学生对字母的理解:历史相似性研究

Children’s Understanding of the Letters: An Empirical Study of Historical Parallelism

用＂用字母表示数＂的测试卷对初中预备班学生进行测试.测试结果表明：（1）为数不少的学生对＂用字母表示数＂仍停留在＂修辞代数＂和＂缩略代数＂阶段;对字母意义的认知水平多数停留在＂记数符号＂及＂未知量＂的层次,只有少部分学生理解并能用＂一类量＂思想解决问题;（2）学生对于符号代数的＂一类量＂思想存在认知困难;（3）学生对＂用字母表示数＂的认知发展过程和＂字母表示数＂意义演进的历史发展过程之间存在一定的相似性.因此,借鉴字母意义的历史演进过程设计教学,将史料及其蕴含的思想、方法等重构后应用于课堂教学,将能够有效解决学生学习过程中存在的问题与障碍.

We test the preparatory class students of junior high school in Shanghai with the paper on letters used to represent numbers. The results indicates that： （1） a large number of students＇ cognition on letters used to represent numbers still remain at the stage of＂rhetorical algebra＂ or ＂abbreviated Algebra＂; a majority of students＇ cognitive levels to the letters meaning stay in the levels of ＂notations of numbers＂ and ＂unknowns＂, only a small number of students understand and are able to solve the problem with the thought of ＂a type of quantities＂; （2） the students have cognitive difficulties in the ＂a type of quantities＂ of symbolic algebra; （3） to a certain extent there exists parallelism between students＇ cognitive development process and the historical evolution process of the letters meaning. Learning from the historical evolution of letters meaning and reconstructing the historical materials and their idea and methods to design instruction, we will be able to effectively solve the problems and obstacles that exist in the students＇ learning process.