Let Me Try Again: Examining Replay Behavior by Tracing Students' Latent Problem-Solving Pathways

TL;DR

The paper addresses how replay and problem-solving pathways unfold in a game-based algebra learning platform and how these dynamics relate to learning. By applying Markov chains and Hidden Markov Models to log data from FH2T with 777 seventh graders, it identifies four latent states and demonstrates that immediate replay and replay-dominant/optimal-ending pathways predict higher conceptual knowledge, flexibility, and performance, with timing being crucial. Regression analyses further reveal that latent-state engagement across within- and across-problem contexts robustly predicts proximal and distal outcomes, while immediate replay consistently benefits learning and delayed replay shows weaker or negative associations. The work provides actionable insights for digital-learning design to promote productive exploration, rapid iteration, and smooth transitions toward efficient strategies in algebra.

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.

Figures (3)

• Figure 1: Example Problem 14 from FH2T with sample solution steps (Start State: $47+33+b+52+68$ Goal State: $99+b+101$
• Figure 2: Transition matrices for within-problem (top row) and across-problem (bottom row) Markov Chain analyses. Each row shows transition probabilities (P) and average log(Time) (T).
• Figure 3: HMM results for Across-problem analysis: (a) emission distributions, and (b) transition probabilities.