even when they are well-defined, often have open-ended solutions. Coupled with that is the added aspect of uncertainty associated with the solver's problem solving strategies. As introduced earlier, an important dimension of RWPS is the continuous interaction between the solver and their environment. During these interactions, the solver might be inspired or arrive at an “aha!” moment. However, more often than not, the solver experiences dozens of minor discovery events— “hmmm, interesting…” or “wait, what?…” moments. Like discovery events, there's typically never one singular impasse or distraction event. The solver must iterate through the problem solving process experiencing and managing these sorts of intervening events (including impasses and discoveries). In summary, RWPS is quite messy and involves a tight interplay between problem solving, creativity, and insight. Next, I explore each of these processes in more detail and explicate a possible role of memory, attention, conflict management and perception.

2.2. Analytical problem-solving

In psychology and neuroscience, problem-solving broadly refers to the inferential steps taken by an agent 4 that leads from a given state of affairs to a desired goal state (Barbey and Barsalou, 2009 ). The agent does not immediately know how this goal can be reached and must perform some mental operations (i.e., thinking) to determine a solution (Duncker, 1945 ).

The problem solving literature divides problems based on clarity (well-defined vs. ill-defined) or on the underlying cognitive processes (analytical, memory retrieval, and insight) (Sprugnoli et al., 2017 ). While memory retrieval is an important process, I consider it as a sub-process to problem solving more generally. I first focus on analytical problem-solving process, which typically involves problem-representation and encoding, and the process of forming and executing a solution plan (Robertson, 2016 ).

2.2.1. Problem definition and representation

An important initial phase of problem-solving involves defining the problem and forming a representation in the working memory. During this phase, components of the prefrontal cortex (PFC), default mode network (DMN), and the dorsal anterior cingulate cortex (dACC) have been found to be activated. If the problem is familiar and well-structured, top-down executive control mechanisms are engaged and the left prefrontal cortex including the frontopolar, dorso-lateral (dlPFC), and ventro-lateral (vlPFC) are activated (Barbey and Barsalou, 2009 ). The DMN along with the various structures in the medial temporal lobe (MTL) including the hippocampus (HF), parahippocampal cortex, perirhinal and entorhinal cortices are also believed to have limited involvement, especially in episodic memory retrieval activities during this phase (Beaty et al., 2016 ). The problem representation requires encoding problem information for which certain visual and parietal areas are also involved, although the extent of their involvement is less clear (Anderson and Fincham, 2014 ; Anderson et al., 2014 ).

2.2.1.1. Working memory

An important aspect of problem representation is the engagement and use of working memory (WM). The WM allows for the maintenance of relevant problem information and description in the mind (Gazzaley and Nobre, 2012 ). Research has shown that WM tasks consistently recruit the dlPFC and left inferior frontal cortex (IC) for encoding an manipulating information; dACC for error detection and performance adjustment; and vlPFC and the anterior insula (AI) for retrieving, selecting information and inhibitory control (Chung and Weyandt, 2014 ; Fang et al., 2016 ).

2.2.1.2. Representation

While we generally have a sense for the brain regions that are functionally influential in problem definition, less is known about how exactly events are represented within these regions. One theory for how events are represented in the PFC is the structured event complex theory (SEC), in which components of the event knowledge are represented by increasingly higher-order convergence zones localized within the PFC, akin to the convergence zones (from posterior to anterior) that integrate sensory information in the brain (Barbey et al., 2009 ). Under this theory, different zones in the PFC (left vs. right, anterior vs. posterior, lateral vs. medial, and dorsal vs. ventral) represent different aspects of the information contained in the events (e.g., number of events to be integrated together, the complexity of the event, whether planning, and action is needed). Other studies have also suggested the CEN's role in tasks requiring cognitive flexibility, and functions to switch thinking modes, levels of abstraction of thought and consider multiple concepts simultaneously (Miyake et al., 2000 ).

Thus, when the problem is well-structured, problem representation is largely an executive control activity coordinated by the PFC in which problem information from memory populates WM in a potentially structured representation. Once the problem is defined and encoded, planning and execution of a solution can begin.

2.2.2. Planning

The central executive network (CEN), particularly the PFC, is largely involved in plan formation and in plan execution. Planning is the process of generating a strategy to advance from the current state to a goal state. This in turn involves retrieving a suitable solution strategy from memory and then coordinating its execution.

2.2.2.1. Plan formation

The dlPFC supports sequential planning and plan formation, which includes the generation of hypothesis and construction of plan steps (Barbey and Barsalou, 2009 ). Interestingly, the vlPFC and the angular gyrus (AG), implicated in a variety of functions including memory retrieval, are also involved in plan formation (Anderson et al., 2014 ). Indeed, the AG together with the regions in the MTL (including the HF) and several other regions form a what is known as the “core” network. The core network is believed to be activated when recalling past experiences, imagining fictitious, and future events and navigating large-scale spaces (Summerfield et al., 2010 ), all key functions for generating plan hypotheses. A recent study suggests that the AG is critical to both episodic simulation, representation, and episodic memory (Thakral et al., 2017 ). One possibility for how plans are formulated could involve a dynamic process of retrieving an optimal strategy from memory. Research has shown significant interaction between striatal and frontal regions (Scimeca and Badre, 2012 ; Horner et al., 2015 ). The striatum is believed to play a key role in declarative memory retrieval, and specifically helping retrieve optimal (or previously rewarded) memories (Scimeca and Badre, 2012 ). Relevant to planning and plan formation, Scimeca & Badre have suggested that the striatum plays two important roles: (1) in mapping acquired value/utility to action selection, and thereby helping plan formation, and (2) modulation and re-encoding of actions and other plan parameters. Different types of problems require different sets of specialized knowledge. For example, the knowledge needed to solve mathematical problems might be quite different (albeit overlapping) from the knowledge needed to select appropriate tools in the environment.

Thus far, I have discussed planning and problem representation as being domain-independent, which has allowed me to outline key areas of the PFC, MTL, and other regions relevant to all problem-solving. However, some types of problems require domain-specific knowledge for which other regions might need to be recruited. For example, when planning for tool-use, the superior parietal lobe (SPL), supramarginal gyrus (SMG), anterior inferior parietal lobe (AIPL), and certain portions of the temporal and occipital lobe involved in visual and spatial integration have been found to be recruited (Brandi et al., 2014 ). It is believed that domain-specific information stored in these regions is recovered and used for planning.

2.2.2.2. Plan execution

Once a solution plan has been recruited from memory and suitably tuned for the problem on hand, the left-rostral PFC, caudate nucleus (CN), and bilateral posterior parietal cortices (PPC) are responsible for translating the plan into executable form (Stocco et al., 2012 ). The PPC stores and maintains “mental template” of the executable form. Hemispherical division of labor is particularly relevant in planning where it was shown that when planning to solve a Tower of Hanoi (block moving) problem, the right PFC is involved in plan construction whereas the left PFC is involved in controlling processes necessary to supervise the execution of the plan (Newman and Green, 2015 ). On a separate note and not the focus of this paper, plan execution and problem-solving can require the recruitment of affective and motivational processing in order to supply the agent with the resolve to solve problems, and the vmPFC has been found to be involved in coordinating this process (Barbey and Barsalou, 2009 ).

2.3. Creativity

During the gestalt movement in the 1930s, Maier noted that “most instances of “real” problem solving involves creative thinking” (Maier, 1930 ). Maier performed several experiments to study mental fixation and insight problem solving. This close tie between insight and creativity continues to be a recurring theme, one that will be central to the current discussion. If creativity and insight are linked to RWPS as noted by Maier, then it is reasonable to turn to the creativity and insight literature for understanding the role played by the environment. A large portion of the creativity literature has focused on viewing creativity as an internal process, one in which the solvers attention is directed inwards, and toward internal stimuli, to facilitate the generation of novel ideas and associations in memory (Beaty et al., 2016 ). Focusing on imagination, a number of researchers have looked at blinking, eye fixation, closing eyes, and looking nowhere behavior and suggested that there is a shift of attention from external to internal stimuli during creative problem solving (Salvi and Bowden, 2016 ). The idea is that shutting down external stimuli reduces cognitive load and focuses attention internally. Other experiments studying sleep behavior have also noted the beneficial role of internal stimuli in problem solving. The notion of ideas popping into ones consciousness, suddenly, during a shower is highly intuitive for many and researchers have attempted to study this phenomena through the lens of incubation, and unconscious thought that is internally-driven. There have been several theories and counter-theories proposed to account specifically for the cognitive processes underlying incubation (Ritter and Dijksterhuis, 2014 ; Gilhooly, 2016 ), but none of these theories specifically address the role of the external environment.

The neuroscience of creativity has also been extensively studied and I do not focus on an exhaustive literature review in this paper (a nice review can be found in Sawyer, 2011 ). From a problem-solving perspective, it has been found that unlike well-structured problems, ill-structured problems activate the right dlPFC. Most of the past work on creativity and creative problem-solving has focused on exploring memory structures and performing internally-directed searches. Creative idea generation has primarily been viewed as internally directed attention (Jauk et al., 2012 ; Benedek et al., 2016 ) and a primary mechanism involved is divergent thinking , which is the ability to produce a variety of responses in a given situation (Guilford, 1962 ). Divergent thinking is generally thought to involve interactions between the DMN, CEN, and the salience network (Yoruk and Runco, 2014 ; Heinonen et al., 2016 ). One psychological model of creative cognition is the Geneplore model that considers two major phases of generation (memory retrieval and mental synthesis) and exploration (conceptual interpretation and functional inference) (Finke et al., 1992 ; Boccia et al., 2015 ). It has been suggested that the associative mode of processing to generate new creative association is supported by the DMN, which includes the medial PFC, posterior cingulate cortex (PCC), tempororparietal juntion (TPJ), MTL, and IPC (Beaty et al., 2014 , 2016 ).

That said, the creativity literature is not completely devoid of acknowledging the role of the environment. In fact, it is quite the opposite. Researchers have looked closely at the role played by externally provided hints from the time of the early gestalt psychologists and through to present day studies (Öllinger et al., 2017 ). In addition to studying how hints can help problem solving, researchers have also looked at how directed action can influence subsequent problem solving—e.g., swinging arms prior to solving the two-string puzzle, which requires swinging the string (Thomas and Lleras, 2009 ). There have also been numerous studies looking at how certain external perceptual cues are correlated with creativity measures. Vohs et al. suggested that untidiness in the environment and the increased number of potential distractions helps with creativity (Vohs et al., 2013 ). Certain colors such as blue have been shown to help with creativity and attention to detail (Mehta and Zhu, 2009 ). Even environmental illumination, or lack thereof, have been shown to promote creativity (Steidle and Werth, 2013 ). However, it is important to note that while these and the substantial body of similar literature show the relationship of the environment to creative problem solving, they do not specifically account for the cognitive processes underlying the RWPS when external stimuli are received.

2.4. Insight problem solving

Analytical problem solving is believed to involve deliberate and conscious processing that advances step by step, allowing solvers to be able to explain exactly how they solved it. Inability to solve these problems is often associated with lack of required prior knowledge, which if provided, immediately makes the solution tractable. Insight, on the other hand, is believed to involve a sudden and unexpected emergence of an obvious solution or strategy sometimes accompanied by an affective aha! experience. Solvers find it difficult to consciously explain how they generated a solution in a sequential manner. That said, research has shown that having an aha! moment is neither necessary nor sufficient to insight and vice versa (Danek et al., 2016 ). Generally, it is believed that insight solvers acquire a full and deep understanding of the problem when they have solved it (Chu and Macgregor, 2011 ). There has been an active debate in the problem solving community about whether insight is something special. Some have argued that it is not, and that there are no special or spontaneous processes, but simply a good old-fashioned search of a large problem space (Kaplan and Simon, 1990 ; MacGregor et al., 2001 ; Ash and Wiley, 2006 ; Fleck, 2008 ). Others have argued that insight is special and suggested that it is likely a different process (Duncker, 1945 ; Metcalfe, 1986 ; Kounios and Beeman, 2014 ). This debate lead to two theories for insight problem solving. MacGregor et al. proposed the Criterion for Satisfactory Progress Theory (CSPT), which is based on Newell and Simons original notion of problem solving as being a heuristic search through the problem space (MacGregor et al., 2001 ). The key aspect of CSPT is that the solver is continually monitoring their progress with some set of criteria. Impasses arise when there is a criterion failure, at which point the solver tries non-maximal but promising states. The representational change theory (RCT) proposed by Ohlsson et al., on the other hand, suggests that impasses occur when the goal state is not reachable from an initial problem representation (which may have been generated through unconscious spreading activation) (Ohlsson, 1992 ). In order to overcome an impasse, the solver needs to restructure the problem representation, which they can do by (1) elaboration (noticing new features of a problem), (2) re-encoding fixing mistaken or incomplete representations of the problem, and by (3) changing constraints. Changing constraints is believed to involve two sub-processes of constraint relaxation and chunk-decomposition.

The current position is that these two theories do not compete with each other, but instead complement each other by addressing different stages of problem solving: pre- and post-impasse. Along these lines, Ollinger et al. proposed an extended RCT (eRCT) in which revising the search space and using heuristics was suggested as being a dynamic and iterative and recursive process that involves repeated instances of search, impasse and representational change (Öllinger et al., 2014 , 2017 ). Under this theory, a solver first forms a problem representation and begins searching for solutions, presumably using analytical problem solving processes as described earlier. When a solution cannot be found, the solver encounters an impasse, at which point the solver must restructure or change the problem representation and once again search for a solution. The model combines both analytical problem solving (through heuristic searches, hill climbing and progress monitoring), and creative mechanisms of constraint relaxation and chunk decomposition to enable restructuring.

Ollingers model appears to comprehensively account for both analytical and insight problem solving and, therefore, could be a strong candidate to model RWPS. However, while compelling, it is nevertheless an insufficient model of RWPS for many reasons, of which two are particularly significant for the current paper. First, the model does explicitly address mechanisms by which external stimuli might be assimilated. Second, the model is not sufficiently flexible to account for other events (beyond impasse) occurring during problem solving, such as distraction, mind-wandering and the like.

So, where does this leave us? I have shown the interplay between problem solving, creativity and insight. In particular, using Ollinger's proposal, I have suggested (maybe not quite explicitly up until now) that RWPS involves some degree of analytical problem solving as well as the post-impasse more creative modes of problem restructuring. I have also suggested that this model might need to be extended for RWPS along two dimensions. First, events such as impasses might just be an instance of a larger class of events that intervene during problem solving. Thus, there needs to be an accounting of the cognitive mechanisms that are potentially influenced by impasses and these other intervening events. It is possible that these sorts of events are crucial and trigger a switch in attentional focus, which in turn facilitates switching between different problem solving modes. Second, we need to consider when and how externally-triggered stimuli from the solver's environment can influence the problem solving process. I detail three different mechanisms by which external knowledge might influence problem solving. I address each of these ideas in more detail in the next two sections.

3. Event-triggered mode switching during problem-solving

3.1. impasse.

When solving certain types of problems, the agent might encounter an impasse, i.e., some block in its ability to solve the problem (Sprugnoli et al., 2017 ). The impasse may arise because the problem may have been ill-defined to begin with causing incomplete and unduly constrained representations to have been formed. Alternatively, impasses can occur when suitable solution strategies cannot be retrieved from memory or fail on execution. In certain instances, the solution strategies may not exist and may need to be generated from scratch. Regardless of the reason, an impasse is an interruption in the problem solving process; one that was running conflict-free up until the point when a seemingly unresolvable issue or an error in the predicted solution path was encountered. Seen as a conflict encountered in the problem-solving process it activates the anterior cingulate cortex (ACC). It is believed that the ACC not only helps detect the conflict, but also switch modes from one of “exploitation” (planning) to “exploration” (search) (Quilodran et al., 2008 ; Tang et al., 2012 ), and monitors progress during resolution (Chu and Macgregor, 2011 ). Some mode switching duties are also found to be shared with the AI (the ACC's partner in the salience network), however, it is unclear exactly the extent of this function-sharing.

Even though it is debatable if impasses are a necessary component of insight, they are still important as they provide a starting point for the creativity (Sprugnoli et al., 2017 ). Indeed, it is possible that around the moment of impasse, the AI and ACC together, as part of the salience network play a crucial role in switching thought modes from analytical planning mode to creative search and discovery mode. In the latter mode, various creative mechanisms might be activated allowing for a solution plan to emerge. Sowden et al. and many others have suggested that the salience network is potentially a candidate neurobiological mechanism for shifting between thinking processes, more generally (Sowden et al., 2015 ). When discussing various dual-process models as they relate to creative cognition, Sowden et al. have even noted that the ACC activation could be useful marker to identify shifting as participants work creative problems.

3.2. Defocused attention

As noted earlier, in the presence of an impasse there is a shift from an exploitative (analytical) thinking mode to an exploratory (creative) thinking mode. This shift impacts several networks including, for example, the attention network. It is believed attention can switch between a focused mode and a defocused mode. Focused attention facilitates analytic thought by constraining activation such that items are considered in a compact form that is amenable to complex mental operations. In the defocused mode, agents expand their attention allowing new associations to be considered. Sowden et al. ( 2015 ) note that the mechanism responsible for adjustments in cognitive control may be linked to the mechanisms responsible for attentional focus. The generally agreed position is that during generative thinking, unconscious cognitive processes activated through defocused attention are more prevalent, whereas during exploratory thinking, controlled cognition activated by focused attention becomes more prevalent (Kaufman, 2011 ; Sowden et al., 2015 ).

Defocused attention allows agents to not only process different aspects of a situation, but to also activate additional neural structures in long term memory and find new associations (Mendelsohn, 1976 ; Yoruk and Runco, 2014 ). It is believed that cognitive material attended to and cued by positive affective state results in defocused attention, allowing for more complex cognitive contexts and therefore a greater range of interpretation and integration of information (Isen et al., 1987 ). High attentional levels are commonly considered a typical feature of highly creative subjects (Sprugnoli et al., 2017 ).

4. Role of the environment

In much of the past work the focus has been on treating creativity as largely an internal process engaging the DMN to assist in making novel connections in memory. The suggestion has been that “individual needs to suppress external stimuli and concentrate on the inner creative process during idea generation” (Heinonen et al., 2016 ). These ideas can then function as seeds for testing and problem-solving. While true of many creative acts, this characterization does not capture how creative ideas arise in many real-world creative problems. In these types of problems, the agent is functioning and interacting with its environment before, during and after problem-solving. It is natural then to expect that stimuli from the environment might play a role in problem-solving. More specifically, it can be expected that through passive and active involvement with the environment, the agent is (1) able to trigger an unrelated, but potentially useful memory relevant for problem-solving, (2) make novel connections between two events in memory with the environmental cue serving as the missing link, and (3) incorporate a completely novel information from events occuring in the environment directly into the problem-solving process. I explore potential neural mechanisms for these three types of environmentally informed creative cognition, which I hypothesize are enabled by defocused attention.

4.1. Partial cues trigger relevant memories through context-shifting

I have previously discussed the interaction between the MTL and PFC in helping select task-relevant and critical memories for problem-solving. It is well-known that pattern completion is an important function of the MTL and one that enables memory retrieval. Complementary Learning Theory (CLS) and its recently updated version suggest that the MTL and related structures support initial storage as well as retrieval of item and context-specific information (Kumaran et al., 2016 ). According to CLS theory, the dentate gyrus (DG) and the CA3 regions of the HF are critical to selecting neural activity patterns that correspond to particular experiences (Kumaran et al., 2016 ). These patterns might be distinct even if experiences are similar and are stabilized through increases in connection strengths between the DG and CA3. Crucially, because of the connection strengths, reactivation of part of the pattern can activate the rest of it (i.e., pattern completion). Kumaran et al. have further noted that if consistent with existing knowledge, these new experiences can be quickly replayed and interleaved into structured representations that form part of the semantic memory.

Cues in the environment provided by these experiences hold partial information about past stimuli or events and this partial information converges in the MTL. CLS accounts for how these cues might serve to reactivate partial patterns, thereby triggering pattern completion. When attention is defocused I hypothesize that (1) previously unnoticed partial cues are considered, and (2) previously noticed partial cues are decomposed to produce previously unnoticed sub-cues, which in turn are considered. Zabelina et al. ( 2016 ) have shown that real-world creativity and creative achievement is associated with “leaky attention,” i.e., attention that allows for irrelevant information to be noticed. In two experiments they systematically explored the relationship between two notions of creativity— divergent thinking and real-world creative achievement—and the use of attention. They found that attentional use is associated in different ways for each of the two notions of creativity. While divergent thinking was associated with flexible attention, it does not appear to be leaky. Instead, selective focus and inhibition components of attention were likely facilitating successful performance on divergent thinking tasks. On the other hand, real-world creative achievement was linked to leaky attention. RWPS involves elements of both divergent thinking and of real-world creative achievement, thus I would expect some amount of attentional leaks to be part of the problem solving process.

Thus, it might be the case that a new set of cues or sub-cues “leak” in and activate memories that may not have been previously considered. These cues serve to reactivate a diverse set of patterns that then enable accessing a wide range of memories. Some of these memories are extra-contextual, in that they consider the newly noticed cues in several contexts. For example, when unable to find a screwdriver, we might consider using a coin. It is possible that defocused attention allows us to consider the coin's edge as being a potentially relevant cue that triggers uses for the thin edge outside of its current context in a coin. The new cues (or contexts) may allow new associations to emerge with cues stored in memory, which can occur during incubation. Objects and contexts are integrated into memory automatically into a blended representation and changing contexts disrupts this recognition (Hayes et al., 2007 ; Gabora, 2016 ). Cue-triggered context shifting allows an agent to break-apart a memory representation, which can then facilitate problem-solving in new ways.

4.2. Heuristic prototyping facilitates novel associations

It has long been the case that many scientific innovations have been inspired by events in nature and the surrounding environment. As noted earlier, Archimedes realized the relationship between the volume of an irregularly shaped object and the volume of water it displaced. This is an example of heuristic prototyping where the problem-solver notices an event in the environment, which then triggers the automatic activation of a heuristic prototype and the formation of novel associations (between the function of the prototype and the problem) which they can then use to solve the problem (Luo et al., 2013 ). Although still in its relative infancy, there has been some recent research into the neural basis for heuristic prototyping. Heuristic prototype has generally been defined as an enlightening prototype event with a similar element to the current problem and is often composed of a feature and a function (Hao et al., 2013 ). For example, in designing a faster and more efficient submarine hull, a heuristic prototype might be a shark's skin, while an unrelated prototype might be a fisheye camera (Dandan et al., 2013 ).

Research has shown that activating the feature function of the right heuristic prototype and linking it by way of semantic similarity to the required function of the problem was the key mechanism people used to solve several scienitific insight problems (Yang et al., 2016 ). A key region activated during heuristic prototyping is the dlPFC and it is believed to be generally responsible for encoding the events into memory and may play an important role in selecting and retrieving the matched unsolved technical problem from memory (Dandan et al., 2013 ). It is also believed that the precuneus plays a role in automatic retrieval of heuristic information allowing the heuristic prototype and the problem to combine (Luo et al., 2013 ). In addition to semantic processing, certain aspects of visual imagery have also been implicated in heuristic prototyping leading to the suggestion of the involvement of Broadman's area BA 19 in the occipital cortex.

There is some degree of overlap between the notions of heuristic prototyping and analogical transfer (the mapping of relations from one domain to another). Analogical transfer is believed to activate regions in the left medial fronto-parietal system (dlPFC and the PPC) (Barbey and Barsalou, 2009 ). I suggest here that analogical reasoning is largely an internally-guided process that is aided by heuristic prototyping which is an externally-guided process. One possible way this could work is if heuristic prototyping mechanisms help locate the relevant memory with which to then subsequently analogize.

4.3. Making physical inferences to acquire novel information

The agent might also be able to learn novel facts about their environment through passive observation as well as active experimentation. There has been some research into the neural basis for causal reasoning (Barbey and Barsalou, 2009 ; Operskalski and Barbey, 2016 ), but beyond its generally distributed nature, we do not know too much more. Beyond abstract causal reasoning, some studies looked into the cortical regions that are activated when people watch and predict physical events unfolding in real-time and in the real-world (Fischer et al., 2016 ). It was found that certain regions were associated with representing types of physical concepts, with the left intraparietal sulcus (IPS) and left middle frontal gyrus (MFG) shown to play a role in attributing causality when viewing colliding objects (Mason and Just, 2013 ). The parahippocampus (PHC) was associated with linking causal theory to observed data and the TPJ was involved in visualizing movement of objects and actions in space (Mason and Just, 2013 ).

5. Proposed theory

I noted earlier that Ollinger's model for insight problem solving, while serving as a good candidate for RWPS, requires extension. In this section, I propose a candidate model that includes some necessary extensions to Ollinger's framework. I begin by laying out some preliminary notions that underlie the proposed model.

5.1. Dual attentional modes

I propose that the attention-switching mechanism described earlier is at the heart of RWPS and enables two modes of operation: focused and defocused mode. In the focused mode, the problem representation is more or less fixed, and problem solving proceeds in a focused and goal directed manner through search, planning, and execution mechanisms. In the defocused mode, problem solving is not necessarily goal directed, but attempts to generate ideas, driven by both internal and external items.

At first glance, these modes might seem similar to convergent and divergent thinking modes postulated by numerous others to account for creative problem solving. Divergent thinking allows for the generation of new ideas and convergent thinking allows for verification and selection of generated ideas. So, it might seem that focused mode and convergent thinking are similar and likewise divergent and defocused mode. They are, however, quite different. The modes relate less to idea generation and verification, and more to the specific mechanisms that are operating with regard to a particular problem at a particular moment in time. Convergent and divergent processes may be occurring during both defocused and focused modes. Some degree of divergent processes may be used to search and identify specific solution strategies in focused mode. Also, there might be some degree of convergent idea verification occuring in defocused mode as candidate items are evaluated for their fit with the problem and goal. Thus, convergent and divergent thinking are one amongst many mechanisms that are utilized in focused and defocused mode. Each of these two modes has to do with degree of attention placed on a particular problem.

There have been numerous dual-process and dual-systems models of cognition proposed over the years. To address criticisms raised against these models and to unify some of the terminology, Evans & Stanovich proposed a dual-process model comprising Type 1 and Type 2 thought (Evans and Stanovich, 2013 ; Sowden et al., 2015 ). Type 1 processes are those that are believed to be autonomous and do not require working memory. Type 2 processes, on the other hand, are believed to require working memory and are cognitively decoupled to prevent real-world representations from becoming confused with mental simulations (Sowden et al., 2015 ). While acknowledging various other attributes that are often used to describe dual process models (e.g., fast/slow, associative/rule-based, automatic/controlled), Evans & Stanovich note that these attributes are merely frequent correlates and not defining characteristics of Type 1 or Type 2 processes. The proposed dual attentional modes share some similarities with the Evans & Stanovich Type 1 and 2 models. Specifically, Type 2 processes might occur in focused attentional mode in the proposed model as they typically involve the working memory and certain amount of analytical thought and planning. Similarly, Type 1 processes are likely engaged in defocused attentional mode as there are notions of associative and generative thinking that might be facilitated when attention has been defocused. The crucial difference between the proposed model and other dual-process models is that the dividing line between focused and defocused attentional modes is the degree of openness to internal and external stimuli (by various networks and functional units in the brain) when problem solving. Many dual process models were designed to classify the “type” of thinking process or a form of cognitive processing. In some sense, the “processes” in dual process theories are characterized by the type of mechanism of operation or the type of output they produced. Here, I instead characterize and differentiate the modes of thinking by the receptivity of different functional units in the brain to input during problem solving.

This, however, raises a different question of the relationship between these attentional modes and conscious vs. unconscious thinking. It is clear that both the conscious and unconscious are involved in problem solving, as well as in RWPS. Here, I claim that a problem being handled is, at any given point in time, in either a focused mode or in a defocused mode. When in the focused mode, problem solving primarily proceeds in a manner that is available for conscious deliberation. More specifically, problem space elements and representations are tightly managed and plans and strategies are available in the working memory and consciously accessible. There are, however, secondary unconscious operations in the focused modes that includes targeted memory retrieval and heuristic-based searches. In the defocused mode, the problem is primarily managed in an unconscious way. The problem space elements are broken apart and loosely managed by various mechanisms that do not allow for conscious deliberation. That said, it is possible that some problem parameters remain accessible. For example, it is possible that certain goal information is still maintained consciously. It is also possible that indexes to all the problems being considered by the solver are maintained and available to conscious awareness.

5.2. RWPS model

Returning to Ollinger's model for insight problem solving, it now becomes readily apparent how this model can be modified to incorporate environmental effects as well as generalizing the notion of intervening events beyond that of impasses. I propose a theory for RWPS that begins with standard analytical problem-solving process (See Figures ​ Figures1, 1 , ​ ,2 2 ).

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Summary of neural activations during focused problem-solving (Left) and defocused problem-solving (Right) . During defocused problem-solving, the salience network (insula and ACC) coordinates the switching of several networks into a defocused attention mode that permits the reception of a more varied set of stimuli and interpretations via both the internally-guided networks (default mode network DMN) and externally guided networks (Attention). PFC, prefrontal cortex; ACC, anterior cingulate cortex; PCC, posterior cingulate cortex; IPC, inferior parietal cortex; PPC, posterior parietal cortex; IPS, intra-parietal sulcus; TPJ, temporoparietal junction; MTL, medial temporal lobe; FEF, frontal eye field.

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Proposed Model for Real World Problem Solving (RWPS). The corresponding neural correlates are shown in italics. During problem-solving, an initial problem representation is formed based on prior knowledge and available perceptual information. The problem-solving then proceeds in a focused, goal-directed mode until the goal is achieved or a defocusing event (e.g., impasse or distraction) occurs. During focused mode operation, the solver interacts with the environment in directed manner, executing focused plans, and allowing for predicted items to be activated by the environment. When a defocusing event occurs, the problem-solving then switches into a defocused mode until a focusing event (e.g., discovery) occurs. In defocused mode, the solver performs actions unrelated to the problem (or is inactive) and is receptive to a set of environmental triggers that activate novel aspects using the three mechanisms discussed in this paper. When a focusing event occurs, the diffused problem elements cohere into a restructured representation and problem-solving returns into a focused mode.

5.2.1. Focused problem solving mode

Initially, both prior knowledge and perceptual entities help guide the creation of problem representations in working memory. Prior optimal or rewarding solution strategies are obtained from LTM and encoded in the working memory as well. This process is largely analytical and the solver interacts with their environment through focused plan or idea execution, targeted observation of prescribed entities, and estimating prediction error of these known entities. More specifically, when a problem is presented, the problem representations are activated and populated into working memory in the PFC, possibly in structured representations along convergence zones. The PFC along with the Striatum and the MTL together attempt at retrieving an optimal or previously rewarded solution strategy from long term memory. If successfully retrieved, the solution strategy is encoded into the PPC as a mental template, which then guides relevant motor control regions to execute the plan.

5.2.2. Defocusing event-triggered mode switching

The search and solve strategy then proceeds analytically until a “defocusing event” is encountered. The salience network (AI and ACC) monitor for conflicts and attempt to detect any such events in the problem-solving process. As long as no conflicts are detected, the salience network focuses on recruiting networks to achieve goals and suppresses the DMN (Beaty et al., 2016 ). If the plan execution or retrieval of the solution strategy fails, then a defocusing event is detected and the salience network performs mode switching. The salience network dynamically switches from the focused problem-solving mode to a defocused problem-solving mode (Menon, 2015 ). Ollinger's current model does not account for other defocusing events beyond an impasse, but it is not inconceivable that there could be other such events triggered by external stimuli (e.g., distraction or an affective event) or by internal stimuli (e.g., mind wandering).

5.2.3. Defocused problem solving mode

In defocused mode, the problem is operated on by mechanisms that allow for the generation and testing of novel ideas. Several large-scale brain networks are recruited to explore and generate new ideas. The search for novel ideas is facilitated by generally defocused attention, which in turn allows for creative idea generation from both internal as well as external sources. The salience network switches operations from defocused event detection to focused event or discovery detection, whereby for example, environmental events or ideas that are deemed interesting can be detected. During this idea exploration phase, internally, the DMN is no longer suppressed and attempts to generate new ideas for problem-solving. It is known that the IPC is involved in the generation of new ideas (Benedek et al., 2014 ) and together with the PPC in coupling different information together (Simone Sandkühler, 2008 ; Stocco et al., 2012 ). Beaty et al. ( 2016 ) have proposed that even this internal idea-generation process can be goal directed, thereby allowing for a closer working relationship between the CEN and the DMN. They point to neuroimaging evidence that support the possibility that the executive control network (comprising the lateral prefrontal and inferior parietal regions) can constrain and direct the DMN in its process of generating ideas to meet task-specific goals via top down monitoring and executive control (Beaty et al., 2016 ). The control network is believed to maintain an “internal train of thought” by keeping the task goal activated, thereby allowing for strategic and goal-congruent searches for ideas. Moreover, they suggest that the extent of CEN involvement in the DMN idea-generation may depend on the extent to which the creative task is constrained. In the RWPS setting, I would suspect that the internal search for creative solutions is not entirely unconstrained, even in the defocused mode. Instead, the solver is working on a specified problem and thus, must maintain the problem-thread while searching for solutions. Moreover, self-generated ideas must be evaluated against the problem parameters and thereby might need some top-down processing. This would suggest that in such circumstances, we would expect to see an increased involvement of the CEN in constraining the DMN.

On the external front, several mechanisms are operating in this defocused mode. Of particular note are the dorsal attention network, composed of the visual cortex (V), IPS and the frontal eye field (FEF) along with the precuneus and the caudate nucleus allow for partial cues to be considered. The MTL receives synthesized cue and contextual information and populates the WM in the PFC with a potentially expanded set of information that might be relevant for problem-solving. The precuneus, dlPFC and PPC together trigger the activation and use of a heuristic prototype based on an event in the environment. The caudate nucleus facilitates information routing between the PFC and PPC and is involved in learning and skill acquisition.

5.2.4. Focusing event-triggered mode switching

The problem's life in this defocused mode continues until a focusing event occurs, which could be triggered by either external (e.g., notification of impending deadline, discovery of a novel property in the environment) or internal items (e.g., goal completion, discovery of novel association or updated relevancy of a previously irrelevant item). As noted earlier, an internal train of thought may be maintained that facilitates top-down evaluation of ideas and tracking of these triggers (Beaty et al., 2016 ). The salience network switches various networks back to the focused problem-solving mode, but not without the potential for problem restructuring. As noted earlier, problem space elements are maintained somewhat loosely in the defocused mode. Thus, upon a focusing event, a set or subset of these elements cohere into a tight (restructured) representation suitable for focused mode problem solving. The process then repeats itself until the goal has been achieved.

5.3. Model predictions

5.3.1. single-mode operation.

The proposed RWPS model provides several interesting hypotheses, which I discuss next. First, the model assumes that any given problem being worked on is in one mode or another, but not both. Thus, the model predicts that there cannot be focused plan execution on a problem that is in defocused mode. The corollary prediction is that novel perceptual cues (as those discussed in section 4) cannot help the solver when in focused mode. The corollary prediction, presumably has some support from the inattentional blindness literature. Inattentional blindness is when perceptual cues are not noticed during a task (e.g., counting the number of basketball passes between several people, but not noticing a gorilla in the scene) (Simons and Chabris, 1999 ). It is possible that during focused problem solving, that external and internally generated novel ideas are simply not considered for problem solving. I am not claiming that these perceptual cues are always ignored, but that they are not considered within the problem. Sometimes external cues (like distracting occurrences) can serve as defocusing events, but the model predicts that the actual content of these cues are not themselves useful for solving the specific problem at hand.

When comparing dual-process models Sowden et al. ( 2015 ) discuss shifting from one type of thinking to another and explore how this shift relates to creativity. In this regard, they weigh the pros and cons of serial vs. parallel shifts. In dual-process models that suggest serial shifts, it is necessary to disengage one type of thought prior to engaging the other or to shift along a continuum. Whereas, in models that suggest parallel shifts, each of the thinking types can operate in parallel. Per this construction, the proposed RWPS model is serial, however, not quite in the same sense. As noted earlier, the RWPS model is not a dual-process model in the same sense as other dual process model. Instead, here, the thrust is on when the brain is receptive or not receptive to certain kinds of internal and external stimuli that can influence problem solving. Thus, while the modes may be serial with respect to a certain problem, it does not preclude the possibility of serial and parallel thinking processes that might be involved within these modes.

5.3.2. Event-driven transitions

The model requires an event (defocusing or focusing) to transition from one mode to another. After all why else would a problem that is successfully being resolved in the focused mode (toward completion) need to necessarily be transferred to defocused mode? These events are interpreted as conflicts in the brain and therefore the mode-switching is enabled by the saliency network and the ACC. Thus, the model predicts that there can be no transition from one mode to another without an event. This is a bit circular, as an event is really what triggers the transition in the first place. But, here I am suggesting that an external or internal cue triggered event is what drives the transition, and that transitions cannot happen organically without such an event. In some sense, the argument is that the transition is discontinuous, rather than a smooth one. Mind-wandering is good example of when we might drift into defocused mode, which I suggest is an example of an internally driven event caused by an alternative thought that takes attention away from the problem.

A model assumption underlying RWPS is that events such as impasses have a similar effect to other events such as distraction or mind wandering. Thus, it is crucial to be able to establish that there exists of class of such events and they have a shared effect on RWPS, which is to switch attentional modes.

5.3.3. Focused mode completion

The model also predicts that problems cannot be solved (i.e., completed) within the defocused mode. A problem can be considered solved when a goal is reached. However, if a goal is reached and a problem is completed in the defocused mode, then there must have not been any converging event or coherence of problem elements. While it is possible that the solver arbitrarily arrived at the goal in a diffused problem space and without conscious awareness of completing the task or even any converging event or problem recompiling, it appears somewhat unlikely. It is true that there are many tasks that we complete without actively thinking about it. We do not think about what foot to place in front of another while walking, but this is not an instance of problem solving. Instead, this is an instance of unconscious task completion.

5.3.4. Restructuring required

The model predicts that a problem cannot return to a focused mode without some amount of restructuring. That is, once defocused, the problem is essentially never the same again. The problem elements begin interacting with other internally and externally-generated items, which in turn become absorbed into the problem representation. This prediction can potentially be tested by establishing some preliminary knowledge, and then showing one group of subjects the same knowledge as before, while showing the another group of subjects different stimuli. If the model's predictions hold, the problem representation will be restructured in some way for both groups.

There are numerous other such predictions, which are beyond the scope of this paper. One of the biggest challenges then becomes evaluating the model to set up suitable experiments aimed at testing the predictions and falsifying the theory, which I address next.

6. Experimental challenges and paradigms

One of challenges in evaluating the RWPS is that real world factors cannot realistically be accounted for and sufficiently controlled within a laboratory environment. So, how can one controllably test the various predictions and model assumptions of “real world” problem solving, especially given that by definition RWPS involves the external environment and unconscious processing? At the expense of ecological validity, much of insight problem solving research has employed an experimental paradigm that involves providing participants single instances of suitably difficult problems as stimuli and observing various physiological, neurological and behavioral measures. In addition, through verbal protocols, experimenters have been able to capture subjective accounts and problem solving processes that are available to the participants' conscious. These experiments have been made more sophisticated through the use of timed-hints and/or distractions. One challenge with this paradigm has been the selection of a suitable set of appropriately difficult problems. The classic insight problems (e.g., Nine-dot, eight-coin) can be quite difficult, requiring complicated problem solving processes, and also might not generalize to other problems or real world problems. Some in the insight research community have moved in the direction of verbal tasks (e.g., riddles, anagrams, matchstick rebus, remote associates tasks, and compound remote associates tasks). Unfortunately, these puzzles, while providing a great degree of controllability and repeatability, are even less realistic. These problems are not entirely congruent with the kinds of problems that humans are solving every day.

The other challenge with insight experiments is the selection of appropriate performance and process tracking measures. Most commonly, insight researchers use measures such as time to solution, probability of finding solution, and the like for performance measures. For process tracking, verbal protocols, coded solution attempts, and eye tracking are increasingly common. In neuroscientific studies of insight various neurological measures using functional magnetic resonance imaging (fMRI), electroencephalography (EEGs), transcranial direct current stimulation (tDCS), and transcranial magnetic stimulation (tMS) are popular and allow for spatially and temporally localizing an insight event.

Thus, the challenge for RWPS is two-fold: (1) selection of stimuli (real world problems) that are generalizable, and (2) selection of measures (or a set of measures) that can capture key aspects of the problem solving process. Unfortunately, these two challenges are somewhat at odds with each other. While fMRI and various neuroscientific measures can capture the problem solving process in real time, it is practically difficult to provide participants a realistic scenario while they are laying flat on their back in an fMRI machine and allowed to move nothing more than a finger. To begin addressing this conundrum, I suggest returning to object manipulation problems (not all that different from those originally introduced by Maier and Duncker nearly a century ago), but using modern computing and user-interface technologies.

One pseudo-realistic approach is to generate challenging object manipulation problems in Virtual Reality (VR). VR has been used to describe 3-D environment displays that allows participants to interact with artificially projected, but experientially realistic scenarios. It has been suggested that virtual environments (VE) invoke the same cognitive modules as real equivalent environmental experience (Foreman, 2010 ). Crucially, since VE's can be scaled and designed as desired, they provide a unique opportunity to study pseudo-RWPS. However, a VR-based research approach has its limitations, one of which is that it is nearly impossible to track participant progress through a virtual problem using popular neuroscientific measures such as fMRI because of the limited mobility of connected participants.

Most of the studies cited in this paper utilized an fMRI-based approach in conjunction with a verbal or visual task involving problem-solving or creative thinking. Very few, if any, studies involved the use physical manipulation, and those physical manipulations were restricted to limited finger movements. Thus, another pseudo-realistic approach is allowing subjects to teleoperate robotic arms and legs from inside the fMRI machine. This paradigm has seen limited usage in psychology and robotics, in studies focused on Human-Robot interaction (Loth et al., 2015 ). It could be an invaluable tool in studying real-time dynamic problem-solving through the control of a robotic arm. In this paradigm a problem solving task involving physical manipulation is presented to the subject via the cameras of a robot. The subject (in an fMRI) can push buttons to operate the robot and interact with its environment. While the subjects are not themselves moving, they can still manipulate objects in the real world. What makes this paradigm all the more interesting is that the subject's manipulation-capabilities can be systematically controlled. Thus, for a particular problem, different robotic perceptual and manipulation capabilities can be exposed, allowing researchers to study solver-problem dynamics in a new way. For example, even simple manipulation problems (e.g., re-arranging and stacking blocks on a table) can be turned into challenging problems when the robotic movements are restricted. Here, the problem space restrictions are imposed not necessarily on the underlying problem, but on the solver's own capabilities. Problems of this nature, given their simple structure, may enable studying everyday practical creativity without the burden of devising complex creative puzzles. Crucial to note, both these pseudo-realistic paradigms proposed demonstrate a tight interplay between the solver's own capabilities and their environment.

7. Conclusion

While the neural basis for problem-solving, creativity and insight have been studied extensively in the past, there is still a lack of understanding of the role of the environment in informing the problem-solving process. Current research has primarily focused on internally-guided mental processes for idea generation and evaluation. However, the type of real world problem-solving (RWPS) that is often considered a hallmark of human intelligence has involved both a dynamic interaction with the environment and the ability to handle intervening and interrupting events. In this paper, I have attempted to synthesize the literature into a unified theory of RWPS, with a specific focus on ways in which the environment can help problem-solve and the key neural networks involved in processing and utilizing relevant and useful environmental information. Understanding the neural basis for RWPS will allow us to be better situated to solve difficult problems. Moreover, for researchers in computer science and artificial intelligence, clues into the neural underpinnings of the computations taking place during creative RWPS, can inform the design the next generation of helper and exploration robots which need these capabilities in order to be resourceful and resilient in the open-world.

Author contributions

The author confirms being the sole contributor of this work and approved it for publication.

Conflict of interest statement

The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Acknowledgments

I am indebted to Professor Matthias Scheutz, Professor Elizabeth Race, Professor Ayanna Thomas, and Professor. Shaun Patel for providing guidance with the research and the manuscript. I am also grateful for the facilities provided by Tufts University, Medford, MA, USA.

1 My intention is not to ignore the benefits of a concentrated internal thought process which likely occurred as well, but merely to acknowledge the possibility that the environment might have also helped.

2 The research in insight does extensively use “hints” which are, arguably, a form of external influence. But these hints are highly targeted and might not be available in this explicit form when solving problems in the real world.

3 The accuracy of these accounts has been placed in doubt. They often are recounted years later, with inaccuracies, and embellished for dramatic effect.

4 I use the term “agent” to refer to the problem-solver. The term agent is more general than “creature” or “person” or “you" and is intentionally selected to broadly reference humans, animals as well as artificial agents. I also selectively use the term “solver.”

Funding. The research for this Hypothesis/Theory Article was funded by the authors private means. Publication costs will be covered by my institution: Tufts University, Medford, MA, USA.

  • Abraham A. (2013). The promises and perils of the neuroscience of creativity . Front. Hum. Neurosci. 7 :246. 10.3389/fnhum.2013.00246 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
  • Anderson J. R., Fincham J. M. (2014). Discovering the sequential structure of thought . Cogn. Sci. 38 , 322–352. 10.1111/cogs.12068 [ PubMed ] [ CrossRef ] [ Google Scholar ]
  • Anderson J. R., Seung H., Fincham J. M. (2014). Neuroimage discovering the structure of mathematical problem solving . Neuroimage 97 , 163–177. 10.1016/j.neuroimage.2014.04.031 [ PubMed ] [ CrossRef ] [ Google Scholar ]
  • Ash I. K., Wiley J. (2006). The nature of restructuring in insight: an individual-differences approach . Psychon. Bull. Rev. 13 , 66–73. 10.3758/BF03193814 [ PubMed ] [ CrossRef ] [ Google Scholar ]
  • Barbey A. K., Barsalou L. W. (2009). Reasoning and problem solving : models , in Encyclopedia of Neuroscience , ed Squire L. (Oxford: Academic Press; ), 35–43. [ Google Scholar ]
  • Barbey A. K., Krueger F., Grafman J. (2009). Structured event complexes in the medial prefrontal cortex support counterfactual representations for future planning . Philos. Trans. R. Soc. Lond. B Biol. Sci. 364 , 1291–1300. 10.1098/rstb.2008.0315 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
  • Beaty R. E., Benedek M., Silvia P. J., Schacter D. L. (2016). Creative cognition and brain network dynamics . Trends Cogn. Sci. 20 , 87–95. 10.1016/j.tics.2015.10.004 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
  • Beaty R. E., Benedek M., Wilkins R. W., Jauk E., Fink A., Silvia P. J., et al.. (2014). Creativity and the default network: a functional connectivity analysis of the creative brain at rest . Neuropsychologia 64 , 92–98. 10.1016/j.neuropsychologia.2014.09.019 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
  • Benedek M., Jauk E., Beaty R. E., Fink A., Koschutnig K., Neubauer A. C. (2016). Brain mechanisms associated with internally directed attention and self-generated thought . Sci. Rep. 6 :22959. 10.1038/srep22959 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
  • Benedek M., Jauk E., Fink A., Koschutnig K., Reishofer G., Ebner F., et al.. (2014). To create or to recall? Neural mechanisms underlying the generation of creative new ideas . Neuroimage 88 , 125–133. 10.1016/j.neuroimage.2013.11.021 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
  • Boccia M., Piccardi L., Palermo L., Nori R., Palmiero M. (2015). Where do bright ideas occur in ourbrain? Meta-analytic evidence from neuroimaging studies of domain-specific creativity . Front. Psychol. 6 :1195. 10.3389/fpsyg.2015.01195 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
  • Brandi M. l., Wohlschläger A., Sorg C., Hermsdörfer J. (2014). The neural correlates of planning and executing actual tool use . J. Neurosci. 34 , 13183–13194. 10.1523/JNEUROSCI.0597-14.2014 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
  • Cass S. (2005). Apollo 13, we have a solution , in IEEE Spectrum On-line, 04 , 1. Available online at: https://spectrum.ieee.org/tech-history/space-age/apollo-13-we-have-a-solution
  • Chu Y., Macgregor J. N. (2011). Human performance on insight problem solving : a review J. Probl. Solv. 3 , 119–150. 10.7771/1932-6246.1094 [ CrossRef ] [ Google Scholar ]
  • Chung H. J., Weyandt L. L. (2014). The physiology of executive functioning , Handbook of Executive Functioning (Springer; ), 13–28. [ Google Scholar ]
  • Dandan T., Haixue Z., Wenfu L., Wenjing Y., Jiang Q., Qinglin Z. (2013). Brain activity in using heuristic prototype to solve insightful problems . Behav. Brain Res. 253 , 139–144. 10.1016/j.bbr.2013.07.017 [ PubMed ] [ CrossRef ] [ Google Scholar ]
  • Danek A. H., Wiley J., Öllinger M. (2016). Solving classical insight problems without aha! experience: 9 dot, 8 coin, and matchstick arithmetic problems . J. Probl. Solv. 9 :4 10.7771/1932-6246.1183 [ CrossRef ] [ Google Scholar ]
  • Duncker K. (1945). On problem-solving . Psychol. Monogr. 58 , i–113. [ Google Scholar ]
  • Evans J. S., Stanovich K. E. (2013). Dual-process theories of higher cognition: advancing the debate . Perspect. Psychol. Sci. 8 , 223–241. 10.1177/1745691612460685 [ PubMed ] [ CrossRef ] [ Google Scholar ]
  • Fang X., Zhang Y., Zhou Y., Cheng L., Li J., Wang Y., et al.. (2016). Resting-state coupling between core regions within the central-executive and salience networks contributes to working memory performance . Front. Behav. Neurosci. 10 :27. 10.3389/fnbeh.2016.00027 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
  • Finke R. A., Ward T. B., Smith S. M. (1992). Creative Cognition: Theory, Research, and Applications . Cambridge, MA: MIT press. [ Google Scholar ]
  • Fischer J., Mikhael J. G., Tenenbaum J. B., Kanwisher N. (2016). Functional neuroanatomy of intuitive physical inference . Proc. Natl. Acad. Sci. U.S.A. 113 , E5072–E5081. 10.1073/pnas.1610344113 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
  • Fleck J. I. (2008). Working memory demands in insight versus analytic problem solving . Eur. J. Cogn. Psychol. 20 , 139–176. 10.1080/09541440601016954 [ CrossRef ] [ Google Scholar ]
  • Foreman N. (2010). Virtual reality in psychology . Themes Sci. Technol. Educ. 2 , 225–252. Available online at: http://earthlab.uoi.gr/theste/index.php/theste/article/view/33 [ Google Scholar ]
  • Gabora L. (2016). The neural basis and evolution of divergent and convergent thought . arXiv preprint arXiv:1611.03609 . [ Google Scholar ]
  • Gazzaley A., Nobre A. C. (2012). Top-down modulation: bridging selective attention and working memory . Trends Cogn. Sci. 60 , 830–846. 10.1016/j.tics.2011.11.014 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
  • Gilhooly K. J. (2016). Incubation and intuition in creative problem solving . Front. Psychol. 7 :1076. 10.3389/fpsyg.2016.01076 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
  • Guilford J. P. (1962). Creativity: its measurement and development , in A Source Book for Creative Thinking (New York, NY: Charles Scribner's Sons; ), 151–167. [ Google Scholar ]
  • Hao X., Cui S., Li W., Yang W., Qiu J., Zhang Q. (2013). Enhancing insight in scientific problem solving by highlighting the functional features of prototypes: an fMRI study . Brain Res. 1534 , 46–54. 10.1016/j.brainres.2013.08.041 [ PubMed ] [ CrossRef ] [ Google Scholar ]
  • Hayes S. M., Nadel L., Ryan L. (2007). The effect of scene context on episodic object recognition: parahippocampal cortex mediates memory encoding and retrieval success . Hippocampus 9 , 19–22. 10.1002/hipo.20319 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
  • Heinonen J., Numminen J., Hlushchuk Y., Antell H., Taatila V., Suomala J. (2016). Default mode and executive networks areas: association with the serial order in divergent thinking . PLoS ONE 11 :e0162234. 10.1371/journal.pone.0162234 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
  • Horner A. J., Bisby J. A., Bush D., Lin W.-J., Burgess N. (2015). Evidence for holistic episodic recollection via hippocampal pattern completion . Nat. Commun. 6 :7462. 10.1038/ncomms8462 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
  • Isen A. M., Daubman K. A., Nowicki G. P. (1987). Positive affect facilitates creative problem solving . J. Pers. Soc. Psychol. 52 , 1122–1131. 10.1037/0022-3514.52.6.1122 [ PubMed ] [ CrossRef ] [ Google Scholar ]
  • Jauk E., Benedek M., Neubauer A. C. (2012). Tackling creativity at its roots: evidence for different patterns of EEG alpha activity related to convergent and divergent modes of task processing . Int. J. Psychophysiol. 84 , 219–225. 10.1016/j.ijpsycho.2012.02.012 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
  • Kaplan C. A., Simon H. A. (1990). In search of insight . Cogn. Psychol. 22 , 374–419. [ Google Scholar ]
  • Kaufman S. B. (2011). Intelligence and the cognitive unconscious , in The Cambridge Handbook of Intelligence (New York, NY: Cambridge University Press; ), 442–467. [ Google Scholar ]
  • Kounios J., Beeman M. (2014). The cognitive neuroscience of insight . Annu. Rev. Psychol. 65 , 71–93. 10.1146/annurev-psych-010213-115154 [ PubMed ] [ CrossRef ] [ Google Scholar ]
  • Kumaran D., Hassabis D., McClelland J. L. (2016). What learning systems do intelligent agents need? complementary learning systems theory updated . Trends Cogn. Sci. 20 , 512–534. 10.1016/j.tics.2016.05.004 [ PubMed ] [ CrossRef ] [ Google Scholar ]
  • Loth S., Jettka K., Giuliani M., De Ruiter J. P. (2015). Ghost-in-the-machine reveals human social signals for human–robot interaction . Front. Psychol. 6 :1641. 10.3389/fpsyg.2015.01641 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
  • Lovell J., Kluger J. (2006). Apollo 13 . New York, NY: Houghton Mifflin Harcourt. [ Google Scholar ]
  • Luo J., Li W., Qiu J., Wei D., Liu Y., Zhang Q. (2013). Neural basis of scientific innovation induced by heuristic prototype . PLoS ONE 8 :e49231. 10.1371/journal.pone.0049231 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
  • MacGregor J. N., Ormerod T. C., Chronicle E. P. (2001). Information processing and insight: a process model of performance on the nine-dot and related problems . J. Exp. Psychol. Learn. Mem. Cogn. 27 :176. 10.1037/0278-7393.27.1.176 [ PubMed ] [ CrossRef ] [ Google Scholar ]
  • Maier N. R. (1930). Reasoning in humans. i. on direction . J. Comp. Psychol. 10 :115. [ Google Scholar ]
  • Mason R. A., Just M. A. (2013). Neural representations of physics concepts . Psychol. Sci. 27 , 904–913. 10.1177/0956797616641941 [ PubMed ] [ CrossRef ] [ Google Scholar ]
  • Mehta R., Zhu R. J. (2009). Blue or red? exploring the effect of color on cognitive task performances . Science 323 , 1226–1229. 10.1126/science.1169144 [ PubMed ] [ CrossRef ] [ Google Scholar ]
  • Mendelsohn G. (1976). Associative and attentional processes in creative performance . J. Pers. 44 , 341–369. [ Google Scholar ]
  • Menon V. (2015). Salience network , in Brain Mapping: An Encyclopedic Reference, Vol. 2 , ed Toga A. W. (London: Academic Press; Elsevier; ), 597–611. [ Google Scholar ]
  • Metcalfe J. (1986). Premonitions of insight predict impending error . J. Exp. Psychol. Learn. Mem. Cogn. 12 , 623. [ Google Scholar ]
  • Miyake A., Friedman N. P., Emerson M. J., Witzki A. H., Howerter A., Wager T. D. (2000). The unity and diversity of executive functions and their contributions to complex “Frontal Lobe” tasks: a latent variable analysis . Cogn. Psychol. 41 , 49–100. 10.1006/cogp.1999.0734 [ PubMed ] [ CrossRef ] [ Google Scholar ]
  • Newman S. D., Green S. R. (2015). Complex problem solving . Brain Mapp. 3 , 543–549. 10.1016/B978-0-12-397025-1.00282-7 [ CrossRef ] [ Google Scholar ]
  • Ohlsson S. (1992). Information-processing explanations of insight and related phenomena . Adv. Psychol. Think. 1 , 1–44. [ Google Scholar ]
  • Öllinger M., Fedor A., Brodt S., Szathmáry E. (2017). Insight into the ten-penny problem: guiding search by constraints and maximization . Psychol. Res. 81 , 925–938. 10.1007/s00426-016-0800-3 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
  • Öllinger M., Jones G., Knoblich G. (2014). The dynamics of search, impasse, and representational change provide a coherent explanation of difficulty in the nine-dot problem . Psychol. Res. 78 , 266–275. 10.1007/s00426-013-0494-8 [ PubMed ] [ CrossRef ] [ Google Scholar ]
  • Operskalski J. T., Barbey A. K. (2016). Cognitive neuroscience of causal reasoning , in Oxford Handbook of Causal Reasoning , ed Waldmann M. R. (New York, NY: Oxford University Press; ), 217–242. [ Google Scholar ]
  • Quilodran R., Rothé M., Procyk E. (2008). Behavioral shifts and action valuation in the anterior cingulate cortex . Neuron 57 , 314–325. 10.1016/j.neuron.2007.11.031 [ PubMed ] [ CrossRef ] [ Google Scholar ]
  • Ritter S. M., Dijksterhuis A. (2014). Creativity the unconscious foundations of the incubation period . Front. Hum. Neurosci. 8 :215. 10.3389/fnhum.2014.00215 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
  • Robertson S. (2016). Problem Solving: Perspectives from Cognition and Neuroscience . New York, NY: Psychology Press. [ Google Scholar ]
  • Salvi C., Bowden E. M. (2016). Looking for creativity: where do we look when we look for new ideas? Front. Psychol. 7 :161. 10.3389/fpsyg.2016.00161 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
  • Sawyer K. (2011). The cognitive neuroscience of creativity: a critical review . Creat. Res. J. 23 , 137–154. 10.1080/10400419.2011.571191 [ CrossRef ] [ Google Scholar ]
  • Scimeca J. M., Badre D. (2012). Striatal contributions to declarative memory retrieval Jason . Neuron 75 , 380–392. 10.1016/j.neuron.2012.07.014 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
  • Simone Sandkühler J. B. (2008). Deconstructing insight: EEG correlates of insightful problem solving . PLoS ONE 3 :e1459. 10.1371/journal.pone.0001459 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
  • Simons D. J., Chabris C. F. (1999). Gorillas in our midst: sustained inattentional blindness for dynamic events . Perception 28 , 1059–1074. [ PubMed ] [ Google Scholar ]
  • Sowden P. T., Pringle A., Gabora L. (2015). The shifting sands of creative thinking: connections to dual-process theory . Think. Reason. 21 , 40–60. 10.1080/13546783.2014.885464 [ CrossRef ] [ Google Scholar ]
  • Sprugnoli G., Rossi S., Emmendorfer A., Rossi A., Liew S.-L., Tatti E., et al. (2017). Neural correlates of Eureka moment . Intelligence 62 , 99–118. 10.1016/j.intell.2017.03.004 [ CrossRef ] [ Google Scholar ]
  • Steidle A., Werth L. (2013). Freedom from constraints: darkness and dim illumination promote creativity . J. Environ. Psychol. 35 , 67–80. 10.1016/j.jenvp.2013.05.003 [ CrossRef ] [ Google Scholar ]
  • Stocco A., Lebiere C., O'Reilly R. C., Anderson J. R. (2012). Distinct contributions of the caudate nucleus, rostral prefrontal cortex, and parietal cortex to the execution of instructed tasks . Cogn. Affect. Behav. Neurosci. 12 , 611–628. 10.3758/s13415-012-0117-7 [ PubMed ] [ CrossRef ] [ Google Scholar ]
  • Summerfield J. J., Hassabis D., Maguire E. A. (2010). Differential engagement of brain regions within a corenetwork during scene construction . Neuropsychologia 48 , 1501–1509. 10.1016/j.neuropsychologia.2010.01.022 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
  • Tang Y.-Y., Rothbart M. K., Posner M. I. (2012). Neural Correlates of stablishing, maintaining and switching brain states . Trends Cogn. Sci. 16 , 330–337. 10.1016/j.tics.2012.05.001 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
  • Team M. E. (1970). Mission Operations Report apollo 13 . [ Google Scholar ]
  • Thakral P. P., Madore K. P., Schacter D. L. (2017). A role for the left angular gyrus in episodic simulation and memory . J. Neurosci. 37 , 8142–8149. 10.1523/JNEUROSCI.1319-17.2017 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
  • Thomas L. E., Lleras A. (2009). Swinging into thought: directed movement guides insight in problem solving . Psychon. Bull. Rev. 16 , 719–723. 10.3758/PBR.16.4.719 [ PubMed ] [ CrossRef ] [ Google Scholar ]
  • Vohs K. D., Redden J. P., Rahinel R. (2013). Physical order produces healthy choices, generosity, and conventionality, whereas disorder produces creativity . Psychol. Sci. 24 , 1860–1867. 10.1177/0956797613480186 [ PubMed ] [ CrossRef ] [ Google Scholar ]
  • Wegbreit E., Suzuki S., Grabowecky M., Kounios J., Beeman M. (2012). Visual attention modulates insight versus analytic solving of verbal problems . J. Probl. Solv. 144 , 724–732. 10.7771/1932-6246.1127 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
  • Yang W., Dietrich A., Liu P., Ming D., Jin Y., Nusbaum H. C., et al. (2016). Prototypes are key heuristic information in insight problem solving . Creat. Res. J. 28 , 67–77. 10.1080/10400419.2016.1125274 [ CrossRef ] [ Google Scholar ]
  • Yoruk S., Runco M. A. (2014). Neuroscience of divergent thinking . Activ. Nervosa Superior 56 , 1–16. 10.1007/BF03379602 [ CrossRef ] [ Google Scholar ]
  • Zabelina D., Saporta A., Beeman M. (2016). Flexible or leaky attention in creative people? Distinct patterns of attention for different types of creative thinking . Mem Cognit . 44 , 488–498. 10.3758/s13421-015-0569-4 [ PubMed ] [ CrossRef ] [ Google Scholar ]
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Two elementary students work together

Using Mathematical Modeling to Get Real With Students

Unlike canned word problems, mathematical modeling plunges students into the messy complexities of real-world problem solving.  

How do you bring math to life for kids? Illustrating the boundless possibilities of mathematics can be difficult if students are only asked to examine hypothetical situations like divvying up a dessert equally or determining how many apples are left after sharing with friends, writes third- and fourth- grade teacher Matthew Kandel for Mathematics Teacher: Learning and Teaching PK-12 .

In the early years of instruction, it’s not uncommon for students to think they’re learning math for the sole purpose of being able to solve word problems or help fictional characters troubleshoot issues in their imaginary lives, Kandel says. “A word problem is a one-dimensional world,” he writes. “Everything is distilled down to the quantities of interest. To solve a word problem, students can pick out the numbers and decide on an operation.” 

But through the use of mathematical modeling, students are plucked out of the hypothetical realm and plunged into the complexities of reality—presented with opportunities to help solve real-world problems with many variables by generating questions, making assumptions, learning and applying new skills, and ultimately arriving at an answer.

In Kandel’s classroom, this work begins with breaking students into small groups, providing them with an unsharpened pencil and a simple, guiding question: “How many times can a pencil be sharpened before it is too small to use?”

Setting the Stage for Inquiry 

The process of tackling the pencil question is not unlike the scientific method. After defining a question to investigate, students begin to wonder and hypothesize—what information do we need to know?—in order to identify a course of action. This step is unique to mathematical modeling: Whereas a word problem is formulaic, leading students down a pre-existing path toward a solution, a modeling task is “free-range,” empowering students to use their individual perspectives to guide them as they progress through their investigation, Kandel says. 

Modeling problems also have a number of variables, and students themselves have the agency to determine what to ignore and what to focus their attention on. 

After inter-group discussions, students in Kandel’s classroom came to the conclusion that they’d need answers to a host of other questions to proceed with answering their initial inquiry: 

  • How much does the pencil sharpener remove? 
  • What is the length of a brand new, unsharpened pencil? 
  • Does the pencil sharpener remove the same amount of pencil each time it is used?

Introducing New Skills in Context

Once students have determined the first mathematical question they’d like to tackle (does the pencil sharpener remove the same amount of pencil each time it is used?), they are met with a roadblock. How were they to measure the pencil if the length did not fall conveniently on an inch or half inch? Kandel took the opportunity to introduce a new target skill which the class could begin using immediately: measuring to the nearest quarter inch. 

“One group of students was not satisfied with the precision of measuring to the nearest quarter inch and asked to learn how to measure to the nearest eighth of an inch,” Kandel explains. “The attention and motivation exhibited by students is unrivaled by the traditional class in which the skill comes first, the problem second.” 

Students reached a consensus and settled on taking six measurements total: the initial length of the new, unsharpened pencil as well as the lengths of the pencil after each of five sharpenings. To ensure all students can practice their newly acquired skill, Kandel tells the class that “all group members must share responsibility, taking turns measuring and checking the measurements of others.” 

Next, each group created a simple chart to record their measurements, then plotted their data as a line graph—though exploring other data visualization techniques or engaging students in alternative followup activities would work as well.

“We paused for a quick lesson on the number line and the introduction of a new term—mixed numbers,” Kandel explains. “Armed with this new information, students had no trouble marking their y-axis in half- or quarter-inch increments.” 

Sparking Mathematical Discussions

Mathematical modeling presents a multitude of opportunities for class-wide or small-group discussions, some which evolve into debates in which students state their hypotheses, then subsequently continue working to confirm or refute them. 

Kandel’s students, for example, had a wide range of opinions when it came to answering the question of how small of a pencil would be deemed unusable. Eventually, the class agreed that once a pencil reached 1 ¼ inch, it could no longer be sharpened—though some students said they would be able to still write with it. 

“This discussion helped us better understand what it means to make an assumption and how our assumptions affected our mathematical outcomes,” Kandel writes. Students then indicated the minimum size with a horizontal line across their respective graphs. 

Many students independently recognized the final step of extending their line while looking at their graphs. With each of the six points representing their measurements, the points descended downward toward the newly added horizontal “line of inoperability.” 

With mathematical modeling, Kandel says, there are no right answers, only models that are “more or less closely aligned with real-world observations.” Each group of students may come to a different conclusion, which can lead to a larger class discussion about accuracy. To prove their group had the most accurate conclusion, students needed to compare and contrast their methods as well as defend their final result. 

Developing Your Own Mathematical Models

The pencil problem is a great starting point for introducing mathematical modeling and free-range problem solving to your students, but you can customize based on what you have available and the particular needs of each group of students.

Depending on the type of pencil sharpener you have, for example, students can determine what constitutes a “fair test” and set the terms of their own inquiry. 

Additionally, Kandel suggests putting scaffolds in place to allow students who are struggling with certain elements to participate: Simplified rulers can be provided for students who need accommodations; charts can be provided for students who struggle with data collection; graphs with prelabeled x- and y-axes can be prepared in advance.

Math concepts

.css-1sk4066:hover{background:#d1ecfa;} 7 Real-World Math Strategies

Students can also explore completely different free-range problem solving and real world applications for math . At North Agincourt Jr. Public School in Scarborough, Canada, kids in grades 1-6 learn to conduct water audits. By adding, subtracting, finding averages, and measuring liquids—like the flow rate of all the water foundations, toilets, and urinals—students measure the amount of water used in their school or home in a single day. 

Or you can ask older students to bring in common household items—anything from a measuring cup to a recipe card—and identify three ways the item relates to math. At Woodrow Petty Elementary School in Taft, Texas, fifth-grade students display their chosen objects on the class’s “real-world math wall.” Even acting out restaurant scenarios can provide students with an opportunity to reinforce critical mathematical skills like addition and subtraction, while bolstering an understanding of decimals and percentages. At Suzhou Singapore International School in China, third- to fifth- graders role play with menus, ordering fictional meals and learning how to split the check when the bill arrives. 

how can you solve real world problems

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

More specific topics in solve real-life and mathematical problems using numerical and algebraic expressions and equations..

  • Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.

Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

  • Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.
  • Solve word problems leading to inequalities of the form px + q > r or px + q

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Using research to solve real world problems

Peter Blair Henry of Stern Business School

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By Rebecca Knight

Roula Khalaf, Editor of the FT, selects her favourite stories in this weekly newsletter.

In India, a country with a population of 1.2bn, fewer than 30 per cent of citizens have a passport, driver’s licence or other form of identification.

It may seem a minor point, except that the absence of these documents makes it difficult to apply for a bank account, obtain a mobile phone or even receive the government subsidies for education and food that individuals are entitled to.

But according to a new survey led by Arun Sundararajan, an associate professor of information, operations and management sciences at New York University’s Stern School of Business and a group of his students, that is changing. A government-sponsored project that began towards the end of 2010 to give every person in India a unique 12-digit ID number is showing signs of success. If enrolment continues according to projections, Prof Sundararajan reckons that about 300m citizens who previously did not have a portable ID will have one by the end of the year.

“It’s a moon-shot project,” says Prof Sundararajan. “It’s having a transformative impact on the lives of hundreds of millions of people.”

It is also, he hopes, a project that will have a transformative impact on the careers of the dozen MBA students who are working with him on the survey. The survey, which is analysing the impact of India’s Unique Identity project, is part of the Stern Consulting Corps programme.

International trips provide hands-on experience

To try to better prepare students to operate in the global economy, a number of leading business schools have introduced courses for MBAs to embark on international consulting projects.

The courses are designed to give students an applied learning experience that is very different from the one they receive on campus.

Harvard Business School , for instance, recently launched a year-long required course for its first-year students called “Field Immersion Experiences for Leadership Development”, or Field for short. The capstone of the course is a week-long trip to a developing country where student teams work closely with a company to develop an idea for a product or service.

Last year, projects were based in cities including Cape Town, Mumbai, Shanghai, Warsaw and Buenos Aires.

“Our aspiration is that it becomes so self-evident about how valuable this is that other schools do it too,” says Youngme Moon, who chairs HBS’s MBA programme.

Massachusetts Institute of Technology’s Sloan School , meanwhile, has expanded its G-Lab course in which students work with the management of overseas start-ups. Student teams work remotely from MIT for three months and full-time at their host companies for at least three weeks. Last year students worked on projects in Kenya, Colombia, Indonesia and other countries.

While some schools may view courses with an international consulting component as a way to “teach students how to be [a] consultant, it’s very much meant to be an interesting learning challenge,” says Michellana Jester, director of Sloan’s action learning programme.

According to her, business schools are using these courses to strike the right balance between academic rigour and relevance. “Scholarship is important and research is important, but how do you make it relevant for students in business schools today?

“It’s a transition for business schools right now in terms of how we navigate this,” she says.

SCC, an elective course now in its 10th year, began as a programme that placed students with local non-profits on 10-week project engagements. This year, for the first time, students worked on projects in emerging markets linked to faculty research. This new element provides students with vivid illustrations of how academic research can be used to solve real world problems.

“What [students] are gaining from this is an understanding of the potential of business to be an agent of social change,” says Prof Sundararajan. “It’s one thing to be exposed to examples of this in a textbook, it’s another to witness it first hand.”

As top schools strive to infuse their curricula with more hands-on learning experiences by adding overseas exchange programmes and class consulting projects in far-flung corners of the world, SCC stands out for its emphasis on research.

The new focus of the SCC programme reflects the increasing interest from MBA students in using their degrees to work on social policy issues. The programme is popular on campus: more than 100 students participated in the programme this past academic year and applications to the SCC rose 117 per cent this spring compared with last year.

Academic research is often accused of being ponderous, narrow and detached from the real world. But there is a new wave of research coming out of schools today that concerns how government and business can work together to solve big social problems, according to Professor Peter Henry, Stern’s dean.

There is also a growing recognition on the part of management faculty that the type of research they conduct about corporations has potentially broad applications for other kinds of organisations.

“There is a false dichotomy between research and the real world,” says Prof Henry. “Research can have a real impact.”

One group of students, for instance, worked on a business plan for a city that is being developed in Honduras. Because the city is a new concept, the business plan will have a direct effect on policy decisions in the country.

The students, under the supervision of Professor Paul Romer who heads the Urbanization Project, a research centre at Stern that focuses on urban growth and governance in the developing world, spent the semester devising potential scenarios for the city, such as population growth models and potential financial rules and regulations, as well as working up infrastructure estimates and writing policy briefs. Some of their findings were presented in a meeting Prof Romer had with Octavio Sánchez, chief of staff to the Honduran president.

“We’re getting students into the world through the lens of research,” says Prof Henry. “We’re giving students the chance to say, ‘I didn’t just take a set of classes. I built something’.”

Throughout the projects, students work closely with a faculty member and often develop the type of mentoring relationship that has typically been the province of PhD programmes. Teams also work with an outside mentor from a top-tier consulting company.

Students hone their analytical skills, but are also able to practise their professional responsibilities such as meeting a timeline and soliciting feedback from a client.

“The learning experience for the students was better than I expected,” says Prof Romer. “What they learnt was not just how to think abstractly about governance and fiscal policy – the kind of things you have to think about when you’re creating a new city – but also how will you work in teams, how will you divide tasks, what will you do when one sub-team gets stuck.”

The fact that students were working on a project with real world implications “lent more urgency to the group effort”, he says. “People are taking real decisions on [the students’ work]. A term paper doesn’t really matter. This goes out of the realm of a pretend exercise and makes it real.”

For students, the risk of working on such an engrossing project is that it can make other business school assignments seem dull or unworthy by comparison.

But Benjamin Wise, a student who worked on the Honduras project, says that it forced him to think about how to apply concepts learnt in the classroom.

“I’d be sitting in my corporate finance class on the edge of my seat because we were learning about a financial model that I couldn’t wait to plug in to [one of the models in] my project,” he says.

Prof Sundararajan says that spending a week in India was an eye-opening experience for his students.

“I could see them immersed in the context. They gained a clearer understanding of the breadth of vision and they could see what the problem was.

“This is the kind of immersive experiential learning that alters the worldview of students.”

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26 Snappy Answers to the Question “When Are We Ever Going to Use This Math in Real Life?”

Next time they ask, you’ll be ready.

how can you solve real world problems

As a math teacher, how many times have you heard frustrated students ask, “When are we ever going to use this math in real life!?” We know, it’s maddening! Especially for those of us who love math so much we’ve devoted our lives to sharing it with others.

It may very well be true that students won’t use some of the more abstract mathematical concepts they learn in school unless they choose to work in specific fields. But the underlying skills they develop in math class—like taking risks, thinking logically and solving problems—will last a lifetime and help them solve work-related and real-world problems.

Here are 26 images and accompanying comebacks to share with your students to get them thinking about all the different and unexpected ways they might use math in their futures!

1. If you go bungee jumping, you might want to know a thing or two about trajectories.

https://giphy.com/gifs/funny-fail-5OuUiP0we57b2

Source: GIPHY

2. When you invest your money, you’ll do better if you understand concepts such as interest rates, risk vs. reward, and probability.

3. once you’re a driver, you’ll need to be able to calculate things like reaction time and stopping distance., 4. in case of a zombie apocalypse, you’re going to want to explore geometric progressions, interpret data and make predictions in order to stay human..

Trigger an outbreak of learning and infectious fun in your classroom with this Zombie Apocalypse activity from TI’s STEM Behind Hollywood series.

5. Before you tackle that home wallpaper project, you’ll need to calculate just how much wall paper glue you need per square foot.

6. when you buy your first house and apply for a 30-year mortgage, you may be shocked by the reality of what interest compounded over 30 years looks like., 7. to be a responsible pet owner, you’ll need to calculate how much hamster food to have on hand., 8. even if you’re just an armchair athlete, you can’t believe the math involved in kicking field goals.

Check out this Field Goal for the Win activity that encourages students to model, explore and explain the dynamics of kicking a football through the uprights.

9. When you double a recipe, you’re going to need to understand ratios so your dinner guests don’t look like this.

10. before you take that family road trip , you’re going to want to calculate time and distance., 11. before you go candy shopping, you’re going to have to figure out x trick or treaters times x pieces of candy equals…, 12. if  you grow up to be an ice cream scientist, you’re going to have to understand the effect of temperature and pressure at the molecular level..

https://giphy.com/gifs/ice-lick-cream-3Z1kRYmLRQm5y

Explore states of matter and the processes that change cow milk into a cone of delicious decadence with this Ice Cream, Cool Science activity .

13. Once you have little ones, you’ll need to know how many diapers to buy for the month.

14. because what if it’s your turn to organize the annual ping pong tournament, and there are 7 players at a club with 4 tables, where each player plays against each other player, 15. when dressing for the day, you might want to consider the percent likelihood of rain., 16. if you go into medical research, you’re going to have to know how to solve equations..

Learn more about inspiring careers that improve lives with STEM Behind Health , a series of free activities from TI.

17. Understanding percentages will help you get the best deal at the mall. For example, how much will something cost with 40% off? What about once the 8% tax is added? What if it’s advertised as half-off?

https://giphy.com/gifs/blue-kawaii-pink-5aplc3D2G0IrC

18. Budgeting for vacation will require figuring out how many hours at your pay rate you’ll have to work to afford the trip you want.

19. when you volunteer to host the company holiday party, you’ll need to figure out how much food to get., 20. if you grow up to be a super villain, you’re going to need to use math to determine the most effective way to slow down the superhero and keep him from saving the day..

Put your students in the role of an arch-villain’s minions with Science Friction, a STEM Behind Hollywood activity .

21. You’ll definitely want to understand how to budget your money so you don’t look like this at the grocery checkout.

22. if you don’t work the numbers out in advance, you might at some point regret choosing that expensive out-of-state college., 23. before taking on a building project, remember the old saying—measure twice, cut once., 24. if have aspirations of being a fashion designer, you’ll have to understand geometry in order to make the perfect twirling skirt.

https://giphy.com/gifs/loop-bunny-ballet-yarFJggnH24da

Geometry and fashion design intersect in this STEM Behind Cool Careers activity .

25. Everyone loves a good bargain! Figuring out the best deal is not only fun, it’s smart!

26. if you can’t manage calculations, running the numbers at the car dealership might leave you feeling like this:, you might also like.

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Algebra in Real Life

Table of Contents

Have you ever wondered how Algebra may be applied to solve real-life problems?

We regularly see people using Algebra in many parts of everyday life; for instance, it is utilized in our morning schedule each day to measure the time you will spend in the shower, making breakfast, or driving to work.

The absence of "X" or "Y" doesn't imply that algebra is not around us; algebra’s actual occurrences are uncountable. This exact and compact numerical language works wonderfully with practically all different subjects and everyday life. 

In this article, we will grasp instances in real life where applications of algebra are needed and examples of applications of algebra in real life.  

  • How to factorise a polynomial?

What is Algebra?

Algebra is a part of mathematics that deals with symbols and the standards for controlling those symbols. The more basic parts of algebra are called elementary algebra, and the more abstract types are called Abstract Algebra or modern algebra. 

Algebraic Expression

Let us consider the pattern below. It has been created using marbles. Here we see that the first column has 2 marbles, the second column has 3 marbles, the third column has 4 marbles and so on.

Algebraic expression image

Thus we observe that every new column increases by 1 marble. We can write the representation as 

The number of marbles used in a column =

position of the column + 1

or as 

the number of marbles used in a column = n + 1.

Here n represents the position of the column. So ‘n’ is an example for a variable that can take any value 1,2,3… so on. Thus n + 1 is the algebraic expression formed with n as variable and constant 1.

Speed of a car image

A variable is a number that does not have a fixed value. The picture and the list below show some real-life examples, where the value of a variable changes with the change in place and time. 

  • The temperature in different places also change.
  • The height of a growing child changes with time.        
  • The speed of a car changes with time.
  • The age of people keeps on increasing year by year.

Constant 

The value remains fixed for specific numbers that represent quantities or ideas that will not change. For example, the date of birth of a particular person, the normal human body temperature and capacity of a given container.

Framing algebraic expressions with given conditions

Now we will see how to frame an algebraic expression. The rules are that variables are to be represented with alphabetic letters, say lower case a-z and constants in numeric form.

1. Amanda has 10 storybooks more than Alex. Express the number of storybooks Amanda has in terms of the number of storybooks Alex has. 

Let the number of storybooks Alex has = y

Therefore the number of storybooks Amanda has = y + 10

2. Sweets from a big box are equally distributed in 10 small boxes. Express the number of sweets in one small box in terms of the total number of sweets.

Let x be the total number of sweets. 

Number of sweet boxes = 10

Therefore, the number of sweets in one box is = x/10

Solving Equations

Let us see how practical applications of algebra can be used to solve equations. You will often see equations like 3x + 4 = 5, where you want to find x.

Consider a situation from our daily life.

The cost of a book is £5 more than the cost of a pen. Let us take the cost of the pen as £x. Then the cost of the book is £ (x + 5) . If the cost of the book is £20, what is the cost of the pen?

We know that the book’s cost is x + 5 and it is given that x + 5 = 20. This is an equation in the variable x.

A table is prepared as shown below for various values of x:

It is clear from the table that x + 5 = 20 only for x = 15. So, the cost of the pen is £15. 

In general we say that x = 15 is the solution of the equation x + 5 = 20. This is the trial and error method where we substitute different values for the variable that satisfies the given equation.

An equation has two parts which are connected by an equal to sign. The two parts or sides of an equation are denoted as LHS (Left Hand Side) and RHS (Right Hand Side). If LHS = RHS we get an equation. 2x = 6 is an

algebraic equation, whereas 3x > 10 or 4x < 12 are not equations.

Solving an equation using the Principle of Balances

Consider the balance given in the figure.

Image 1

Four circles balance one square and a circle on the other side. The idea is we have to find out how many circles will balance a square. If we remove the circle from the left pan, we have only the square there. Since we removed a circle from the left pan, we have to remove the circle from the right pan also. Then there will be three circles in the right pan.

Now the balance looks like the one shown on the right. This is called the principle of balances. Using balancing equations, we can solve equations in a systematic way.

Solve using the principle of balances:

Benjamin's mother is three times as old as Benjamin. If Benjamin's mother is 39 years old, find Benjamin's age. 

Let Benjamin's age be x. 

Benjamin’s mother's age 3x = 39

3x/3 = 39/3 {Dividing by 3 on both the sides }

So, Benjamin’s age = 13.

The same quantity can be added or subtracted to both sides of the equation. If the same amount is multiplied or divided on both the sides of an equation, it remains the same.

Forming an equation to find the unknown

Translating verbal descriptions into algebraic expressions is an essential initial step in solving word problems. So let’s see another real-life example in the form of a puzzle.

Image 1 example

Detailed Solution:

Our first supposition is that Uma buys at least one ball of each kind. Now let’s say she buys x footballs, y cricket balls, and z table-tennis balls.

The question requires x + y + z = 100  [ 1 ]

It also requires 15 x + 1y + z/4 = 100  [ 2 ]Since we have 3 variables but only 2 equations we’ll have to use the trial and error method to get at the solution.

Let’s vary x the number of footballs and see what we get:

Suppose x = 1, then 

y + z =99 and y + z/ 4 = 83z/4 = 14 3z = 56 z = 56/3 which is not a whole number.

Trying for x = 2 also fails and now

If x = 3, then  z = 97 and y + z / 4 = 55 3z/4 =42 3z= 168 z = 168/3 = 56  which is a whole number! 

And if z = 56  then y = 97 - z = 97 - 56 = 41 

So the set of balls Uma buys is { 3 footballs, 41 cricket balls and 56 table tennis balls }

Algebra in Geometry

In Algebraic Geometry we study geometric objects and their assortment that are characterized by polynomial equations. 

Examples of algebraic varieties’ most studied classes are plane algebraic curves, including lines, circles, parabolas, ellipses, hyperbolas. There are also cubic curves like elliptic curves and quartic curves like lemniscates and Cassini ovals.

In real life, algebraic geometry can be used to study the dynamics properties of robotics mechanisms.

Algebraic geometry image

   Source: Pinterest

A robot can move in continuous space with an infinite set of possible actions and states. When the robot has arms and legs that must also be controlled and the search space becomes many-dimensional. Robot’s kinematics can be formulated as a polynomial equation system that can be solved using algebraic geometry tools.

Algebraic geometry is also widely used in statistics, control theory, and geometric modelling. There are also connections to string theory, game theory, graph matchings and integer programming.

Algebra in Computer Programming

The mathematical languages unite fields such as science, technology, and engineering into itself. That is why an individual intrigued by the field of computer programming and coding should figure out how to comprehend and control mathematical logic.

Strong comprehension of algebra incorporates characterizing the connections between objects, critical thinking with restricted factors, and analytical skill development to help execute decision making. 

One such use of Algebra can be seen in Inference procedures used in Knowledge engineering. Variables and constant symbols are used as terms representing objects in real life. 

The knowledge engineer adds a set of facts and specifies what is true, and the inference procedure figures out how to turn the facts into a solution to the problem. 

Besides, because a fact is true regardless of what task one is trying to solve, knowledge bases can be reused for various tasks without modification. 

Example for the  task of inference

Take a sentence,

Everyone likes ice cream.

It is represented in First-order logic as 

 x Likes ( x, ice cream ) 

where x is the variable and is the universal quantifier that generalizes to all persons liking icecream. 

If another sentence found in the knowledge base is as follows:

    John likes ice cream

It is represented as Likes( John, ice cream)

The inference procedure will reason out from x Likes ( x, ice cream ) with the substitution {x/John} and infers Likes(John, ice cream) and concludes that John likes icecreams.

                                                                                                                                                      Biostatistics University of Florida

Other uses of algebra in programming are  Ontology, error correction algorithms, Natural language processing, Neural networks,  designing artificial intelligence programming languages such as LISP and PROLOG and theorem provers such as OTTER.

In real life there are a plethora of instances where Algebra is being used. It’s utility is being universally quantified in all walks of our lives. For instance, take a shopping domain where we need to be budgeted with the cart items and some algebraic formulation is applied.

Algebra in real life image

The economy of every country is analysed with the help of economists taking the help of algebra to solve the problems related to debts or loans.

Tom Evans's ANALOGY program (1968) solved geometric analogy problems that appear in IQ tests such as the one shown below.

Anology image 1

                                                                                                                                                 Source: Artificial Intelligence by Stuart Russell

The use of algebra is multipurpose, and it goes handy in every sphere of our lives.  It isn't just mathematicians, however, even most academicians, educationists, researchers, and experts from all different backgrounds collectively

agree with the adaptability of algebra. 

Real-World Applications of Linear Algebra

What is linear algebra.

Linear algebra is the branch of mathematics concerning linear equations such as linear maps and their representations in vector spaces and matrices.

The concept of classification can be simulated with the help of neural network structures that use a linear regression model. Here the training set is compared with the test data so that the learning algorithms generate outcomes to predict data related to decision making, medical diagnosis, statistical inferences, etc.

Example 1

Applications

The most generally utilized use of linear algebra is certainly optimization, and the most broadly utilized sort of advancement is linear algebra. You can upgrade spending plans, your eating regimen, and your course to work 

utilizing linear algebra, and this uniqueness starts to expose a lot of applications. 

Other real-world applications of linear algebra include ranking in search engines, decision tree induction, testing software code in software engineering, graphics, facial recognition, prediction and so on.

In real life, algebra can be compared to a universally handy device or a sorcery wand that can help manage regular issues of life. Whenever life throws a maths problem at you, for example when you have to solve an equation or work out a geometrical problem, algebra is usually the best way to attack it. 

Written by Jesy Margaret, Cuemath teacher

About Cuemath

Cuemath, a student-friendly mathematics and coding platform, conducts regular Online Classes for academics and skill-development, and their Mental Math App, on both iOS and Android , is a one-stop solution for kids to develop multiple skills. Understand the Cuemath Fee structure and sign up for a free trial.

HOW STEM IS ACTIVELY SOLVING REAL-WORLD PROBLEMS

  • STEM EDUCATION ARTICLES & OPINIONS
  • How STEM is Actively Solving Real-World Problems

How STEM is Actively Solving Real-World Problems

STEM education has been a topic of hot debate for a few years now and its existence is under unending scrutiny. At a first glance this “third-degree” may feel like an annoying, rude, and uneducated attack on what is arguably one of the most progressive ideas to be set into action in schools in over 100 years. However, this scrutiny is actually proof that STEM is making its intended impact on the future generation of innovative, thoughtful, and resourceful leaders. Science, technology, engineering, and mathematics all require that individuals employ critical thinking skills in a variety of settings to accomplish tasks both big and small. You may thank those in the STEM fields for everything from shoes that protect your feet from whatever is on the ground to the mobile device that you have likely used at least once today for your own personal purposes. Beyond these useful, but not vital, components in your everyday life, STEM is actively being used to help solve some of the world’s greatest and most demanding problems.

Taming World Hunger

World hunger is an issue that is facing thousands of communities all over the world. Entire villages, towns, and cities are facing food shortages for various reasons including: dry seasons, climate change, changes in the environment, animal disturbances in farms and gardens, and simply lack of money. STEM is stepping up and solving these problems on a regular basis by teaching individuals how to grow gardens and providing communities in adverse situations with greenhouses and farming technology to help combat this very real problem.

Facilitating Worldwide Communications

If you are using a computer, tablet, smartphone, or other mobile device to view this page, then you are witnessing first-hand how the internet is connecting you with people, places, businesses, and products all over the world. The device that you are using to view this material is a prime example of how technology has been used to facilitate worldwide communication efforts around the world. This helps to inform individuals of disasters, politics, travel, and social situations across the world without physically having to travel. It is a much cheaper, faster, and more efficient way to spread important information than what was used just a few decades ago.

Safer World Travel

Have you ever booked a flight only to have it canceled or delayed by a winter storm? Not only are you annoyed, upset, or concerned about having to wait to get wherever you are going, you are actually facing the reality that you could be entering into a dangerous situation once you finally do board that plane. Why? Planes that fly in wintery, frozen precipitation accumulate ice on the wings. To combat this problem, flights are delayed, and the plane is sprayed down with an antifreeze-type substance to keep ice from forming on the wings. Unfortunately, this substance wears down and some planes are forced into emergency landings. Science is currently researching the possibility of planes releasing this anti-freezing liquid in mid-air and making travel a safer experience for all involved.

Life Saving Medicine

All areas of STEM education are currently working together to research the medical procedures and medications that are given to individuals in order to save their lives. Vaccines for conditions like Polio have nearly eradicated these deadly diseases. Heart, lung, and kidney transplants have literally saved lives thanks to the efforts made by individuals in STEM-related fields. Researchers have an entire list of diseases and conditions that they are working on tackling in the future as new and bright minds enter these STEM careers.

Decreasing Homelessness

3D printing is one of the newest, most innovative, and relatively inexpensive methods of providing strong homes for people in areas of the world that are highly populated. These homes can be built in as little as one day and can be customized to meet all of the requirements that an individual could ever need or want. These homes are sturdy, readily available, and incredibly affordable. Communities in places like Japan are already utilizing these 3D printed homes and efforts around the world have taken place to raise the money necessary to build such homes for the truly homeless to use.

Saving Wildlife

In places like New York City where skyscrapers are plentiful and glass walls are everywhere, birds and other flying animals are dying in the thousands. These animals do not see the glass and will literally fly into it, fall to the ground, and die either from the impact of flying into the glass or from the impact of hitting the ground from such a high altitude. Researchers are currently testing different types of glass with different patterns in an effort to design an aesthetically pleasing glass that birds can see and avoid. As of now, there STEM researchers have discovered that birds do see certain patterns in glass and the journey to providing these types of glass at an affordable price to the public is moving forward.

Providing Fresh Water

Dry, hot, and barren areas of the world are constantly faced with a lack of quality, clean, drinking water. It is often easier to access saltwater than freshwater in these areas, and the little freshwater that is available is usually too dirty to consume. To solve this issue, researchers are actively working on technology that can desalinate saltwater for the purpose of turning it into safe drinking water.

Creating “Green” Alternative, Renewable Energy Sources

You have probably heard that you have what is called a “carbon footprint”. This means that a portion of your daily life is made possible by the burning of limited carbon resources like coal. Individuals in the STEM field have committed their time to finding resources that can replace carbon-based fossil fuels without harsh negative ecological effects. Once a viable source has been discovered [such as water or wind sources], it takes an entire crew of people to develop the technology necessary to harness that energy and distribute it to communities all around the world. Not only are these resources viable "green" alternatives, but they are renewable and therefore feasibly sustainable methods of powering everyday life.

STEM is providing young generations with the incentive to tackle world problems like those listed above. While it is impossible to get everyone on the same page with agreeing opinions of its structure, it is worth noting that STEM-oriented individuals are making a difference in the world.

For those that question whether a STEM education is worth pursuing because of its exclusion of other important topics like arts, physical education, history, and language arts, try and point out to them that every STEM career can incorporate those subjects and their lessons. No topic in life is ever as cut and dry as it may seem on the surface. All subjects are important in making students well-rounded and active citizens in their communities, but STEM-oriented students simply choose to focus more of their attention to the areas of science, technology, engineering, and mathematics than in other areas.

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7 Examples of Algebra in Everyday Life (Simplified Real-Life Applications)

Do you ever feel like algebra is just a bunch of meaningless equations and symbols? Well, think again! Algebra is actually all around us in everyday life. In this blog post, we will discuss seven examples of how algebra is used in the real world.

We will also provide real-life applications for each example. So whether you’re a student trying to understand why you’re learning this stuff or a teacher looking for ways to make it more relevant to your students, read on!

Examples of Algebra in everyday life

Whilst algebra has many applications in daily life, here are my favorite ways of using algebra to solve problems.

1. Calculating discounts at the store

You’re at the store and you see a shirt that’s on sale for 20% off. How much will it cost? This is a great opportunity to use some algebra!

Here’s how we can set this up:

Let x represent the original price of the shirt

Then, we know that:

x – 0.20x = the new price of the shirt

We can simplify x – 0.20x to 0.8x.

So then the new price of the shirt is 0.8x

If the original price of the shirt is $30,

then the new price of the shirt = 0.8 x 30 = $24

2. Are we there yet? Calculating how long it will take to get somewhere

Remember Bart Simpson asking ‘Are we there yet?’ on repeat.

Well, we can use algebra, specifically the formula linking distance, speed and time, to calculate how long it will take to arrive at your destination.

how can you solve real world problems

Say your car is traveling at 60 miles per hour, then the formula would be:

how can you solve real world problems

So instead of asking ‘Are we there yet?’, you could look out the window for a sign that shows how many miles to your destination then use the Distance-Speed-Time formula.

The Sign Says You've Got 72 Miles to Go Before the End of Your Road Trip.  It's Lying. - Bloomberg

So the time to get to Las Vegas will be 72 divided by 60 which is just over 1. So it will be just over 1 hour to get there.

how can you solve real world problems

The distance – speed – time formula is a useful math formula to remember.

3. Figuring out how many pizzas to order

You’re having 7 friends over and you want pizza.

You each can eat at least 4 slices.

If there are 8 slices in a pizza, how many pizzas should you order?

You can use algebra to find how many pizzas you should order by writing an equation and solving it.

Let x represent the number of pizzas you should order.

So then you and 7 friends is 1 + 7, which is 8.

If each person eats 4 slices, the total number of slices is 8 x 4 = 32

Since each pizza has 8 slices, the number of slices in total will be 8x.

Here’s what it looks like as an algebraic equation:

how can you solve real world problems

So you will need to order at least 4 pizzas.

If your friend eat more than 4 slices each you need to order more pizzas.

If your mom and dad, brothers & sisters want pizza too, you will need to order more.

So we could write it as an algebraic inequality like this:

how can you solve real world problems

4. Calculating how many hours you need to work

Imagine there is a new pair of jeans you want that cost $75.

If your parents give you $25 towards them, how many hours of babysitting do you have to work in order to buy them?

Well you only need $50 right because $75 – $25 = $50

Let us say you earn $5 an hour for babysitting.

Then you will need to work for 10 hours.

Here’s what it looks like in algebra:

how can you solve real world problems

5. When adjusting amounts in a recipe when cooking

Let’s say you want to make some choc-chip cookies but the recipe requires 2 eggs and you only have 1 egg.

You will need to adjust the amounts of the rest of the ingredients.

This is a simple example where you can simply halve each ingredient.

Alternatively, you could use your knowledge of algebra to write an algebraic equation to calculate all the other quantities.

This is useful when its not a simple case of doubling or halving amounts.

For example if you wanted to make choc-chip cookies but you only have 2 cups of flour and you need 3 cups.

This means your recipe will be 2/3 of the original recipe.

So your formula will be:

new amount = 2/3 x recipe amount

how can you solve real world problems

6. Planning a budget and sticking to it

Budgeting is so important, whether you’re an individual, a family or a business. And algebra can help!

Let’s say you have $200 income in a month. You want to budget this out so that you don’t overspend and can even save money each month. Perhaps for an end-of-school holiday, a car or college.

List all your expenses, for example:

  • $16 cell phone
  • $30 monthly bus pass
  • $50 going out with friends

Add up your expenses to find your monthly expenses.

16 + 30 +50 = 96

You should track your expenses in an app or spreadsheet to see what you are actually spending your money on. These days with apple pay and a cashless society it is very easy to spend money and not realize how much we are spending over. a month.

Subtract your total monthly expenses from your income to calculate the amount leftover that you can save (or invest).

Using algebra this could be done like this:

Let x represent your monthly expenditure.

Then we know that:

200-x = the amount we can save each month

Of course, this is just a simple example. In reality, you may use a spreadsheet (which is what I use). But you will need to understand the mathematics so you can enter a formula in your spreadsheet. This way when your expenses vary each month your savings will be automatically calculated.

So algebra can help you to create a budget, stick to it and even save or invest.

how can you solve real world problems

7. Comparing cell phone plans

The time will come when your parents stop paying your cell bill. In order to find the best value for money, you need to be able to compare different cell phone plans.

Algebra can help you do this!

Let’s say you’re looking at two different cell phone plans:

Plan A: $60/month with unlimited talk and text and 5GB data

Plan B: $20/month with unlimited talk and text and 1GB data plus $10/GB over this amount.

In order to compare cell phone plans, we need to find out how much data we use each month. You may need to look at past statements for this information.

Just say you use roughly 3GB of data each month.

On Plan A, the 3GB is included so your total bill would be $60

On Plan B, 3GB is over the 1GB of included data so you will need to pay extra. Each plan will have different costs.

The amount you will pay is calculated as follows:

# of GB over plan = 3GB minus 1GB = 2 GB

Cost for extra GB = 2 x $10/GB = $20

Total monthly cost = $20 + $20 = $40

So plan B ends up being $20 cheaper.

You could write this as a formula as:

Total monthly cost = 20 + (# GB used – 1GB) x 10

Since the amount of data used each month may vary, it Is called a variable.

Different plans may charge different excess data costs too.

You could set up a spreadsheet to calculate the different monthly costs for the varying amount of data used to help you decide which cell phone plan is best for your needs.

Using Algebra to compare cell phone plans in a spreadsheet

You can see that once you use over 5GB of data the monthly cost for plan B will be more than $60. This is when plan A is the best value.

So knowing how to write a formula can help you compare cell phone plans.

Wrapping up and my experience with using examples of Algebra in everyday life in the classroom.

There are countless other examples of how algebra is used in daily life. These are just a few of the ways that I use it on a regular basis to problem solve. I’m sure you can think of many more!

From my 14+ years of teaching high school mathematics to students of all abilities, I have observed that some students need to see the relevance of abstract concepts like Algebra in order to be interested.

Start the lesson with a hook or example of how they can use algebra in real life so they buy into the topic and are more engaged.

If you’re a teacher, try incorporating some real-life examples into your lessons. And if you’re a student, pay attention to the ways that you use algebra in your daily life. It will help you to better understand the concepts and make them more relevant to your own life.

I hope this article has helped you to see how algebra is used in everyday life.

Related posts:

x 3 8 factor

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5 Real Life Algebra Problems That You Solve Everyday

Algebra has a reputation for not being very useful in daily life. In fact, in my experience as a high school math teacher, the complaint that I get the most often is that we don’t spend enough time solving real life algebra problems.

You might be surprised to hear that I understand the frustration that my students experience. Unless we are solving real life algebra problems related to money in some way, algebra can feel very “artificial” or disconnected from real life.

My goal here is to walk you through 5 real life algebra problems that will give you a whole new appreciation for the application of algebra to the real-world. I am excited to help you see how many algebraic equations and algebraic concepts are applicable beyond just algebra word problems in your math class!

What is an Example of Algebra in Real Life?

While it is often seen as an abstract branch of mathematics, there are many real-life applications of algebra in everyday life. Now, it is unlikely that you will be solving quadratic equations while walking your dog, or solving real-world problems with linear equations while you play video games. But you can see examples of real life algebra problems all around you!

A simple example is when you want to quickly determine the total cost of a product including taxes, or the total cost after a discount from the original price. Knowing the total amount of money something will cost is a real-life scenario that everyone can relate to!

Depending on your chosen career path, you may see the use of algebra more often than others (I know I see it a lot in my daily life as a math teacher…!).

For example, if you are a business owner, you may use algebra to determine the number of labor hours to spread amongst your staff, or the lowest price you can sell your product for to break even.

For more uses of algebra, check out my list of 20  examples of algebra in real life !

What is an Example of an Algebra Problem in Real Life?

An algebra problem is a mathematical problem that requires the use of algebraic concepts and strategies to determine unknown values or unknown variables. Much like how the order of operations are required to evaluate numerical expressions, algebra problems require the problem solver to apply a set of rules in order to arrive at a solution.

Real world problems that require the use of algebra usually involve modelling real-life situations with  algebraic formulas . A formula is a specific equation that can be applied to solve a problem. Formulas make it possible to make predictions about a given real-life scenario.

For example, consider the following problem:

You are saving up for a new smartphone and currently have $200 in your savings account. Your plan is to save a certain amount of money each week from your allowance. If the smartphone costs $600, and you want to have enough money to buy it in 8 weeks, how much money should you save each week?

cell phone pixel art

To solve this problem, we first need to use the information provided in the problem to create an equation that models the real-life scenario. Thinking about the problem in terms of variables, we can define T as the total of the savings, and variable x as the amount saved each week.

Since we know that we have a fixed value of 200, we can use the following equation to model this real world problem:

$$T=200+8x$$

This equation says “the total saved is equal to the original $200 plus whatever amount is saved per week, for 8 weeks”.

Substituting the total of the smartphone allows us to begin solving for the unknown variable x. Remember, when solving algebraic equations, you must apply the same operation to both sides of the equation.

$$ \begin{split} T&=200+8x  \\ \\ 600&=200+8x  \\ \\ 600-200 &= 8x \\ \\ 400 &= 8x \\ \\ \frac{400}{8} &= \frac{8x}{8} \\\\ 50 &= x \end{split} $$

Therefore, since x = 50, you should save $50 each week in order to save enough money for the smartphone. For more practice with the algebra used in this solution, check out this free collection of  solving two step equations worksheets !

5 Real Life Algebra Problems with Step-By-Step Solutions

There are so many real-life examples of algebra problems, but I want to focus on 5 here that I believe will convince you of just how applicable algebra is to the real-world! So let’s dig into these 5 real-world algebraic word problems!

Example #1: Comparing Cell Phone Plans

Link is considering two different cell phone plans. Plan A charges a monthly fee of $30 and an additional $0.10 per minute of talk time. Plan B charges a monthly fee of $45 regardless of how much time is used talking. How many minutes of total time talking will make the plans equal in cost?

The best way to start this problem is by writing two equations to represent each scenario. If C represents total cost, and x represents minutes of talk time used, the equations can be written as follows:

  • Plan A: \(C=30+0.1x\)
  • Plan B: \(C=45\)

Setting the first equation equal to the second equation will allow us to employ algebra to solve for the number of minutes that makes the two plans equal.

$$ \begin{split}  30+0.1x&=45 \\ \\ 30-30+0.1x&=45-30 \\ \\ 0.1x&=15 \\ \\ \frac{0.1x}{0.1}&=\frac{15}{0.1} \\ \\ x&=150 \end{split} $$

Therefore, the two cell phone plans are equal when 150 minutes of total time talking are used.

Example #2: Calculating Gallons of Gas

Zelda is driving from Hyrule to the Mushroom Kingdom, which are 180 miles apart. Her car can travel 30 miles per gallon of gas. Write an equation to represent the number of gallons of gas, G, that Zelda needs for the trip in terms of the distance, d, she needs to travel. Then calculate how many gallons of gas she needs for this trip.

jerry can pixel art

The number of gallons of gas (G) Zelda needs for any trip can be represented by the equation \(G = \frac{d}{30}\). Since the distance between Hyrule and the Mushroom Kingdom is 180 miles, we can substitute 180 into the equation for  d  to determine the number of gallons of gas needed:

$$G=\frac{180}{30}=6$$

Therefore, Zelda needs 6 gallons of gas for her trip.

Example #3: Basketball Players in Action!

A basketball player shoots a basketball from a height of 6 feet above the ground. Unfortunately he completely misses the net and the ball bounces off court. A sports analyst models the path of the basketball using the equation \(h(t) = -16t^2 + 16t + 6\), where h(t) represents the height of the basketball above the ground in feet at time t seconds after the shot. Determine the time it takes for the basketball to hit the ground.

basketball pixel art

Since we are asked for when the ball hits the ground and  h(t)  is given as the height above the ground, we know that we are looking for the x-intercepts of this quadratic function. We therefore set the equation equal to zero and solve for x. 

Note that we cannot use  trinomial factoring  here since the quadratic is not factorable! Thankfully quadratic equations are solvable using the quadratic formula!

$$ \begin{split}  x&=\frac{-b \pm \sqrt{b^2-4ac}}{2a} \\\\ &=\frac{-16 \pm \sqrt{16^2-4(-16)(6)}}{2(-16)}\\\\ &=\frac{-16 \pm \sqrt{640}}{-32}\\\\ x&=-0.291 \\\\ x&=1.291 \end{split}$$

Therefore, the ball hits the ground after approximately 1.3 seconds. Remember that time cannot be negative, so the first answer is inadmissible and rejected!

Example #4: Saving for a Computer Game

You are saving to buy a new computer game that costs $90. You decide to save up for the computer game by depositing some money into a savings account that earns an annual interest rate of 5% (compounded monthly). You start with an initial deposit of $30 and plan to save for 22 months. Will you have enough to purchase the computer game?

pixel art cd

This is an example of a math problem that connects to financial problems people encounter everyday! Since the account you chose earns  interest , we can apply a compound interest formula to help us out here:

$$A=P(1+i)^n$$

In this formula:

  • A(t)  is the total amount of money.
  • P  is the initial deposit (which is $30 in this case).
  • i  is the monthly interest rate (5% annual interest, compounded monthly means that  i  is approximately 0.004167).
  • n  is the time that has elapsed (since we are working with months, we multiply by 12)

We can set up our equation and see if our total amount of money is greater than $90:

$$\begin{split}  A(22)&=30(1.004167)^{22 \times 12} \\\\ &=$89.93 \end{split} $$

Remember to always include a dollar sign in your answer and to round to two decimal places when working with money!

Since our answer is approximately equal to $90, we can say that you will have enough money after 22 months! It’s time to get saving!

Example #5: How Many Tickets Did the Movie Theater Sell?

A movie theater charges $10 per ticket for adults and $6 per ticket for children. On a particular day, the theater sold a total of 150 tickets, and the total revenue for the day was $1350. Write a system of equations to represent this real-life scenario and then solve for the number of adult and child tickets sold.

movie tickets pixel art

Let’s assume that variable  x  represents the number of adult tickets sold and variable  y  represents the number of child tickets sold. We can set up two linear equations as follows:

  • First Equation (the total number of tickets sold): \(x+y=150\) 
  • Second Equation (the total revenue from ticket sales is 1350): \(10x+6y=1350\) 

We can use substitution to solve this linear system by rearranging the first equation and substituting it into the second equation. You can catch a quick overview of the substitution process by checking out  this substitution video  on my YouTube channel!

Rearranging the first equation into a different form to solve for  y  results in \(y=-x+150\). Substituting this expression for  y  into the second equation results in: 

$$ \begin{split}  10x+6(-x+150)&=1350 \\ \\ 10x-6x+900&=1350 \\ \\ 4x&=450\\ \\ x&=112.5\\ \\ \end{split}  $$

We then substitute this value for  x  into our expression for  y: 

$$ \begin{split}  y&=-x+150 \\ \\ &=-112.50+150 \\ \\ &=37.5\\ \\ \end{split}  $$

Since we can’t have fractional ticket sales, we can say that approximately 112 adult tickets were sold and 38 child tickets were sold.

Appreciating Real Life Algebra Problems

While algebra is often seen as an abstract topic, I am hopeful that I have shown you just how applicable it can be to real-life situations! Some of these examples you may have even encountered in your own life!

Even if you aren’t drawing up complex equations and solving them while you are playing basketball, combining basic math and problem solving is one of the most important skills people can have in both their work and their lives. 

I hope that I have helped you further your understanding of algebra, while growing an appreciation for the different ways it can be used in your own life!

Did you find this guide to real life algebra problems helpful? Share this post and subscribe to Math By The Pixel on YouTube for more helpful mathematics content!

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Solving Systems of Equations Real World Problems

Wow! You have learned many different strategies for solving systems of equations! First we started with Graphing Systems of Equations . Then we moved onto solving systems using the Substitution Method . In our last lesson we used the Linear Combinations or Addition Method to solve systems of equations.

Now we are ready to apply these strategies to solve real world problems! Are you ready? First let's look at some guidelines for solving real world problems and then we'll look at a few examples.

Steps For Solving Real World Problems

  • Highlight the important information in the problem that will help write two equations.
  • Define your variables
  • Write two equations
  • Use one of the methods for solving systems of equations to solve.
  • Check your answers by substituting your ordered pair into the original equations.
  • Answer the questions in the real world problems. Always write your answer in complete sentences!

Ok... let's look at a few examples. Follow along with me. (Having a calculator will make it easier for you to follow along.)

Example 1: Systems Word Problems

You are running a concession stand at a basketball game. You are selling hot dogs and sodas. Each hot dog costs $1.50 and each soda costs $0.50. At the end of the night you made a total of $78.50. You sold a total of 87 hot dogs and sodas combined. You must report the number of hot dogs sold and the number of sodas sold. How many hot dogs were sold and how many sodas were sold?

1.  Let's start by identifying the important information:

  • hot dogs cost $1.50
  • Sodas cost $0.50
  • Made a total of $78.50
  • Sold 87 hot dogs and sodas combined

2.  Define your variables.

  • Ask yourself, "What am I trying to solve for? What don't I know?

In this problem, I don't know how many hot dogs or sodas were sold. So this is what each variable will stand for. (Usually the question at the end will give you this information).

Let x = the number of hot dogs sold

Let y = the number of sodas sold

3. Write two equations.

One equation will be related to the price and one equation will be related to the quantity (or number) of hot dogs and sodas sold.

1.50x + 0.50y = 78.50    (Equation related to cost)

 x + y = 87   (Equation related to the number sold)

4.  Solve! 

We can choose any method that we like to solve the system of equations. I am going to choose the substitution method since I can easily solve the 2nd equation for y.

Solving a systems using substitution

5. Think about what this solution means.

x is the number of hot dogs and x = 35. That means that 35 hot dogs were sold.

y is the number of sodas and y = 52. That means that 52 sodas were sold.

6.  Write your answer in a complete sentence.

35 hot dogs were sold and 52 sodas were sold.

7.  Check your work by substituting.

1.50x + 0.50y = 78.50

1.50(35) + 0.50(52) = 78.50

52.50 + 26 = 78.50

35 + 52 = 87

Since both equations check properly, we know that our answers are correct!

That wasn't too bad, was it? The hardest part is writing the equations. From there you already know the strategies for solving. Think carefully about what's happening in the problem when trying to write the two equations.

Example 2: Another Word Problem

You and a friend go to Tacos Galore for lunch. You order three soft tacos and three burritos and your total bill is $11.25. Your friend's bill is $10.00 for four soft tacos and two burritos. How much do soft tacos cost? How much do burritos cost?

  • 3 soft tacos + 3 burritos cost $11.25
  • 4 soft tacos + 2 burritos cost $10.00

In this problem, I don't know the price of the soft tacos or the price of the burritos.

Let x = the price of 1 soft taco

Let y = the price of 1 burrito

One equation will be related your lunch and one equation will be related to your friend's lunch.

3x + 3y = 11.25  (Equation representing your lunch)

4x + 2y = 10   (Equation representing your friend's lunch)

We can choose any method that we like to solve the system of equations. I am going to choose the combinations method.

Solving Systems Using Combinations

5. Think about what the solution means in context of the problem.

x = the price of 1 soft taco and x = 1.25.

That means that 1 soft tacos costs $1.25.

y = the price of 1 burrito and y = 2.5.

That means that 1 burrito costs $2.50.

Yes, I know that word problems can be intimidating, but this is the whole reason why we are learning these skills. You must be able to apply your knowledge!

If you have difficulty with real world problems, you can find more examples and practice problems in the Algebra Class E-course.

Take a look at the questions that other students have submitted:

how can you solve real world problems

Problem about the WNBA

Systems problem about ages

Problem about milk consumption in the U.S.

Vans and Buses? How many rode in each?

Telephone Plans problem

Systems problem about hats and scarves

Apples and guavas please!

How much did Alice spend on shoes?

All about stamps

Going to the movies

Small pitchers and large pitchers - how much will they hold?

Chickens and dogs in the farm yard

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Real World Examples of Quadratic Equations

A Quadratic Equation looks like this:

Quadratic equations pop up in many real world situations!

Here we have collected some examples for you, and solve each using different methods:

  • Factoring Quadratics
  • Completing the Square
  • Graphing Quadratic Equations
  • The Quadratic Formula
  • Online Quadratic Equation Solver

Each example follows three general stages:

  • Take the real world description and make some equations
  • Use your common sense to interpret the results

ball throw

Balls, Arrows, Missiles and Stones

When you throw a ball (or shoot an arrow, fire a missile or throw a stone) it goes up into the air, slowing as it travels, then comes down again faster and faster ...

... and a Quadratic Equation tells you its position at all times!

Example: Throwing a Ball

A ball is thrown straight up, from 3 m above the ground, with a velocity of 14 m/s. when does it hit the ground.

Ignoring air resistance, we can work out its height by adding up these three things: (Note: t is time in seconds)

Add them up and the height h at any time t is:

h = 3 + 14t − 5t 2

And the ball will hit the ground when the height is zero:

3 + 14t − 5t 2 = 0

Which is a Quadratic Equation !

In "Standard Form" it looks like:

−5t 2 + 14t + 3 = 0

It looks even better when we multiply all terms by −1 :

5t 2 − 14t − 3 = 0

Let us solve it ...

There are many ways to solve it, here we will factor it using the "Find two numbers that multiply to give ac , and add to give b " method in Factoring Quadratics :

ac = −15 , and b = −14 .

The factors of −15 are: −15, −5, −3, −1, 1, 3, 5, 15

By trying a few combinations we find that −15 and 1 work (−15×1 = −15, and −15+1 = −14)

The "t = −0.2" is a negative time, impossible in our case.

The "t = 3" is the answer we want:

The ball hits the ground after 3 seconds!

Here is the graph of the Parabola h = −5t 2 + 14t + 3

It shows you the height of the ball vs time

Some interesting points:

(0,3) When t=0 (at the start) the ball is at 3 m

(−0.2,0) says that −0.2 seconds BEFORE we threw the ball it was at ground level. This never happened! So our common sense says to ignore it.

(3,0) says that at 3 seconds the ball is at ground level.

Also notice that the ball goes nearly 13 meters high.

Note: You can find exactly where the top point is!

The method is explained in Graphing Quadratic Equations , and has two steps:

Find where (along the horizontal axis) the top occurs using −b/2a :

  • t = −b/2a = −(−14)/(2 × 5) = 14/10 = 1.4 seconds

Then find the height using that value (1.4)

  • h = −5t 2 + 14t + 3 = −5(1.4) 2 + 14 × 1.4 + 3 = 12.8 meters

So the ball reaches the highest point of 12.8 meters after 1.4 seconds.

Example: New Sports Bike

bike

You have designed a new style of sports bicycle!

Now you want to make lots of them and sell them for profit.

Your costs are going to be:

  • $700,000 for manufacturing set-up costs, advertising, etc
  • $110 to make each bike

Based on similar bikes, you can expect sales to follow this "Demand Curve":

Where "P" is the price.

For example, if you set the price:

  • at $0, you just give away 70,000 bikes
  • at $350, you won't sell any bikes at all
  • at $300 you might sell 70,000 − 200×300 = 10,000 bikes

So ... what is the best price? And how many should you make?

Let us make some equations!

How many you sell depends on price, so use "P" for Price as the variable

Profit = −200P 2 + 92,000P − 8,400,000

Yes, a Quadratic Equation. Let us solve this one by Completing the Square .

Solve: −200P 2 + 92,000P − 8,400,000 = 0

Step 1 Divide all terms by -200

Step 2 Move the number term to the right side of the equation:

Step 3 Complete the square on the left side of the equation and balance this by adding the same number to the right side of the equation:

(b/2) 2 = (−460/2) 2 = (−230) 2 = 52900

Step 4 Take the square root on both sides of the equation:

Step 5 Subtract (-230) from both sides (in other words, add 230):

What does that tell us? It says that the profit is ZERO when the Price is $126 or $334

But we want to know the maximum profit, don't we?

It is exactly half way in-between! At $230

And here is the graph:

The best sale price is $230 , and you can expect:

  • Unit Sales = 70,000 − 200 x 230 = 24,000
  • Sales in Dollars = $230 x 24,000 = $5,520,000
  • Costs = 700,000 + $110 x 24,000 = $3,340,000
  • Profit = $5,520,000 − $3,340,000 = $2,180,000

A very profitable venture.

Example: Small Steel Frame

Your company is going to make frames as part of a new product they are launching.

The frame will be cut out of a piece of steel, and to keep the weight down, the final area should be 28 cm 2

The inside of the frame has to be 11 cm by 6 cm

What should the width x of the metal be?

Area of steel before cutting:

Area of steel after cutting out the 11 × 6 middle:

Let us solve this one graphically !

Here is the graph of 4x 2 + 34x :

The desired area of 28 is shown as a horizontal line.

The area equals 28 cm 2 when:

x is about −9.3 or 0.8

The negative value of x make no sense, so the answer is:

x = 0.8 cm (approx.)

Example: River Cruise

A 3 hour river cruise goes 15 km upstream and then back again. the river has a current of 2 km an hour. what is the boat's speed and how long was the upstream journey.

There are two speeds to think about: the speed the boat makes in the water, and the speed relative to the land:

  • Let x = the boat's speed in the water (km/h)
  • Let v = the speed relative to the land (km/h)

Because the river flows downstream at 2 km/h:

  • when going upstream, v = x−2 (its speed is reduced by 2 km/h)
  • when going downstream, v = x+2 (its speed is increased by 2 km/h)

We can turn those speeds into times using:

time = distance / speed

(to travel 8 km at 4 km/h takes 8/4 = 2 hours, right?)

And we know the total time is 3 hours:

total time = time upstream + time downstream = 3 hours

Put all that together:

total time = 15/(x−2) + 15/(x+2) = 3 hours

Now we use our algebra skills to solve for "x".

First, get rid of the fractions by multiplying through by (x-2) (x+2) :

3(x-2)(x+2) = 15(x+2) + 15(x-2)

Expand everything:

3(x 2 −4) = 15x+30 + 15x−30

Bring everything to the left and simplify:

3x 2 − 30x − 12 = 0

It is a Quadratic Equation!

Let us solve it using the Quadratic Formula :

Where a , b and c are from the Quadratic Equation in "Standard Form": ax 2 + bx + c = 0

Solve 3x 2 - 30x - 12 = 0

Answer: x = −0.39 or 10.39 (to 2 decimal places)

x = −0.39 makes no sense for this real world question, but x = 10.39 is just perfect!

Answer: Boat's Speed = 10.39 km/h (to 2 decimal places)

And so the upstream journey = 15 / (10.39−2) = 1.79 hours = 1 hour 47min

And the downstream journey = 15 / (10.39+2) = 1.21 hours = 1 hour 13min

Example: Resistors In Parallel

Two resistors are in parallel, like in this diagram:

The total resistance has been measured at 2 Ohms, and one of the resistors is known to be 3 ohms more than the other.

What are the values of the two resistors?

The formula to work out total resistance "R T " is:

1 R T   =   1 R 1 + 1 R 2

In this case, we have R T = 2 and R 2 = R 1 + 3

1 2   =   1 R 1 + 1 R 1 +3

To get rid of the fractions we can multiply all terms by 2R 1 (R 1 + 3) and then simplify:

Yes! A Quadratic Equation!

Let us solve it using our Quadratic Equation Solver .

  • Enter 1, −1 and −6
  • And you should get the answers −2 and 3

R 1 cannot be negative, so R 1 = 3 Ohms is the answer.

The two resistors are 3 ohms and 6 ohms.

Quadratic Equations are useful in many other areas:

parabolic dish

For a parabolic mirror, a reflecting telescope or a satellite dish, the shape is defined by a quadratic equation.

Quadratic equations are also needed when studying lenses and curved mirrors.

And many questions involving time, distance and speed need quadratic equations.

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A screenshot from an AI-generated video of woolly mammoths.

Sora: OpenAI launches tool that instantly creates video from text

Model from ChatGPT maker ‘simulates physical world in motion’ up to a minute long based on users’ subject and style instructions

OpenAI revealed a tool on Thursday that can generate videos from text prompts.

The new model, nicknamed Sora after the Japanese word for “sky”, can produce realistic footage up to a minute long that adheres to a user’s instructions on both subject matter and style. According to a company blogpost, the model is also able to create a video based on a still image or extend existing footage with new material.

“We’re teaching AI to understand and simulate the physical world in motion, with the goal of training models that help people solve problems that require real-world interaction,” the blogpost reads.

One video included among several initial examples from the company was based on the prompt: “A movie trailer featuring the adventures of the 30-year-old space man wearing a red wool knitted motorcycle helmet, blue sky, salt desert, cinematic style, shot on 35mm film, vivid colors.”

The company announced it had opened access to Sora to a few researchers and video creators. The experts would “red team” the product – test it for susceptibility to skirt OpenAI’s terms of service, which prohibit “extreme violence, sexual content, hateful imagery, celebrity likeness, or the IP of others”, per the company’s blogpost. The company is only allowing limited access to researchers, visual artists and film-makers, though CEO Sam Altman responded to users’ prompts on Twitter after the announcement with video clips he said were made by Sora. The videos bear a watermark to show they were made by AI.

Introducing Sora, our text-to-video model. Sora can create videos of up to 60 seconds featuring highly detailed scenes, complex camera motion, and multiple characters with vibrant emotions. https://t.co/7j2JN27M3W Prompt: “Beautiful, snowy… pic.twitter.com/ruTEWn87vf — OpenAI (@OpenAI) February 15, 2024

The company debuted the still image generator Dall-E in 2021 and generative AI chatbot ChatGPT in November 2022, which quickly accrued 100 million users. Other AI companies have debuted video generation tools, though those models have only been able to produce a few seconds of footage that often bears little relation to their prompts. Google and Meta have said they are in the process of developing generative video tools, though they have not released them to the public. On Wednesday, it announced an experiment with adding deeper memory to ChatGPT so that it could remember more of its users’ chats.

https://t.co/uCuhUPv51N pic.twitter.com/nej4TIwgaP — Sam Altman (@sama) February 15, 2024

OpenAI did not disclose how much footage was used to train Sora or where the training videos may have originated, other than telling the New York Times that the corpus contained videos that were both publicly available and licensed from copyright owners. The company has been sued multiple times for alleged copyright infringement in the training of its generative AI tools, which digest gargantuan amounts of material scraped from the internet and imitate the images or text contained in those datasets.

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  • \mathrm{Lauren's\:age\:is\:half\:of\:Joe's\:age.\:Emma\:is\:four\:years\:older\:than\:Joe.\:The\:sum\:of\:Lauren,\:Emma,\:and\:Joe's\:age\:is\:54.\:How\:old\:is\:Joe?}
  • \mathrm{Kira\:went\:for\:a\:drive\:in\:her\:new\:car.\:She\:drove\:for\:142.5\:miles\:at\:a\:speed\:of\:57\:mph.\:For\:how\:many\:hours\:did\:she\:drive?}
  • \mathrm{The\:sum\:of\:two\:numbers\:is\:249\:.\:Twice\:the\:larger\:number\:plus\:three\:times\:the\:smaller\:number\:is\:591\:.\:Find\:the\:numbers.}
  • \mathrm{If\:2\:tacos\:and\:3\:drinks\:cost\:12\:and\:3\:tacos\:and\:2\:drinks\:cost\:13\:how\:much\:does\:a\:taco\:cost?}
  • \mathrm{You\:deposit\:3000\:in\:an\:account\:earning\:2\%\:interest\:compounded\:monthly.\:How\:much\:will\:you\:have\:in\:the\:account\:in\:15\:years?}
  • How do you solve word problems?
  • To solve word problems start by reading the problem carefully and understanding what it's asking. Try underlining or highlighting key information, such as numbers and key words that indicate what operation is needed to perform. Translate the problem into mathematical expressions or equations, and use the information and equations generated to solve for the answer.
  • How do you identify word problems in math?
  • Word problems in math can be identified by the use of language that describes a situation or scenario. Word problems often use words and phrases which indicate that performing calculations is needed to find a solution. Additionally, word problems will often include specific information such as numbers, measurements, and units that needed to be used to solve the problem.
  • Is there a calculator that can solve word problems?
  • Symbolab is the best calculator for solving a wide range of word problems, including age problems, distance problems, cost problems, investments problems, number problems, and percent problems.
  • What is an age problem?
  • An age problem is a type of word problem in math that involves calculating the age of one or more people at a specific point in time. These problems often use phrases such as 'x years ago,' 'in y years,' or 'y years later,' which indicate that the problem is related to time and age.

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Read our research on: Immigration & Migration | Podcasts | Election 2024

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How americans view the situation at the u.s.-mexico border, its causes and consequences, 80% say the u.s. government is doing a bad job handling the migrant influx.

how can you solve real world problems

Pew Research Center conducted this study to understand the public’s views about the large number of migrants seeking to enter the U.S. at the border with Mexico. For this analysis, we surveyed 5,140 adults from Jan. 16-21, 2024. Everyone who took part in this survey is a member of the Center’s American Trends Panel (ATP), an online survey panel that is recruited through national, random sampling of residential addresses. This way nearly all U.S. adults have a chance of selection. The survey is weighted to be representative of the U.S. adult population by gender, race, ethnicity, partisan affiliation, education and other categories. Read more about the ATP’s methodology .

Here are the questions used for the report and its methodology .

The growing number of migrants seeking entry into the United States at its border with Mexico has strained government resources, divided Congress and emerged as a contentious issue in the 2024 presidential campaign .

Chart shows Why do Americans think there is an influx of migrants to the United States?

Americans overwhelmingly fault the government for how it has handled the migrant situation. Beyond that, however, there are deep differences – over why the migrants are coming to the U.S., proposals for addressing the situation, and even whether it should be described as a “crisis.”

Factors behind the migrant influx

Economic factors – either poor conditions in migrants’ home countries or better economic opportunities in the United States – are widely viewed as major reasons for the migrant influx.

About seven-in-ten Americans (71%), including majorities in both parties, cite better economic opportunities in the U.S. as a major reason.

There are wider partisan differences over other factors.

About two-thirds of Americans (65%) say violence in migrants’ home countries is a major reason for why a large number of immigrants have come to the border.

Democrats and Democratic-leaning independents are 30 percentage points more likely than Republicans and Republican leaners to cite this as a major reason (79% vs. 49%).

By contrast, 76% of Republicans say the belief that U.S. immigration policies will make it easy to stay in the country once they arrive is a major factor. About half as many Democrats (39%) say the same.

For more on Americans’ views of these and other reasons, visit Chapter 2.

How serious is the situation at the border?

A sizable majority of Americans (78%) say the large number of migrants seeking to enter this country at the U.S.-Mexico border is eithera crisis (45%) or a major problem (32%), according to the Pew Research Center survey, conducted Jan. 16-21, 2024, among 5,140 adults.

Related: Migrant encounters at the U.S.-Mexico border hit a record high at the end of 2023 .

Chart shows Border situation viewed as a ‘crisis’ by most Republicans; Democrats are more likely to call it a ‘problem’

  • Republicans are much more likely than Democrats to describe the situation as a “crisis”: 70% of Republicans say this, compared with just 22% of Democrats.
  • Democrats mostly view the situation as a major problem (44%) or minor problem (26%) for the U.S. Very few Democrats (7%) say it is not a problem.

In an open-ended question , respondents voice their concerns about the migrant influx. They point to numerous issues, including worries about how the migrants are cared for and general problems with the immigration system.

Yet two concerns come up most frequently:

  • 22% point to the economic burdens associated with the migrant influx, including the strains migrants place on social services and other government resources.
  • 22% also cite security concerns. Many of these responses focus on crime (10%), terrorism (10%) and drugs (3%).

When asked specifically about the impact of the migrant influx on crime in the United States, a majority of Americans (57%) say the large number of migrants seeking to enter the country leads to more crime. Fewer (39%) say this does not have much of an impact on crime in this country.

Republicans (85%) overwhelmingly say the migrant surge leads to increased crime in the U.S. A far smaller share of Democrats (31%) say the same; 63% of Democrats instead say it does not have much of an impact.

Government widely criticized for its handling of migrant influx

For the past several years, the federal government has gotten low ratings for its handling of the situation at the U.S.-Mexico border. (Note: The wording of this question has been modified modestly to reflect circumstances at the time).

Chart shows Only about a quarter of Democrats and even fewer Republicans say the government has done a good job dealing with large number of migrants at the border

However, the current ratings are extraordinarily low.

Just 18% say the U.S. government is doing a good job dealing with the large number of migrants at the border, while 80% say it is doing a bad job, including 45% who say it is doing a very bad job.

  • Republicans’ views are overwhelmingly negative (89% say it’s doing a bad job), as they have been since Joe Biden became president.
  • 73% of Democrats also give the government negative ratings, the highest share recorded during Biden’s presidency.

For more on Americans’ evaluations of the situation, visit Chapter 1 .

Which policies could improve the border situation?

There is no single policy proposal, among the nine included on the survey, that majorities of both Republicans and Democrats say would improve the situation at the U.S.-Mexico border. There are areas of relative agreement, however.

A 60% majority of Americans say that increasing the number of immigration judges and staff in order to make decisions on asylum more quickly would make the situation better. Only 11% say it would make things worse, while 14% think it would not make much difference.

Nearly as many (56%) say creating more opportunities for people to legally immigrate to the U.S. would make the situation better.

Chart shows Most Democrats and nearly half of Republicans say boosting resources for quicker decisions on asylum cases would improve situation at Mexico border

Majorities of Democrats say each of these proposals would make the border situation better.

Republicans are less positive than are Democrats; still, about 40% or more of Republicans say each would improve the situation, while far fewer say they would make things worse.

Opinions on other proposals are more polarized. For example, a 56% majority of Democrats say that adding resources to provide safe and sanitary conditions for migrants arriving in the U.S. would be a positive step forward.

Republicans not only are far less likely than Democrats to view this proposal positively, but far more say it would make the situation worse (43%) than better (17%).

Chart shows Wide partisan gaps in views of expanding border wall, providing ‘safe and sanitary conditions’ for migrants

Building or expanding a wall along the U.S.-Mexico border was among the most divisive policies of Donald Trump’s presidency. In 2019, 82% of Republicans favored expanding the border wall , compared with just 6% of Democrats.

Today, 72% of Republicans say substantially expanding the wall along the U.S. border with Mexico would make the situation better. Just 15% of Democrats concur, with most saying either it would not make much of a difference (47%) or it would make things worse (24%).

For more on Americans’ reactions to policy proposals, visit Chapter 3 .

Facts are more important than ever

In times of uncertainty, good decisions demand good data. Please support our research with a financial contribution.

Report Materials

Table of contents, fast facts on how greeks see migrants as greece-turkey border crisis deepens, americans’ immigration policy priorities: divisions between – and within – the two parties, from the archives: in ’60s, americans gave thumbs-up to immigration law that changed the nation, around the world, more say immigrants are a strength than a burden, latinos have become less likely to say there are too many immigrants in u.s., most popular.

About Pew Research Center Pew Research Center is a nonpartisan fact tank that informs the public about the issues, attitudes and trends shaping the world. It conducts public opinion polling, demographic research, media content analysis and other empirical social science research. Pew Research Center does not take policy positions. It is a subsidiary of The Pew Charitable Trusts .

ncesc-gaming-faq

Can video games help solve real world problems?

A lot. Well, there is a couple of how video games help solve real- world problems faster : Learning from your mistakes You go through deep practice You get to try different things Learning when to give up You face a lot of different problems All the benefits We all make mistakes on a daily basis.

How do video games help with real world problem-solving?

Unlike the well-structured problems that students face in formal learning settings, well-designed games provide students with challenging scenarios that promote problem-solving skills by requiring players to generate new knowledge from challenging scenarios within interactive environments, while also providing …

Can video games help you solve problems?

Problem solving skills/decision making skills

Traditionally video games train problem solving and strategy development skills by getting the player solve increasingly complicated problems. In many cases there is a time pressure which develops speed and decision making skills.

Do video games improve real life skills?

But new and ongoing studies prove that gaming can improve important life skills , such as “superior sensorimotor decision-making skills” and enhanced brain activity, according to a recent study in 2022 at Georgia State University.

What games can improve problem-solving?

Examples include sudoku, murder mysteries, and spaghetti towers. These games are also known as “problem solving exercises”, “problem and solution games” and “group problem solving activities.”

Life is a video game & you are playing it wrong.

How do video games help critical thinking.

In video games, sometimes surprising events occur that “catch” players off guard, forcing them to think quickly to overcome the obstacles that arise. Playing video games improves one’s ability to make effective decisions in dynamic environments, a valuable skill in the real world as well.

What is the hardest game to solve?

Top 10 hardest puzzle video games you’ve played

  • Baba is you.
  • Can of wormholes.
  • Picross 3d.
  • The Witness.

What is the real life benefit of video games?

However, the benefits of videogames include improved powers of concentration, creativity, memory, languages and teamwork. Videogames can make it easier to learn educational contents and develop cognitive skills.

How do video games help kids the real world?

Social connections

Some kids have trouble fitting in and making friends in real life. Video games can be a refuge for them to find people to connect with in positive way. In our busy lives, games offer virtual playdates with real-life friends. Video games also give kids something to talk about at school.

Can video games teach you life lessons?

Video games can entertain us, help us deal with stress, strengthen friendships, and of course, teach us valuable life lessons. These lessons can come to mark the life of gamers and change its course. You may not have consciously paid attention to them, but I assure you they are there.

How do video games help kids problem solve?

One of the most significant benefits of video games is their ability to improve their problem-solving. Many games require players to solve puzzles, overcome obstacles, and make decisions that affect the game’s outcome.

Do video games improve strategy?

Different game types build other sorts of skills. Puzzle games teach problem-solving. Real-time action games improve fine motor skills, memory, response time and the aforementioned hand-eye coordination. Strategy games encourage players to make plans, manage resources and balance competing objectives.

How do video games improve social skills?

Online video games can allow players to talk to others and make friends at their current ability level even when they are not emotionally or physically able to leave their homes. This can help build the skills and confidence necessary to try it in-person.

Are video games helpful or harmful?

It’s true that some studies have shown certain video games can improve hand–eye coordination, problem-solving skills, and the mind’s ability to process information. But too much video game playing may cause problems. It’s hard to get enough active play and exercise if you’re always inside playing video games.

How long should a 12 year old play video games per day?

It’s good to set video game time limits by age. For kids over the age of 6, the American Academy of Pediatrics says no more than 60 minutes on school days and 2 hours on non-school days. Kids under 6 should spend closer to 30 minutes.

Is Roblox good for kids?

Roblox can provide a fun and innovative gaming experience. Unfortunately, however, it’s not always safe for children. While the platform is working hard to keep kids safe with filters and age restrictions, it’s not enough.

What are the pros and cons of video games?

Video games can be used to help improve test scores, teach life and job skills, improve brain function, and encourage physical exercise. Because video game addiction can negatively impact social and physical health, parents should be aware of the symptoms.

Is gaming a sport yes or no?

The Merriam-Webster dictionary defines a sport as a physical activity engaged in for pleasure. While playing a video game requires skill and some coordination, it does not incorporate enough physical aspects to be a sport.

How video games affect children?

To put it mildly, these games can have a marked effect on a child showing excessive violence and aggressive behavior, social anxiety, insomnia, hostility, the risk of neuropsychiatric illness, phobia, and even drug abuse along with Gaming addiction.

What is the name of the hardest game ever?

Contra may be the hardest video game ever once set the tone in terms of raw difficulty remains absolutely hard as nails to this day. Those who get stressed easily should avoid it at all costs. However, those who fancy a real challenge should set aside some time and prove their metal.

Who made the hardest game on earth?

About This Game

It’s hard from the start, but difficulty increases as you progress through the levels. This is a remake of a classic flash game from 2008 “browser gaming” era. “The World’s Hardest Game – On Steam” powered by GameMaker. Original game was made by “Snubby Land” @ArmorGames.

What is the world’s toughest puzzle?

List of Clear Puzzles

  • Impossible Magma, Gemturt, 240 pieces (2022)
  • Impossible Ocean, Gemturt, 240 pieces (2022)
  • Impossible Unicorn, Gemturt, 100 pieces (2022)
  • Impossible Unicorn, Gemturt, 180 pieces (2022)
  • The Clearly Impossible Puzzle, 1000, 500, 250, 100 pieces (2021)
  • Broken Glass Puzzle, 161 pieces (2020)

Do video games train your brain?

Essentially, the more you learn, the more your brain can adapt. “Like stimulants, video gaming can increase gray matter in the brain,” says Dr. Manos. “Gray matter provides interconnectivity and allows parts of your brain to communicate with other parts of your brain and advance your self-perception.”

Can gaming benefit your brain?

Gaming is really a workout for your mind disguised as fun. Studies have shown that playing video games regularly may increase gray matter in the brain and boost brain connectivity. (Gray matter is associated with muscle control, memories, perception, and spatial navigation.)

How does the brain react to gaming?

Gaming activates dopamine – the brain’s reward system

Dopamine is a feel-good neurotransmitter that’s part of the brain’s reward system. Whenever the brain is expecting a reward from a certain activity, it starts producing dopamine which makes us feel good.

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COMMENTS

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  26. Can video games help solve real world problems?

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