The balance model: Hindrance or support for the solving of linear equations with one unknown
The balance model: Hindrance or support for the solving of linear equations with one unknown
复制标题
平衡模型：对求解具有一个未知数的线性方程的阻碍或支持
DOI：
10.1023/a:1020229023965
复制
发表时间：
2002
影响因子：
3.2
通讯作者：
Joëlle Vlassis
中科院分区：
文献类型：
--
作者：
Joëlle Vlassis
使用具体模型来教学生如何求解方程在科学文献中经常引起争议。本文旨在研究平衡模型并找出导致科学家分歧的问题。我们的思考基于实证研究的结果以及对该模型的支持者和反对者提出的各种论点的分析。我们描述了实证研究主题的学习情境，该研究涉及两个八年级班级的 40 名学生。目的是教授形式求解方法，其中涉及使用平衡模型在方程两边执行相同的运算。对学生推理的分析表明，负数的存在导致了很多错误。八个月后，在对从参加实验的学生中选出的五名学生的采访中，我们回顾了负数带来的困难。在此背景下，我们讨论了平衡模型的相关性，并分析了捍卫或拒绝其使用的研究人员提出的论点。
The use of concrete models for teaching students how to solve equations is often debated in scientific literature. This article aims to examine the balance model and to identify the issues that divide scientists. We based our reflections on the results of an empirical study and analysis of the various arguments put forward by supporters and opponents of the model. We describe learning situations that were the subject of the empirical study, which involved forty students in two 8th-grade classes. The aim was to teach the formal solving method, which involved performing the same operations on both sides of the equation using, notably, the balance model. Analysis of students' reasoning showed that the presence of negative numbers gave rise to many errors. The difficulties presented by negative numbers were reviewed, eight months later, during an interview with five students, chosen from those who took part in the experiment. Within that context, we discuss the relevance of the balance model and analyse the arguments put forward by researchers who either defend or reject its use.