<![CDATA[Mathematics achievement is frequently constrained by students' difficulty in connecting abstract symbolic procedures with the physical phenomena they describe, particularly in topics such as vectors, rates of change, and motion. This study presents and evaluates an Artificial Intelligence (AI)-enhanced learning environment, referred to as PhysMath-AI, which integrates an interactive physics simulation of motion and vector quantities with an adaptive knowledge-tracing engine to support conceptual understanding of mathematics. Two complementary models underlie the platform: an AI adaptive learning model based on a bidirectional long short-term memory (LSTM) network with an attention mechanism that estimates each learner's mastery of mathematical sub-skills from interaction data, and a physics-based mathematical model that represents position, velocity, and acceleration as time-dependent vector quantities linked directly to the mathematical operations being taught. A quasi-experimental pretest-posttest design was conducted with 120 secondary school students (60 experimental, 60 control) over an eight-week period. The experimental group achieved a significantly higher mean post-test score (78.4%) than the control group (61.2%), with a large normalized learning gain (⟨g⟩ = 0.58) compared with the control group (⟨g⟩ = 0.23). Paired-sample t-tests confirmed statistically significant pre-post improvements (p < 0.001) for both groups, while the independent-sample comparison confirmed the experimental group's advantage (p < 0.001, Cohen's d = 1.42). Weekly engagement surveys showed sustained motivational increases for the experimental group. These findings suggest that coupling AI-driven adaptive sequencing with physics-grounded visualizations of motion and vectors can meaningfully strengthen students' conceptual and procedural understanding of mathematics.]]>
