From Prompting to Epistemic Proactivity: Temporal Trajectories of Student-AI Interaction in Mathematics Learning

Technical Summary: From Prompting to Epistemic Proactivity

Problem Statement
While Generative AI (GenAI) systems are increasingly adopted as learning companions, particularly in mathematics, there is a critical gap in understanding how students utilize these tools in open-ended learning environments. Existing research often relies on static metrics (e.g., usage frequency, aggregate prompt quality) or surveys, which fail to capture the dynamic process of learning within the interaction. A central concern is "epistemic offloading," where students may rely on AI to perform the cognitive work required for genuine learning (e.g., identifying gaps, formulating questions, evaluating solutions) rather than engaging in it themselves. The paper posits that the quality of AI-supported learning depends not merely on the quality of individual prompts, but on whether students sustain "epistemically proactive" behaviors—strategic, self-regulated, and understanding-oriented engagement—over time. The study seeks to determine whether specific temporal trajectories of student-AI interaction predict subsequent independent (AI-free) performance.

Methodology

• Participants: 112 Grade-9 students (aged 14–15) from German Gymnasium schools. 97 students completed the full protocol, including pre- and post-tests.
• Task & Setting: Students engaged in a 40-minute, open-ended practice session with a web-based general-purpose LLM (Mistral Large) to prepare for a curriculum-aligned assessment on mathematical modeling (MM) involving linear and quadratic functions. The task was explicitly framed as skill improvement rather than task completion.
• Data Collection:
  • Pre/Post-Tests: Validated MM items from the IQB VERA pool to measure prior knowledge and AI-free post-intervention performance.
  • Conversational Data: Full chat transcripts were analyzed.
  • Coding Framework: A theory-driven, turn-level coding scheme was developed based on three dimensions:
    1. Self-Regulated Learning (SRL): Coded using Zimmerman's cyclical model (PLAN, MONITOR, REQUEST, EVALUATE).
    2. Help-Seeking (HS): Coded for orientation (instrumental vs. executive) and content (conceptual, procedural, verification, answer-seeking).
    3. Mathematical Modeling (MM): Coded using Blum's framework (understanding situation, identifying variables, mathematizing, working with model, interpreting, validating).
  • Validation: Automated coding via LLM (Gemini 2.5 Pro) was validated against human expert coders, showing acceptable agreement (Cohen's Kappa > 0.5 for most dimensions).
• Analytical Approach:
  • Static Analysis: Whole-session proportions of codes and behavioral diversity (Shannon entropy) were tested against post-test scores using ANCOVA, controlling for prior knowledge.
  • Temporal Analysis: The session was divided into early and late phases. Three "Proactivity Shift" indicators were calculated to measure the change in orientation from early to late phases:
    1. Regulation Proactivity Shift: Shift from REQUEST to (PLAN + MONITOR + EVALUATE).
    2. Help-Seeking Proactivity Shift: Shift from (Verification + Answer-seeking) to (Conceptual + Procedural).
    3. Mathematical Proactivity Shift: Shift from (Interpret + Validate) to (Understand + Structure + Mathematize + Work).

Key Results

• Descriptive Patterns: Interactions were dominated by REQUEST turns (74%), with instrumental help-seeking accounting for 70% of requests. Explicit regulatory moves (MONITOR, EVALUATE) were rare (5% and 3%, respectively). Mathematical modeling turns concentrated on "Understanding" (43%) and "Working" (32%), with "Validating" being rare initially.
• Static Predictors: Static summaries of interaction (whole-session proportions of SRL functions, request types, MM stages, and behavioral diversity) did not predict AI-free post-test performance after controlling for prior knowledge.
• Temporal Predictors: Temporal indicators were significant predictors of learning outcomes.
  • On average, students shifted away from proactive orientations over time (negative shifts in HS and MM proactivity), moving toward verification and validation.
  • However, students who exhibited a positive shift toward epistemically proactive orientations (increasing conceptual/procedural help-seeking and constructive mathematical work relative to verification/validation) achieved significantly higher post-test scores.
  • Specifically, the Help-Seeking Proactivity Shift ($\beta = .250, p = .009$) and Mathematical Proactivity Shift ($\beta = .209, p = .031$) significantly predicted post-test performance beyond prior knowledge.
  • The Regulation Proactivity Shift showed a positive but non-significant trend ($p = .090$).
• Group Differences: A trajectory grouping based on these shifts revealed that students maintaining or increasing proactive behaviors (Group 1) outperformed those shifting toward reactive behaviors (Group 0), with a significant difference in post-test residuals ($p = .014$).

Significance and Claims
The paper argues that productive AI-supported learning is best understood as a domain-specific trajectory of epistemic proactivity rather than a collection of isolated, high-quality prompts.

• Theoretical Contribution: The study demonstrates that static aggregates of interaction are insufficient for predicting learning outcomes. Instead, the direction of behavioral change over time is the critical indicator. Learning is a developing process where the ability to sustain or strengthen proactive engagement (regulation, understanding-oriented help-seeking, and domain-specific work) is more predictive of success than the mere presence of these behaviors.
• Implications for Design: AI tutors should move beyond evaluating individual prompt quality to monitoring the temporal evolution of interaction. Systems should detect reactive trajectories (e.g., increasing reliance on verification without further mathematical work) and provide scaffolding only when such patterns emerge, rather than reacting to isolated instances of answer-seeking.
• Implications for Practice: Teachers can use interaction traces to diagnose specific struggles in the mathematical modeling cycle (e.g., difficulty in structuring a model vs. validating results) and guide students to distinguish between tasks suitable for AI delegation and those requiring epistemic responsibility.

Limitations
The authors note that the study is correlational, preventing causal claims regarding the temporal indicators. The interaction duration was short (40 minutes), and coding reliability for specific MM steps was moderate. Future work is needed to test these findings longitudinally and to evaluate whether adaptive scaffolds can actively promote epistemically proactive trajectories.