[论文解读] Let Me Try Again: Examining Replay Behavior by Tracing Students' Latent Problem-Solving Pathways

Shan Zhang, Siddhartha Pradhan+3 more|arXiv (Cornell University)|Jan 3, 2026

Educational Games and Gamification被引用 0

一句话总结

该论文使用马尔可夫链和隐马尔可夫模型来分析七年级学生在 FH2T 中解决问题的路径和回放行为与就近与远期代数学习结果的关系。

ABSTRACT

Prior research has shown that students' problem-solving pathways in game-based learning environments reflect their conceptual understanding, procedural knowledge, and flexibility. Replay behaviors, in particular, may indicate productive struggle or broader exploration, which in turn foster deeper learning. However, little is known about how these pathways unfold sequentially across problems or how the timing of replays and other problem-solving strategies relates to proximal and distal learning outcomes. This study addresses these gaps using Markov Chains and Hidden Markov Models (HMMs) on log data from 777 seventh graders playing the game-based learning platform of From Here to There!. Results show that within problem sequences, students often persisted in states or engaged in immediate replay after successful completions, while across problems, strong self-transitions indicated stable strategic pathways. Four latent states emerged from HMMs: Incomplete-dominant, Optimal-ending, Replay, and Mixed. Regression analyses revealed that engagement in replay-dominant and optimal-ending states predicted higher conceptual knowledge, flexibility, and performance compared with the Incomplete-dominant state. Immediate replay consistently supported learning outcomes, whereas delayed replay was weakly or negatively associated in relation to Non-Replay. These findings suggest that replay in digital learning is not uniformly beneficial but depends on timing, with immediate replay supporting flexibility and more productive exploration.

研究动机与目标

• 研究学生在 FH2T 中在解题策略之间以及在不同题目之间的转换。
• 识别来自完整题序列的潜在解题状态。
• 检验潜在状态对就近和远期学习结果的预测力。
• 评估回放时机（即时与延迟）与学习结果的关系。

提出的方法

• 使用12个带标签的尝试状态，用一阶马尔可夫链对题内与题间转移建模。
• 对12类尝试序列应用带5折交叉验证和BIC的隐马尔可夫模型以识别潜在状态。
• 解码隐含状态并分析发射分布和转移矩阵，以解释动态路径。
• 计算状态百分比和跑长以将潜在状态与就近后测构建及远期状态测试联系起来。
• 使用回归分析（OLS）在控制前测分数和参与度变量的情况下，将状态参与度与学习结果相关联。
• 将回放分解为即时、延迟和非回放，并比较它们与结果的关联。

Figure 1 . Example Problem 14 from FH2T with sample solution steps (Start State: $47+33+b+52+68$ Goal State: $99+b+101$

实验结果

研究问题

• RQ1 研究问题1：学生在题内及题间如何在不同解题策略之间转换？
• RQ2 研究问题2：在建模完整题序时，会出现哪些潜在解题状态，以及这些状态之间发生了哪些转变？
• RQ3 研究问题3：潜在解题状态如何预测就近与远期学习结果？
• RQ4 研究问题4：学生的回放行为（即时与延迟）与就近与远期学习结果之间有什么关联？

主要发现

• 回放主导和最优结尾的潜在状态相较于不完整主导状态，能预测更高的概念性知识、灵活性和状态测试表现。
• 跨题分析显示，具有回放主导和最优结尾模式的状态，与多项结果在FDR校正后存在正向关联。
• 即时回放与更好的学习结果一致相关，而延迟回放在与非回放的关系中表现较弱甚至呈负相关。
• 题内转移表现出状态和回放序列的持续性，而题间转移表现出跨题策略的强持续性。
• 隐马尔可夫模型识别出四个潜在状态：混合型、非完整主导型、最优结尾型和回放主导型，具有不同的转移模式和跑长。

(a) Within-problem Transition Probabilities