Analysis of a Mathematical Problem-Solving Test on Speed and Students' Strategies: A Mixed Item Response Theory Approach

The present study used the mixed item response theory (IRT) model to identify qualitatively distinct subgroups of sixth-grade students with respect to their performance on word problems on speed. A total of 345 Singaporean students and 361 Chinese students took a problem-solving test on speed. The mixed IRT analysis revealed two latent classes — the algebra proficient group and the algebra novice group. The algebra proficient group was more likely to use traditional algebraic and arithmetic strategies to solve the problems, whereas the algebra novice group was more likely to use model drawing, unitary, and guess-and-check strategies, in addition to using traditional arithmetic and algebraic strategies. Findings of the study indicate that a greater variety of problem-solving strategies could be encouraged in upper primary schools to help students make connections among these strategies, in particular, between these strategies and the abstract algebraic strategies, and finally to achieve a successful transition from arithmetic to algebra learning.