Evidence-aware Mastery

Every concept tracks five dimensions instead of one number: exposure (you met the material), supported performance (you succeeded with in-app assistance), independent performance (you succeeded without it), retention (you succeeded again after a delay), and transfer (you applied it in a different context than you learned it).

Concept cards show the proportions and a timeline of your recent evidence, plus one actionable sentence — "You last solved this with in-app assistance yesterday. We haven’t yet checked whether you can do it without assistance."

A 2024 field experiment in high-school mathematics found a troubling asymmetry: students with unrestricted AI assistance performed better during practice but worse when the assistance was taken away — and learning-oriented safeguards largely prevented the harm. Practice success alone is a poor proxy for learning.

The same logic applies to your own records: if the tutor helped, the twin should not quietly claim you know it. And metacognition research shows self-reported confidence drifts from actual performance — so the twin keeps your confidence rating and its own evidence in separate columns and shows you both.

Every mastery update is an evidence event with a unique key per question, evaluation, or completion — the same interaction can never be counted twice through chat analysis, teach-back, or synthesis. Assistance is recorded as what the platform can actually observe: hint chats and answer reviews inside the app. It cannot see tools you use outside, and the interface never claims otherwise.

Misconceptions inferred from conversation are marked "suspected" until an assessment confirms them; you can challenge any inference with one click, and your challenge is displayed rather than silently discarded.

Every concept starts at 0.40. Each piece of evidence updates it with one rule: new = old + step × (outcome − old), where outcome is 1 for a correct answer, 0 for a wrong one, 0.7 for completing a lesson. Being right pushes the score toward 1; being wrong pulls it toward 0.

The step starts at 0.25 on a concept’s first piece of evidence and shrinks to a floor of 0.08 as evidence piles up: early answers move the score a lot, later ones fine-tune it. Two multipliers scale every step — question difficulty (easy ×0.8, medium ×1.0, hard ×1.25) and how centrally the lesson covers the concept (up to ×1.0).

The displayed score also settles back toward 0.40 with a 21-day half-life when a concept goes unpractised — your stored score never changes, only the display does. Bands: below 0.35 struggling, 0.35–0.70 developing, above 0.70 mastered.

What it powers: your tutor builds on what you struggled with and skips what you have mastered, quiz hints adapt their depth, and the weekly plan targets your weakest concepts first.

In your twin panel, every concept card shows its dimension chips, timeline, and the "what we haven’t checked yet" line. The weekly plan deliberately schedules "re-test unaided" steps for concepts you have only solved with help.