Math Circle Home

1. Pedagogical lineage is explicit

This is not invented from scratch. It draws from a documented tradition of cognitive-development math education:

2. The four magic prompts, baked in

Every problem ends with one or more of these. They are the most reliably underused tools in early math instruction:

1. "How do you know?" — even after a right answer.
2. "Can you show it another way?" — fingers, drawing, ten-frame, story.
3. "What if it were different?" — what if the number were 8 instead of 7? what if there were 3 baskets?
4. "What did you notice?" — at the end of every session.

Each problem in the bank carries an explain_prompt field. A child can reach the right answer without articulation, but the conversation is what builds long-term mathematical thinking.

3. Strategy tracking + an optional AI tutor's-eye-view

Most apps track whether a child got the answer. Math Circle Home tracks how they thought about it.

• Each problem ships with a list of possible strategies a child might use ("count up", "near-doubles", "decompose", "balance model", "work backwards", etc.). These are hand-authored by the curriculum.
• Parents type a free-text strategy note per attempt. The system stores the verbatim text.
• Every attempt receives a parent rating: easy, good struggle, or too hard. This rating directly drives level adaptation — targeting the productive-confusion zone.

Optionally, you can opt in to a weekly AI digest: a short, parent-facing note that reads the past seven days of attempts + strategy notes + parent ratings, and surfaces patterns a parent might miss skimming the raw data. Powered by Amazon Bedrock with Anthropic's Claude Haiku 4.5. Data does not leave the AWS region; the model is not trained on your prompts; child names are anonymized to "Child" before being sent.

"Praise the strategy, not the speed." — the principle behind every UX choice in this app.

4. Math Circle Night mode

Modeled on the Soviet/Russian after-school math circle: a 20–30 minute session for siblings or small mixed-age groups, working cooperatively on a shared problem. The system composes a mixed-level plan automatically — the older child explains, the younger spots patterns, both contribute.

This is the underrated dimension of the math-circle tradition: math is a social activity. The home version of "math night" can be ten minutes at the kitchen table, but it changes how children identify with the subject.

5. Open longitudinal data (JSON / CSV export)

Every attempt, every strategy note, every parent rating, every session plan is exportable as JSON or CSV from the parent dashboard. No proprietary lock-in, no walled garden. A teacher, researcher, or curious parent can:

• See which strategies a child returns to over time.
• Track when "good struggle" turns into mastery, by strand.
• Look for stalled levels and target conversations there.
• Hand the data to another tool — anki, a spreadsheet, a research project.

The promise: your child's mathematical thinking belongs to you.

6. A living curriculum that grows with the child

Per-strand adaptive levels. Each child has 10 strand skills tracked independently, each on a 7-level scale (Level 1 ≈ Pre-K, Level 7 ≈ mid-2nd-grade enrichment). A child can be at Level 4 in Patterns and Level 2 in Geometry at the same time — and that's the whole point. The system shows progress per strand on the parent dashboard.

The parent rating is the dial. After every problem, the parent rates it easy, good struggle, or too hard. The system uses that — plus rolling accuracy across the last 5 attempts and consecutive-correct streaks — to move the strand level up or down before the next session. "Too hard" twice → ease down. "Easy" twice in a row → step up. The child never sees this; the parent sees the level change on the dashboard.

Cooldown + parametric variants prevent staleness. A problem the child has seen in the last 4 sessions won't reappear. 22 parametric generators produce fresh variants on demand (new numbers, new objects, new contexts) and each generated problem is persisted — so the bank grows organically with use rather than draining.

Pre-K has its own depth. Pre-K runs Level 1 (foundational: subitize 1–3, AB patterns, one-attribute sorting, vertical symmetry) and Level 2 (subitize to 6, ABCABC / AABB / two-attribute patterns, multi-attribute sorting, shape-constancy-under-rotation, count-on, decomposition of 5 and 7). Same parent-led format at both levels — but the cognitive demand at Level 2 maps to late Pre-K / pre-K-to-K-bridge work, not a re-skin of the foundational set. Per-strand skill tracking is on for Pre-K too: a child can be at L2 in Patterns and L1 in Measurement, just like K–2.

Pre-K-to-K graduation, on real evidence. The dashboard surfaces a "Ready for Kindergarten?" prompt only when a Pre-K child has reached Level 2 in at least 7 of the 10 strands, with 25+ attempts logged and no recent "too hard" pattern. That's "meaningfully engaged with the deeper Pre-K material," not "clicked through a few foundational warm-ups." One click promotes them and the K–2 7-level adaptive engine takes over from there.

Open-source, auto-deploy. Every push to main triggers a GitHub Action that pulls and restarts the live service within ~15 seconds. Curriculum changes ship as I write them, not on a release cadence.

Bank-size projection (parametric growth × 365 sessions × typical generation rate) lands in the ~2,000–6,000 problem range over 1–3 years of daily use; the exact figure depends on which strands a child gravitates toward.