Exploring Recommendation Patterns in Calculus Learning: An Achievement-Based Evaluation of the Funk-SVD System

Abstract

This study applies a Funk-SVD collaborative filtering model to analyze calculus learning data across student groups with varying achievement levels. By examining recommended items, recommendation intensity, and conceptual focus, the study aims to explore students’ knowledge structures and identify group-specific learning difficulties. The results indicate that high-achieving students were frequently recommended advanced theorems and integrative tasks; medium-achieving students were presented with items involving conditional reasoning and representational shifts; while low-achieving students primarily received reinforcement on basic definitions and common conceptual misconceptions. Although all three groups demonstrated certain shared difficulties in core topics such as integration and differentiability, they exhibited distinct cognitive demands overall. Based on these findings, it is recommended that instructors utilize the results to inform differentiated instructional design and make pedagogical adjustments tailored to students’ learning profiles. In addition, future research may further address the recommendation gap caused by data sparsity and confidence asymmetry, aiming to optimize the system for enhancing access to key conceptual content across achievement levels.