Math Ladder AI is an expert system: it emulates the moment-to-moment decisions of a skilled tutor — what should this student work on right now? — using a knowledge graph and the cognitive-science learning strategies with the strongest research evidence: mastery learning, spaced repetition, and interleaved practice.
Every topic in the course is a node, connected by weighted prerequisite edges. “Two-Step Equations” points back to “One-Step Equations”, which points back to “Negative Numbers”, and so on. The graph is what lets the system reason about your knowledge instead of just recording scores.
Instead of testing all topics, the diagnostic bisects the graph. Each question targets the topic of median depth among the still-undecided ones. Answer correctly and the topic plus every prerequisite beneath it is marked known; miss it and the topic plus everything built on it is marked unknown. A handful of questions places the whole graph and finds your knowledge frontier.
You only get a lesson when every one of its prerequisites is mastered, and you must score at least 75% on a lesson's practice to master it. No moving on with gaps — gaps are what make later math feel impossible.
And when you miss a problem, the system doesn't just show the answer and move on. It re-teaches the method with a worked example and immediately hands you a fresh problem of the same type to work — active correction, right at the moment of the mistake, before you continue.
Each mastered topic has a repetition number; every successful review raises it and roughly doubles the time until the next review (2 → 4 → 8 → 16 days…). Fail a review and the topic comes back immediately.
Crucially, knowledge in math is hierarchical: solving two-step equations is practice of one-step equations. So when you advance a topic, fractional credit trickles down its prerequisite edges (scaled by each edge's weight), postponing reviews of skills you just practiced implicitly. You never waste time reviewing something you used five minutes ago inside a harder problem.
Every time you ask for work, the engine picks the highest-value task:
| Review | Overdue spaced reviews come first — up to three topics interleaved in one task, which is harder but builds far more durable memory than blocked practice. |
| Quiz | After every six lessons, a timed-feel quiz over recent material. Missed topics get targeted remediation: their reviews are rescheduled to now. |
| Lesson | Otherwise, the next frontier topic — always something you have the prerequisites for, never something you've already shown you know. |
One XP is calibrated to roughly one minute of focused work. You set a daily XP goal; hitting it every day builds a streak. Progress is measured in work completed, not time spent staring at the screen.
From trigonometry onward, answers stop being plain numbers. Math Ladder AI
grades by mathematical equivalence using a computer-algebra system:
pi/6, sqrt(2)/2, 1/sqrt(2),
3x^2+sin(2x) — any correct form counts, and "+C" on an
indefinite integral is optional.
Once you're into the calculus units, the AP Practice tab generates timed sections at real AP pacing: no-calculator multiple choice (2 min/question), calculator multiple choice (3 min/question), and multi-part free-response questions scored against 9-point rubrics with the scoring breakdown revealed after each part. Recent section results combine into a projected AP score on a BC-style curve, and questions are drawn from the topics you've actually mastered — so the projection reflects you, not a generic test bank.