Why hand-author anything?
The obvious approach for seeding an adaptive math tutor is to generate problems programmatically. Pick two random numbers, subtract them, done. I tried this first and it failed for a specific reason: generated problems don't have meaningful hints.
A hint like "Try subtracting the ones column first" is generic. A hint like "2 ones minus 9 is impossible without borrowing — take a ten from the 3 tens" is diagnostic. It names the exact step where a dyscalculic student is likely to get stuck, and it names the operation they need to perform. That second kind of hint requires a human who understands the problem.
NumPath's Phase 1 seeds 100 problems across 5 Knowledge Components, each with two progressive hints, a calibrated difficulty score, and structured metadata that the MistakeClassifier uses to diagnose errors. Every one is hand-authored.
The content schema
