Abstract Research and practitioner articles advocate the use of visual representations in scaffolding elementary students’ learning of multiplication and division. Prior research suggests students use different strategies when provided with different visualized representations of multiplication and division. However, there is relatively little study examining how children’s multiplicative reasoning corresponds with different representations. The present study collected data from 182 elementary students responding to set, area, and length representations of multiplication/division. Rasch modeling was used to estimate item difficulty statistics to measure differences between visual representations. Results suggest that visual representations differed primarily in how unit was represented and quantified, and not regarding the form of representation (set, area, length).

中文翻译：

---

视觉表现传达的乘法意义

摘要 研究和从业者文章提倡在小学生学习乘法和除法的过程中使用视觉表征。先前的研究表明，当为乘法和除法提供不同的可视化表示时，学生会使用不同的策略。然而，关于儿童乘法推理如何与不同表征相对应的研究相对较少。本研究收集了 182 名小学生对乘法/除法的集合、面积和长度表示做出反应的数据。Rasch 模型用于估计项目难度统计以测量视觉表示之间的差异。结果表明，视觉表示的不同主要在于单位的表示和量化方式，