Elementary Preservice Teachers’ Transitional Conceptions of Partitive Division with Proper-Fraction Divisors
Elementary Preservice Teachers’ Transitional Conceptions of Partitive Division with Proper-Fraction Divisors
复制标题
小学职前教师对真分数除法的过渡观念
DOI：
10.1080/10986065.2017.1346452
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发表时间：
2017
影响因子：
1.6
通讯作者：
Amanda Jansen
中科院分区：
文献类型：
--
作者：
Charles Hohensee;Amanda Jansen
摘要对整除的理解是许多其他数学主题的基础，包括单位率，斜率和概率。然而，研究表明，当除数是一个真分数时，学习者对整除的理解往往有限。为了扩展本研究中对部分划分概念的研究，我们使用Moschkovich（1999）的过渡概念视角来考察部分划分概念是如何演变的。本研究以国小数学课程为对象，探讨17位国小教师在探究整除法前后，对整除法的概念。我们的分析前和后的采访揭示了一个初步的过渡概念和两个层次的细化他们的概念。此外，我们还确定了CST在完善其概念过程中经历的两种干扰。通过识别有序的细化和相关的扰动水平，这个探索性的研究扩展了过渡概念的角度。此外，这项研究增加了新的见解的概念复杂性，分割模型的分数提出的PST（和一般的学习者），并提出了新的假设的方式，分割的概念进行细化。
ABSTRACT An understanding of partitive division is foundational for numerous other mathematics topics, including unit rate, slope, and probability. However, research has shown that learners tend to have a limited understanding of partitive division when the divisor is a proper fraction. To extend research on conceptions of partitive division in this study, we used Moschkovich’s (1999) transitional conceptions perspective to examine how conceptions of partitive division evolve. This article reports on preservice teachers’ (PSTs) conceptions of partitive division with proper-fraction divisors before and after they explored partitive division in a mathematics content course for elementary teachers (N = 17). Our analysis of pre- and post-interviews revealed an initial transitional conception and two levels of refinement of their conceptions. Furthermore, we identified two perturbations that PSTs experienced during refinement of their conceptions. By identifying ordered levels of refinement and associated perturbations, this exploratory study extends the transitional conceptions perspective. Furthermore, this study adds new insights into the conceptual complexities that the partitive model for division of fractions presents to PSTs (and to learners in general) and suggests new hypotheses about ways that conceptions of partitive division undergo refinement.