Making sense of the minus sign or becoming flexible in “negativity”
Making sense of the minus sign or becoming flexible in “negativity”
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DOI：
10.1016/j.learninstruc.2004.06.012
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发表时间：
2004-10
影响因子：
6.2
通讯作者：
Joëlle Vlassis
中科院分区：
文献类型：
--
作者：
Joëlle Vlassis
这篇文章关注的是学生在处理初等代数运算中的负数时所产生的概念变化。对12名8年级学生进行了访谈，这些学生是根据他们在要求减少多项式的测试中的结果选出的。这些问题适用于他们的策略以及他们对负号的理解。对学生口头和书面话语的分析证明存在两种主要的概念变化：第一种是由于学生试图调和他们对自然数的算术假设和与负数运算所需的代数规则。第二种概念变化的本质与负号有关，并通过扩大理解和灵活使用我们所谓的“消极性”来发展。我们认为，如果学生对自己的符号化活动没有形成元概念意识，这两种概念变化就不可能完全发生。
This article focuses on the kinds of conceptual changes that occur when students have to deal with negative numbers in elementary algebraic operations. Interviews were carried out with twelve 8th-grade level students who were selected on the basis of their results in a test where they were required to reduce polynomials. The questions applied to their strategies and to the meaning they gave to the minus sign. The analysis of the students’ oral and written discourse attests to the presence of two major kinds of conceptual change: the first one results from students’ attempts to reconcile their arithmetical presuppositions about natural numbers and the algebraic rules required to operate with negatives. The nature of the second kind of conceptual change relates to the minus sign and develops through an enlarged understanding and a flexible use of what we called ‘negativity’. We argue that these two kinds of conceptual change cannot fully occur without the students developing a meta-conceptual awareness of their symbolizing activities.