Guest post by:

Sharon A. Edwards

Sai Gattupalli

University of Massachusetts Amherst

Everyone wants to improve math learning for elementary school-age children. Computation, calculation, and problem-solving skills are essential tools for young learners to have. Each builds the mathematical foundations, conceptual building blocks, for future understandings of math instruction in middle school, high school, college, and careers. But national test scores are lower than pre-pandemic as are interest and engagement of many young learners.

To develop tools to support math learning for students, teachers, and families, we and our University of Massachusetts Amherst colleague Robert Maloy, are developing a free open for use online system called Usable Math:

Usable Math provides a unique interactive problem-solving model of activities for youngsters learning mathematical reasoning and computation skills with word problems. Using computers, tablets, smartphones, students, and teachers can access standardized test questions from the Massachusetts MCAS tests and receive multiple learning strategies from four virtual coaches we call learning coaches. Estella Explainer, Chef Math Bear, How-to Hound, and Visual Vicuna are the characters offering words, images, pictures, charts, graphs, animations, and gifs to engage students’ thinking as they read, compute, and strategically solve word problems. The model supports estimating, comparing, understanding vocabulary, and identifying ways to be math solvers seeking right answers in different ways.

To date, we have published interactive modules about fractions, addition, rounding/estimation, geometry, money, data analysis, measurement, and more are on the way.

The name * Usable Math* encompasses our goals and purposes for the system design:

**U Able**meaning you (every young math learner) can be a math problem solver.**Us Able**meaning together all of us (students, teachers, and family members in classrooms and homes) can be a team of math problem solvers.**Usable**meaning anyone (young or older) is able to develop their math problem-solving skills with curiosity, practice, and clues for thinking from the online coaches. For this reason, the system is open and free and works on multiple digital devices, including desktops, laptops, tablets, and smartphones.

Usable Math is designed so users control the process of what learners see and how quickly they see each problem, the coaching clues, answer choices and the answer to the problem. A click-to-see approach lets children and adults use a mouse or a tap to reveal the inner workings of the math word problems one step at a time. Each click of the mouse or return key reveals additional strategies for youngsters to use in solving math problems strategically.

Click-to-see proceeds like this. With the first click, a problem appears on the screen, some with and others without their answer choices being shown depending on what the problem is asking learners to do. In this example, seeing the answers is necessary to problem-solving it.

Click a second time and the system displays Estella Explainer’s hint, a reading strategy intended to reframe the math question in more straightforward, kid-accessible language. The math problem continues to display at the top of the screen, while each hint appears in the bottom section of the screen. The idea is to engage children in actively conversing about the problem from the lens of Estella Explainer’s scaffolding hint.

With another click, Chef Math Bear offers a computational strategy. With another click, a strategic thinking idea appears from How-to-Hound. And with another click, a hint in the form of a movie, chart, graph, or picture appears from Visual Vicuna. In each instance, students and adults have opportunities to analyze and discuss with one another what they think or know, or have learned from the coaches to help them answer the question. When all of the coaching hints are visible on the screen below the question, another click either shows the answer choices or if those are part of the question already, highlights the solution to the problem from among the answer choices. Then before continuing to the next word problem, a motivational statement (“You know parallel lines when you see them” or “You SOLVED the puzzle”) appears along with a surprising visual, a gif, or an image to elicit smiles or delight or laughter to emphasize the accomplishment and encourage viewing the next problem.

Enabling children and adults to choose how quickly or slowly they see information when analyzing problem-solving strategies from the coaches is a deliberate different practice from expectations in many classroom settings. In math, youngsters have mistakenly been taught that being “smart” with math means being the first or one of the first to answer questions correctly or to complete practice worksheets swiftly. By not taking the time needed to read and think through possible problem-solving strategies, students make mistakes, confuse key concepts, and begin to believe that math is a skill only some are competent to learn.

We want Usable Math to be different for several reasons. First, the design of the system makes it possible for children and adults to have productive collaborative problem-solving discussions before choosing an answer. They can “work” the problem, discussing what each puzzle teaches and how it might be solved using different ways. This focuses on the math concepts of the problem and the illustration instead of immediately identifying a procedure to use to find an answer.

Second, the presence of four coaches, with their own problem-solving points of view or perspectives offers choice for students. They can, and do, find a coach who becomes their math friend whose ideas help them to approach problem-solving with confidence. The use of animations and visuals allows the coaches to offer information along with surprising, engaging learning. Children keep coming back to see what the coaches have to say and do. Engagement produces learning.

Third, youngsters and adults discover how math is really about all maths. Look again at that term “maths.” Putting the “s” on math broadens its meaning and changes how it is to be taught and learned. While maths is a term used by educators throughout the world, it is not used or thought of often in classrooms in this country. Maths indicates that there is not one single subject called math, but many ways to think about mathematical topics and concepts. Maths urges children and adults to think like solvers of problems, not recallers of formulas. Maths stresses conceptual understanding with procedural knowledge.

It is our goal to have Usable Math promote maths learning for students, teachers, and families in all topics of maths. We welcome your thoughts and responses and your suggestions for how to revise this coaching system in the future.

**Sharon A. Edwards** is a Clinical Faculty in the College of Education at the University of Massachusetts Amherst. Retired from public school teaching, she taught primary grades for 32 years at the Mark’s Meadow Demonstration Laboratory School, a public school in Amherst, Massachusetts.

**Sai Gattupalli** is a Learning Sciences doctoral student in the College of Education at the University of Massachusetts Amherst. His research interests are broadly focused on learner culture, learning through game play, and game design.

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