Development and evaluation of mathematics lessons by exploring mathematical notations that foster proportional reasoning

在本研究中，我分析了学生对数学符号的意义建构与比例，并探讨了培养他们的比例推理的情况。结果显示，学生在发展适当的意义，以表，公式和图形的比例的困难。另一方面，学生对表格的熟悉程度高于公式和图形，他们使用表格作为脚手架来构建其他表达的意义。研究结果还表明，学生通过自主开发的符号作为媒介相互交流的情况下的意义。基于这些结果，我提出了学生与数学符号积极互动的课程的建议。

In this study, I analyzed student's construction of meaning to mathematical notations with respect to proportion and explored the situations that foster their proportional reasoning. Results showed students' difficulties in developing appropriate meanings to tables, formulas and graphs for proportion. On the other hand, students were more familiar with tables compared with formulas and graphs and their use of tables functioned as scaffolding to construct meanings to other expressions. Results also showed the significance of situations in which students communicate each other through self-developed notations as medium. Based on the results, I made implications for lessons in which students interact positively with their mathematical notations.