通过比较算法学习乘法:“一乘一,但实际上是十乘十”

IF 1 Q3 EDUCATION & EDUCATIONAL RESEARCH
Anna Ethelwyn Baccaglini-Frank , Silvia Funghi , Mirko Maracci , Alessandro Ramploud
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引用次数: 0

摘要

小学时代的乘法算法仍然经常被引入,很少关注意义。我们展示了一个案例研究,重点是一个三年级的班级,该班级参与了两种算法的比较,并讨论了“为什么它们都有效”。教学干预的目的是培养学生对乘法算法的数学意义的发展,以及他们判断和比较不同算法的价值和效率的态度。基本假设是,就教学干预的目标而言,有可能促进两种被视为文化产物的算法的符号学潜力的同时展开,并在这两种算法之间建立富有成效的协同作用。结果,本研究揭示了“桥接符号”的新理论结构,揭示了学生涉及多个人工制品的意义形成过程;并且它提供了对算法的假设潜力的实际展开的重要见解。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Learning about multiplication by comparing algorithms: “One times one, but actually they are ten times ten”

Multiplication algorithms in primary school are still frequently introduced with little attention to meaning. We present a case study focusing on a third grade class that engaged in comparing two algorithms and discussing “why they both work”. The objectives of the didactical intervention were to foster students' development of mathematical meanings concerning multiplication algorithms, and their development of an attitude to judge and compare the value and efficiency of different algorithms. Underlying hypotheses were that it is possible to promote the simultaneous unfolding of the semiotic potential of two algorithms, considered as cultural artifacts, with respect to the objectives of the didactical intervention, and to establish a fruitful synergy between the two algorithms. As results, this study sheds light onto the new theoretical construct of “bridging sign”, illuminating students’ meaning-making processes involving more than one artifact; and it provides important insight into the actual unfolding of the hypothesized potential of the algorithms.

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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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