A gradient-matching algorithm decomposes almost any composite student equation into primitive physics equations¶

Claim · All claims
Evidence · 1 study · design r2 · q2
Currency · newest study 2015 · not yet checked against its sources · not reviewed by a person

Subclaims¶

q2 i? Shapiro's algorithm can decompose almost any composite equation into its primitive constituents by searching for primitive equations whose gradient combination matches the student equation's gradient. → VanLehn 2015

Evidence¶

VanLehn 2015¶

VanLehn, K. (2015). Reflections on Andes' Goal-free User Interface. International Journal of Artificial Intelligence in Education. https://doi.org/10.1007/s40593-015-0067-7

q2 · i? · design · r2

A mathematical algorithm developed by sabbatical visitor Joel Shapiro for the Andes system, replacing combinatorial pre-generation of algebraic combinations, which "exploded combinatorially". The article says it decomposed almost any composite equation and calls it one of the small treasures of ITS research.

"The algorithm searched for a set of primitive equations such that a linear combination of their gradients at the solution point equaled the gradient of the student’s equation at the solution point."

Discussion¶

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