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

1. Problem Statement

The study addresses the challenge of identifying and understanding Learned Helplessness (LH) in mathematics learning within Intelligent Tutoring Systems (ITS). While ITS can adapt to student needs, they often reveal negative behavioral patterns—such as avoidance, skipping problems, and help-seeking avoidance—that limit learning gains.

• Gap: Existing research on LH relies heavily on surveys or experimental tasks. There is a lack of studies using detailed interaction logs from tutoring systems to uncover specific behavioral co-occurrences associated with LH.
• Specific Need: There is limited comparative analysis of these behavioral patterns across different LH levels (low vs. high) and between students with and without system-based interventions. Without this data, adaptive features cannot be effectively designed to target specific disengagement behaviors.

2. Methodology

Dataset

• Source: Data was extracted from AES (Adaptive Equation Sensei), a mathematics tutoring system used by Grade 8 students in the Philippines.
• Sample Size: 3,696 interaction sessions generated by 246 students.
• Groups:
  • Intervention Group (n=133): Received automated hints, motivational messages, and engagement prompts upon errors.
  • Without-Intervention Group (n=113): Used the same system but without these specific support features.
• Timeframe: Data collected between 2024 and early 2025.

Variables

• Behavioral Indicators (Binary/Categorical):
  • MistakeOccurred: Whether an error was made.
  • HintUsed: Whether a hint was accessed.
  • Skipped: Whether the problem was skipped.
  • Status: Problem outcome (Solved vs. Unsolved).
  • Session-level counts: TotalSteps, TotalHints, TotalAnswerAttempts.
• Grouping Variables:
  • With Intervention (Yes/No).
  • Label (Low LH vs. High LH).
  • Note on LH Labeling: The LH classification was not self-reported but derived from a Random Forest machine learning model (trained in prior work) using Yates's (2009) teacher-rated scale as ground truth. The model achieved 92% accuracy and 98% recall for high LH cases.

Analytical Approach

• Algorithm: The Apriori algorithm (implemented via Python's mlxtend library) was used for Association Rule Mining.
• Rationale for Apriori: Selected over predictive models (e.g., logistic regression) because it produces explicit "if-then" rules (Support, Confidence, Lift) that are interpretable by educators and designers. It is suited for session-level transactional data where temporal ordering is less critical than co-occurrence.
• Parameters:
  • Minimum Support: 0.20 (pattern must appear in ≥20% of sessions).
  • Minimum Confidence: 0.60 (rule must hold true in ≥60% of relevant transactions).
  • Minimum Lift: >1.0 (association must be stronger than chance).
  • Sensitivity Analysis: Conducted across nine threshold combinations to ensure pattern stability.

3. Key Contributions

1. Operationalization of LH in Logs: Successfully applied a machine-learning-derived LH label to mining association rules in educational logs, bridging psychological constructs with behavioral data.
2. Granular Behavioral Segmentation: Provided a comparative analysis of behavioral patterns across three distinct dimensions: LH level, intervention status, and problem-solving outcome.
3. Identification of Avoidance Markers: Isolated specific behavioral signatures (e.g., skipping without hints) that strongly predict unsolved outcomes, distinguishing between persistence and avoidance strategies.
4. Methodological Validation: Demonstrated the stability of key association rules across varying support and confidence thresholds, ensuring the findings are not artifacts of specific parameter choices.

4. Key Results

General Findings

• Dominant Pattern: The most frequent pattern linked to unsolved outcomes was skipping problems without using hints.
• Persistence: Persistence behaviors (not skipping) were less dominant overall but strongly linked to success in specific subgroups.
• Help Avoidance: Skipping without hints predicted unsolved outcomes across all groups.

By Learned Helplessness (LH) Level

• Low-LH Students:
  • Showed strong positive associations between persistence (not skipping) and solved problems (Lift = 2.33).
  • Demonstrated a positive link between hint use and solved outcomes (Lift = 1.39).
• High-LH Students:
  • Exhibited stronger avoidance patterns. Skipping was strongly tied to unsolved outcomes (Lift = 1.39).
  • Showed a pattern of skipping even without prior mistakes, indicating a tendency toward disengagement rather than just error correction.

By Intervention Status

• Without Intervention:
  • Exhibited the strongest persistence-success link (Not Skipped → Solved, Lift = 2.85).
  • Showed a notable pattern connecting hint use to mistakes (Lift = 1.77).
• With Intervention:
  • The group showed stronger patterns where skipping led to unsolved outcomes.
  • Caveat: The study notes that since groups were from different schools without randomization, these differences may reflect pre-existing group characteristics rather than the causal effect of the intervention.

Stability Check

• The primary avoidance rules ({Skipped} → {Unsolved} and {Skipped, No Hint} → {Unsolved}) maintained identical Lift values across all nine threshold combinations, confirming their robustness.

5. Significance and Implications

Theoretical Implications

• The study validates that behavioral logs can serve as effective proxies for psychological constructs like Learned Helplessness.
• It supports Attribution Theory and Self-Determination Theory by showing that students who attribute failure to uncontrollable causes (High LH) exhibit distinct avoidance behaviors (skipping, no help-seeking) compared to Low LH students.

Practical Implications for ITS Design

• Early Detection: Systems can detect early signs of avoidance (repeated skipping, low hint usage) to trigger timely interventions.
• Targeted Support:
  • For High-LH Students: Interventions should focus on guiding them toward productive hint use and reinforcing persistence after mistakes to break the cycle of helplessness.
  • For Low-LH Students: Systems can focus on sustaining engagement and gradually increasing difficulty to build resilience.
• Adaptive Feedback: The findings suggest that simply providing hints is insufficient; the system must actively encourage the use of hints and discourage skipping behaviors that lead to unsolved outcomes.

Limitations & Future Work

• Causality: Due to the lack of randomization between intervention groups, findings are correlational, not causal.
• Unit of Analysis: The study analyzed session-level co-occurrences, not individual student trajectories. Future work should use multilevel modeling to account for within-student dependencies.
• Context: The study was limited to Grade 8 students in the Philippines; results may vary by educational level or culture.
• Data Depth: Logs capture what happened but not why. Future studies should integrate logs with self-reports or think-aloud protocols to understand the motivational drivers behind skipping.