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.

翻译：针对数学文本的预训练编码器已在公式分类和信息检索等任务上取得了显著进展。然而，它们在表示和捕捉学生完整解题路径的策略方面仍存在局限。此前，这一目标要么通过劳动密集型的人工标注来实现（该方法难以规模化），要么通过学习与平台特定行为绑定的表示（这限制了泛化能力）。在本研究中，我们提出了一种新颖的方法，用于学习整个代数解题路径的问题不变表示。我们首先通过计算由高容量预训练模型编码的连续代数状态之间的向量差异来构建转换嵌入，该方法强调变换而非问题特定特征。随后，利用SimCSE通过对比学习目标学习序列级嵌入，使语义相似的解题路径在嵌入空间中靠近，同时将不相似的策略分离。我们通过多项任务评估这些嵌入，包括多标签动作分类、解题效率预测和序列重建，并展示了它们编码有意义的策略信息的能力。此外，我们推导了基于嵌入的策略独特性、多样性和一致性度量，这些度量与短期及长期学习成果相关，为数学创造力和发散性思维提供了可扩展的代理指标。该方法促进了对学生解题行为的平台无关和跨问题分析，展示了基于转换的序列嵌入在教育数据挖掘和自动评估中的有效性。