100% FREE TO USE

# 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 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

## Math Problem-solving and Design Modules

## More coming soon!

## HOW TO USE

### 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 and Presentations

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

College of Education, University of Massachusetts Amherst

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)

College of Education, University of Massachusetts Amherst

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 better 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.

### Sara **Shea**

Graduate Student, Math and Digital Media Research Assistant

College of Education, University of Massachusetts Amherst

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

College of Education, University of Massachusetts Amherst

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.

### Thank you.

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