Connecting operation-choice problems by the variation principle: Sixth graders’ operational or deeper relational pathways

IF 1 Q3 EDUCATION & EDUCATIONAL RESEARCH
Cristina Zorrilla , Anna-Katharina Roos , Ceneida Fernández , Salvador Llinares , Susanne Prediger
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引用次数: 0

Abstract

Many empirical studies documented students’ challenges with operation-choice problems, in particular for multiplication and division with rational numbers. The design principle of problem variation was suggested to overcome these challenges by engaging students in making connections between inverse operation-choice problems of multiplication and division, and between problems with natural numbers and fractions/decimals, but so far, this approach was hardly investigated empirically. In this study, we investigate 17 sixth graders’ modelling pathways through sets of operation-choice problems that are systematically designed according to the variation principle. In the qualitative analysis, we identify five pathways by which students solve the problems and sometimes connect them. While one pathway uses deep relational connections, others only draw superficial and operational connections and others stay with informal strategies without connecting them to formal operations.

用变异原理连接操作选择问题:六年级学生的操作或更深的关系路径
许多实证研究记录了学生在操作选择问题上的挑战,特别是有理数的乘法和除法。问题变化的设计原则建议通过让学生在乘法和除法的逆操作选择问题之间以及自然数和分数/小数问题之间建立联系来克服这些挑战,但到目前为止,这种方法几乎没有实证研究。本研究以17名六年级学生为研究对象,透过根据变分原理设计的作业选择问题,探讨他们的建模路径。在定性分析中,我们确定了学生解决问题的五种途径,有时将它们联系起来。一种途径使用深层的关系联系,其他途径只绘制表面的和可操作的联系,而其他途径则停留在非正式的策略上,而不将它们与正式的操作联系起来。
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来源期刊
Journal of Mathematical Behavior
Journal of Mathematical Behavior EDUCATION & EDUCATIONAL RESEARCH-
CiteScore
2.70
自引率
17.60%
发文量
69
期刊介绍: The Journal of Mathematical Behavior solicits original research on the learning and teaching of mathematics. We are interested especially in basic research, research that aims to clarify, in detail and depth, how mathematical ideas develop in learners. Over three decades, our experience confirms a founding premise of this journal: that mathematical thinking, hence mathematics learning as a social enterprise, is special. It is special because mathematics is special, both logically and psychologically. Logically, through the way that mathematical ideas and methods have been built, refined and organized for centuries across a range of cultures; and psychologically, through the variety of ways people today, in many walks of life, make sense of mathematics, develop it, make it their own.
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