用“问题提出”诊断和评估数学教师的概念性理解

Using Problem Posing to Diagnose and Assess Teachers’ Conceptual Understanding

对数学知识的程序性理解和概念性理解一直以来都是数学教育领域的重要研究内容,然而直至今时关于这两类理解的关系研究仍然没有明确的结论,尤其是从具体可操作的方法入手诊断和评估学习者的数学理解情况.研究采用对学生代数发展非常重要的分数除法内容作为工具,从分数除法的计算、作图表示分数除法的解答过程、以及对给定分数除法算式提出数学问题等3个角度,了解教师对分数除法的概念性理解情况.研究发现,分数除法问题是了解教师数学理解情况很好的知识内容;教师对分数除法意义的概念性理解较为缺乏;以及“问题提出”是一种诊断和评估教师数学理解的有效手段.

Conceptual and procedural understanding of mathematics was an important research topic in the field of mathematics education.However,research about the relationships between the two types of understanding lacks a clear conclusion and operational approach for diagnosing and assessing learners’mathematics understanding.This study employs a fraction division question,which was significant to students’learning,to investigate teachers’understanding in three ways:calculating the division of a fraction,using a graph to represent the fraction division solution process,and posing mathematical problems based on the expression of the fraction division.This study highlights the usefulness of fraction division for understanding and assessing teachers’mathematical understanding,teachers’lack of conceptual understanding of fraction division,and the effectiveness of problem posing as a way to diagnose and assess teachers’mathematical understanding.