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28 Online Interactive Math Games Kids Will Love

K through 12 … it all adds up to fun!

Looking for fun ways to get kids to do some math practice? Try these online interactive math games! They’re perfect for at-home enrichment or homework assignments. In the classroom, use them for fast finishers, or play as a group using your interactive projector or whiteboard.

• Elementary School Online Interactive Math Games
• Middle School Online Interactive Math Games
• High School Online Interactive Math Games

Best Online Interactive Math Games for Elementary School

It’s important to spark an interest in math at a young age and build confidence in skills quickly. Fun interactive math games are a great way to do it.

Penalty Kick

What students practice: Multi-digit multiplication

The game is simple enough: Each player takes a turn kicking a soccer ball or defending the goal. When they’re successful, they get to solve a math equation for a chance at a bonus point.

Play it: Penalty Kick at Coolmath Games

Puzzle Pics

What students practice: Basic addition and subtraction

Click and drag the puzzle pieces to answer the math questions, revealing a cool picture at the end. There are multiple versions for different skills and levels, and you can change the target sums too.

Play it: Puzzle Pics at Math Playground

Bar Graphing With Eggs

What students practice: Sorting, graphing

First, move the frying pan to catch the colored eggs as they fall from the chickens. Then, sort the eggs by pattern. Finally, use the eggs to create a basic bar graph.

Play it: Bar Graphing With Eggs at Education.com

Math Baseball

What students practice: Arithmetic skills

It’s a simple concept: Students solve addition, subtraction, multiplication, and division equations, then take a swing. You can change the difficulty from easy to “super brain,” so this is a game that grows with kids.

Play it: Math Baseball at Funbrain

Practice math facts with a fun squirrel who needs your help to gather as many acorns as possible!

Play it: Going Nuts at Multiplication.com

Number Bonds

What students practice: Addition and number bonds

Choose a target sum between 10 and 20. Then, aim and shoot the center number ball at one of the balls circling the track to make the target sum. Repeat until all the balls are gone.

Play it: Number Bonds at Math Playground

Candy Cashier

What students practice: Adding up money and making change

Help the monsters in your candy shop buy candy! As each monster comes in to make a purchase, add up the cost. Then, use their money to make the appropriate payment.

Play it: Candy Cashier at Math Playground

Estimation Contraption

What students practice: Estimation and addition

Estimation seems simple, but it can give some kids real trouble. Play this simple game to get practice rounding and adding numbers.

Play it: Estimation Contraption

Coin Weighing

What students practice: Comparison, weights

Students have four chances to weigh coins to determine which one is fake. In addition to practicing weights, kids have to think carefully to solve the problem.

Play it: Coin Weighing at Math Game Time

Math Pac-Man

What students practice: Arithmetic equations

Classic arcade game meets math! You’ll have to think fast to solve the equation and eat the right ghost. Try this one in pairs with one student solving and the other moving Pac-Man as fast as they can.

Play it: Math Pac-Man at Math Game Time

Canoe Puppies

Can your puppy-filled canoe beat the others to the finish line? Solve the equations quickly to paddle your way to victory. Students practice two-digit addition with this game.

Play it: Canoe Puppies at Math Playground

Kangaroo Hop

Hop from shape to shape faster than your opponents. Students need to know both 2D and 3D shapes to master this one. Kids learn geometric shapes with this game.

Play it: Kangaroo Hop at Math Game Time

Best Online Interactive Math Games for Middle School

As math becomes more challenging, it can also become more difficult to have student engagement. Entertaining math games help students sharpen their skills without feeling like a bore.

Move Here Move There

Use logical reasoning to create a path from the dark blue tile to the green target tile. Part coding, part logic game, this one is excellent for building deductive-reasoning skills.

Play it: Move Here Move There at Coolmath Games

Orbit Integers

What students learn: Adding and subtracting positive and negative integers

Can you win the space race? Students need to solve the equations faster than everyone else in the competition to soar into first.

Play it: Orbit Integers at Math Playground

Math in Music

What students practice: Real-world algebra skills

Students always ask how they’ll use math in real life, and this game gives an example. The challenge is to adjust the music tracks so they align. First, though, they have to figure out how many beats per minute in each. How will they solve the problem?

Play it: Math in Music at Get the Math

Fruit Splat

Practice identifying prime and composite numbers with this simple game. Move the target around the screen and SPLAT the fruit matching the description.

Play it: Fruit Splat at Sheppard Software

Puppy Chase

What students practice: Decimals and equivalent fractions

Click the equivalent decimal from the fraction given. The faster you find the answers, the more you move ahead to win the race!

Play it: Puppy Chase at Math Playground

Find the Quark

What students practice: Coordinate graphing

If kids have played Battleship, they’ll recognize this game. This time, they’re looking for the Quarks hidden somewhere on the board.

Play it: Find the Quark at JLab

High-Stakes Heist

What students practice: Order of operations

Crack the safe by solving an equation, one step at a time, using the correct order of operations. If you make a mistake, you can go back to the previous step to fix it.

Play it: High-Stakes Heist at ABCYa

Algebraic Reasoning Sweet Shop

What students practice: Mental math, writing equations

Using the stacks of various candies that add up to certain amounts, determine how much each individual candy is worth. This can be done as mental math or by writing out and solving equations.

Play it: Algebraic Reasoning Sweet Shop at Math Playground

Boat Coordinates

Enter the coordinates to send the boat on its way to the finish line. Stop along the way to pick up coins but be sure to avoid obstacles. You have a limited amount of time, so think fast! This game can be customized with single-quadrant or four-quadrant boards.

Play it: Boat Coordinates at MathNook

Best Online Interactive Math Games for High School

Higher-level math doesn’t have to be all work and no play. Online math games for high school students are harder to find, but these games give students the chance to practice their skills in unique ways.

Exponents Jeopardy

What students practice: Exponents

You know the drill: Pick a category, solve the equation, earn the points. Be careful though! If you’re wrong, you can lose all the points you’ve earned.

Play it: Exponents Jeopardy at Math Play

Wrecks Factor

What students practice: Factoring quadratic equations

Ships sail onto the board and wreck, displaying a quadratic equation. Factor the equation, then click and drag the correct answer to the points on the grid that surround the boat. More boats continue to arrive, and if one sinks before you solve the equation, you lose a life.

Where to find it: Wrecks Factor at Mangahigh

Math in Fashion

What students practice: Decimals, multiplication, problem-solving

See how math plays a role in fashion design as you try to alter the design of a blouse to meet the target price. This is a fun game to play together in groups so you can see how others would make the changes.

Play it: Math in Fashion at Get the Math

Transformation Golf

What students practice: Translation and transformation in a coordinate plane

Pick a transformation and then a factor choice of that transformation to get the golf ball into the hole. Includes translation, rotation, reflection, and dilation.

Play it: Transformation Golf at Hooda Math

Sortify: Angles

What students practice: Types of angles, basic geometry

Sort the cards by dragging them into bins and placing the correct label on them. Some cards need to be linked together, like those that form complementary or supplementary angles. Submit the bins to be checked and earn points for correct answers.

Play it: Sortify Angles at BrainPOP

Math in Videogames

What students practice: Graphing on a coordinate plane

Students practice graphing linear paths on a coordinate plane with this game, and keep the spaceship from crashing into the asteroid.

Play it: Math in Videogames at Get the Math

What students practice: Geometry

While not a game per se, we love the interactive site GeoGebra for creating graphs, 3D shapes, and more. It’s a perfect way to add an interactive touch to your geometry lessons.

Where to find it: GeoGebra

Looking for more online math content? Check out our big list of the best math websites for students K-12.

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Math Playground | Fun Math Games | Free

Discover the Joys of Learning with Math Playground

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Learning mathematics can be a daunting task for many. Yet, it doesn’t have to be! Welcome to Math Playground, your one-stop destination for making math fun, engaging, and accessible for learners of all ages. Improve your math skills with our Math Playground and see what kind of fun games you can play for free!

Math Skills

At our Math Playground, we’re passionate about transforming the often-feared subject into a delightful experience. We offer a variety of interactive games and problem-solving activities designed to help children grasp mathematical concepts easily.

Gameplay Meets Math Learning on Math Playground

Our educational website platform employs a unique blend of learning and play, allowing children and adults to learn mathematics in a stress-free environment. Games on Math Playground are meticulously designed to present mathematical concepts in a playful and engaging manner.

Math Concepts

Whether it’s addition and subtraction for younger learners or algebra and geometry for the older ones, Math Playground has something for everyone.

Middle School Students

Tired of those printable worksheets? Play our features games designed for middle school students using best games math concepts. Students recommend our math playground because its the best place to go for any age. Read the sign, we dont hand out the grades you learned these basic skills as an elementary student.

Math Playground: A Platform for Every Math Learner

Math Playground is more than just a platform for learning mathematics. It’s a community of learners, educators, and parents who believe that learning mathematics can be as fun and exciting as playing a game. Here, learners can explore different aspects of mathematics at their own pace, enhancing their ability to problem-solve, think critically, and grasp complex concepts with ease.

Conclusion = Answers

At Math Playground, we aim to make every child’s math learning journey enjoyable and rewarding. Come, join us on this exciting mathematical adventure and discover a new love for learning.

Remember, at Math Playground, we turn the ‘Meh’ in Math into ‘Yay!’ So why wait? Dive into the vibrant world of Math Playground today!

In addition to these cool math games we also have word problems as word problems offer another level of cognitive growth on the math playground. What pop ups in your mind when your teacher’s class has a difficult but relevant lesson to explain whole numbers and geometry.

Kids at grade level struggle with math problem logic and logic puzzles at the math playground we aim to help children of all age or teachers. Multiplication, decimals, and fractions make solving math problems a higher difficulty level.

Security Practices

We help adjust your analytical thinking, problem solving skills, with both math word problems, logic games, data, math videos, fraction games, like a google classroom.

Our collection is an excellent tool and web site created by scientists for the student. Find out why teachers, parents, and students all around the world use the CogniFit Math Playground. Our services increase the probability you may enjoy math a bit more. Students often complain about math, break that cycle on the math playground today and have some fun!!

Download our free app with no ads – created for parents, teachers, and students of all age.

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Math Games offers online games and printable worksheets to make learning math fun. Kids from pre-K to 8th grade can practice math skills recommended by the Common Core State Standards in exciting game formats. Never associated learning algebra with rescuing animals or destroying zombies? Time to think again!

Kids learn better when they're having fun . They also learn better when they get to practice new skills repeatedly . Math Games lets them do both - in school or at home .

Teachers and parents can create custom assignments that assess or review particular math skills. Activities are tailored so pupils work at appropriate grade levels . Worksheets can be downloaded and printed for classroom use , or activities can be completed and automatically graded online .

Best of all? It's completely free! Click on any of our games above to get started.

Get updates on what we do by following us on Twitter at @mathgames . Send us your comments, queries or suggestions here .

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Usable Math

(formerly 4mality), a digital playground for math learning through problem solving and design.

Usable Math provides interactive problem solving practice for 3rd through 6th grade students learning mathematical reasoning and computation through creative writing, NoCode slideshow design, and human-AI collaboration.

• MATH MODULES

Math Friends

Featuring four coaches Estella Explainer, Chef Math Bear, How-to Hound, and Visual Vicuna who offer reading, computation, strategy, and visual strategies for solving math problems.

Estella Explainer

"I help children understand the language and meaning of questions using kid-friendly vocabulary."

Chef Math Bear

"I provide computational strategies (addition, subtraction, multiplication and division) for solving problems."

How-to-Hound

" I present strategic thinking clues (rounding, estimation, elimination of wrong answers). "

Visual Vicuna

" I offer ways to see problems and their solutions using animations, pictures, charts and graphs. "

The coaches annotate hints and provide feedback to help students with various levels of knowledge solve mathematical word problems using a wide range of strategies.

Math and ISTE Standards Based

Usable Math aims to teach mathematics concepts and problem solving skills based on the Massachusetts Mathematics Curriculum Framework and the Common Core State Standards for Mathematics. Usable Math supports ISTE Standards for Students : Empowered Learner (1.1), Knowledge Constructor (1.3), and Computational Thinker (1.5).

Open Education Resource

Usable Math is an open education resource project developed in the College of Education, University of Massachusetts Amherst. Usable Math received a 2023 classroom grant from MassCUE (Massachusetts Computer Using Educators) . An initial version called 4mality was developed with funding support from the Verizon Foundation and a grant from the US Department of Education, Institute of Education (IES).

BROWSE MATH MODULES

Storywriting, history, and science modules, a jenny-the-fisher math and citizen scientist adventure, math & science, a tai-the-math historian time travel adventure, math & history, ai-enhanced, a sofia-the-forester adventure, math & storywriting, math problem-solving and design modules, area and perimeter, total problems: 6.

Total problems: 8

Multiplication and Division

Algebraic Thinking

Total problems: 7

Measurement

Total problems: 10.

Geometry: Lines and Lines of Symmetry

Geometry: Maps + Grids + Ordered Pairs

Charts & Graphs

Geometry: Figures, Shapes and Angles

Total problems: 11

Add & Take Away

Place Value

Total problems: 14.

Total problems: 9

Total problems: 5

More coming soon, welcome to usable math. in this interactive website, you will find learning modules designed to develop mathematical problem solving skills among young learners in grades 3 to 6..

Our Modules explore standards-based math concepts including Fractions, Measurement, Geometry, Decimals, Money, and more. Usable Math is free to access using a computer, smartphone, or iPad.

What do we mean by Usable Math?

The word Usable can read as follows:

U Able meaning you can do math problem solving.

Us Able meaning together all of us can do math problem solving.

Usable meaning anyone is able to learn math problem solving - with practice, effort, and support.

What are the Usable Math Learning Modules?

Each learning module in Usable Math consists of a group of math word problems related to a specific mathematical concept. The problems are based on the Massachusetts Mathematics Curriculum Framework↗ as well as Common Core Standards↗ .

Each problem within a module consists of a question, three to four possible answer choices, and problem solving ideas and strategies provided by our four coaches: Estella Explainer, Chef Math Bear, How-to-Hound, and Visual Vicuna.

How are the Modules Displayed online?

Each module has been developed using Google Slides.

Click. Pause. Solve.

View each module in Slideshow.

How do teachers, students and families use each module?

We strive to make every module on Usable Math kid friendly . Clicking on a module from the selections on the Modules Homepage , each user controls what happens during the learning experience by clicking to open strategies and spending time thinking about them before answering the question. The goal is for students, by themselves, in small groups, or with a teacher, or a family member, to analyze and understand what the problem is asking them to solve before providing an answer.

A question appears without its answer choices or any problem solving strategies.

Click one time and Estella offers a problem solving strategy.

Click again and the Bear offers a different strategy.

Click again and the Hound presents a strategy.

Click again and the Vicuna has an additional strategy approach.

The next click gives the four answer choices, but not yet the correct answer.

The final click highlights the correct answer from among the answer choices.

Before going to the next problem, a motivational statement and gif appears offering encouragement to the users.

What is the purpose of the Motivational Statements between Problems?

Each motivational statement is intended to provide feedback and encouragement to students using the system. Following the insights of researchers into the use of praise and the development of growth mindsets in young learners, these motivational statements are designed to reward students’ effort, hard work, persistence, and belief in one’s self as a learner. We want youngsters to realize that they can learn anything with the right tools, the right beliefs, the right coaches, and their own work and practice.

Need more help? Or have a question?

Reach out to us and we will do our best to get back to you within 12 hours.

RESEARCH AND RESOURCES

We believe that every child deserves a strong foundation in mathematics. our platform is designed to provide engaging and effective math instruction to elementary school students, and we are proud to say that there is science behind the way we deliver this instruction..

UsableMath was formerly known as 4MALITY. As a result of our commitment to providing the best possible math instruction to elementary school students, we have rebranded our platform as UsableMath.com to better reflect our mission and approach to teaching mathematics.

Our platform is designed to provide engaging and effective math instruction to students in grades K-5, using a unique approach that emphasizes hands-on, problem-solving activities. We use interactive, multimedia elements such as videos, games, and simulations to help students understand key mathematical concepts and build a strong foundation of knowledge.

Math Coaches

The use of virtual coaches that provides students with personalized support and feedback, has become increasingly popular in the field of math education. Research has shown that learning companions can be effective in improving student engagement and motivation, as well as helping students to better understand mathematical concepts and build a stronger foundation of knowledge. UsableMath employs the concept of learning companions to help students succeed in mathematics. Our virtual math coaches serve as personal guides, providing students with individualized support and feedback as they work through mathematical concepts and problems. These coaches, or learning companions, are designed to be like friends or mentors, helping students to build their confidence, overcome challenges, and achieve their full potential.

How are we using Generative AI to enhance Usable Math Modules?

As developers of Usable Math, we are aware of both the educational potentials and complexities of Generative AI technologies. In our system, ChatGPT is used to support teachers and other adults to expand and enhance how math can be understood and taught in schools and homes. When you click on the AI icon, you are linked to a blog where we have recorded how AI proposes to solve selected math word problems found in Usable Math modules in a side-by-side view next to the hints we have authored from the perspectives of our four math coaches: Estella Explainer, Chef Math Bear, How-to-Hound, and Visual Vicuna. Our hope is that our strategies along with the AI-developed strategies will give adults more ways to inspire math learning among students.

Look for this icon for AI-enhanced guides.

Prompts for ChatGPT, BingAI and Other Generative AI Tools

Estella Explainer Prompt:

Take the personality of a math coach who provides strategies for understanding language and meaning of questions using kid-friendly vocabulary. The coach’s motto is "My job is to explain the math questions clearly so you know what you are supposed to do to solve the problem. Sometimes there are unfamiliar or confusing terms in the question. I will help you understand what they mean. The first math problem is {replace math word problem here}

Chef Math Bear Prompt:

Take the personality of a math coach who provides computational strategies (addition, subtraction, multiplication and division) for solving problems. The coach’s motto is “I am here to make sure that you know how to do the math needed to answer these questions. Sometimes you need to do addition, subtraction, multiplication or division. Some questions ask you to use fractions, decimals, large numbers, and probability. When you need ideas for what to do, I am ready.

How-to-Hound Prompt:

Take the personality of a math coach who uses strategic thinking clues (rounding, estimation, elimination of wrong answers) to solve math problems. The coach’s motto is “Answering math questions means you need a plan and my role is to help you figure out different strategies for solving problems. Sometimes you can get the correct answer by crossing out the wrong answers; other times you can round numbers up or down to make figuring a problem easier. I know other strategies as well.

Visual Vicuna Prompt:

Take the personality of a math coach who offers ways to see problems and their solutions using animations, pictures, charts and graphs. The coach’s motto is “I find math is a lot clearer when I take the numbers and words and put them into pictures and drawings or move objects around so I can see how to answer a question. When you find yourself unsure about a question, see if one of my ideas will explain what to do.

Growth Mindset Statements

As education researchers, we understand the important role that a positive attitude and motivation play in learner success. That's why we’ve integrated the use of growth mindset and motivational cues in Usable Math. After every math challenge, students receive messages that encourage them to adopt a growth mindset, reinforcing the idea that with effort and persistence, they can improve their math skills and achieve success.

A sample motivational cue from the Fractions module.

Collaborative Problem Solving

We believe in the power of collaboration and teamwork when it comes to learning mathematics. Our platform creates a learning climate that promotes collaborative problem solving, providing students with opportunities to work together and explore mathematical concepts in a supportive and inclusive environment. Whether you are a student, teacher, or parent, we invite you to explore our platform and experience the science behind the way we deliver math instruction to elementary school students. Read more about our work on the Journal of STEM Education↗

Papers, Presentations and Blogs

UsableMath GenAI Prompts: Learn Math with Our Tailor-Made Prompts for ChatGPT, Claude, and other GenAI tools. Usable Math Blog. https://blog.usablemath.org/usablemath-genai-prompts .

Maloy, R. W. & Gattupalli, S. (2024). Prompt Literacy. EdTechnica: The Open Encyclopedia of Educational Technology . https://edtechbooks.org/encyclopedia/prompt_literacy

Gattupalli, S., & Maloy, R. W. (2024). On Human-Centered AI in Education. https://doi.org/10.7275/KXAP-FN13

Gattupalli, S., Edwards, S.A, Maloy, R. W., & Rancourt, M. (2023, October). Designing for Learning: Key Decisions for an Open Online Math Tutor for Elementary Students. Digital Experiences in Mathematics Education . https://doi.org/10.1007/s40751-023-00128-3 .

Gattupalli, S., Maloy, R.W., Edwards, S.A. & Gearty, A. (2023, August 23). Prompt Literacy for STEM Educators: Enhance Your Teaching and Learning with Generative AI. Berkshire Resources for Learning and Innovation (BRLI) Teaching with Technology Conference, Pittsfield, MA. ScholarWorks@UMass.

Blending Gardens and Geometry: Socio-cultural Approaches in Math Ed. Usable Math Blog. https://blog.usablemath.org/blending-gardens-and-geometry-socio-cultural-approaches-in-math-education .

Maloy, R. W., Gattupalli, S., & Edwards, S. A. (2023). Developing Usable Math Online Tutor for Elementary Math Learners with NoCode Tools . Scholarworks@UMass.

Gattupalli, S., Maloy, R. W., & Edwards, S. A. (2023). Prompt Literacy: A Pivotal Educational Skill in the Age of AI . Scholarworks@UMass.

Gattupalli, S., Maloy, R. W., & Edwards, S. (2023). Comparing Teacher-Written and AI-Generated Math Problem Solving Strategies for Elementary School Students: Implications for Classroom Learning . https://doi.org/10.7275/8sgx-xj08

Making Math Usable for Young Learners . Guest post on Rachelle Dené Poth's EdTech blog Learning as I go: Experiences, Reflections, Lessons Learned . January, 2023.

Math Learning Digital Choice Board (2020) . ScholarWorks, University of Massachusetts Amherst.

Maloy, R.W., Razzaq, L., & Edwards, S.A. (2014). Learning by Choosing: Fourth Graders Use of an Online Multimedia Tutoring System for Math Problem Solving . Journal of Interactive Learning Research , 25(1), 51-64.

Razzaq, L., Maloy, R. W., Edwards, S. A., Arroyo, I., & Woolf, B.P. (2011). “4MALITY: Coaching Students with Different Problem Solving Strategies Using an Online Tutoring System” (p. 359-364). In J. A. Konstan, Ricardo Conejo, Jose L, Marzo & Nuria Oliver, User Modeling, Adaptation and Personalization: 19th International Conference, UMAP 2011, Girona, Spain, July 11-15 Proceedings . Berlin: Springer Verlag.

Maloy, R.W., Edwards,S. A. & Anderson G. (2010, January-June). “Teaching Math Problem Solving Using a Web-based Tutoring System, Learning Games, and Students’ Writing .” Journal of STEM Education: Innovations and Research, 11 (1&2).

Edwards, S. A., Maloy, R.W., & Anderson G. (2010, February). “Classroom Characters Coach Students to Success.” Teaching Children Mathematics, 16 (6), 342-349.

Edwards, S. A., Maloy, R. W., & Anderson G. (2009, Summer). “Reading Coaching of Math Word Problems.” Literacy Coaching Clearinghouse . http://www.literacycoachingonline.org/briefs.html .

MEET OUR TEAM

Sharon Edwards , Ph.D.

Teacher Education & Curriculum Studies

College of Education, University of Massachusetts Amherst

Sharon (she/her) is a clinical faculty in the Department of Teacher Education and Curriculum Studies in the College of Education at the University of Massachusetts Amherst. Sharon is the big brains behind the development of Usable Math online math tutor.

Email : sae at umass dot edu

Robert Maloy , Ph.D.

Elementary Math and History

Bob (he/him) is a history and math senior lecturer in the Department of Teacher Education and Curriculum Studies in the College of Education at the University of Massachusetts Amherst. Bob is the creative math content creator and storytelling artist behind Usable Math.

Email : rwm at umass dot edu

Sai Gattupalli

Math, Science & Learning Technologies (MSLT)

Sai (he/him) is a PhD candidate at the University of Massachusetts Amherst, where he researches education technology to make STEM teaching and learning and more effective. Sai is passionate about understanding learner culture to create effective learning experiences. Email : sgattupalli at umass dot edu Website : gattupalli.com

Marguerite Rancourt

Lead Teacher, Discovery School at Four Corners

Greenfield, Massachusetts

Marguerite (she/her) teaches fourth grade at the Discovery School in addition to serving as Lead Teacher for the school. She has created and taught professional development workshop for other elementary school teachers. In 2018, she received the Pioneer Valley Excellence in Teaching Award. Students in her class have been contributing to the design of system throughout the 2022-2023 school year.

Aubrey Coyne

Math Content Designer and Reviewer

College of Education, Commonwealth Honors College, University of Massachusetts Amherst.

Aubrey Coyne (she/her) is a sophomore at the University of Massachusetts Amherst. She is a math tutor and is studying to be an elementary teacher. Aubrey is passionate about finding ways to make learning accessible and enjoyable for all students.

Graduate Student, Math and Digital Media Research Assistant

Sara Shea (she/her) is a graduate student at the University of Massachusetts Amherst. She is currently part of the university’s Collaborative Teacher Education Pathway program, working towards earning her master’s degree in elementary education.

Katie Allan

Math and Digital Media Research Assistant

Katie Allan (she/her) is a senior at the University of Massachusetts Amherst. She is a math major with a concentration in education and passionate about math education.

SUGGESTIONS AND FEEDBACK

We welcome ideas from teachers, students, and families about the usable math system..

Please complete our UsableMath Module Review and Feedback↗ form.

Your responses will help us to improve how the system works instructionally and technically. Let us know any additional thoughts about the problems, characters, hints, gifs, mindset statements and more.

Your message has been received. We will get back to you shortly. The average response time is approximately 6 hours.

K-5 Math Centers

K-5 math ideas, 3rd grade math, need help organizing your k-5 math block, 5 ways to include math problem solving activities in your classroom.

Are you looking for math problem solving activities that are not too easy and not too hard, but juuust right? I’ve got something just for you and your students.

Solve and Explain Problem Solving Tasks are open-ended math tasks that provide just the right amount of challenge for your kids. Here’s a little more about them.

Open-ended math problem solving tasks:

• promote multiple solution paths and/or multiple solutions
• boost critical thinking and math reasoning skills
• increase opportunities for developing perseverance
• provide opportunities to justify answer choices
• strengthen kids written and oral communication skills

What Makes These So Great?

• All Common Core Standards are covered for your grade level
• 180+ Quality questions that are rigorous yet engaging
• They are SUPER easy to assemble
• Provide opportunities for meaningful math discussions
• Perfect for developing a growth mindset
• Easily identify student misconceptions so you can provide assistance
• Very versatile (check out the different ways to use them below)

You can find out more details for your grade level by clicking on the buttons below.

I’m sure you really want to know how can you use these with your kids. Check out the top 5 ideas on how to use Solve and Explain Problem Solving Tasks in your classroom.

How and When Can I Use Them?

Solve and Explain Tasks Cards are very versatile. You can use them for:

• Math Centers  – This is my favorite way to use these! Depending on your grade level, there are at least two (Kinder – 2nd) or three (3rd-5th) tasks types per Common Core standard. And each task type has 6 different questions. Print out each of the different tasks types on different color paper. Then, let students choose which one question from each task type they want to solve.

• Problem of the Day  – Use them as a daily math journal prompt. Print out the recording sheet and project one of the problems on your white board or wall.  Students solve the problem and then glue it in their spiral or composition notebooks.

• Early Finisher Activities  -No more wondering what to do next!Create an early finishers notebook where students can grab a task and a recording sheet. Place the cards in sheet protectors and make copies of the Early Finisher Activity Check-Off card for your kids to fill out BEFORE they pull a card out to work on. We want to make sure kids are not rushing through there first assignment before moving on to an early finisher activity.

• Weekly Math Challenges  – Kids LOVE challenges! Give students copies of one of the problems for homework. Then give them a week to complete it. Since many of the questions have multiple solutions and students have to explain how they got their answers, you can have a rich whole group discussion at the end of the week (even with your kindergarten and 1st grade students).

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• Formative Assessments  – Give your students a problem to solve. Then use the Teacher Scoring Rubric to see how your kids are doing with each standard. Since they have to explain their thinking, this is a great way to catch any misconceptions and give feedback to individual students.

So this wraps up the top 5 ways that you can use problem solving tasks in your classroom.  Click your grade level below to get Solve and Explain problem solving tasks for your classroom.

• Read more about: K-5 Math Ideas

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10 Fun Math Problem Solving Activities

I love using fun games and activities to get my kids excited about math. That’s why I was so excited to discover Beast Academy Playground! The site includes a wide variety of math problem solving activities, games, puzzles, and ideas that can be used with your current homeschool curriculum. If you’re looking for some fun ways to get your child interested in math again or some new ideas for teaching math at home, this is a great place to start.

I received compensation in exchange for my honest review, but all the opinions in this post are my own.

What is Beast Academy Playground?

As a homeschool parent, I know that fun math problem solving activities are hard to come by. Practicing math can be frustrating and boring for kids. And, it’s not enough to just teach math facts – children need to learn how to solve complex problems too!

Beast Academy Playground is the perfect solution. This site was created by Beast Academy, a homeschool curriculum for kids ages 8-13 that’s written as a comic book. Beast Academy Playground is a website that includes a growing library of fun activity ideas for kids ages 4-11.

The site includes both tabletop games that can be played with paper and pencil and more active games that can be played outside. Parents can sort the activities by concept, age, number of players, and more to find the perfect activity to complement any math lesson. New activities, games, and crafts are added to the site weekly.

Key Features of Beast Academy Playground

I love that every game on the site includes variations. These are different ways to adapt the game to fit the number of kids in your family or the age and grade level of your child.

In addition, most of the games can be played alone or in small groups. This makes Beast Academy Playground so easy for the whole family to use together!

Beast Academy Playground was developed by the experts at Art of Problem Solving, who are global leaders in K-12 math education. Each activity is intentionally designed to help kids learn new math concepts.

I was excited to see that each game also includes learning notes. This section helps parents understand what their kids will be learning when they play the game. I felt like I was prepared to be a better math teacher after I read the tips in this section!

Check out Beast Academy Playground and learn more now!

How to use Math Problem Solving Activities in Your Homeschool

Introduce a new concept.

One way to use problem-solving activities in your math lessons is to help introduce a new concept. For example, when we were learning about even and odd numbers, we started our math lesson by playing the Odds vs. Evens game from Beast Academy Playground. This simple math problem solving activity is a variation on the game Rock Paper Scissors. This was a fun way to help us review addition facts while introducing the concept of odd and even numbers.

Practice Problem-Solving Skills

Another great way to use Beast Academy Playground is to help kids practice their problem-solving skills. One fun problem solving game that my kids love is the Fox and Hare game. In this outdoor game, the fox needs to use strategy to try to catch the hare on a grid, while the hare tries to avoid capture. You can change the size of the grid to create a variety of problems for kids to solve.

Practice Math Facts

If your kids need extra practice with their math facts, games and math puzzles can be a fun way to practice these important skills. Beast Academy Playground has games for addition and subtraction, as well as concepts like skip counting that will help kids learn their multiplication facts.

One favorite that we enjoyed was Troll Hole . In this game, we took turns writing numbers on a special game board. In the end, we had to add up all the numbers to see who was the winner. My kids had so much fun with the theme of this game and loved getting to draw the troll in the hole!

Independent learning

As homeschool parents, we always need ideas for independent learning activities. Beast Academy Playground includes some great math problem solving games that are perfect for self-directed math learning. The many different activities on the site include several fun activities for one player that kids can work through independently to reinforce their math skills.

For extra review

Hands-on activities are also helpful when kids need a little extra review on a topic. For example, we played Kanga Ruler to help review skip counting. The kids loved this game because it was active and fun!

Top 10 Math Problem Solving Activities from Beast Academy Playground

Here are 10 of our favorite games that help kids develop a deeper understanding of mathematical concepts, all while having fun at the same time.

Trashketball

In this game, kids aim and try to score a basket into a trash can. Then, they add up the points they score. You can modify this game to add extra intellectual challenges for older kids or adapt the math so that younger kids can play too!

Trashketball was my kids’ favorite Beast Academy game, hands down. They loved trying to score as many baskets as they could. They had so much fun that they decided to keep playing even after our math lesson was finished!

Learn how to play Trashketball here.

In this math game for young children, kids race to stack towers of number cards. This is a great way to review numbers and counting. My kids really enjoyed trying to build the tallest tower that they could!

Learn how to play Towers here.

Bumper Cars

Although it took us a few tries to understand the strategy behind this game, my kids loved the concept of trying to figure out new ways to move the cars on the road. This was another great mathematical practice for strategy and solving difficult math problems.

Learn how to play Bumper Cars here.

Hungry Monster

This was a great way to practice inequalities and comparing numbers, and my kids loved feeding the correct answer in each inequality to the hungry monster!

Learn how to play Hungry Monster here.

Fruit Flies

In this math game for older problem solvers, kids try to claim as many grapes as they can for themselves, while blocking their opponent from getting any. This game is like an interactive logic puzzle, and it’s a good way for kids to learn critical thinking skills.

Learn how to play Fruit Flies here.

Blind Heist

In this game, Battleship meets addition as kids try to build the highest towers on their own secret side of the board. There are many different solutions and strategies to be successful, and my kids loved trying different solutions to this open-ended problem.

Learn how to play Blind Heist here.

Möbius Madness

This is a classic brain teaser for a reason- my kids were fascinated by the magic of a piece of paper with only one side. My kids were able to follow the directions easily and afterwards, they were excited to show their magical piece of paper to everyone who would watch.

Learn how to play Möbius Madness here.

This fast-paced card game was the perfect way to help my kids practice their addition facts.

Learn how to play Fifteen here.

Cookie Cutter

This game helps kids practice both spatial reasoning skills and fine motor skills at the same time. And, the result is a fun picture that they can color!

Learn how to play Cookie Cutter here.

Odd Knights

This was a fun way to practice even and odd (and it even led to a history lesson about the Knights of the Round Table!)

Learn how to play Odd Knights here.

What math problem solving activities will you use?

Whether it’s for extra practice or math review , Beast Academy Playground has something for every math learner. This site is a great resource to find exciting games that help kids develop number sense, problem solving, and logical thinking skills. If you want fun and engaging math activities that don’t require a textbook, this is the place to go. For more math problem solving activities and fun math games, check out Beast Academy Playground !

Find hands on activities to teach spelling and reading here!

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Math and Logic Puzzles

If you REALLY like exercising your brain, figuring things 'round and 'round till you explode, then this is the page for you !

Whosoever shall solve these puzzles shall Rule The Universe!

... or at least they should ...

What is Geometry?

Geometry is the study of shapes and their properties. It involves understanding and working with various shapes, sizes, patterns, and spaces. In elementary school, geometry starts with recognizing and naming simple two-dimensional shapes like circles, squares, and triangles, and three-dimensional shapes like cubes, spheres, and cylinders. As students progress, they begin to explore more complex concepts such as area, perimeter, volume, angles, symmetry, and coordinate geometry.

Why Teach Geometry to Elementary Students?

Teaching geometry at an early age is crucial for several reasons:

• Develops Spatial Reasoning: Geometry helps children develop spatial reasoning skills, which are important for everyday tasks like packing a bag, reading a map, or assembling a piece of furniture.
• Enhances Problem-Solving Skills: Working with geometric shapes and concepts requires students to think critically and solve problems, enhancing their problem-solving skills.
• Links to Real-World Concepts: Geometry is all around us – in buildings, nature, art, and more. Teaching geometry helps students understand and appreciate the world around them.
• Foundation for Advanced Math: A solid understanding of geometry is necessary for more advanced math topics taught in high school and beyond, including trigonometry and calculus.

Strategies for Teaching Geometry

Here are some strategies that can make teaching geometry more effective:

• Use Real-World Examples: Using real-world examples is an excellent way to make geometry more relatable and less abstract for students. You can start by discussing different shapes seen in everyday life. For instance, you could talk about how a stop sign is an octagon, a wheel is a circle, or a pyramid of oranges at the grocery store is a pyramid. Discussing architecture is another great way to introduce geometric concepts. Many buildings incorporate various geometric shapes and principles, and children’s familiarity with these structures can ground their understanding of these concepts.
• Visual Learning: Visual aids play a crucial role in teaching geometry. Diagrams, models, and drawings can illustrate concepts and make abstract ideas more tangible. For example, you could use a diagram to explain how to find the area of a triangle or use blocks to demonstrate the concept of volume. Interactive whiteboards can also be a useful tool for visually demonstrating geometric concepts and allowing students to interact with the shapes and figures.
• Hands-On Activities: Hands-on activities can make learning geometry interactive and fun. These activities allow students to physically engage with geometric concepts, which can enhance understanding and retention. For instance, using manipulatives like blocks or tangrams can help students explore concepts of shape, size, and symmetry. Building models of three-dimensional shapes can also deepen their understanding of these figures’ properties.

Activities for Teaching Geometry

Here are some engaging activities for teaching geometry:

• Shape Hunt: A shape hunt is an engaging way for students to apply their knowledge of geometric shapes in a real-world context. To do this activity, create a list of different shapes that students have learned about. Then, ask them to go on a “hunt” around the classroom, school, or their home to find objects that match the shapes on the list. They can draw or take pictures of the objects they find and present them to the class. This activity not only reinforces their understanding of shapes but also helps them see how geometry is used in the world around them.
• Shape Art: Creating art using different geometric shapes can be both fun and educational. Provide students with different shapes (either pre-cut or have them cut out their own) and ask them to create a picture or design using only those shapes. This activity can help reinforce shape recognition and also spark creativity. You can extend this activity by asking students to identify and discuss the different shapes used in their artwork.
• Geometric Construction: Building geometric shapes and structures can provide hands-on experience with geometry. Provide students with materials such as straws and connectors or toothpicks and marshmallows and challenge them to build different shapes or structures. For example, they could build a cube, a pyramid, or a more complex structure like a bridge. This activity not only enhances their understanding of geometric shapes and their properties but also encourages problem-solving and critical thinking skills.
• Symmetry Drawings: Symmetry is a crucial concept in geometry. To introduce this concept, provide students with pictures or shapes that are symmetrical along a line (the line of symmetry). Then, ask them to complete the other half of the picture or shape to make it symmetrical. This activity can help students understand the concept of symmetry in a visual and interactive way.
• Area and Perimeter with Grid Paper: Grid paper is a useful tool for teaching area and perimeter. Ask students to draw different shapes on the grid paper, then calculate their area and perimeter. This activity can provide a visual representation of these concepts, making them easier to understand. You could also challenge students to draw shapes with a specific area or perimeter, promoting further critical thinking and problem-solving skills.

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The Algebra Problem: How Middle School Math Became a National Flashpoint

Top students can benefit greatly by being offered the subject early. But many districts offer few Black and Latino eighth graders a chance to study it.

By Troy Closson

From suburbs in the Northeast to major cities on the West Coast, a surprising subject is prompting ballot measures, lawsuits and bitter fights among parents: algebra.

Students have been required for decades to learn to solve for the variable x, and to find the slope of a line. Most complete the course in their first year of high school. But top-achievers are sometimes allowed to enroll earlier, typically in eighth grade.

The dual pathways inspire some of the most fiery debates over equity and academic opportunity in American education.

Do bias and inequality keep Black and Latino children off the fast track? Should middle schools eliminate algebra to level the playing field? What if standout pupils lose the chance to challenge themselves?

The questions are so fraught because algebra functions as a crucial crossroads in the education system. Students who fail it are far less likely to graduate. Those who take it early can take calculus by 12th grade, giving them a potential edge when applying to elite universities and lifting them toward society’s most high-status and lucrative professions.

But racial and economic gaps in math achievement are wide in the United States, and grew wider during the pandemic. In some states, nearly four in five poor children do not meet math standards.

To close those gaps, New York City’s previous mayor, Bill de Blasio, adopted a goal embraced by many districts elsewhere. Every middle school would offer algebra, and principals could opt to enroll all of their eighth graders in the class. San Francisco took an opposite approach: If some children could not reach algebra by middle school, no one would be allowed to take it.

The central mission in both cities was to help disadvantaged students. But solving the algebra dilemma can be more complex than solving the quadratic formula.

New York’s dream of “algebra for all” was never fully realized, and Mayor Eric Adams’s administration changed the goal to improving outcomes for ninth graders taking algebra. In San Francisco, dismantling middle-school algebra did little to end racial inequities among students in advanced math classes. After a huge public outcry, the district decided to reverse course.

“You wouldn’t think that there could be a more boring topic in the world,” said Thurston Domina, a professor at the University of North Carolina. “And yet, it’s this place of incredibly high passions.”

“Things run hot,” he said.

In some cities, disputes over algebra have been so intense that parents have sued school districts, protested outside mayors’ offices and campaigned for the ouster of school board members.

Teaching math in middle school is a challenge for educators in part because that is when the material becomes more complex, with students moving from multiplication tables to equations and abstract concepts. Students who have not mastered the basic skills can quickly become lost, and it can be difficult for them to catch up.

Many school districts have traditionally responded to divergent achievement levels by simply separating children into distinct pathways, placing some in general math classes while offering others algebra as an accelerated option. Such sorting, known as tracking, appeals to parents who want their children to reach advanced math as quickly as possible.

But tracking has cast an uncomfortable spotlight on inequality. Around a quarter of all students in the United States take algebra in middle school. But only about 12 percent of Black and Latino eighth graders do, compared with roughly 24 percent of white pupils, a federal report found .

“That’s why middle school math is this flashpoint,” said Joshua Goodman, an associate professor of education and economics at Boston University. “It’s the first moment where you potentially make it very obvious and explicit that there are knowledge gaps opening up.”

In the decades-long war over math, San Francisco has emerged as a prominent battleground.

California once required that all eighth graders take algebra. But lower-performing middle school students often struggle when forced to enroll in the class, research shows. San Francisco later stopped offering the class in eighth grade. But the ban did little to close achievement gaps in more advanced math classes, recent research has found.

As the pendulum swung, the only constant was anger. Leading Bay Area academics disparaged one another’s research . A group of parents even sued the district last spring. “Denying students the opportunity to skip ahead in math when their intellectual ability clearly allows for it greatly harms their potential for future achievement,” their lawsuit said.

The city is now back to where it began: Middle school algebra — for some, not necessarily for all — will return in August. The experience underscored how every approach carries risks.

“Schools really don’t know what to do,” said Jon R. Star, an educational psychologist at Harvard who has studied algebra education. “And it’s just leading to a lot of tension.”

In Cambridge, Mass., the school district phased out middle school algebra before the pandemic. But some argued that the move had backfired: Families who could afford to simply paid for their children to take accelerated math outside of school.

“It’s the worst of all possible worlds for equity,” Jacob Barandes, a Cambridge parent, said at a school board meeting.

Elsewhere, many students lack options to take the class early: One of Philadelphia’s most prestigious high schools requires students to pass algebra before enrolling, preventing many low-income children from applying because they attend middle schools that do not offer the class.

In New York, Mr. de Blasio sought to tackle the disparities when he announced a plan in 2015 to offer algebra — but not require it — in all of the city’s middle schools. More than 15,000 eighth graders did not have the class at their schools at the time.

Since then, the number of middle schools that offer algebra has risen to about 80 percent from 60 percent. But white and Asian American students still pass state algebra tests at higher rates than their peers.

The city’s current schools chancellor, David Banks, also shifted the system’s algebra focus to high schools, requiring the same ninth-grade curriculum at many schools in a move that has won both support and backlash from educators.

And some New York City families are still worried about middle school. A group of parent leaders in Manhattan recently asked the district to create more accelerated math options before high school, saying that many young students must seek out higher-level instruction outside the public school system.

In a vast district like New York — where some schools are filled with children from well-off families and others mainly educate homeless children — the challenge in math education can be that “incredible diversity,” said Pedro A. Noguera, the dean of the University of Southern California’s Rossier School of Education.

“You have some kids who are ready for algebra in fourth grade, and they should not be denied it,” Mr. Noguera said. “Others are still struggling with arithmetic in high school, and they need support.”

Many schools are unequipped to teach children with disparate math skills in a single classroom. Some educators lack the training they need to help students who have fallen behind, while also challenging those working at grade level or beyond.

Some schools have tried to find ways to tackle the issue on their own. KIPP charter schools in New York have added an additional half-hour of math time to many students’ schedules, to give children more time for practice and support so they can be ready for algebra by eighth grade.

At Middle School 50 in Brooklyn, where all eighth graders take algebra, teachers rewrote lesson plans for sixth- and seventh-grade students to lay the groundwork for the class.

The school’s principal, Ben Honoroff, said he expected that some students would have to retake the class in high school. But after starting a small algebra pilot program a few years ago, he came to believe that exposing children early could benefit everyone — as long as students came into it well prepared.

Looking around at the students who were not enrolling in the class, Mr. Honoroff said, “we asked, ‘Are there other kids that would excel in this?’”

“The answer was 100 percent, yes,” he added. “That was not something that I could live with.”

Troy Closson reports on K-12 schools in New York City for The Times. More about Troy Closson

iOS 18’s Big AI Update Could Automatically Solve Math Problems for You

Like predictive text, but for math equations.

WWDC 2024 hype season is upon us! We’re a little over a week away from Apple’s annual developer conference, where the company is expected to announce new versions of all of its platforms, including iOS 18 .

All rumors point to iOS 18 being the biggest update to the iPhone software in years, with generative AI as the headlining act. We’ve already heard of some obvious AI updates, like smart summaries, photo retouching, and automatic replies . However, a new report from AppleInsider suggests there’s even more AI in store. The Apple-focused publication says iOS 18 will get a “Catch Up” feature where Siri can provide an overview of recent notifications, cross-device media controls where you can activate Siri on one device to control another, and even the ability to create and edit images within iMessage using generative AI.

With all these leaked AI features, it might be easy to overlook perhaps the most underrated one: AI that can automatically solve math problems.

The Calculator functionality is going to be integrated into the Notes app.

No Need to Open Up the Calculator App

According to AppleInsider , a new feature called “Keyboard Math Predictions” will detect and automatically solve math equations that are entered as text. Think of this like your iPhone’s predictive text that finishes your sentences for you, but for math problems. On top of that, the Notes app will get a crash course in math, with the ability to recognize math equations and offer solutions with help from the Calculator app’s integration. Apple is also reportedly working on a way to generate graphs within the Notes app.

Apple’s AI isn’t the only one that can handle some math thrown its way. OpenAI previously announced GPT-4o, and the AI chatbot made easy work of an equation looking to solve for x. GPT-4o can even act as more of a personal tutor for more involved problems.

WWDC 2024 will finally reveal all the AI things that Apple has been working on.

Big AI Reveal on June 10

Fortunately, we only have to wait until Apple kicks off its WWDC 2024 on June 10 to see what’s in store with iOS 18. The software update won’t officially arrive until the fall, but Apple will share installable developer and public betas shortly after WWDC if you’re willing to deal with bugs and such throughout the summer.

With Apple hopping on the wave, generative AI chatbots are proving that they can handle math just as well as they can understand natural language. You could argue that AI-assisted math could make us all dumber, but that’s also what people said about calculators and computers. Sure, technology has made some people lazier, but it’s also helped save us time and solve even more complex problems. Adding AI that can solve math into the iPhone will only strengthen its purpose as do-it-all device.

May 31, 2024

10 min read

Math Can Help Solve Social Justice Problems

Mathematicians are working on ways to use their field to tackle major social issues, such as social inequality and the need for gender equity

By Rachel Crowell & Nature magazine

MicroStockHub/Getty Images

When Carrie Diaz Eaton trained as a mathematician, they didn’t expect their career to involve social-justice research. Growing up in Providence, Rhode Island, Diaz Eaton first saw social justice in action when their father, who’s from Peru, helped other Spanish-speaking immigrants to settle in the United States.

But it would be decades before Diaz Eaton would forge a professional path to use their mathematical expertise to study social-justice issues. Eventually, after years of moving around for education and training, that journey brought them back to Providence, where they collaborated with the Woonasquatucket River Watershed Council on projects focused on preserving the local environment of the river’s drainage basin, and bolstering resources for the surrounding, often underserved communities.

By “thinking like a mathematician” and leaning on data analysis, data science and visualization skills, they found that their expertise was needed in surprising ways, says Diaz Eaton, who is now executive director of the Institute for a Racially Just, Inclusive, and Open STEM Education at Bates College in Lewiston, Maine.

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For example, the council identified a need to help local people to better connect with community resources. “Even though health care and education don’t seem to fall under the purview of a watershed council, these are all interrelated issues,” Diaz Eaton says. Air pollution can contribute to asthma attacks, for example. In one project, Diaz Eaton and their collaborators built a quiz to help community members to choose the right health-care option, depending on the nature of their illness or injury, immigration status and health-insurance coverage.

“One of the things that makes us mathematicians, is our skills in logic and the questioning of assumptions”, and creating that quiz “was an example of logic at play”, requiring a logic map of cases and all of the possible branches of decision-making to make an effective quiz, they say.

Maths might seem an unlikely bedfellow for social-justice research. But applying the rigour of the field is turning out to be a promising approach for identifying, and sometimes even implementing, fruitful solutions for social problems.

Mathematicians can experience first-hand the messiness and complexity — and satisfaction — of applying maths to problems that affect people and their communities. Trying to work out how to help people access much-needed resources, reduce violence in communities or boost gender equity requires different technical skills, ways of thinking and professional collaborations compared with breaking new ground in pure maths. Even for an applied mathematician like Diaz Eaton, transitioning to working on social-justice applications brings fresh challenges.

Mathematicians say that social-justice research is difficult yet fulfilling — these projects are worth taking on because of their tremendous potential for creating real-world solutions for people and the planet.

Data-driven research

Mathematicians are digging into issues that range from social inequality and health-care access to racial profiling and predictive policing. However, the scope of their research is limited by their access to the data, says Omayra Ortega, an applied mathematician and mathematical epidemiologist at Sonoma State University in Rohnert Park, California. “There has to be that measured information,” Ortega says.

Fortunately, data for social issues abound. “Our society is collecting data at a ridiculous pace,” Ortega notes. Her mathematical epidemiology work has examined which factors affect vaccine uptake in different communities. Her work has found, for example, that, in five years, a national rotavirus-vaccine programme in Egypt would reduce disease burden enough that the cost saving would offset 76% of the costs of the vaccine. “Whenever we’re talking about the distribution of resources, there’s that question of social justice: who gets the resources?” she says.

Lily Khadjavi’s journey with social-justice research began with an intriguing data set.

About 15 years ago, Khadjavi, a mathematician at Loyola Marymount University in Los Angeles, California, was “on the hunt for real-world data” for an undergraduate statistics class she was teaching. She wanted data that the students could crunch to “look at new information and pose their own questions”. She realized that Los Angeles Police Department (LAPD) traffic-stop data fit that description.

At that time, every time that LAPD officers stopped pedestrians or pulled over drivers, they were required to report stop data. Those data included “the perceived race or ethnicity of the person they had stopped”, Khadjavi notes.

When the students analysed the data, the results were memorable. “That was the first time I heard students do a computation absolutely correctly and then audibly gasp at their results,” she says. The data showed that one in every 5 or 6 police stops of Black male drivers resulted in a vehicle search — a rate that was more than triple the national average, which was about one out of every 20 stops for drivers of any race or ethnicity, says Khadjavi.

Her decision to incorporate that policing data into her class was a pivotal moment in Khadjavi’s career — it led to a key publication and years of building expertise in using maths to study racial profiling and police practice. She sits on California’s Racial Identity and Profiling Advisory Board , which makes policy recommendations to state and local agencies on how to eliminate racial profiling in law enforcement.

In 2023, she was awarded the Association for Women in Mathematics’ inaugural Mary & Alfie Gray Award for Social Justice, named after a mathematician couple who championed human rights and equity in maths and government.

Sometimes, gaining access to data is a matter of networking. One of Khadjavi’s colleagues shared Khadjavi’s pivotal article with specialists at the American Civil Liberties Union. In turn, these specialists shared key data obtained through public-records requests with Khadjavi and her colleague. “Getting access to that data really changed what we could analyse,” Khadjavi says. “[It] allowed us to shine a light on the experiences of civilians and police in hundreds of thousands of stops made every year in Los Angeles.”

The data-intensive nature of this research can be an adjustment for some mathematicians, requiring them to develop new skills and approach problems differently. Such was the case for Tian An Wong, a mathematician at the University of Michigan-Dearborn who trained in number theory and representation theory.

In 2020, Wong wanted to know more about the controversial issue of mathematicians collaborating with the police, which involves, in many cases, using mathematical modelling and data analysis to support policing activities. Some mathematicians were protesting about the practice as part of a larger wave of protests around systemic racism , following the killing of George Floyd by police in Minneapolis, Minnesota. Wong’s research led them to a technique called predictive policing, which Wong describes as “the use of historical crime and other data to predict where future crime will occur, and [to] allocate policing resources based on those predictions”.

Wong wanted to know whether the tactics that mathematicians use to support police work could instead be used to critique it. But first, they needed to gain some additional statistics and data analysis skills. To do so, Wong took an online introductory statistics course, re-familiarized themself with the Python programming language, and connected with colleagues trained in statistical methods. They also got used to reading research papers across several disciplines.

Currently, Wong applies those skills to investigating the policing effectiveness of a technology that automatically locates gunshots by sound. That technology has been deployed in parts of Detroit, Michigan, where community members and organizations have raised concerns about its multimillion-dollar cost and about whether such police surveillance makes a difference to public safety.

Getting the lay of the land

For some mathematicians, social-justice work is a natural extension of their career trajectories. “My choice of mathematical epidemiology was also partially born out of out of my love for social justice,” Ortega says. Mathematical epidemiologists apply maths to study disease occurrence in specific populations and how to mitigate disease spread. When Ortega’s PhD adviser mentioned that she could study the uptake of a then-new rotovirus vaccine in the mid-2000s, she was hooked.

Mathematicians, who decide to jump into studying social-justice issues anew, must do their homework and dedicate time to consider how best to collaborate with colleagues of diverse backgrounds.

Jonathan Dawes, an applied mathematician at the University of Bath, UK, investigates links between the United Nations’ Sustainable Development Goals (SDGs) and their associated target actions. Adopted in 2015, the SDGs are “a universal call to action to end poverty, protect the planet, and ensure that by 2030 all people enjoy peace and prosperity,” according to the United Nations , and each one has a number of targets.

“As a global agenda, it’s an invitation to everybody to get involved,” says Dawes. From a mathematical perspective, analysing connections in the complex system of SDGs “is a nice level of problem,” Dawes says. “You’ve got 17 Sustainable Development Goals. Between them, they have 169 targets. [That’s] an amount of data that isn’t very large in big-data terms, but just big enough that it’s quite hard to hold all of it in your head.”

Dawes’ interest in the SDGs was piqued when he read a 2015 review that focused on how making progress on individual goals could affect progress on the entire set. For instance, if progress is made on the goal to end poverty how does that affect progress on the goal to achieve quality education for all, as well as the other 15 SDGs?

“If there’s a network and you can put some numbers on the strengths and signs of the edges, then you’ve got a mathematized version of the problem,” Dawes says. Some of his results describe how the properties of the network change if one or more of the links is perturbed, much like an ecological food web. His work aims to identify hierarchies in the SDG networks, pinpointing which SDGs should be prioritized for the health of the entire system.

As Dawes dug into the SDGs, he realized that he needed to expand what he was reading to include different journals, including publications that were “written in very different ways”. That involved “trying to learn a new language”, he explains. He also kept up to date with the output of researchers and organizations doing important SDG-related work, such as the International Institute for Applied Systems Analysis in Laxenburg, Austria, and the Stockholm Environment Institute.

Dawes’ research showed that interactions between the SDGs mean that “there are lots of positive reinforcing effects between poverty, hunger, health care, education, gender equity and so on.” So, “it’s possible to lift all of those up” when progress is made on even one of the goals. With one exception: managing and protecting the oceans. Making progress on some of the other SDGs could, in some cases, stall progress for, or even harm, life below water.

Collaboration care

Because social-justice projects are often inherently cross-disciplinary, mathematicians studying social justice say it’s key in those cases to work with community leaders, activists or community members affected by the issues.

Getting acquainted with these stakeholders might not always feel comfortable or natural. For instance, when Dawes started his SDG research, he realized that he was entering a field in which researchers already knew each other, followed each other’s work and had decades of experience. “There’s a sense of being like an uninvited guest at a party,” Dawes says. He became more comfortable after talking with other researchers, who showed a genuine interest in what he brought to the discussion, and when his work was accepted by the field’s journals. Over time, he realized “the interdisciplinary space was big enough for all of us to contribute to”.

Even when mathematicians have been invited to join a team of social-justice researchers, they still must take care, because first impressions can set the tone.

Michael Small is an applied mathematician and director of the Data Institute at the University of Western Australia in Perth. For much of his career, Small focused on the behaviour of complex systems, or those with many simple interacting parts, and dynamical systems theory, which addresses physical and mechanical problems.

But when a former vice-chancellor at the university asked him whether he would meet with a group of psychiatrists and psychologists to discuss their research on mental health and suicide in young people, it transformed his research. After considering the potential social impact of better understanding the causes and risks of suicide in teenagers and younger children, and thinking about how the problem meshed well with his research in complex systems and ‘non-linear dynamics’, Small agreed to collaborate with the group.

The project has required Small to see beyond the numbers. For the children’s families, the young people are much more than a single data point. “If I go into the room [of mental-health professionals] just talking about mathematics, mathematics, mathematics, and how this is good because we can prove this really cool theorem, then I’m sure I will get push back,” he says. Instead, he notes, it’s important to be open to insights and potential solutions from other fields. Listening before talking can go a long way.

Small’s collaborative mindset has led him to other mental-health projects, such as the Transforming Indigenous Mental Health and Wellbeing project to establish culturally sensitive mental-health support for Indigenous Australians.

Career considerations

Mathematicians who engage in social-justice projects say that helping to create real-world change can be tremendously gratifying. Small wants “to work on problems that I think can do good” in the world. Spending time pursuing them “makes sense both as a technical challenge [and] as a social choice”, he says.

However, pursuing this line of maths research is not without career hurdles. “It can be very difficult to get [these kinds of] results published,” Small says. Although his university supports, and encourages, his mental-health research, most of his publications are related to his standard mathematics research. As such, he sees “a need for balance” between the two lines of research, because a paucity of publications can be a career deal breaker.

Diaz Eaton says that mathematicians pursuing social-justice research could experience varying degrees of support from their universities. “I’ve seen places where the work is supported, but it doesn’t count for tenure [or] it won’t help you on the job market,” they say.

Finding out whether social-justice research will be supported “is about having some really open and transparent conversations. Are the people who are going to write your recommendation letters going to see that work as scholarship?” Diaz Eaton notes.

All things considered, mathematicians should not feel daunted by wading into solving the world’s messy problems, Khadjavi says: “I would like people to follow their passions. It’s okay to start small.”

This article is reproduced with permission and was first published on May 22, 2024 .