Apriori-based Analysis of Learned Helplessness in Mathematics Tutoring: Behavioral Patterns by Level, Intervention, and Outcome

Sustained effort is essential for realizing the benefits of intelligent tutoring systems (ITS), yet many learners disengage or underuse available practice time. We introduce engagement forecasting as a supervised prediction task based on ITS logs, targeting two outcomes central to effort and learning progress: minutes practiced per week and new skills mastered per week. Using interaction log data from 425 middle-school students over a school year, we benchmark fifteen predictors including regressions, decision trees, and neural networks. We show that these feature-based models reduce mean absolute error (MAE) by 22-33% relative to heuristic baselines, including fixed-percentile rules adapted from prior work in other behavioral domains. We find that percentile heuristics systematically overpredict, whereas feature-based models better track student practice trajectories across weeks. To support explainability, we analyze feature importance and ablations, revealing target-specific patterns: effort forecasting is driven mainly by recent activity features, while progress forecasting depends more on learner-state and content difficulty signals. Finally, in a semi-structured user interview case study with eight college tutors, we examine how tutors reasoned about system-generated predictive features when setting goals with students. We find that tutors reasoned differently about effort versus progress goals in ways that mirror our pattern analysis. Together, these results establish a reproducible benchmark for forecasting weekly effort and learning progress in ITS. By making patterns of sustained effort and progress visible at a weekly timescale, engagement forecasting offers a foundation for supporting tutor-learner goal setting and timely instructional decisions.

Aligning LLMs for math tutoring typically requires RL-based training with multi-GPU infrastructure. We investigate whether training-free prompt optimization-evolving only the system prompt via API calls-can serve as a practical alternative. We adapt 7 published methods and propose 5 education-specialized methods, evaluating these 12 methods under 5 conditions on 2 OOD benchmark suites. All 12 best-per-method configurations surpass the strongest RL-trained baseline (R_total = 0.633), and our ParetoGrad achieves the best Pareto balance across post-test solve rate, leak control, and helpfulness, rather than dominating any single component. Behavioral analysis with an 82-code educational codebook reveals that training-free methods rely on teaching-knowledge patterns at 2-3x the rate of RL-trained models, with a compensating ~10 percentage-point reduction in intent-level scaffolding. We also find a task-dependent reasoning mode effect consistent across training-free and RL-based paradigms. Our approach enables efficient development of pedagogically aligned LLM tutors with prompts alone and minimal compute.

Tool-integrated reasoning (TIR) has become a key approach for improving large reasoning models (LRMs) on complex problems. Prior work has mainly studied when to invoke tools, while overlooking how tools are applied. We identify two common patterns: a calculator pattern that uses code for direct computation, and an algorithmic pattern that encodes problems as programs. Misaligned choices often cause failures even when reasoning is sound. We propose a two-stage framework that first builds code competence from both patterns and then aligns pattern selection with teacher preferences. Across challenging math datasets, our pattern-aware method substantially improves both code usage and accuracy, for instance raising Code@1 on MATH500 from 64.0% to 70.5% and on AIME24 from 26.7% to 50.0%. These gains highlight the effectiveness of a pattern-aware approach for tool-integrated reasoning.