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流程，该流程为师生提供了通过图示建构除法运算意义的路径，其核心是界定参考单元（divisor）、参考整体¹（reference whole）与被除数（dividend）。本研究引入了一种基于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建构解题流程，从而实现有意义学习。本研究招募九组师生参与基于Excel的干预教学实验，对比分析了学生在学习前后对分数除法的理解水平。学生层面的研究结果表明，Excel软件可帮助学生运用精准的数学术语，刻画并建构除法运算的意义；具体而言，学生能够透彻理解应用题的题意，进而能够解释其他同学的解题错误。此外，教师对学生作业的分析结果显示，该计算机化动态教学环境的使用，助力教师提升了数学学科知识、教学知识与技术教学知识。