About Math Trail
Math Trail is a math practice companion for children in grades 4 to 6. A child answers out loud, the problem is drawn as folded paper, the child explains one step in their own words, and a parent is told what to practise next.
Why this matters
- Grades 4 to 6 are where math turns from facts into ideas. Fractions, decimals and multi-digit multiplying and dividing ask a child to understand why a method works, not only to remember it.
- Mistakes at this age are rarely random. Researchers have studied children's arithmetic errors for decades and found that many follow rules that make sense to the child: adding the bottoms of two fractions, or thinking that 0.35 is bigger than 0.4 because 35 is bigger than 4. A worksheet marks such an answer wrong and moves on. A good tutor asks "How did you get that?" and finds the rule.
- Explaining out loud is one of the best-studied ways to learn. Saying a step in your own words shows where the thinking goes off track, for the child and for the grown-up listening.
- Parents want to help but often cannot see where the trouble is. "Six out of ten" does not say what to do on Thursday evening. A tutor for every child is not something every family can have.
- Voice is already in many homes. A child can answer a smart speaker or display while their hands are busy with paper, and a screen can show the picture that makes the idea clear.
What makes it different
- Code decides right and wrong. Fractions and decimals use exact arithmetic, so "three quarters", "3 over 4" and "6/8" are all understood. A language model never marks an answer.
- A wrong answer has a name. Every question is built with the mistakes children really make, such as "added the bottom numbers" or "forgot to carry". The system knows why an answer was wrong, not only that it was.
- Pictures made of folded paper. Bars, groups and place-value blocks show the structure of the problem without giving the answer away. Each picture is checked by a program for leaked answers.
- Speech is treated gently. If what a child said could mean two numbers, Math Trail asks again. It is never counted as a mistake.
- An agent that reads counts, not words. After a session an analyst agent sees only counts and kinds of mistakes, never the questions or what the child said, and proposes one next step. Code checks it against a chain of prerequisites, and plain rules take over if the model fails. The parent sees who decided.
- It teaches checking, too. In Spot the Mistake the child finds which kind of mistake a student made. Finding a mistake is a different skill from avoiding one.
- It never compares children. Progress is each child's own path, with a line that marks where a skill counts as mastered.
Who it is for
Children in grades 4 to 6 (ages 9 to 12) and the adults who help them. Three missions are open today: Fractions, Multiply and Divide, and Decimals. Place Value and Measurement are planned. The interface is in English.
How it was built
Math Trail was made for the Amazon Developer Hackathon 2026, in the Alexa+ track, with Amazon Bedrock for the analyst agent. It is an MCP server written in Rust that speaks protocol 2025-11-25 over Streamable HTTP, a folded-paper learning card served as an MCP App, and a web simulation of a smart display that talks to the same server. A coding assistant (Code Assistant) was used to speed up development and debugging, under the author's direction and review. The source code is open under the MIT license.
What we do not claim
- No child has used it yet, so we claim no learning gain.
- It has not run on a real Alexa+ device. The simulation stands in for a smart display and is not an Amazon product.
- It is not a diagnosis of any learning difficulty and not an official assessment. Its suggestions are ideas for practice.
Ideas we started from
These works shaped the design. They are the starting ideas, not evidence that Math Trail works.
- Brown, J. S. and Burton, R. R. (1978). Diagnostic models for procedural bugs in basic mathematical skills. Cognitive Science, 2(2).
- Resnick, L. B., Nesher, P., Leonard, F., Magone, M., Omanson, S., and Peled, I. (1989). Conceptual bases of arithmetic errors: the case of decimal fractions. Journal for Research in Mathematics Education, 20(1).
- Chi, M. T. H., de Leeuw, N., Chiu, M.-H., and LaVancher, C. (1994). Eliciting self-explanations improves understanding. Cognitive Science, 18(3).
- Bloom, B. S. (1984). The 2 sigma problem: the search for methods of group instruction as effective as one-to-one tutoring. Educational Researcher, 13(6).
Who made it
Muhammad Zia ul Haq, EZI EDUTECH, zia@eziedutech.dev. Source code: github.com/eziedutech/mathtrail.