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<p>Reversal errors—where students incorrectly transpose relationships when translating word problems into algebraic equations—represent a persistent challenge in mathematics educations. This study examined how sentence structures variations influenced Chinese middle school students’ performance on algebraic word problems. We administered paper-and-pencil tests featuring three problem types: Type I (“There are six times as many students as professors”), Type II (“There are six students for every professor”), and Type III (“The ratio of students to professors is 6:1”). Response accuracy and error patterns were analyzed using latent class analysis to identify distinct learning profiles. Results showed that students achieved significantly higher accuracy on Type III problems compared to Type II problems, with reversal errors reduced by 50%. Four distinct problem-solving profiles emerged: Adaptive solvers, developing algebraic solvers, surface-feature matching solvers, and direct-translation solvers. These profiles revealed substantial individual differences in cognitive approaches to algebraic translation. The findings support instructional strategies that consider both problem presentation format and individual learner characteristics, providing practical guidance for mathematics educators working in diverse linguistic contexts.</p>

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Understanding individual differences in algebraic word problem solving: A latent class analysis of Chinese students’ performance across different problem formats

  • 期刊论文

  • 发表日期：

    2026年3月21日

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  • Zongzhao Mo,
  • Ronghuan Jiang,
  • Xiaodong Li

摘要

Reversal errors—where students incorrectly transpose relationships when translating word problems into algebraic equations—represent a persistent challenge in mathematics educations. This study examined how sentence structures variations influenced Chinese middle school students’ performance on algebraic word problems. We administered paper-and-pencil tests featuring three problem types: Type I (“There are six times as many students as professors”), Type II (“There are six students for every professor”), and Type III (“The ratio of students to professors is 6:1”). Response accuracy and error patterns were analyzed using latent class analysis to identify distinct learning profiles. Results showed that students achieved significantly higher accuracy on Type III problems compared to Type II problems, with reversal errors reduced by 50%. Four distinct problem-solving profiles emerged: Adaptive solvers, developing algebraic solvers, surface-feature matching solvers, and direct-translation solvers. These profiles revealed substantial individual differences in cognitive approaches to algebraic translation. The findings support instructional strategies that consider both problem presentation format and individual learner characteristics, providing practical guidance for mathematics educators working in diverse linguistic contexts.