Building a computerized dynamic representation as an instrument for mathematical explanation of division of fractions

This study describes a teaching process that offers teachers and pupils ways of constructing the division operation through illustration based on defining the reference unit (divisor), the reference whole1 and the dividend. We introduce a computerized dynamic environment, using an Excel spreadsheet, in which both teachers and pupils can independently construct the solution process in a manner that leads to meaningful learning. Nine pairs of teachers and pupils underwent an intervention process using Excel, comparing pupils’ understanding of division of fractions before and after the learning process. Findings from the pupils indicate the Excel software enabled them to portray and construct the meaning of the division process while applying accurate mathematical terms. Specifically, they could thoroughly understand the meaning of a word problem, so as to explain another student’s mistake. Furthermore, teachers’ analyses of the pupils’ work indicate that the use of this computerized dynamic environment helped the teachers develop mathematical knowledge, pedagogical knowledge and technological pedagogical knowledge.本研究阐述了一种教学范式，该范式为师生提供了通过具象化途径构建除法运算的方法，其核心为先定义参考单位（除数divisor）、参考整体1（reference whole1）与被除数dividend。本研究引入了基于Excel电子表格的计算机化动态教学环境，师生可在此环境中自主搭建解题流程，以此实现有意义学习。研究招募九组师生配对开展Excel辅助干预教学，对比分析了学生在学习前后对分数除法的理解水平。学生端的研究结果显示，Excel软件可帮助他们借助精准的数学术语，具象化并建构除法运算的内在含义。具体而言，学生能够充分理解文字应用题的题意，进而能够解释其他学生的解题失误。此外，教师对学生作业的分析结果表明，该计算机化动态教学环境能够助力教师发展数学学科知识、教学知识与技术教学知识。