Abstract The aim of this study is to investigate relationships between students’ arithmetical knowledge and their proportional reasoning. Two of seven students for whom we conducted clinical interviews were selected as participants in the study. An analysis of their solutions to four different types of multiplicative problems (equal sharing, reversible multiplicative relationship, fraction composition, and proportional relationship) was conducted. Based on the analysis, we found that the student who coordinated two three-level units structures prior to activity in the first three problem types could also solve the proportion problem using the units coordination. In contrast, the student who coordinated two three-level units structures only in activity in the first three problem types could not solve the proportion problem. Given the importance of units coordinating operations in solving diverse problems, implications for further research on students’ construction of proportional reasoning are discussed.

中文翻译：

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两个不同单元协调水平的中学生的解题活动

摘要 本研究旨在探讨学生算术知识与比例推理之间的关系。我们为其进行临床访谈的七名学生中有两名被选为研究参与者。对他们对四种不同类型的乘法问题（平等共享、可逆乘法关系、分数组成和比例关系）的解决方案进行了分析。根据分析，我们发现在前三个问题类型的活动之前协调两个三级单元结构的学生也可以使用单元协调解决比例问题。相比之下，仅在前三个问题类型的活动中协调两个三级单元结构的学生无法解决比例问题。