结构映射引导的自我解释用于数学程序学习
Structure-Mapping-Guided Self-Explanation for Learning Mathematical Procedures
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中文总结 AI 辅助
本研究提出结构映射引导的自我解释模型，利用关系结构锚定溯因搜索，高效恢复数学变换程序，显著减少搜索组合，为程序学习提供可解释计算框架。
中文摘要 AI 辅助
工作示例是一种强大的教学形式，但学习者必须推断出演示步骤是如何产生的。对这一自我解释过程的朴素模拟可以生成数千个数值解释，这些解释重现了一个观察到的变化，却没有捕捉其背后的程序。我们提出结构映射引导的自我解释，作为认知偏差的计算模型，这些偏差减少了搜索工作量并使这种推断变得可行。该模型将数学表达式表示为类型化关系结构，并使用结构映射来识别对应的源区域和目标区域。对于每个变化的目标值，相应的源区域作为锚点：它引导溯因搜索优先考虑结构相关的值和操作，然后再考虑更广泛的替代方案，从而产生有序、可执行的候选程序，并带有可检查的源证据。在包含120个变化数值组件的70个数学变换中，该模型恢复了每一个预期程序。在104个子问题（86.7%）中，它返回了预期程序，早于任何其他产生相同目标值的计算，而100次未引导运行（以随机顺序测试候选计算）的中位数为32（26.7%）。我们提出的模型在达到预期程序之前，也比未引导搜索测试了少93.8%的值和操作组合。这些结果为关系结构如何引导程序学习提供了一个高效、可解释的说明，并为人类从工作示例中进行自我解释提供了一个可测试的假设。
英文摘要
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.
