Chunlian Jiang

本研究使用混合项目反应理论(IRT)模型将六年级学生在数学问题解决的行程问题测试中的表现分为几个有着质的区别的群组。来自新加坡的345名学生和来自中国的361名学生参加了行程问题的测试。混合IRT分析表明存在两个潜在的组别，其中一组学生（我们称为代数熟手组）倾向于用传统的代数和算术策略去解决问题，而另一组学生（我们称为代数初学组）除了使用传统的代数和算术策略外，更倾向于运用模型化方法、单位元方法和猜测-检验方法等策略。本研究表明在小学数学教学中可以提倡使用多种不同的问题解决策略，小学高年级的数学教学需要帮助学生建立这些策略之间的联系，特别是它们和抽象的代数策略之间的联系，以便顺利过渡到代数的学习。

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.