A symbolizing activity for constructing personal expressions and its impact on a student’s understanding of the sequence of partial sums

IF 1 Q3 EDUCATION & EDUCATIONAL RESEARCH
Derek Eckman , Kyeong Hah Roh
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引用次数: 0

Abstract

This paper reports the results from a set of exploratory teaching interviews in which students constructed individualized algebraic expressions (called personal expressions) to describe their meanings for partial sums. Our analysis focused on one student, Emily, who constructed two distinct personal expressions for partial sums, one novel and one based on her image of summation notation. Emily created her novel expression to denote the process of generating the summands to compute the value of a partial sum. Emily adopted summation notation to describe the value of the partial sum. After reflecting on her inscription for a series’ general term of summation, Emily constructed a single expression to describe either the process of computing an arbitrary partial sum or the value of the sum itself. Using Emily’s story, we propose three categories for students’ coordination of their meanings for partial sums with a corresponding representation.

构建个人表达式的符号化活动及其对学生理解部分相加顺序的影响
本文报告了一组探索性教学访谈的结果,在这些访谈中,学生们构建了个性化的代数表达式(称为个人表达式)来描述他们对部分和的意义。我们的分析集中在一位名叫艾米丽的学生身上,她为部分和构建了两种不同的个人表达式,一种是新颖的,另一种是基于她对求和符号的印象。艾米丽创造了新颖的表达方式,用来表示生成求和以计算部分和值的过程。艾米丽采用求和符号来描述部分和的值。在反思了她为数列的一般求和术语所做的题词后,艾米丽构建了一个单一表达式来描述计算任意部分和的过程或和本身的值。通过艾米丽的故事,我们提出了学生将其对部分和的意义与相应的表达式进行协调的三个类别。
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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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