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How we teach

What this is built on

Four questions, answered plainly: what actually happens in a lesson, where our sequence comes from, what rules our tutor is held to, and what we have not proven yet.

336hand-built lessons
10full courses
25,376practice problems
100checks on every single reply
11,582automated checks per release

Counted, not claimed — figures as of August 2026. Every number above is machine-counted from the app itself, by the same test run that has to pass before anything ships. They go up as we build; none of them is an estimate.

1. What actually happens in a lesson

No mystery, no hand-waving. Here is the whole thing, plainly.

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An AI teacher talks with your student — really talks

Mr. Cadabra speaks out loud, draws each step on the whiteboard as he says it, and your student answers him — out loud, or by tapping, or by typing. He teaches the idea first, working a problem all the way through, and then hands one over. If the student is stuck, he gives more help: a hint before a smaller step, a smaller step before the answer, and never the same question the same way twice. Every lesson follows a plan we wrote and tested by hand — what to teach, in what order, with which problems — and the AI walks your student through that plan, listening and adapting as it goes. That blend is deliberate: the curriculum is not improvised, and the conversation is not canned.

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The AI is powerful — so we built machinery to keep it accurate

Artificial intelligence is what makes a real conversation possible, and we use it proudly. We also do not simply trust it. Every practice problem's answer is computed by a math engine, never typed in by a person. When the tutor speaks, every mathematical claim in the reply is re-computed by that same engine to confirm it is literally true, and 100 separate automated checks read the reply before your student sees it — a reply that fails one is rejected and rewritten, not shipped. Then a second, independent AI reviews what the first one wrote. Two AIs and a math engine, checking each other, on every single reply.

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Feedback everywhere — all of it built to encourage

Learning runs on feedback, so it comes from every direction: spoken in the moment, in a warm voice that says what was right before what to fix; written on the board, where the running tally is honest arithmetic, never judgment; and on the site, where progress, practice, and streaks each earn their own recognition. Parents see it too — a plain-English dashboard of what their student has mastered and where to help next — and teachers get the same for a whole class. All of it is positively structured: your student is compared to nobody but themselves, effort is praised on its own terms, and practice can never hurt a mastery record — it can only show how hard they worked.

2. What we teach, and where the order comes from

A curriculum is a sequence before it is anything else. Get the order wrong and a student meets an idea before the one it stands on.

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The elementary sequence follows the Common Core State Standards for Mathematics

For our two youngest courses we worked against A Story of Units — the Pre-K through Grade 5 curriculum map, curriculum overview and CCSS checklist published by Great Minds. We used it the way a teacher uses a scope-and-sequence document: to decide what comes before what, which fluencies each grade owes the next, and where the usual gaps open up. Counting comes before adding; adding before carrying; carrying before regrouping. That order is not our invention and we did not want it to be. A Story of Units: Curriculum Map, Curriculum Overview, and CCSS Checklist for Grades P–5. © 2015 Great Minds, eureka-math.org (SOU-1.3.0-07.2015). We are not affiliated with Great Minds and claim no endorsement by them.

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The teaching practices come from the MAA Instructional Practices Guide

Published by the Mathematical Association of America, this is a professional body's own account of what good mathematics instruction looks like. It is written for undergraduate teaching, so we treat it as it is: directly relevant to our Calculus and Differential Equations courses, and a sound guide to teaching practice everywhere else. Three of its sections shaped this product more than anything else — wait time, developing persistence in problem solving, and the selection of appropriate mathematical tasks. MAA Instructional Practices Guide. © 2018 The Mathematical Association of America. Open access under CC BY-NC 4.0. Print ISBN 978-0-88385-198-2. We are not affiliated with the MAA and claim no endorsement by them.

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The courses between them follow the standard progression

Pre-Algebra, Algebra I, Geometry, Algebra II, Trigonometry and Pre-Calculus, and Probability and Statistics follow the conventional United States course sequence, nine units each, in the order these subjects are normally taught. Where a course depends on an earlier one, we say so inside the lesson rather than assuming the student remembers.

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The teaching moves in those courses come from the federal What Works Clearinghouse

The What Works Clearinghouse, run by the U.S. Department of Education's Institute of Education Sciences, publishes practice guides that grade classroom techniques by the strength of the research behind them. Three of those guides were open on the desk while our teaching rules were written — and the rules carry the guide numbers to this day:

  • Improving Mathematical Problem Solving in Grades 4–8 — its recommendation that students monitor and reflect while they solve, one of only two the guide rates at Strong Evidence, is our rule "teach the student to check themselves." Its multiple-strategies recommendation is our rule "two ways, one board, then 'which would you choose?'"
  • Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students (grades 6–12) — its solved-problems recommendation is our rule "find the error: a wrong solution, clearly labeled, is a problem type of its own," and its strategy-choice recommendation (the guide's best-evidenced) is the "which would you choose?" question our tutor asks after showing two ways.
  • Assisting Students Struggling with Mathematics (2021) — all six of its recommendations carry the Clearinghouse's strongest evidence rating. Its number-line recommendation is our rule "the number line is a tool you use on purpose, not a decoration." Its word-problems recommendation is our rule "a word problem has a type — name the type, never teach key words." Its mathematical-language recommendation is two of ours: "one name per thing, all lesson" and "vocabulary is taught, never assumed."

We did not adopt these guides as decoration. Each mapping above names a written rule in our tutor, and most of those rules are enforced by code on every reply — the same release checks that count the numbers at the top of this page verify them. What Works Clearinghouse practice guides: Improving Mathematical Problem Solving in Grades 4 Through 8 (NCEE 2012-4055, revised 2018); Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students (NCEE 2015-4010, revised 2019); Assisting Students Struggling with Mathematics: Intervention in the Elementary Grades (WWC 2021006). All are public documents of the U.S. Department of Education, Institute of Education Sciences, available free at ies.ed.gov. No endorsement by the Department or the Institute is claimed or implied.

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The statistics course follows the GAISE II framework

For Probability & Statistics we checked our unit sequence against GAISE II — the Pre-K–12 guidelines for statistics education published by the American Statistical Association with the National Council of Teachers of Mathematics. Its four-step investigative process — formulate a statistical question, collect the data, analyze the data, interpret the results — is the arc of our course: exploring and describing data first, then how data is collected, then probability as the tool for quantifying randomness, and inference last, once the student has everything inference stands on. Pre-K–12 Guidelines for Assessment and Instruction in Statistics Education II (GAISE II), © 2020 American Statistical Association. Available free at amstat.org. Consulted for our course's sequence; no content is reproduced and no endorsement is claimed or implied.

3. How we teach — and the rules we hold ourselves to

Our tutor works from 65 written teaching rules. Thirty-three of them are not merely written down — they are enforced by code, and 100 separate checks read every reply before a student ever sees it. A reply that breaks one is rejected and rewritten, not shipped and apologised for. Here are the ones that matter most.

Teach it before you ask it

A lesson demonstrates the idea worked all the way through — out loud, on the board — before the student is asked to do one. Opening with a question is not teaching, it is testing. This is the MAA guide's I do, then you do, and it is the rule we break least. The tutor is allowed to take the length teaching needs, even though every other reply is kept short.

No cold quizzes

Before any quiz counts toward mastery, the student must have got two problems right on that topic without hints. If they have not, the tutor teaches another one instead and says why in a way that sounds like confidence rather than delay. Without this rule a quiz score is a coin flip written permanently onto a student's record.

One more try before anyone is told the answer

A wrong answer earns a second attempt at the same problem before the answer is given. When a student misses twice, the teaching restarts rather than the score simply falling. The MAA guide calls this developing persistence, and describes the instructor resisting the urge to tell and asking a guiding question instead. That is exactly the moment our tutor is designed for.

The same word for the same idea, every time

If a student learns "over nine, carry", they will not hear "ten or more, carry" four turns later. The first phrasing a student meets is recorded and it is the one that comes back — for as long as they use the app. To an adult those are the same sentence. To a seven-year-old they are two different rules, and nobody taught the second one.

Every problem is checked before a student sees it

Every one of our 25,376 practice problems is put through the same validator: the answer is computed, never typed; the numbers stay inside the range the lesson promises; the difficulty only ever climbs; and every sentence is read aloud against a fixed vocabulary. This is the MAA guide's selecting appropriate mathematical tasks, done in advance rather than hoped for.

A student is compared to nobody but themselves

There are no leaderboards, no class rankings, and no percentiles. Progress is measured against where that student was, and effort is rewarded on its own terms — practice and streaks earn their own awards, separately from mastery. Mastery is earned on quizzes. Practice is for getting better, and it is counted so a student can show somebody how hard they worked.

4. What we have not proven

There is no efficacy study of this product. We have not run a trial, we do not have outcome data across a population of students, and we are not going to point at somebody else's research and let you assume it was about us. This app has not yet been in enough students' hands for anyone to make that claim honestly — including us.

What we can tell you is exactly what we built, what we built it from, and what it refuses to do. Those are the things on this page, and every one of them is checkable.

We are in beta, and that is the honest word for it. If you want to know whether this works for your student, the only real answer available today is to try a lesson and judge it yourself — which is why a lesson is free and needs no card.

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Sources named on this page were read in full before they were cited. We reproduce no third-party content, and neither organisation has reviewed or endorsed this product.