Structure mapping reduces effort in learning math procedures from examples
Structure-Mapping-Guided Self-Explanation for Learning Mathematical Procedures
Artificial Intelligence
Summary
Figuring out how math steps work just by watching examples can be very hard because many possible explanations fit the numbers. The authors created a computer method that looks at the structure of math expressions to guide the search for the real steps taken. This method finds the intended math procedure much faster and checks fewer wrong guesses than random trying. Their results suggest that understanding the relationships in math expressions helps people learn procedures more efficiently from examples.
What this means in practice
- •For educational software developers: Design math tutoring systems that efficiently infer students’ problem-solving steps using structure-based guidance.
- •For intelligent tutoring system builders: Improve automatic feedback by reducing guesswork when reconstructing student math procedures from their answers.
Authors
Shinhaeng Lee, Christopher J. MacLellan, Daniel Weitekamp
Abstract
Worked examples are a powerful form of instruction, but learners must infer how the demonstrated steps were produced. A naive simulation of this self-explanation process can generate thousands of numerical explanations that reproduce one observed change without capturing its underlying procedure. We propose structure-mapping-guided self-explanation as a computational account of the cognitive biases that reduce search effort and make this inference tractable. The model represents mathematical expressions as typed relational structures and uses structure mapping to identify corresponding source and target regions. For each changed target value, the corresponding source region serves as an anchor: it guides abductive search toward structurally relevant values and operations before broader alternatives, yielding ordered, executable candidate procedures with inspectable source evidence. Across 70 mathematical transformations containing 120 changed numeric components, the model recovered every intended procedure. It returned the intended procedure before any other computation producing the same target value in 104 subproblems (86.7%), compared with a median of 32 (26.7%) across 100 unguided runs that tested candidate calculations in random order. Our proposed model also tested 93.8% fewer combinations of values and operations than unguided search before reaching the intended procedures. These results provide an efficient, interpretable account of how relational structure can guide procedural learning and a testable hypothesis about human self-explanation from worked examples.