arXiv:2604.08693cs.CYcs.HC2026-04

用数学解题过程的转换特征,建模通用解题策略。

Towards Generalizable Representations of Mathematical Strategies

  • 通过前后步骤向量差提取解题转换特征
  • 在多任务上验证策略信息编码能力,相关性显著
  • 适合教育数据挖掘与跨平台学生行为分析

预训练数学文本编码器在公式分类和信息检索等任务中表现优异,但在捕捉学生完整解题路径的策略方面仍受限。以往方法依赖人工标注(难扩展)或平台特定动作表示(泛化性差)。本文提出一种新方法,学习跨问题的代数解题路径通用表示:先用高容量预训练模型编码连续解题状态,计算其向量差得到转换嵌入;再通过SimCSE对比目标,使语义相似路径在嵌入空间中靠近,不同策略分离。在多标签动作分类、解题效率预测和序列重构任务上评估,证明其能有效编码策略信息。进一步构建基于嵌入的策略独特性、多样性与一致性度量,与短期及长期学习成果显著相关,提供数学创造力与发散思维的可扩展代理指标。该方法支持无平台依赖的跨问题分析,展示了转换型序列嵌入在教育数据挖掘与自动化评估中的有效性。

原文摘要 · Abstract (English)

Pretrained encoders for mathematical texts have achieved significant improvements on various tasks such as formula classification and information retrieval. Yet they remain limited in representing and capturing student strategies for entire solution pathways. Previously, this has been accomplished either through labor-intensive manual labeling, which does not scale, or by learning representations tied to platform-specific actions, which limits generalizability. In this work, we present a novel approach for learning problem-invariant representations of entire algebraic solution pathways. We first construct transition embeddings by computing vector differences between consecutive algebraic states encoded by high-capacity pretrained models, emphasizing transformations rather than problem-specific features. Sequence-level embeddings are then learned via SimCSE, using contrastive objectives to position semantically similar solution pathways close in embedding space while separating dissimilar strategies. We evaluate these embeddings through multiple tasks, including multi-label action classification, solution efficiency prediction, and sequence reconstruction, and demonstrate their capacity to encode meaningful strategy information. Furthermore, we derive embedding-based measures of strategy uniqueness, diversity, and conformity that correlate with both short-term and distal learning outcomes, providing scalable proxies for mathematical creativity and divergent thinking. This approach facilitates platform-agnostic and cross-problem analyses of student problem-solving behaviors, demonstrating the effectiveness of transition-based sequence embeddings for educational data mining and automated assessment.

数学教育策略表示教育数据挖掘序列嵌入

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