To shed light on the value of the area model as a tool to elicit pre-service teachers’ (PSTs’) understanding of fractions and area, we explored their understanding of the fractional knowledge and geometric measurement knowledge incorporated in the area model by providing PSTs area models in an atypical way. We administered a written questionnaire to 82 PSTs at a large Midwestern university in the USA. We used an inductive content analysis approach, including both qualitative and quantitative analyses, to analyze the data. Almost half of the PSTs provided incorrect answers and faulty reasoning. We identified two main strategies for correct reasoning and five sources of the misconceptions embedded in the PSTs’ incorrect reasoning. Finally, we drew implications from our analysis for designing mathematics methods courses that support effective use of area models.

为了阐明面积模型作为一种工具来激发职前教师 (PST) 对分数和面积的理解的价值，我们通过提供 PST 来探索他们对面积模型中包含的分数知识和几何测量知识的理解非典型区域模型大大地。我们对美国中西部一所大型大学的 82 名 PST 进行了书面问卷调查。我们使用归纳内容分析方法，包括定性和定量分析，来分析数据。几乎一半的 PST 提供了错误的答案和错误的推理。我们确定了正确推理的两个主要策略和嵌入在 PST 错误推理中的误解的五个来源。最后，我们从我们的分析中得出了设计支持有效使用面积模型的数学方法课程的启示。