中学生对“字母表示数”认知发展的历史相似性研究

A Study of Historical Parallelism on Middle School Students' Understanding of the Letters Representing Numbers

"用字母表示数"是中学数学的重要内容,同时也是中学生从文字代数向符号代数过渡的重要阶段.运用测试卷对七年级和高一年级学生关于"用字母表示数"的理解进行抽样测试的结果显示,学生对"用字母表示数"的认知发展过程与"字母表示数"意义演进的历史发展过程存在显著的相似性.这种历史相似性对"用字母表示数"相关内容的教学与教材的编写都有着重要的启示意义.

＂ Letters Represent Numbers ＂ is an important part of middle school mathematics,and also a significant stage for middle school students to learn the transition from rhetorical algebra to symbolic algebra.Sample tests for the Seventh Grade students and Senior Grade One students on their understanding of ＂ Letters Represent Numbers ＂ have been conducted. The results indicated that the development process of students＇ understanding of ＂ Letters Represent Numbers＂ is similar to the historical evolvement process of the meaning of ＂Letters Represent Numbers＂ itself. Such similarity is essential to assist the preparation of teaching method and learning materials that are related to the topic of ＂ Letters Represent Numbers＂.