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The 6 Best Apps to Improve Your Problem-Solving Skills

Want to improve your problem-solving skills and become more solution-oriented in your daily routine? Here are some apps to try.

Your ability to solve problems is a valuable skill you cannot do without if you want to succeed in your career, business, and life. While most people learn to solve problems primarily through exposure to challenging situations and having to find solutions almost immediately, others don't.

As such, not everyone is skilled at effective problem-solving. However, there is an easy way to improve your problem-solving skills using technology. Today, there are several fun ways to do so, including playing brain games on your mobile. Here are six game apps you can use to develop problem-solving skills while having fun.

1. Lumosity

Lumosity is a web app that helps you improve your mental skills. It is programmed with activities that help people improve their memory, flexibility, rate of processing information, and concentration levels. Thus, Lumosity is a great tool to help you develop problem-solving capabilities.

Lumosity was launched in 2007 and had over 70 million users as of January 2015. The app is available in English, French, Spanish, and German.

Download : Lumosity for Android | iOS (Free, in-app purchases available)

Happify is a company that works to enhance personal, organizational, and healthcare effectiveness by improving the emotional health of its users.

The Happify app incorporates scientific experiments into gaming activities designed to improve resilience and mindfulness and tackle health conditions like mood disorders, depression, anxiety, severe pain, and insomnia. Thus, it is a great healthcare software platform for improving your mental and physical conditions.

Download : Happify for Android | iOS (Free, in-app purchases available)

Launched by Elevate Labs in 2014, Elevate is a brain game app that focuses on improving its users' reading, writing, speaking, listening, and math skills. It is also one of the best android apps to help you solve math problems .

Seeing you already possess the skills mentioned above, you may wonder, is the Elevate brain training app worth your time ? The truth is, there is always room for improvement, hence, the need for you to keep developing these skills. And, as you pass each assessment in the training sessions, the difficulty level increases. This way, you can test whether your abilities are basic or strong.

Download : Elevate for Android | iOS (Free, in-app purchases available)

4. Neuronation

Neuronation is a cognitive training site and app that was made public in 2011. Since then, over 10 million people have used the app. The Neuronation app focuses on improving users' cognitive abilities, such as thinking, learning, understanding, and remembering, through its specialized training activities in the program.

Although native to Germany, the app is available in over eight languages, including English, French, Spanish, Italian, Portuguese, Russian, Turkish, and German. Additionally, the app enjoys widespread use, especially among German healthcare practitioners.

Download: Neuronation for Android | iOS (Free, in-app purchases available)

The Peak brain training app is designed to correct cognitive disorders with the help of short, interactive games. To get started on the Peak brain game app, you will be required to set goals on areas you want to improve, like mental processing, emotional strength, linguistic skills, recollection, concentration levels, and problem-solving.

Once you complete this stage, a virtual coach will be assigned to guide you through the program, and you will be given an assessment. Immediately after you finish each assessment, you will receive feedback based on your result.

You can start using the app for free with the basic version, but it has a limited number of daily exercises that are randomly selected. On the other hand, with the paid version, Peak Pro, you enjoy unlimited access to over 40+ exercises, alongside detailed feedback and personalized training sessions.

Download : Peak for Android | iOS (Free, in-app purchases available)

6. New York Times Crossword

The New York Times Crossword is a daily puzzle published by the renowned New York Times magazine on their website and mobile apps. The New York Times Crossword puzzle dates back to 1942. The first puzzle was published on Sunday, 15 February 1942.

Several freelance puzzle developers generate the puzzle. The puzzle gets tougher as each day goes by in a week, so the simplest puzzles are on Mondays, and the hardest are on Saturdays. Sunday's crossword puzzle is a 21×21 square matrix, whereas the daily crossword puzzle is a 15×15 square matrix. The crossword and other free puzzle games greatly improve critical thinking, learning, and reasoning abilities.

Download : New York Times Crossword for Android | iOS (Free, in-app purchases available)

Have Fun While Improving Your Problem-solving Skills

Developing cognitive abilities, emotional well-being, and problem-solving skills are no longer challenging. Thanks to these brain game apps, you can develop and improve your mental and emotional abilities more easily, faster, and while having fun.

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6 Best Math Problem Solver Apps

By Med Kharbach, PhD | Last Update: March 23, 2024

Tackling math homework can be a daunting task, but with the right tools at your fingertips, it doesn’t have to be. We’ve curated a list of exceptional math problem-solving apps that can turn complex equations into understandable steps, making math homework less of a hurdle.

These math problem solver apps span a broad range of mathematical topics, from the foundational principles of algebra and trigonometry to the intricate complexities of calculus and statistics. They offer comprehensive instructions to help students navigate through math problems, ensuring a deep and effective understanding of the subject.

For websites that offer math homework help, check out best math homework solver tools for students .

Best math problem solver apps

Here are some of the best math problem solver apps out there:

1. Mathway Mathway

Mathway is a problem solver app that includes advanced math calculators for algebra, graphing, and calculus. Simply type in your math problem or point the camera of your device and take a picture of it and the app instantly generates step by step solutions. 

Mathway also includes a voice to text feature which enables you to say your math problem and have it converted to text. 

There is also a section where students can access examples of solved math problems. Students can simply type in a math problem or use the categories under the search box to browse these examples. They can also use the Popular Problems column on the right for quick access to examples.

 Compatibility: iPad/iPhone , Android ; Price: Free, offers in-app purchases.  

2. Microsoft Math Solver

Microsoft Math Solver offers free step by step instructions to help you with your math homework. It covers various topics from arithmetic to advanced algebra and calculus. The way it works is simple: you can enter your math problem, scan a math photo or handwrite it, Microsoft Math Solve instantly recognizes it and provides with you guided explanation to solve it including interactive graphs, similar math problems from around the web, and online video tutorials.

 Compatibility:   iPad/iPhone , Android ;  Price:  Free.  

Cymath is a math problem solver app for students of various grades and skill levels. Students can either type their math problems or snap a photo of them and let the app solve it step by step. 

Math topics covered include: Algebra (e.g., equation solving, factoring, logarithms, exponents, complex numbers, quadratic equations, trigonometry, etc), Calculus (e.g., quotient rule, chain rule, u-substitution, integration by parts, integration by partial fraction, trigonometric substitution, and more), and graphing (e.g., graph generation, intercepts, asymptotes, domains, ranges, etc), and more.

 Compatibility:   iPad/iPhone , Android ;  Price:  Free, offers in-app purchases.  

Gaumath is a math problem solver app that helps you find solutions to complex math equations. Maths topics covered include math word problems, function, geometry, trigonometry, calculus, statistics, matrix, and logic. 

Besides the step by step explanations, Gaumath also offers a 24/7 online math tutors. Simply take a photo of your math problem using the math homework solver app and access instant step-by-step solutions.

5. Photomath

Photomath is another powerful math problem solver app. It offers step by step explanations to math problems covering different topics from geometry to word problems. These explanations are illustrated with interactive graphs and several solution methods. 

This math problem solver app also includes an advanced scientific calculator to facilitate your complex math calculations. Main math topics covered are: numbers and quantity, functions, algebra, trigonometry and angles, sequences, calculus, among others.

Compatibility:  iPad/iPhone , Android ;  Price:  Free, offers in-app purchases.  

6. MathPapa

MathPapa helps you solve your algebra problems step by step. More specifically, it can help you find out solutions to linear equations and quadratic equations, linear and quadratic inequalities, graphs equations, factors quadratic expressions, systems of two equations, order of operations step-by-step, and more. Simply enter your algebra problem into the calculator and click to get step by step explanations.

 Compatibility:  iPad/iPhone , Android ;  Price:  Free, offers in-app purchases.  

It’s worth noting that not all math problem solver apps are created equal. Some may excel in user interface but lack depth in content, while others could offer brilliant insights but come with a steep learning curve. So, it’s essential to take the time to explore and find the one that best fits your or your child’s needs.

On a personal note, I’d argue that these apps also offer a level of independence to learners. In my time researching educational tools, one common thread has been the importance of fostering independent problem-solving skills . These apps can be a stepping stone toward that independence, allowing students to tackle problems on their own before seeking guidance.

However, it’s important to balance this independence with guided instruction. Sometimes the intricacies of math require a human touch—a teacher’s intuition to identify where a student is going wrong and how best to guide them back on track. This delicate balance is something that we, as educators, parents, and students, need to strive for as we navigate the ever-evolving landscape of educational technology.

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Meet Med Kharbach, PhD

Dr. Med Kharbach is an influential voice in the global educational technology landscape, with an extensive background in educational studies and a decade-long experience as a K-12 teacher. Holding a Ph.D. from Mount Saint Vincent University in Halifax, Canada, he brings a unique perspective to the educational world by integrating his profound academic knowledge with his hands-on teaching experience. Dr. Kharbach's academic pursuits encompass curriculum studies, discourse analysis, language learning/teaching, language and identity, emerging literacies, educational technology, and research methodologies. His work has been presented at numerous national and international conferences and published in various esteemed academic journals.

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Best apps for advanced math

• Best Overall
• Best for Algebra
• Best for Graphing

Mathway delivers a great all-around experience for anyone who needs help to pump up their math skills. Whether you need help just finding the solution to homework problems, or you need the step-by-step directions to solve for X, it's got you covered. At its simplest, you'll get the solution to any math problem that you enter into the app, but that definitely isn't everything this app is capable of.Mathway covers math problems from basic math to linear algebra and graphing. That makes it excellent for students from high school up and through college. It's especially handy for students who tend to struggle with math in class and need more hands-on help in order to understand advanced mathematical concepts.When you jump into the app you'll first need to choose the type of math problem that you are solving. From there all you need to do is take a photo of the problem or type it in manually. Mathway will automatically solve the equation for you right there. If your answer differs from the correct one, then you can view the problem step by step to see where you went wrong. This includes an explanation of how to find the correct answer and in some cases even a graph to give you the full answer. Bottom line: Mathway is an excellent aid for anyone who wants to check their answers or who need more in-depth help to master advanced math. It covers everything from simple concepts to advanced problems and can even break everything down step by step to make sure you have a solid grasp on what you are doing. One more thing: In order to access everything Mathway has to offer, specifically step-by-step instructions for solving problems, you'll need to upgrade to the full version of the app for $19.99 a month or $79.99 for the full year.

Why Mathway is the Best

Why you can trust Android Central Our expert reviewers spend hours testing and comparing products and services so you can choose the best for you. Find out more about how we test .

Not everyone can look at math and pick it up without a problem. For some people —myself included— math can seem daunting and confusing. Trying to schedule time with a tutor can be difficult when you are working and going to school, and many teachers and professors don't have the time to devote to helping a student succeed. Mathway is able to fill in those gaps for you.

Whether you're taking a remedial algebra class or you're diving into trigonometry, the app can make sure you find the solution to your problems. With PRO, you're even able to see every step of a problem while working towards a solution. If the free version is more suited to your budget, you still get plenty of help.

Mathway will solve your problem automatically. It will also tell you the rule for solving a specific problem. While it isn't quite as awesome as getting every step along the way, it does help you to figure your way through complicated problems.

Algebra is ostensibly the beginning of college-level math. Whether you've matriculated or you're returning after years of being away, it's a fair bet that algebra will be on your course list. College Algebra aims to work as your own personal tutor while you are working your way through the semester.This app is fully stocked with tons of resources to reduce your anxiety while in math class. There are 56 practice tests to help you prep for test day, and you can take extra time by studying specific concepts, with access to concept-specific flashcards. If you need more specific one-on-one help, you can even find a tutor by inputting your zip code and subject of choice. Bottom line: College Algebra aims to be your very own pocket tutor while you are working your way through Algebra 1 and Algebra 2. It delivers a great way to find a tutor, practice specific concepts, and even prep yourself for test day. One more thing: College Algebra is just one of many apps that Varsity Tutors Llc offers. If you like the experience, you can find more apps to help you with other math courses in the future.

The days of needing a dedicated graphing calculator in order to properly graph out certain math problems are gone. Now instead of having to drop $80 on a calculator, you can download an app to get the job done, and Desmos Graphing Calculator does an excellent job of it. You can plot out equations, and sliders will allow you how to demonstrate function transformations.Desmos Graphing Calculator is chock full of features to make sure you have the ability to fulfill your every graphing need. You can plot out polar, cartesian, and parametric graphs with an unlimited number of expressions for each graph. You can see statistics, crate tables, zoom to scale axes, plot inequalities, and plenty more to boot. Best of all, you never need access to the internet in order to use all of the features. Bottom line: Desmos Graphing Calculator gives you access to everything that you need in order to successfully graph out any problem you need to solve. It's got tons of features to make sure that you don't need to purchase a dedicated graphing calculator, because it has everything you need to be successful in math class. One more thing: By creating an account, you can save your graphs, making them easy to pull up later if necessary.

There are plenty of excellent advanced math apps that are floating around the internet. What we've collected are the best apps to make sure that you are successful at what you do in math class. From graphing calculators to practising advanced concepts to having the ability to practise varying math concepts, these apps will help to make sure you grasp even the advanced stuff.

While there are other apps that can get the job done, none of them do it quite as well as the apps we've listed here. Out of all of them, Mathway does the best job of delivering everything that you need in order to become a serious math whiz and ace your next test.

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15 Best Math Apps for Kids That Engage and Boost Learning (Updated for 2023)

Written by Jordan Nisbet

Parents & Teachers

Inspire a love for math in kids with Prodigy Math.

• Adaptive Learning
• Game-Based Learning
• Parent Resources
• Teacher Resources
• Teaching Tools
• Elephant Learning Math Academy
• DoodleMaths
• Khan Academy
• Rocket Math
• Marble Math Junior
• Twelve a Dozen
• Operation Math
• Motion Math
• Math Learning Center
• Splash Math

21st century education is changing rapidly and educators around the world are having to adapt -- especially with regard to  using technology in the classroom . Naturally, teachers and parents alike are wondering:  What are the  best math apps for kids ?

Radio in the early 1920s sparked a revolutionary wave of learning with on-air classes for students within listening distance.

In 1951, videotapes set the stage for new, visually-engaging instructional methods.

The handheld calculator launched in 1972, enabling students to make on-the-fly calculations without employing  mental math practices . And now with devices like iPhones, iPads and Android tablets, the market for interactive learning experiences has boomed.

As of October 2022,  according to Educational App Store , there are an estimated 520,000 apps categorized as “Educational.”

With an endless sea of educational apps to sift through, finding the best apps that effectively build skills, engage students, and boost learning outcomes can be daunting.

To help you on your mission for quality learning apps, below are 15 of the best math apps for kids.

1.  Prodigy Math

Prodigy is a curriculum-aligned, fantasy-based math game used by more than a million teachers, three million parents, and 50 million students around the world.

It offers content from every major math topic and covers 1,500+ skills from 1st to 8th grade, as well as DoK levels one to three!

As players compete in math duels against in-game characters, it borrows gameplay elements from role-playing games (RPGs) such as Pokemon. To win, they must answer sets of math questions tailored to their curriculum and learning goals.

As a teacher, you can customize these questions to supplement class material. The game also uses adaptive learning and differentiated instruction principles to adjust the content, addressing each student’s trouble spots.

Students battle...

...and students learn!

Prodigy Math also features powerful and immediate reporting tools for both teachers and parents. From Progress Reports to Usage Reports and more, use your student or child’s data to identify where they’re excelling or struggling so you can customize the content in game for them!

I have seen many students improve their understanding of math concepts after reviewing the skills on Prodigy. My students who have the privilege of being able to access Prodigy at home show even more growth. Susan Phillips 2nd grade teacher Miamisburg City Schools

Available : Apple App Store, Google Play, Amazon Appstore, Web

Age : 5 to 14

Cost : Educators get full access for free, optional Parent Memberships starting available at $6.25/mo

2.  Elephant Learning Math Academy

This math platform guarantees children will learn a year’s worth of math in three months when they use it 30 minutes a week.

Elephant Learning’s algorithm provides real-time reports that let you know what your child is working on and how they’re progressing through the growing library of  mathematics activities .

Although they claim to be 100% compatible with all school curriculums -- because they “focus on concepts rather than procedures” -- Elephant Learning is not curriculum-aligned.

Available : App Store, Google Play, Web

Age : 2 to 16

Cost : $35/month

3.  DoodleMaths

According to co-founders Nicola Chilman and Tom Minor, DoodleMaths is like a good tutor. Its  adaptive learning technology  tailors math content based on students’ strengths and weaknesses called “7-a-day” activities.

Using the Parent Dashboard, you can see where your child is excelling and where there’s room for improvement.

Though created in the U.K., DoodleMaths is also aligned to the U.S. Common Core Standards.

Available : Apple App Store, Google Play Store

Age : 4 to 14

Cost : £7.99 per month ($9.22 USD) or £69.99 per year ($80.74 USD)

Note : We converted prices above from the British Pound to the approximate United States Dollar.

A California-based non-profit organization, the goal of CK-12 is to increase access to free and customizable open educational resources.

When a student signs up, they will gain access to a variety of free lessons in STEM subjects. Instead of sifting through traditional hardcopy textbooks, CK-12 breaks them down into easy-to-digest concepts in forms such as:

• Textual descriptions
• Video lectures
• Multimedia simulations
• Photo galleries
• Practical experiments
• Flash cards

Available : Apple App Store, Google Play Store, Web

Age : 4 to 18

Cost : Free

5.  Khan Academy

This self-described “global classroom” contains personalized learning resources for all ages, in and out of the classroom.

Khan Academy provides instructional math videos that help students build basic math skills as they walk through common math problems. Learners then complete a series of questions to test out what they’ve learned.

From practice exercises to instructional videos created by math content specialists, adaptive technology helps identify strengths and learning gaps.

Now, they’ve introduced Khan Academy Kids which they hope will “inspire a lifetime of learning and discovery.” This includes math

6.  Buzzmath

Buzzmath is a math resource broken down into three stages, based on the following age ranges:

• 6-7 years old: Beginning to discover math
• 8-11 years old: In search of lost knowledge
• 12-16 years old: Save Buzzcity

Each stage has a set of missions for students to complete, where they'll answer math questions and progress through a particular curriculum. Buzzmath is aligned with Common Core and have separate paid plans for parents and teachers.

Available : Web

Age : 8 to 14

Cost : Parents pay $20/month or $120/year, teachers and school administrators will need to request a quote

7.  Rocket Math

Complete math missions to build your own rockets and launch them into space!

Dr. Don Crawford, the original paper-and-pencil Rocket Math author, created this app to help children learn math facts in each operation.

There are 26 levels -- A to Z -- and each one has three achievements: take-off, orbit, and universe.

Any time students can’t answer a math fact in three seconds or less, Mission Control gives the problem and answer. Then you have to prove you’ve learned it.

Teachers can create an account and buy seats for their classroom. However, for parents who don’t need a plan with multiple seats and the ability to track student progress, the iOS app store has two apps:

• Add at Home  (and subtract)
• Multiply at Home  (and divide)

Available : App Store

Age : 6 to 14

Cost : $2.99/app

8.  Marble Math Junior

Marble Math Junior is designed to help kids in elementary school practice early math, mastering basic math skills like counting and addition. The game features interactive mazes where students must roll a virtual marble to the correct answer, using problem-solving skills as they go.

Marble Math Junior is pretty hands-on and might even be a fun challenge for gifted students in pre-k.

Available : Apple App Store, Google Play Store, Amazon App Store

Age : 5 to 8

Cost : Free

9.  Operation Math

Earn the latest spy gear on your quest to defeat Mr. Odd! Operation Math creates a learning adventure out of math drills -- from the streets of Paris to the pyramids of Egypt.

Kids will have access to training runs and 105 missions, each with selectable math operations and skill levels.

In case you need a refresher, there are quick reference math tables in game to help them succeed.

Age : 6 to 12

Cost : $3.99

10.  Motion Math

This adaptive game helps students master the most challenging standards from K-6.

Its creators built their instructional math games based on  growth mindset  research to help improve math fluency and conceptual understanding.

Once teachers sign up and provide students with an access code, they gain access to over 900 levels of adaptive math content, including:

• Number line
• Fractions, decimals, percents
• Word problems
• Mental math

Available : Apple App Store, Web

Cost : Free (in-app purchases of $2.99 to $29.99), free pilot for teachers (with subsequent payments)

11.  Math Learning Center

The 11 apps in The Math Learning Center are based on visual models from Bridges in Mathematics, a comprehensive PK–5 curriculum that equips teachers to fully implement the  Common Core State Standards .

Though they aren’t gamified like other math apps in this list, they provide a digital alternative to traditional flashcards and worksheets.

Their list of math apps include:

• Math vocabulary cards
• Money pieces
• Number frames
• Number pieces
• Number rack
• Pattern shapes
• Partial product finder

Available : App Store, Web

Age : 4 to 11

12.  DragonBox

Now owned by quiz app Kahoot, this group of apps covers numbers, addition, subtraction, multiplication, division, algebra, geometry and more.

According to DragonBox, their method “is a unique approach that uses motivation-based learning techniques to give children a deeper understanding of how and why things work.”

They achieve this through helping students engage with, explore, reflect on, and apply what they’re learning and practicing.

Age : 4 to 8+

Cost : Free, with in-app purchases between $9.99 to $89.99

IXL is a learning app and website that provides math exercises for students. As students complete these activities, teachers receive real-time analytics on their class' progress. They can then use this data to identify any struggle points or learning gaps.

IXL has a wide coverage of curriculum levels from pre-K to 12th grade, including in other subjects like language arts and science. The app can also be used in preparation for SATs, ideal for high school students.

Available : Apple App Store, Google Play, Amazon App Store

Cost : Memberships between $9.95 and $19.95 per month, teachers and schools will need a quote.

14.  Splash Math

While Splash Math has single-grade apps available, the All Grades version allows children to practice content from 1st to 5th grade. This way, if your child masters 2nd grade math skills, they can go on to start learning 3rd grade ones.

Curriculum-aligned with 351 math skills to be learned, this app from SplashLearn adapts to your child’s level and encourages self-paced learning.

Using their Parent Connect App, you can get notifications on progress improvement and skill completions.

Cost : Free to sign up, subscriptions available at $7.99 to $11.99 per month

15. Moose Math

Now part of Khan Academy, Moose Math is a free math app that helps kids practice basic math skills. The app follows an adventure format as kids complete 5 different activities:

• Moose Juice:  Create smoothies while practicing counting, addition and subtraction
• Paint Pet:  Paint pets by counting the number of dots
• Pet Bingo:  Solve addition, subtraction and counting problems to get BINGO
• Lost & Found:  Learn and sort through shapes and colors
• Dot to Dot:  Help the Dust Funny find his way home by joining the dots

Moose Math is mostly aimed at younger students, particularly those just starting elementary school or in early learning. All questions shown in Moose Math align with Common Core standards, including on skills like counting and geometry.

Available : Apple App Store

Age : 2 to 7

Cost : Free, with optional donations

How to choose the best math apps for kids

So, you’ve checked out the best math apps for kids but are still unsure which one to use. We understand how challenging it can be to choose the right one.

If you’re in that boat, check out the  nine qualities you must assess when choosing math software :

• Teacher control
• Adaptivity and differentiation
• Curriculum alignment
• Data actionability
• Ease-of-use
• Training and support
• Student engagement

The guide above will walk you through those qualities in detail, ensuring you make the best choice for your students or children as possible!

Want to motivate your child to learn more math?

Our Membership  is a great way to help encourage your child to practice — and love to learn — math!

The Best Math Apps for Kids

Math can be one of the most frightening subjects for kids in school today. 

One of the main reasons that kids find math so anxiety-inducing is that math classes build on themselves, getting more complex and difficult as time goes on and small gaps in knowledge can quickly cause big problems.

Of critical importance to math success is time and practice – some students require more and busy classrooms just can’t always give that to them, causing them to struggle with more complicated math concepts and skills. This can lead to lifelong aversions to math, which can hurt their academic success and limit their choices for future study and careers.

With today’s technology at our fingertips, there’s no reason to allow kids to suffer from math anxiety anymore. 

Properly designed math apps can help reinforce and practice math concepts,  and have been shown to help kids close critical math gaps and develop better math skills and understanding. 

With so many on the market, it can be hard to know which ones can help your student learn math most effectively. To help you find a program that’s right for your student, we’ve put together a list of some of our favorite math apps.

In a rush? Check out our choices for the best math apps for kids

A sophisticated, high tech and standards aligned personalized math learning app for kids in k-12 .

Price : from $9.95 per month

Ages: 3-18 (pre-K to 12)

Available for : Android, iPad, iPhone, PC/Mac

In-App Purchases : No

In-App Advertising: No

Subjects Taught other than Math : Language Arts, Spanish, Social Science and Science

What We Like

But Be Careful

IXL is a personalized, online subscription-based learning platform for students pre-K-12. Available both on desktop and mobile, it covers a variety of subjects from Math to Social Science. 

That said, due to most students’ fear of the subject, the largest amount of content in IXL is Math. In fact, with IXL there are thousands of skills and topics to work on for each grade, even at the lower grades, covering all K-12 math topics in a very comprehensive and standards-aligned manner.

Beyond the sheer amount of math content, at its core IXL is all about personalized learning and skill development. 

IXL’s technology is driven by adaptive technology that helps build a personal learning experience in real time, called the Continuous Diagnostic tool.

As students work on various math topics, the software offers progressively harder or easier practice questions and lessons to hone in on and improve the student’s actual skill and knowledge gaps.

It doesn’t just let them sink or swim either. 

If a student answers a question wrong, the program offers ample on-screen, written step by step explanations of the question, helping them learn the underlying concepts more effectively and help them succeed on that kind of question in the future. 

Additionally, under every skill question IXL also offers recommendations of supporting skills that a student can work on if they’re having a problem with a particular concept. These range from supporting concepts in math to associated math skills that can help boost performance,  and these recommendations are uniquely tailored to the student based on their real time use of the program. 

If this seems like a lot of pressure, IXL does take some of the pressure off by offering kids virtual prizes for meeting certain goals, gamifying the experience and encouraging practice.

On mobile apps, fairly sophisticated handwriting recognition picks up handwriting so users can answer questions directly in the app, and it works pretty well overall, even for students with less than clear handwriting. 

Finally, parents keep track of student progress through fairly sophisticated analytics and progress tracking.

These tools give parents a sort of birds-eye view of what their kids are up to and how they’re doing with the app, such as by letting parents see the students scores for every particular skill for each topic and, at a glance, gives parents a more granular understanding of a child’s mastery of subject material.

To learn more, read our full review of IXL 

Bottom Line: 

IXL is an extremely well-organized and easy to access math learning app that creates a highly personalized learning experience for kids. Using powerful adaptive technology, it can be highly effective at helping students hone in on and target specific math skill gaps through focused practice and step-by-step explanations. 

Thinkster Math 

A math app for kids that combines intensive and personalized math help with live coaching and tutoring.

Price : from $75 per month

Ages: 5-18 (K-12)

Subjects Taught other than Math : No

Thinkster Math is a browser-based math app that specializes in improving math skills with focused and personalized practice for K-12 students. 

Unlike most other math apps out there, Thinkster Math uses a hybrid teaching curriculum that gives subscribers access to both a self-paced online learning program and (for gold plans and up) access to online math tutoring.

When signing up for Thinkster Math, students are given a skills assessment, which forms the basis of a personalized learning plan and is given by one of the company’s academic advisors. 

Based on the results of this assessment, students are given a customized learning plan with practice material and helpful video tutorials to work with, a self-paced system that is then supplemented by one-on-one coaching and even tutoring from the company’s network of qualified educators. 

Curriculum-wise, Thinkster Math is Common Core Standards aligned, and covers all K-12 math, from counting and objects/shapes in kindergarten to Algebra 1 & 2, Geometry and Calculus at the high school level.

Interestingly, it is also fairly different from most other math apps and programs out there in that it is based on the Singapore Math Method. This math teaching method is quite streamlined, focusing more on mastering fewer concepts at a time, but in more depth, than other methods of teaching math. 

The Singapore method is known for being highly effective at rapidly developing and improving math skills in students. It emphasizes problem solving and “thinking through” math problems, which is quite good for teaching “non-math” students, and includes a lot of visual diagrams and aids to help reach students with differently learning styles. 

One thing that stood out to us as being pretty interesting from an educational perspective is that the app uses advanced technology to detect and playback student writing.

 As students work on math problems (and show their work), their coaches and tutors can actually see their thought process in real time, giving them a more complete picture of the students abilities and skill level, rather than just relying on a percentage of right or wrong answers. 

To keep things interesting and engaging, kids earn points for completing worksheets and assignments and can even compete on an online leaderboard to see who has the most math points. Interestingly, students can even win real life gift cards for stores such as Apple and Amazon cards that can be used to buy real items they may want. 

Pricewise, starting at $75 a month, Thinkster Math is somewhat expensive but you do get a lot for your money. 

The app has built-in powerful and easy to use real-time analytics so parents can get insight into their students math skills and keep track of progress, it provides tons of content – well over 100,000 math worksheets, games, video tutorials and word problems on offer, and if you consider that good quality math tutoring and coaching begins around $40-50 per hour, we do think it represents good value.

To learn more, read our full review of Thinkster Math

Guided by custom-built learning plans, tailored to student goals and supplemented by as-needed online tutoring, Thinkster Math goes beyond most other math apps for kids out there and is an effective and complete option for those looking for math help and who can also benefit from math tutoring.

ABCmouse Early Learning Academy

A math app that’s specifically designed for kids under 8.

Available for : Android, iPad, iPhone, PC/Mac (through web browser)

Subjects Taught other than Math : Math, Reading and Language, Art, Social Science/Science

Originally Designed with the help of experienced educational professionals, ABCmouse’s popular Early Learning Academy app and website is a colorful, engaging and effective way to help kids from pre-K to 2nd grade develop better numeracy, arithmetic and math skills.

Recognizing the challenge of reaching younger students, ABCmouse takes creating an engaging and meaningful environment quite seriously

ABCmouse is centered around a cute virtual cartoon “classroom” and a customized, learning path (represented by an actual, cartoon path through various environments). Through these environments, ABCmouse takes young kids through essential math development in a step-by-step, logical manner that is filled with fun books, songs, puzzles, and games. 

All told there are 9,000+ individual learning activities and over 850 lessons, as well as 10 separate learning levels that can be adjusted depending on your child’s level.

In terms of math skills, while the program is not Common Core aligned, it does run through everything a child in pre-K to 2nd grade should need to know, such as numeracy, addition and subtraction, shapes, patterns, measurements, base ten system, 3D shapes and more. 

Underneath an attractive and crisply animated 2D world and adorable virtual cartoon classroom, however, is a well made and well designed educational app that provides an enormous amount of educational content specifically designed for young kids. 

ABCmouse uses a great deal of interactive and multimedia content that are built into the program to teach subject matter, with tons of songs, animations and fun stories as well as some pretty fun math games that kids can play to master the basics. 

In addition to making the app more engaging for younger kids, the variety of content makes ABCmouse very amenable to different learning styles.  

Whether your child learns better through listening and song, by observing and watching, by doing puzzles and reasoning or by taking a hands-on  approach, they can find content that matches how they learn best, which is really critical for early childhood learning.

To make sure kids stay interested in learning math, they can earn “tickets” as they progress along their learning path. As they earn more tickets, kids can then “buy” virtual rewards for their account that are then accessible in specific locations in the program. These are usually virtual items used to decorate their classroom, virtual fish tanks, animals etc.

Also included with the subscription to Early Learning Academy are a number of math-centric apps that can add more focused math content. Mastering math, for example, is a cutting edge math program that introduces over 30 adaptive games and over 100 new activities that can change up the difficulty level in real time to match your child’s actual skill and responses, offering a more personalized and focused math learning experience. 

Finally, parents get a good deal of analytic capability to track their kids progress and usage. There is also the possibility of purchasing an Assessment Center add-on. 

An excellent supplement to the built-in progress tracking, it allows parents to assess their kids skills in math through a variety of short quizzes that have been developed in collaboration with the University of Chicago.

This can help parents get a better understanding of their child’s learning progress, finding areas of strength and finding where kids need more help so that both students and parents can focus their effort and time to where it’s more needed. 

To learn more, read our full review of ABCmouse

Designed around the needs and interests of young kids, ABCmouse is a safe, content-rich and effective way of introducing them to numeracy and math skills in an entertaining and engaging manner. All this makes it a rather unique and extremely useful supplementary math app for kids ages 2 to 8.

Math App for Kids: Our Criteria

Math anxiety is one of the most common fears out there for students and adults alike. As such, there is no shortage of math apps for kids out there these days. Some take the form of games, hoping to hide educational material in the form of Math-Blaster like gaming experiences, while others provide full learning suites for students K-12 (and even higher). 

Generally speaking, to narrow down our list to our finalists we first examined dozens of apps, reading reviews and examining their curricula, pairing down our final selection based on the following criteria:

Obviously price is a factor when it comes to any learning software. It doesn’t really help parents or students if a math app is way too expensive for the content it offers. We looked for apps that could comfortably fit in a family budget.

That said, we were more flexible with price if the app included access to content in more than one subject area, or gave parents and students more personalized or higher value educational assistance.

Engagement and Appeal

Research has shown that engaged learners are more likely to pay attention and focus on the material, and are far more motivated to work on their skill development and understanding, as well as practice higher-level critical thinking. 

Yet, when it comes to math kids, especially those who struggle with it, have a hard time finding intrinsic motivation to study and improve their performance. 

The myriad of math apps that merely focus on drill don’t really help in this matter either, in our opinion. 

That’s we looked for apps that go beyond drill and memorization, and were able to make learning more interesting and appealing to kids through games, visual stimulation, relatability and more.

Comprehensiveness

Because developing proper math fundamentals is often the key to improving math success we went beyond simple math drill programs, looking at math apps and programs that were far more comprehensive in scope, offering full-suite learning rather than focusing on one area of math, for example. 

Having a well-balanced curriculum that touches on all the K-12 math topics is highly valuable as it can act as a general math supplement, giving students the opportunity to access and work on as many different skill sets and math concepts as they need, even giving them the ability to go backwards or forwards in grade level as needed. 

Cross device accessibility.

In today’s world learning can and should take place anywhere a student feels comfortable, be it their bedroom or a coffee shop. 

Similarly, not every family has a dedicated device for every student and and sometimes students have to make room for others, taking their learning from a tablet to a laptop/desktop, or vice versa.

For these reasons, we looked for apps that are supported on the many various platforms found in households, such as tablets, smartphones and desktops/laptops.

Can Math Apps Really Help Kids Learn Math?

When it comes down to it, one of the more fundamental questions parents have with math apps for kids is…well, do they really work?

The answer is that yes, when combined with a well-rounded and thought out curriculum, math apps can help kids develop a strong foundation of numeracy, math and problem solving skills.

This is particularly true when these apps go beyond rote memorization and drill and create more meaningful and deeper learning by integrating math learning and practice into entertaining, interactive and interesting content.

Interactive math apps have actually been found to reduce cognitive demand, making practicing math far less stressful and demanding for struggling students

Apps with animated graphics, fun audio and interactive learning also can make learning multisensory, engaging kids with different learning styles.

Math apps can also be effective by letting students work at their own pace and by providing immediate (and sometimes amusing) feedback to prevent frustration and gently moving the student in the right direction. 

Finally, when combined with adaptive algorithms, math apps can provide an individualised and targeted form of learning and math practice, letting kids and parents hone in on certain skills that need improvement rather than simply reviewing an entire topic. 

About the Author

David Belenky is a freelance writer, former science and math tutor and a tech enthusiast. When he’s not writing about educational tech, he likes to chill out with his family and dog at home.  

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Mental Math & Times Tables 4+

Multiplication flash cards ‪‬, peter schmidt.

• 4.7 • 264 Ratings
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Become a mental math genius - start to practice now! FastMath will turn you into a math genius in no time! It's the ultimate way to master solving math problems quickly in your head. Perfect for students, professionals, brain training, or just for fun, FastMath offers a wide variety of exercise types, number types, and difficulty levels to improve your math skills. Discover the power of mental arithmetic with these fantastic features: - Race against time with standardized tests to evaluate your performance level - Set high scores to motivate and challenge yourself - Compete with friends on leaderboards to achieve math supremacy - Discover cool math tricks for lightning-fast problem solving - Trainer offers maximum flexibility with different number and exercise types - Monitor your progress and statistics to improve daily - Addictive challenges help you develop a lasting habit - Earn unique achievements the more you practice Supported number types: - Natural numbers - Decimal numbers - Giant numbers Supported exercise types: - Addition - Subtraction - Multiplication - Division - Squares - Square roots - Fractions - Percentages - Modulo Join thousands of learners, parents, schools, and teachers around the world who love FastMath! If there's something we can improve, or if you need help, contact our support team: [email protected] Terms of Use: https://www.apple.com/legal/internet-services/itunes/dev/stdeula Privacy Policy: https://www.fastmath.app/privacy

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We continuously improve FastMath to enhance your mental math skills. In this update, we've added new features and optimized performance to keep you swift in pursuing personal best times. Enjoy FastMath? Please consider leaving a review on the App Store. For questions or feedback, reach out to [email protected]

Ratings and Reviews

264 Ratings

If you’re struggling with your mental math, use this.

After just one week I already noticed my abilities improve. It was frustrating that I used to be really good at it, but since I’ve had little practice in recent years, my skills have diminished. This app is clear and straightforward. You can get started immediately improving your math skills. Definitley recommend!

Developer Response ,

Thanks for sharing! We are happy to hear that you like Fast Math and are incredibly motivated to see that it helps you improve your mental math skills. We hope you’ll improve even further :)

Great for keeping skills sharp

Tried multiple apps (free version for all) and this was the most functional and easy to use. Thinking about upgrading to pro to use the trainer mode.

Thanks for the great feedback, we really appreciate it!

Multiplication helper

This is really good for multiplication and adding especially since you get to pick which level you’re on I don’t like that there’s a bunch of in app purchases. it is also a little glitchy when you are trying to answer the question you answer it and it stops and waits but it’s a really good multiplication, adding helper. It really helps every skill I have in math and it strengthens my grades.

Hi and thanks for your review! We are happy that you like FastMath and that it helps you to improve your mental math skills :) As for the glitches you mentioned: We will try to make sure to squash any bugs that might negatively affect the performance of the app … so keep an eye out for future updates.

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I know I'm not the only one who feels just a tad less guilty about extra screen time for my kids when they're engaged with an app that is helping them learn. Having a folder of problem-solving game apps for kids lets them exercise their minds and stretch their imaginations instead of just zoning out like they do while watching endless unboxing videos. (Although, I admit, those videos are oddly fascinating.)

Educational apps for kids aren't necessarily hard to come by and your kids likely already have a few that they love. However, these games will help kids hone in on specific problem-solving skills in various forms to keep their minds sharp and give them the chance to learn new things. The American Academy of Pediatrics (AAP) recommends kids engage with apps that "require more than 'pushing and swiping,'" which these 15 problem-solving game apps certainly do.

Strategy and planning are key components to solving any problem, so it is no surprise that all of these games help to make these concepts come to life for kids in a way that is fun and engaging. STEM-forward games engage physics and engineering to help kids create and invent to solve mechanical and structural problems, while traditional puzzle games allow kids to use their strategical skills to put together digital riddles.

The problem-solving power of puzzles cannot be overstated, and apps like Tozzle bring practice of this skillset right to your toddler's digital-loving fingertips. Instead of tripping over a pile of puzzles in your child's floor and risking losing critical pieces, let them explore the 40+ puzzles available on Tozzle. Designed for kids from toddler through early elementary, Tozzle's puzzles range in complexity so there is truly something for every kid.

Cut The Rope

My own kids adore playing this game. The goal of the game Cut The Rope is to feed a cute little monster named Om Nom as much candy as you can. The trick though is that to feed him, you must strategically cut a rope that the candy is hanging from so that it drops in Om Nom's mouth, dodging obstacles along the way. It's actually harder than it looks and requires quite a bit of critical thinking. Best suited for kids ages 4 and up, I have played this one myself a time or two, and it is actually entertaining and engaging for adults as well.

What do you get when you combine the physics of water with puzzles? The problem-solving app Busy Water . Kids can use their critical thinking skills to use pipes, wheels, blocks, and paddles to help Archie the fish find his way out of the open water and back into his fish tank. Aimed at children ages 6 to 10, this app will help engage children's creativity, as well as stretch their cognitive ability and reasoning skills.

Laugh & Learn Shapes & Colors

Even babies and toddlers can learn through simplistic problem solving apps. Designed for babies ages 6 months and up, this app by Fisher Price features a baby and toddler-friendly design with bright colors and simple shapes to sort. Two levels of play allow babies and toddlers to learn through tapping or tilting the screen to move the shapes and hear their names.

Mystery Math Town

Older kids who could benefit from brushing up on their math skills can do exactly that while enjoying the problem-solving app Mystery Math Town . The app engages kids in a mission to help a friendly ghost rescue fireflies hidden within Mystery Math Town by using math skills like addition, subtraction, multiplication, and division to unlock passages and enter rooms. The app is customizable to fit your child's specific math needs, but recommended for kids aged 7 and up.

Savings Spree

As an adult, I can confidently say that money can sometimes causes big problems that must be solved. Let your kids learn how to mitigate money issues before they get their hands on the real thing with the Savings Spree app . Kids ages 7 and up can practice problem solving skills related to money by engaging in the game show-style format of this game, choosing when to spend, save, invest, or donate their virtual money.

Inventioneers

For kids who love to experiment and invent new things, the Inventioneers app allows them to do so in a digital way. Kids ages 4 and up can build with 50+ objects and tools that utilize physics and engineering to create inventions that solve problems for the three fun Inventioneers characters working within the app.

Where's My Water?

This Disney app allows your kids to practice their problem-solving skills while also bringing attention to the global issue of clean water access. In Where's My Water? players must cut through dirt and manipulate pipes to deliver clean water through a sewer system to Swampy the alligator. Additional scenarios to solve involve creating steam to power another alligator's musical instrument and clearing algae from a picky alligator's plate.

Winky Think Logic Puzzles

The logic puzzles included in the Winky Think app start out easy, but get increasingly harder as the levels progress. From matching shapes and colors, to twisting and switching objects to maneuver through puzzles, each game encourages players to use reasoning skills as they work through each level. The lower levels of the app are best suited for kids around age 5, but older kids and teens can work through the low levels quickly and be challenged through 180 levels.

Shiny Picnic

The Shiny Picnic app provides engaging and fun game play for toddlers and preschoolers to practice their problem-solving skills. Kids can sort and match objects like fruits and vegetables by color, following along with the game's fun animal characters as they help the crew pack for and set up picnics.

'The Cat In The Hat' Builds That

If your kids love The Cat In The Hat , this PBS Kids app will help them hone in on problem-solving skills right alongside their favorite feisty feline. Kids can engineer their own creations to help solve dilemmas using physics and scientific concepts. Preschoolers will love this fun and easy-to-explore app set in a backyard where The Cat In the Hat and friends build tree houses, playgrounds, and more.

When you combine STEM concepts with traditional logic games, you get a game that kids can truly get lost in while learning about engineering, physics, and mechanics. Kids ages 3 to 8 can help the adorable monster creatures in the app Thinkrolls make their way through obstacle courses by manipulating objects to clear paths and trying different methods to finish the game.

Cyberchase 3D Builder

This app from PBS Kids uses geometry and three-dimensional shapes to help take traditional puzzle games to the next level. Kids ages 6 and up are tasked with using shapes to re-build the city of Botropolis after it is accidentally zapped by Delete and Buzz from the classic Cyberchase game .

The Zoombinis app is a recreation of the classic '90s computer game Logical Journey of the Zoombinis , which stars tiny blue creatures attempting to journey home. In this app, kids will solve logic puzzles that engage analyzation skills, pattern creation, and more within each level in order to unlock each additional level until the Zoombinis complete their travels and wind up back at home.

Tami's Tower

The Tami's Tower app allows kids to use their problem-solving skills to build towers that help Tami the tiger reach fruit to eat. Created by the Smithsonian Institute , the game takes basic engineering predicaments and allows kids to stretch their minds to create solutions to those problems by stacking and manipulating objects.

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Raising Early Achievement in Math With Interactive Apps: A Randomized Control Trial

Laura a. outhwaite.

1 School of Psychology, University of Nottingham

Marc Faulder

2 Burton Joyce Primary School, Nottingham

Anthea Gulliford

3 School of Psychology, University of Nottingham

Nicola J. Pitchford

Funding: This work was supported by the Economic and Social Research Council [grant number ES/J500100/1], and a research grant from the School of Psychology, University of Nottingham. The not-for-profit app developers, onebillion , donated the software free of charge to the participating schools. None of the authors have a financial interest in onebillion .

Improving provision and raising achievement in early math for young children is of national importance. Child-centered apps offer an opportunity to develop strong foundations in learning math as they deliver one-to-one instruction. Reported here is the first pupil-level randomized control trial in the United Kingdom of interactive math apps designed for early years education, with 389 children aged 4–5 years. The original and rigorous research design disentangled the impact of the math apps as a form of quality math instruction from additional exposure to math. It was predicted that using the apps would increase math achievement when implemented by teachers in addition to standard math activities (treatment) or instead of a regular small group-based math activity (time-equivalent treatment) compared with standard math practice only (control). After a 12-week intervention period, results showed significantly greater math learning gains for both forms of app implementation compared with standard math practice. The math apps supported targeted basic facts and concepts and generalized to higher-level math reasoning and problem solving skills. There were no significant differences between the 2 forms of math app implementation, suggesting the math apps can be implemented in a well-balanced curriculum. Features of the interactive apps, which are grounded in instructional psychology and combine aspects of direct instruction with play, may account for the observed learning gains. These novel results suggest that structured, content-rich, interactive apps can provide a vehicle for efficiently delivering high-quality math instruction for all pupils in a classroom context and can effectively raise achievement in early math.

Educational Impact and Implications Statement

In a pupil-level randomized control trial we evaluated the effectiveness of a new math app intervention to support young children’s early math development. The results showed children using the math apps either as a supplementary intervention or instead of a small group teacher-led math activity made significant learning gains in comparison with children receiving standard practice only. This study suggests high-quality math apps can be used as a form of quality math instruction in a well-rounded curriculum to raise achievement in early math for all children.

Raising achievement in mathematics is an issue of national importance. In the United Kingdom (U.K.) attainment in early math has been shown to lag behind attainment in early literacy within the same group of children, revealing a significant discrepancy in the development of these two domains in the first year of formal education ( Department for Education, 2016 ; Pitchford, Papini, Outhwaite, & Gulliford, 2016 ). In part, this may be because of the provision of a phonics-based literacy intervention in all elementary schools in the country ( Department for Education, 2010 , 2016 ), whereas a similar strategy for mathematics is not currently implemented. However, developing a strong foundation in early math skills is vital for children’s later educational success ( Duncan et al., 2007 ; Geary, 2011a ) and economic, health, and employment outcomes ( Reyna, Nelson, Han, & Dieckmann, 2009 ). In response, recent research and policy calls for a greater focus on learning math at the start of school ( APPG, 2014 ; Ofsted, 2018 ; Pitchford et al., 2016 ) through effective, efficient, and evidence-based interventions to support early math development and raise math achievement ( Butterworth, Varma, & Laurillard, 2011 ; Jordan & Levine, 2009 ).

Math Development

Math development requires the acquisition of different component skills and processes that range in level of difficulty ( Goswami, 2006 ; Holmes & Dowker, 2013 ). Components of math knowledge can be grouped into four broad categories: factual knowledge (e.g., number bond combinations and properties of shape and patterns) and conceptual understanding (e.g., identifying and applying mathematical procedures), which both encompass basic math skills. In contrast, mathematical reasoning (e.g., making deductions and inferences from mathematical information), and problem solving (e.g., combining and applying different areas of mathematics to solve a problem in a specific context) reflect higher-level mathematical skills that require the application of basic math knowledge to find a solution ( Rutherford-Becker & Vanderwood, 2009 ; Thurber, Shinn, & Smolkowski, 2002 ). Research shows the acquisition and automatization of basic math skills facilitates higher-level mathematical development ( Codding, Archer, & Connell, 2010 ; Gersten & Chard, 1999 ; Mayfield & Chase, 2002 ; VanDerHeyden & Burns, 2005 ). For example, longitudinal research shows early factual and conceptual knowledge, including, number bond combinations, counting, pattern knowledge, and calculation ability predict more complex skills, such as problem solving later in development ( Björn, Aunola, & Nurmi, 2016 ; Fuchs et al., 2006 ; Rittle-Johnson, Fyfe, Hofer, & Farran, 2016 ). In contrast, poor fluency in basic math skills is shown to be commonly associated with mathematical difficulties ( Geary, 1993 ; Jordan, Hanich, & Kaplan, 2003 ). Together, this evidence supports theories of cumulative learning that propose the mastery of basic math facts and concepts are an essential foundation for the acquisition of more complex math skills ( Gagné, 1968 ). It emphasizes the vital, foundational role of strong basic math skills in successful mathematical development.

However, many children struggle to acquire basic math facts and conceptual knowledge ( Geary, 2011b ), which makes them vulnerable to persistent underachievement throughout their education ( Duncan et al., 2007 ; Jordan, Kaplan, Ramineni, & Locuniak, 2009 ). Efficiency in basic math skills can be facilitated through targeted practice, which emphasizes task repetition for effective skill acquisition ( Daly, Martens, Barnett, Witt, & Olson, 2007 ; Imbo & Vandierendonck, 2008 ) and direct instruction ( Chodura, Kuhn, & Holling, 2015 ; Kroesbergen & Van Luit, 2003 ; Swanson & Hoskyn, 1999 ), which is characterized by deliberately sequenced small units of information taught explicitly ( Kirschner, Sweller, & Clark, 2006 ). Intervention studies show that individualized training that places the child at the center of their learning with learning activities that incorporate targeted practice and direct instruction can enhance the development of targeted basic math knowledge and generalize to other more complex math components not included in the intervention ( Fuchs et al., 2009 ; Kidd et al., 2013 ; van der Ven, Segers, Takashima, & Verhoeven, 2017 ). This evidence provides further support for theories of cumulative learning ( Gagné, 1968 ) and the importance of developing a strong foundation in basic math skills. It also suggests well-designed individualized early interventions that include targeted practice and direct instruction are needed to provide all children with the necessary learning opportunities to develop a strong foundation in math ( Stacy, Cartwright, Arwood, Canfield, & Kloos, 2017 ). Such approaches may be particularly beneficial in the first years of schooling ( Clements, Baroody, & Samara, 2013 ) when children show the fastest rates of math development ( Hill, Bloom, Black, & Lipsey, 2008 ).

App Technology

Educational math apps delivered on touch-screen tablets offer an opportunity for individualized math practice targeted to children’s needs. Apps that are grounded in learning science theory ( Hirsh-Pasek et al., 2015 ) and incorporate the principles of universal design and play ( Burgstahler, 2012 ) can provide a blended learning approach ( Naismith, Lonsdale, Vavoula, & Sharples, 2004 ). Specifically, apps that embody the principles of active, engaged, meaningful, and socially interactive learning with a specific learning goal ( Hirsh-Pasek et al., 2015 ) can combine benefits of direct instruction ( Kirschner et al., 2006 ), for example, feedback, repetition, and rewards with features of free play ( Gray, 2015 ) particularly, self-regulation and control. This can help provide an efficient child-centered but scaffolded learning environment ( Mayer, 2004 ; Mayo, 2009 ) tailored to individual needs ( Slavin & Lake, 2008 ) enabling individualized and structured instruction ( Gulliford & Miller, 2015 ) without additional, time-consuming, teaching demands ( Hilton, 2016 ; Kucian et al., 2011 ).

Educational apps delivered on touch-screen tablets are also particularly suited for young children, because they typically find them motivating ( Flewitt, Messer, & Kucirkova, 2015 ) and intuitive to use ( Cooper, 2005 ). Touch-screen tablets are mobile, light weight, and do not rely on dexterity-based motor skills that are needed to use a computer keyboard or mouse ( Kucirkova, 2014 ). Furthermore, access to mobile devices in educational settings is increasing. For example, in the United Kingdom, 70% of elementary schools have access to touch-screen tablets ( Clarke, 2014 ).

Previous Research

Despite the prevalence, popularity, and potential benefits of using app technology to support math development, the current evidence-base is fragmented ( Haßler, Major, & Hennessy, 2015 ) and suffers from a paucity of rigorous scientific investigations ( Cheung & Slavin, 2013 ). Concerns have also been raised about the impact of technology based screen time on early child learning and development ( Greenfield, 2015 ; Palmer, 2007 ; Sigman, 2012 ). To evaluate the impact of app technology in educational settings, practical and high-quality research is needed ( Cheung & Slavin, 2013 ) and should focus on the quality of the educational app content ( Blum-Ross & Livingstone, 2016 ; Falloon, 2013 ).

Emerging experimental evidence demonstrates the effectiveness of different high-quality math apps with early years pupils in a classroom setting ( Outhwaite, Gulliford, & Pitchford, 2017 ; Pitchford, 2015 ; Schacter & Jo, 2016 , 2017 ; van der Ven et al., 2017 ) and increasing time spent on learning math through using educational apps at home positively benefits children’s achievement in school ( Berkowitz et al., 2015 ). All of the math apps evaluated in these studies were grounded in evidence based learning theory, embodying the principles of active, engaged, meaningful, and socially interactive learning with a specific learning goal ( Hirsh-Pasek et al., 2015 ). Common features in these apps include explicit instruction, repetitive and cumulative training in mathematical concepts, immediate feedback, challenge and early reward, and individualized, self-paced learning, which are important components of effective math interventions ( Baker, Gersten, & Lee, 2002 ; Fuchs et al., 2008 ; Gersten et al., 2009 ).

Current Study

Math app intervention.

The math apps at the focus of this study also include many of these features. Active learning in the math apps is fostered through the direct manipulation of virtual objects, verbal labels, and numerical representations ( Lindahl & Folkesson, 2012 ). The simultaneous presentation of auditory and visual inputs engenders multisensory learning and which has been shown to facilitate children’s understanding ( Carr, 2012 ; Pavio, 1986 ). Engaged learning is supported by immediate feedback (positive or negative) given after every interaction with the apps highlighting the potential of app-based learning for motivational enhancement ( Couse & Chen, 2010 ). Furthermore, the multitouch nature of the tablet device affords cognitive embodiment, shown to be influential in mathematical development ( Calder, 2016 ; Duijzer, Shayan, Bakker, Van der Schaaf, & Abrahamson, 2017 ). Meaningful learning through the math apps is promoted through a staged curriculum that builds on the child’s previous knowledge ( Magliaro, Lockee, & Burton, 2005 ) and extends children beyond their current ability level ( Inal & Cagiltay, 2007 ; Vygotsky, 1978 ). Moreover, the math apps include continuous assessment of knowledge acquired through the different topics taught. This engenders retrieval-based learning, shown to improve learning outcomes ( Dunlosky, Rawson, Marsh, Nathan, & Willingham, 2013 ; Grimaldi & Karpicke, 2014 ). When using the math apps children can regulate their pace of learning within their own in-app profile, which can provide effective scaffolding for pupils with differing needs and create an individualized learning environment ( Gulliford & Miller, 2015 ; Slavin & Lake, 2008 ). This can promote learner autonomy, shown to be effective for improving educational outcomes ( Morrison, Ross, & Baldwin, 1992 ). Socially interactive learning is evident in the math apps with the on-screen teacher providing demonstrations and task instructions, which children have the opportunity to repeat when needed ( Troseth, 2010 ). This can offer the efficient and effective delivery of one-to-one instruction, which has been shown to be an important component of math interventions ( Holmes & Dowker, 2013 ).

Despite recent progress in the emerging evidence base for the effectiveness of educational apps to support the acquisition of early math skills, two important questions still need to be addressed: (a) how are the math apps most effectively implemented in a classroom setting compared to standard instructional practice? (b) Which components of math development are supported by the math apps?

Effectiveness and Implementation

First, there is a need to understand how educational apps are best implemented in a classroom setting. Typically, researchers have implemented app-based interventions (e.g., Schacter & Jo, 2017 ) as a supplementary teaching aid, in addition to standard math practice (e.g., Berkowitz et al., 2015 ). This entails greater instructional time on learning mathematics compared with the comparison groups, rendering it difficult to disentangle the effects of the intervention from the effects of extra time learning math ( Foster, Anthony, Clements, Sarama, & Williams, 2016 ; Ginsburg & Smith, 2016 ). To address this threat, experimental study designs need to include a time-equivalent control group (e.g., Holmes & Dowker, 2013 ). Furthermore, it is critical that teachers implement the intervention, to ensure high ecological validity and to support the generalizability of the intervention beyond the research context ( Clements, Sarama, Wolfe, & Spitler, 2015 ). To address this issue in the current study, two forms of teacher-based implementation of an educational math app intervention were compared to standard math practice. As illustrated in Table 1 , children in Group 1 (treatment) used the math apps in addition to all other standard math activities and so had increased exposure to math instruction. In contrast, children in Group 2 (time-equivalent treatment) used the math apps instead of a daily small group-based math activity, so time spent learning math was equivalent to the children in Group 3 (control) receiving standard teacher-led math instruction that included a daily small group-based activity. Thus, in the current study, all children received whole class math instruction delivered by the teacher, which was embedded into play-based learning, as is standard practice for early years classrooms in the United Kingdom.

In summary, this study asked, do children make more progress when the math app intervention is implemented by teachers in addition to regular math instruction (Group 1) or when implemented instead of a daily small group-based math activity (Group 2) compared with children receiving standard instructional practice (Group 3)? Based on previous research ( Outhwaite et al., 2017 ; Pitchford, 2015 ), it was predicted that children who used the math apps (Group 1 and Group 2) would progress more than children receiving standard math instructional practice (Group 3), and children who received the math apps in addition to their regular math instruction (Group 1) would have the strongest learning gains.

Components of Math Development

Second, there is a need to examine which components of math development are supported by educational apps. Previous research evaluating app interventions has frequently used assessments closely aligned with the intervention content, which typically focuses on specific aspects of math knowledge (e.g., Schacter & Jo, 2017 ). Studies are required to take a broader view of mathematics and consider how educational apps support the acquisition of targeted components of math knowledge and whether this generalizes to higher-level skills. This will help elucidate how math development is supported by interactive, individualized, educational apps. To address this, the math apps evaluated in this current study primarily targeted basic math facts and concept knowledge (see Table 2 ) and a standardized assessment of early mathematical skills that comprised measures of the four components of early mathematical development outlined above was given to all children in the trial, before and after the intervention period. This enabled learning gains for each mathematical component, including targeted basic skills and higher-level knowledge not included in the intervention to be compared across the three intervention groups. Therefore, this study also asked, for each of the four components of math development, do children make more progress with the apps when used in addition to regular math instruction (Group 1) or when implemented instead of a daily small group-based math activity (Group 2) compared with children receiving standard instructional practice (Group 3)?

A pupil-level randomized control trial (RCT) was conducted to evaluate the effectiveness of a new math app intervention compared with standard math classroom practice with children aged 4–5 years, in the first year of compulsory education in the United Kingdom, known as Early Years Foundation Stage II. The study was conducted in the last 14 weeks of the school year, before the children transitioned to the next stage of education, known in the United Kingdom as Key Stage I. There were 12 participating schools across Nottingham and Nottinghamshire in the East Midlands, United Kingdom, representing a range of socioeconomic and multicultural backgrounds and relatively high levels of educational underachievement compared to other regions in the United Kingdom ( Ofsted, 2013 ). Within each class of the 12 participating schools, children were randomly allocated to one of three groups outlined in Table 1 . As randomization occurred at the pupil-level within each class, this controlled against school effects influencing results.

This three-Group RCT design allowed the effects of maturation (Group 3: control) to be disentangled from the effects of the math apps (Group 1 and 2) being investigated. Furthermore, the inclusion of two treatment groups enabled the effects of the math apps as a form of quality instruction (Group 2: time-equivalent treatment) to be differentiated from additional exposure to math instruction (Group 1: treatment). Thus, these two forms of app implementation addressed calls from previous research and policy ( APPG, 2014 ; Ofsted, 2018 ; Pitchford et al., 2016 ) by considering if an increased focus on early math should take the form of additional time learning math (treatment) or if current allocated time can be used more efficiently (time-equivalent treatment).

Children were assessed on the Progress Test in Math, level 5 (PTM5; Maths Assessment Resource Service, 2015 ), a standardized assessment of mathematical skills, before (pretest) and immediately after (posttest) an intervention period in which teachers implemented the math apps for 30 min each day across 12 consecutive weeks. The School of Psychology Ethics Committee at the University of Nottingham granted ethical approval for the study. Opt-in informed parental consent was obtained for all participating children in line with the British Psychological Society ethical guidelines. There were 85% of all available children across the 12 participating schools given parental consent to take part in the study.

Participants

The CONSORT (2010) data in Table 3 summarizes the study sample at each stage of the RCT. In total, 461 children aged 4–5 years were randomly allocated to one of the three groups. There were 153 children assigned to Group 1 (treatment) and received the math app intervention as well as all daily standard math practices. There were 152 children randomly allocated to Group 2 (time-equivalent treatment) and used the math app intervention instead of a daily small group-based math activity that is given as part of standard math practice. The remaining 156 children were assigned to Group 3 (control) and received regular math teaching practice only.

There were 452 children from the 12 schools pretested on the PTM5 ( Math Assessment Resource Service, 2015 ). Nine children were absent at pretest but were still randomized to group. Of the 452 children that were pretested, 389 children from 11 schools were available at posttest and were given the same math assessment immediately after the 12-week intervention period. In total, 63 children who were pretested did not complete the posttest; one child left school, two children were removed from the study by their teachers for reasons unknown, and 60 children were absent at posttest, including 30 children from one school because of a school fieldtrip. It was not possible to follow-up on children that were absent on the day of the posttest because posttesting took place during the last week of the school year. Table 4 details descriptive data for the final sample of 389 children.

The intervention consisted of two math apps, “Maths 3–5” and “Maths 4–6,” developed by onebillion , an educational not-for-profit organization ( www.onebillion.org.uk ). These math apps are based on core mathematical concepts in Number and Shape, and Space and Measure, covered in the Early Years Foundation Stage (EYFS) Profile ( Department for Education, 2013 ; see Table 2 ). The apps also start to introduce children to topics included in the U.K. National Primary Curriculum for Key Stage I ( Department for Education, 2014 ). The apps primarily target factual knowledge and basic conceptual understanding, for example, simple numerical operations, such as addition and subtraction. Table 2 details the topics covered in each app and how the app content maps onto the math curriculum and the components of math development.

Features of the math apps and how they map onto the principles of active, engaged, meaningful, and socially interactive learning are discussed in detail above. Overall, the apps are designed to deliver child-centered tuition through interactive picture, audio, and animation formats with clear objectives, instructions, and immediate formative feedback, consistent for all users. Children work through the apps individually with headphones, at their own pace, and have the opportunity to repeat instructions and activities as often as needed. To complete a topic, children need to achieve 100% pass rate on an end of topic quiz included in the software. The quizzes are designed to assess children’s knowledge of the mathematical concepts covered in the topic activities.

For example, in topic 1 in Maths 3–5 children are taught the concepts of sorting and matching through a range of activities involving sorting and matching different items by type, shape, size, and color. Screenshots of example activity items and task instructions for Topic 1 are displayed in Figure 1 (courtesy of onebillion ). After completing seven sets of activities, children reach the end of topic quiz that includes 10 questions from the previous activities. When children pass the quiz they are awarded a certificate and progress to the next topic.

Example item and task instructions for Topic 1, Sorting and Matching.

As shown in Table 1 children in Group 1 (treatment) and Group 2 (time-equivalent treatment) received the daily math app intervention for 30 min each day over the 12-week intervention period.

Small Group Math Instruction

Small group math instruction was consistent with the Number and Shape, and Space and Measure content covered in the EYFS Profile ( Department for Education, 2013 ; see Table 2 ). Group-based activities were delivered by the class teacher and focused on a particular mathematical concept from the EYFS Profile. Example activities were obtained through observations made during school visits by the first author. For example, shape recognition was taught by the teacher drawing different shapes on the whiteboard and asking the small group of children, “what shape am I?” Children responded by calling out the answer and receiving corrective feedback from the teacher before moving onto the next item. In an activity focused on understanding the concepts of more and less, the teacher utilized a number line visual aid and physically demonstrated “1 more than 18.” The teacher then asked the small group of children, “what is 1 more than 10?” and children responded by writing their answer on an individual mini whiteboard and showing it to the teacher. The teacher would then give corrective feedback before moving onto the next item. As highlighted in Table 1 , children in Group 1 (treatment) and children in Group 3 (control) received instruction through daily small group math activities as part of standard math practice.

Whole Class Embedded Math Activities

In the United Kingdom children in the first year of school (aged 4–5 years old) are typically taught through play. In a whole class setting teachers embed mathematical concepts from the EYFS Profile into play-based activities. Examples of whole-class activities were obtained through observations made during school visits by the first author. For example, children were introduced to the concept of volume in a water play activity with containers of different sizes placed in the wet play area. During times of free play children had the opportunity to explore which of the different containers could hold the most water. The concept of shape recognition was introduced to children by identifying shapes in their environment. In this activity children explored their classroom environment to find examples of different shapes, which were recorded on a teacher-made worksheet. Teaching staff supervised both activities to facilitate and scaffold children’s exploratory play. As shown in Table 1 all children participating in this study received this form of teacher-led embedded instruction.

Math Assessment

Children’s mathematical ability was assessed using the PTM5 ( Math Assessment Resource Service, 2015 ). The PTM5 is a paper-based, age-appropriate, standardized measure of mathematical ability, applicable for children aged 4–5 years old in the summer term of the Early Years Foundation Stage II, when this trial took place. The assessment is designed to be used by schools to track children’s progress and has been used in other evaluation studies of educational interventions ( Jerrim & Vignoles, 2016 ; Worth, Sizmur, Ager, & Styles, 2015 ). It covers a concise selection of items from the EYFS Profile ( Department for Education, 2013 ; see Table 2 ) and is independent of the math app intervention. The PTM5 assessment can be delivered to groups of pupils, but for this study the assessment was administered on a one-to-one basis, to maximize child engagement. Reliability analysis of the PTM5 assessment using a one-to-one administration procedure showed high internal consistency between pretest and posttest scores, r = .67, Cronbach’s α = .80.

The PTM5 is designed to assess the four components of math proficiency outlined in the introduction, with increasing levels of difficulty and application of mathematical knowledge, for example: (a) Fluency in Facts and Procedures using ordinal numbers and recognizing shapes (maximum raw score = 7); (b) Fluency in Conceptual Understanding measures understanding “most” and “least” and recognizing numbers of quantity (maximum raw score = 9); (c) Mathematical Reasoning assesses drawing conclusions from mathematical information (maximum raw score = 7); and (4) Problem Solving assesses making connections between different parts of math to solve a problem in a particular context (maximum raw score = 3). The total maximum raw score was 26 with no discontinuation rule; children completed all questions on this assessment.

School recruitment

A recruitment event was held through the Nottingham Apple Education Regional Training Centre to inform interested schools about the study and the math app intervention being trialed. Participating schools already had access to the required hand-held tablet device hardware (iPads). Participating schools were given access to the math apps, free of charge, by onebillion . Children were recruited through schools that agreed to participate in the study and opt-in parental consent was obtained for all participating children before study commencement.

Implementation monitoring

A teacher manual was produced to provide further guidance on how to implement the math app intervention and included full details of the study protocol to maximize consistency across all participating schools. The manual did not provide instructions for when and how mathematics should be taught in standard practice. The implementation of standard practice was consistent with national guidelines provided in the EYFS Profile ( Department for Education, 2013 ; see Table 2 ) and was at the discretion and autonomy of the teaching and senior staff, as is standard in England (The EYFS Profile is not statutory in Scotland and Wales). The first author also visited each school before the trial commenced to ensure the teaching staff were fully informed of the study protocol and had successfully embedded the math app intervention within their daily school routine. Although, school implementation timetables varied because of iPad availability and individual school routines, the first author visited all schools again during the 12- week intervention period to interview the teaching staff about their experiences of the math apps, observe the math app intervention sessions and ensure intervention compliance. The small group math instruction and whole class embedded math activities were also observed to gain an understanding of standard math practice, however, systematic monitoring of implementation fidelity was not practically possible in the current study.

Group allocation

Within participating schools, children in each class were randomly assigned to one of the three groups (see Table 1 ). This controlled for potential school and teacher effects, as the apps were implemented by the usual teaching staff in the 12 participating schools to optimize ecological validity. As each participating class typically had one teacher and one or two teaching assistants this allowed all children from each class to be taught/supervised by their usual teaching staff that were known to them. To guard against selection bias, each child was given a unique study identification number by class teachers as parental consent was returned, and these were given to the first author who then randomized children to group allocation using a random number generator. This way, the researchers were blind to group allocation. Once group allocation was complete, the first author returned a list of study identification numbers for each group to each of the class teachers taking part in the trial, who were then able to match the study identification number and group allocation to individual children taking part in the study. The group allocations remained fixed throughout the study and the researchers remained blind to the correspondence between study identification number and group allocation throughout.

Assessment administration

The standardized paper-based math assessment (PTM5) was administered immediately before (1 week) and immediately after (1 week) the 12-week intervention period. A team of trained assessors delivered the PTM5 to individual children, on a one-to-one basis, in a quiet area, free from distraction, in the child’s familiar school environment. Before the assessment began, the trained assessor explained the task to the child, ensuring the child felt comfortable and explicitly asked if the child would like to take part in the assessment so as to gain assent. Because of the child’s age, verbal or nonverbal assent (using a smiley face/not smiley face response sheet) was accepted. The trained assessor then read aloud the questions from the PTM5, one at a time, and the child was required to write their response in the response booklet. Each math assessment lasted 10–15 min per child. The trained assessors were recruited from the University of Nottingham and were trained on administration by the first and last author. All trained assessors were blind to group allocation so were unaware which children had received the math app intervention. GL Assessment independently scored all of the completed assessments and was also blind to condition.

Intervention implementation

Children assigned to receive the math app intervention in Group 1 (treatment) and Group 2 (time-equivalent treatment) used the apps for approximately 30 min a day for 12 weeks. Children used the same iPad each day, as they had their own profile in the apps, which saved their progress. To support classroom organization, iPads were color coded or numbered by the teaching staff. The intervention was administered in small groups of between 10 and 15 children, depending on class size. Children worked independently through the apps, using headphones in a quiet area of the classroom, supervised by teaching staff that provided technical support and ensured children remained focused on the tasks.

The intervention was embedded into the daily classroom routine. As highlighted in Table 1 , children assigned to Group 2 (time-equivalent treatment) used the intervention while the other children received a small group-based math input activity. This ensured children in Group 2 (time-equivalent treatment) received the same amount of time on math education as Group 3 (control). Children assigned to Group 1 (treatment) used the intervention at a different time during the school day, for example, during free play sessions, so as not to miss out on core subjects, such as phonics. Despite being implemented during free play, children were supervised and instructed to use the math apps by teaching staff; it was not an optional activity, as is sometimes conventional in free play. As such, children in Group 1 (treatment) had more exposure to math instruction over the 12-week intervention period. At the end of the study, the participating schools continued to have access to the math apps, so the apps were available to all pupils.

Preliminary Analyses

Standardized norms for the PTM5 are based on group administration ( Maths Assessment Resource Service, 2015 ) but as this study used one-to-one administration to maximize child engagement standardized scores were not considered appropriate. Instead, raw scores on the PTM5 were used as the dependent variable. A one-way analysis of variance (ANOVA) showed no significant age differences across the three instruction groups, F (2, 386) = 1.03, p = 0.358, confirming it suitable to use raw scores. There were also no observed gender differences across the three groups, χ(2) = 2.25, p = .324. Despite making directional hypotheses that the math apps would be more effective in supporting the development of early mathematical skills than standard classroom practice, all analyses are reported at a two-tailed level of probability, unless otherwise stated.

To establish which form of implementation of the math app intervention was the most effective compared to standard classroom practice in supporting the acquisition of early math skills and to account for minor differences in pretest math ability across the three groups (see Table 5 ; Van Breukelen, 2006 ), mean math performance for each of the three groups (see Table 5 ) was compared using a 2 (Time: pretest, posttest) × 3 (Group: Group 1, Group 2, Group 3) mixed ANOVA. Results showed a significant interaction between Time and Group, F (2, 386) = 3.10, p = 0.046.

Analysis of simple main effects showed no significant differences between groups at pretest, F (2, 386) = 1.63, p = 0.197, or posttest, F (2, 386) = 0.12, p = 0.888. Over time, significant learning gains were found for Group 1 (treatment), t (125) = 10.54, p < .0001, Group 2 (time-equivalent treatment), t (130) = 8.97, p < .0001, and Group 3 (control), t (131) = 7.03, p < .0001. The largest within-group effect sizes (Cohen’s d with 95% confidence interval [CI]) reflecting the magnitude of progress were observed for Group 1 (treatment; see Table 5 ).

To explore the significant interaction further, planned comparisons with independent samples t tests and between-groups effect sizes (Cohen’s d with 95% CI; Trafimow, 2015 ) were conducted on progress made over time (difference scores; posttest minus pretest). Results showed that pupils in Group 1 (treatment) made significantly more progress over the 12-week intervention period than Group 3 (control), t (256) = 2.46, p = 0.015, between-groups effect size = 0.31, CI = 0.06–0.55. Similarly, pupils in Group 2 (time-equivalent treatment) made significantly greater learning gains compared with pupils in Group 3 (control) in line with the predictions, t (261) = 1.74, p = 0.042, one-tailed, between-groups effect size = 0.21, CI = −0.03–0.46. There was no significant difference in the progress made by Group 1 (treatment) and Group 2 (time-equivalent treatment), t (255) = 0.64, p = 0.525, between groups effect size = 0.08, CI = −0.17–0.33.

Components of Mathematical Proficiency

To examine how effective the math apps were at supporting the acquisition of the four components of mathematical proficiency (Fluency in Facts, Fluency in Concepts, Mathematical Reasoning and Problem Solving) compared with normal classroom practice, mean performance on each component for the three groups (see Table 5 ) were compared using separate 2 (Time: pretest, posttest) × 3 (Group: Group 1, Group 2, Group 3) mixed ANOVAs. Results showed no significant Time × Group interactions for any of the four components; Fluency in Facts F (2, 386) = 0.56, p = 0.570; Fluency in Concepts F (2, 386) = 2.04, p = 0.132; Mathematical Reasoning F (2, 386) = 1.37, p = 0.256; Problem Solving F (2, 386) = 1.42, p = 0.244.

This study reports the first pupil-level RCT to be conducted evaluating the effectiveness of a new math app intervention for children aged 4–5 years old in the United Kingdom. Specifically, this RCT evaluated two forms of math app intervention implementation (treatment and time-equivalent treatment) compared with a standard practice control. This is the first math app intervention study to adopt this novel and rigorous research design. The current findings are of particular significance to the provision of early math instruction and the need to raise math achievement in the early years of education ( APPG, 2014 ; Ofsted, 2018 ; Pitchford et al., 2016 ).

Math App Intervention Effectiveness and Implementation

This study found that combining child-centered, curriculum-based, apps with interactive touch-screen tablet technology for children aged 4–5 years old in the first year of school provides an effective means of delivering quality instruction that promotes the development of early math skills. Specifically, the interpretation of between-groups effect sizes based on normative expectations of change ( Hill et al., 2008 ) showed at the whole sample level, children in Group 1 (treatment) who used the math apps in addition to all normal math practices were 3–4 months ahead of their peers in Group 3 (control) receiving standard practice only (between-groups effect size 0.31). Children in Group 2 (time-equivalent treatment) who used the math apps instead of one daily regular small group math activity were shown to be approximately 2 months ahead of children in Group 3 (control) receiving standard practice only (between-groups effect size 0.21). However, there was no significant difference between implementing the math apps as well as all standard math practices or instead of one regular small group math activity. This indicates the apps are a form of quality math instruction and suggests an increased focus on early math at the class level ( APPG, 2014 ; Ofsted, 2018 ; Pitchford et al., 2016 ) can take the form of efficient instructional practices without the need for extra time learning math, which could potentially detract from other areas of a well-rounded curriculum.

Supporting Components of Math Development

When examining which components of math development are supported by the math app intervention, results showed no significant Time × Group interactions for any of the four components of mathematical proficiency. This suggests all three forms of instruction supported the four areas of math development. However, when comparing within-group effect sizes (see Table 5 ), which reflect the magnitude of progress in each group, larger effect sizes were consistently observed for children who used the math apps (Group 1 and Group 2) compared with children who received standard practice (Group 3) across all four math components. This suggests the math apps strongly support learning in the areas of math development targeted by the intervention (Fluency in Facts and Fluency in Concepts; see Table 2 ) that generalizes to other higher-level skills not extensively or explicitly covered in the app content (Mathematical Reasoning and Problem Solving). These results suggest the math apps go beyond drill-based practice for fact retrieval ( Salminen, Koponen, Leskinen, Poikkeus, & Aro, 2015 ) and help build a strong foundation in basic math skills that enables math facts and simple concepts to become automated and assimilated into a higher-level conceptualization of math knowledge ( Codding et al., 2010 ; Gersten & Chard, 1999 ; Karmiloff-Smith, 1994 ; Mayfield & Chase, 2002 ; VanDerHeyden & Burns, 2005 ). These results are consistent with cumulative learning theory ( Gagné, 1968 ) and agree with previous intervention studies that have also targeted basic math skill acquisition and demonstrated evidence of generalization to higher-level mathematical skills ( Fuchs et al., 2009 ; Kidd et al., 2013 ; van der Ven et al., 2017 ).

Theoretical Implications

Overall, these results corroborate previous research demonstrating proof of concept of this new math app intervention over a series of small scale studies ( Outhwaite et al., 2017 ) and adds to the growing evidence base demonstrating the educational benefits of app content for young children ( Berkowitz et al., 2015 ; Schacter & Jo, 2016 , 2017 ; van der Ven et al., 2017 ) in different educational contexts ( Pitchford, 2015 ). Several features of the math apps may count for their success. In particular, the math apps include features consistent with the principles of active (e.g., multisensory and direct interactions), engaged (e.g., feedback), meaningful (e.g., a staged and scaffolded curriculum), and socially interactive learning (e.g., through the on-screen teacher) as discussed earlier ( Hirsh-Pasek et al., 2015 ). The math apps also include high-quality curriculum based content (see Table 2 ; Blum-Ross & Livingstone, 2016 ; Falloon, 2013 ) and specific learning goals ( Hirsh-Pasek et al., 2015 ). Finally, the math apps draw on different instructional psychology principles, namely direct instruction through feedback, repetition, and reward ( Kirschner et al., 2006 ) and free play through the opportunity for self-regulation and learner control ( Gray, 2015 ). The combination of these app design features may account for the observed learning gains.

An interesting find was that the math app learning gains found in this study conducted in a high-income Western country (within-group effect size >0.65) were comparable with the learning gains (within-subject effect size >0.80) observed in Pitchford’s (2015) study evaluating the same math apps in Malawi, a low-income country with a history of poor child development ( Hubber et al., 2016 ) and extremely low basic math skills ( UNESCO-IBE, 2010 ). Children in Malawi used the same math apps, with instructions delivered in their local language. Although interventions are not typically considered universally effective ( Fuchs et al., 2009 ), this study shows comparable learning gains with the same math apps in two radically different educational contexts, suggesting these app design principles based on science of learning theory may be a common mechanism underpinning learning with high-quality educational app content that transcends culture.

Policy and Practice Implications

The significance of the study results also has two important implications for policy and practice. First, previous intervention research has predominately focused on low-achievers and with small sample sizes (e.g., Outhwaite et al., 2017 ; Räsänen, Salminen, Wilson, Aunio, & Dehaene, 2009 ; Schacter & Jo, 2016 ; Wilson, Revkin, Cohen, Cohen, & Dehaene, 2006 ). In contrast, this study implemented the math app intervention at the whole class level with a final sample of 389 children. This novel approach is important as typically attaining and low-achieving pupils both demonstrate difficulties acquiring early mathematical skills ( Dowker, 2005 ; Geary & Hoard, 2005 ) so high-quality app based math instruction may be suitable for all children in early education. Furthermore, it clearly addresses previous research and policy calling for instructional practices that benefit the math development of all children ( APPG, 2014 ; Ofsted, 2018 ; Pitchford et al., 2016 ) to address the “math-practice” gap ( Stacy et al., 2017 ) and close the gap in math and literacy attainment in the first year of school ( Pitchford et al., 2016 ).

Second, previous research has typically evaluated math app interventions as a supplementary teaching aid (e.g., Berkowitz et al., 2015 ; Outhwaite et al., 2017 ). The application of a three-arm RCT in this study with two forms of intervention implementation (treatment and time-equivalent treatment) compared with a standard practice control enabled the impact of the math apps to be disentangled from additional exposure to math instruction ( Holmes & Dowker, 2013 ). This novel and rigorous research design is particularly beneficial to address concerns raised in response to recent U.K. based early years educational practice recommendations ( Ofsted, 2018 ). Critiques of educational policy have argued that the early years curriculum introduces too much time spent on formal instruction, reducing opportunities for play-based exploratory learning ( Roberts-Holmes, 2015 ). This study shows the math apps were an efficient form of math instruction and shows the apps can be implemented as part of a well-balanced curriculum. It indicates the apps can capitalize on the benefits of play based learning by introducing children to math concepts in a game like format, that is interactive, engaging and child centered, but also draws on the benefits of direct instruction and targeted practice, helping to bridge the gap between formal and informal early math learning opportunities ( Evangelou, Sylva, Kyriacou, Wild, & Glenny, 2009 ).

Limitations and Future Directions

The current study adds to the mounting evidence base evaluating this new math app intervention developed by onebillion as part of a staged scaling of implementation ( Outhwaite et al., 2017 ; Pitchford, 2015 ). Blind group allocation, the inclusion of a time-equivalent treatment group and an independent standardized math assessment help to address potential threats to validity and current concerns regarding the usefulness of RCTs in educational research ( Ginsburg & Smith, 2016 ). However, there are three important limitations to consider when interpreting the results of the current study and directing future research. Further lines of research and implications for classroom practice are also discussed.

First, there were minor differences in the instructional content between the intervention treatment groups and the control group. Specifically, the math apps included a number of topics from the U.K. National Primary Curriculum for Key Stage I (see Table 2 ). This poses a potential threat to validity ( Cheung & Slavin, 2013 ; Ginsburg & Smith, 2016 ; Shadish, Cook, & Campbell, 2002 ) as children in the intervention groups had access to more advanced topics than children in the control group. However, the independent assessment measure only included a concise selection of items from the EYFS Profile ( Department for Education, 2013 ; see Table 2 ). As children were not assessed on the more advanced topics from Key Stage I, for example, odd and even numbers, the intervention groups did not have an unfair advantage over their peers in the control group in the assessment procedure.

Second, as the intervention was implemented toward the end of the first year of school, some of the higher ability children in the two intervention treatment groups may have already mastered some of the math skills covered in topics that are presented early in the apps. The revision of math content may have benefitted their learning ( Dunlosky et al., 2013 ) and boosted their confidence with the app technology. Alternatively, it may have delayed further progress within the 12-week intervention period. In contrast, children in the standard practice control group continued to work through the early years curriculum content, without this revision. To address this issue, entry-level placement strategies should be developed consistent with the curriculum and components of math development ( Kadosh, Dowker, Heine, Kaufmann, & Kucian, 2013 ) and results from future research utilizing this tool should be compared to this study to examine the impact of revision on math progress.

Third, while this study indicates the benefits of this new math app intervention for supporting the development of young children’s mathematics skills, it is important to recognize that technology alone will not lead to success; but is dependent on how the technology is integrated into the school environment ( Beach & O’Brien, 2015 ; Couse & Chen, 2010 ). Detailed qualitative research is needed, therefore, to explore insights into teachers’ perceptions and implementation of using the math apps in their classrooms. Although no main effect or interactions were found in this study when School was entered as an independent variable in the analyses reported above, understanding which school level factors may impact the success of scaling this intervention will provide important insights for recommendations for best practice in implementation. This will help drive theoretical understandings of learning with educational apps and consequently help to optimize learning outcomes for all.

Finally, this study examined the effectiveness of the math app intervention for children of all ability levels. This was in response to previous research revealing a significant discrepancy in math development in the first year of formal education and recent policy calling for an increased focus on math in the early years for all children ( APPG, 2014 ; Department for Education, 2016 ; Ofsted, 2018 ; Pitchford et al., 2016 ). However, when considering the usability of the math app intervention outside of the research context, many of the participating schools have since chosen to implement the math apps as a targeted, supplementary intervention for children struggling to acquire basic math skills. This is particularly interesting as children in this study who were statistically identified as low-achievers based on their pretest math score (≥1.5 SD below the overall group mean; Snowling, 2013 ) showed much stronger learning gains (within-group effect size 4.03, 95% CI = 1.87–6.18) when they used the math apps as well as all standard math practice (Group 1 treatment) relative to low-achieving peers who received standard practice only (Group 3 control, within-group effect size 1.25, 95% CI = −0.10–2.61). This observation raises the possibility that the math app intervention might be particularly beneficial for low-achieving young children who may require supplementary math instruction. However, these observations are based on a small sample of low-achievers ( n = 31 across all three arms of the RCT) and the threats to internal validity associated with identifying low-achievers on baseline performance ( Barnett, van der Pols, & Dobson, 2004 ) render the security of this observation very weak. Nevertheless, it is indicative for a current large scale cluster RCT evaluating these math apps as a targeted intervention for low-achieving children (identified through teacher assessments) aged 5–6 years old across 114 schools in the United Kingdom. This current efficacy trial is being delivered by the University of Nottingham and evaluated by the University of Oxford as part of an Education Endowment Foundation funded trial. The results of this large-scale trial are expected in autumn 2019.

Overall, this study shows the new math app intervention was an efficient form of early math instruction for children aged 4–5 years old in the first year of education in the United Kingdom. The results support the assertion that well-designed and theoretically grounded app content can be effectively integrated into the early years classroom to deliver efficient and effective math instruction ( Hirsh-Pasek et al., 2015 ; Kucirkova, 2014 ) for children of all ability levels and without placing additional time-consuming demands on teaching staff ( Hilton, 2016 ; Kucian et al., 2011 ). Furthermore, through enhancing the development of basic math facts and concepts with targeted practice and direct instruction, the development of higher-level math abilities, including mathematical reasoning and problem solving, can also be supported.

These findings have important implications for addressing recent research and policy highlighting the need to raise early math attainment ( APPG, 2014 ; Ofsted, 2018 ; Pitchford et al., 2016 ) as part of a well-balanced early years curriculum.

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