Students’ conception of infinite series
Students’ conception of infinite series
复制标题
学生对无穷级数的概念
DOI：
--
复制
发表时间：
2012
期刊：
影响因子：
--
通讯作者：
Vanessa Acevedo
中科院分区：
文献类型：
--
作者：
Rafael Martínez;Ana Carmen Gonzalez;G. DiCristina;Vanessa Acevedo
这是一篇关于学生对无穷级数理解的研究报告。它有三重目的：表明学生可以构建两个本质上不同的无穷级数概念，表明其中一个结构对学生来说特别困难，并检查这两个不同结构的构建方式，以便我们可以发现帮助学生提高理解的方法。其理论框架包括行动过程对象图式理论和巴拉切夫的概念、认识和概念理论中的具体概念模型。从这两个不同的理论角度来处理这个问题，使我们能够对观察到的现象提供不同的、同时又是互补的解释。这两种不同的无穷级数的结构，简单地说，系列作为一个无限的无限过程的补充和系列作为一个序列的部分和。学生被发现有困难建立一个系列的理解作为一个序列的部分和，因此往往有困难的问题的情况下，需要这种解释。本研究采用半结构化访谈的方式，对10名研究生进行了访谈。访谈探讨的情况下，可能会给洞察学生的概念的序列部分和。
This is a report of a study of students’ understanding of infinite series. It has a three-fold purpose: to show that students may construct two essentially different notions of infinite series, to show that one of the constructions is particularly difficult for students, and to examine the way in which these two different constructions may be built so that we may uncover ways to help students improve their understanding. The theoretical framework consists of action–process–object–schema theory and the specific model of conceptions in Balacheff’s theory of conception, knowing, and concept. Approaching the problem from these two different theoretical perspectives allows us to provide different and at the same time complementary explanations of observed phenomena. The two different infinite series constructions are, briefly stated, series as an infinite unending process of addition and series as a sequence of partial sums. Students are found to have difficulty building an understanding of series as a sequence of partial sums and thus tend to have difficulty in problem situations that require this interpretation. The study uses semi-structured interviews with 10 graduate students. The interviews explore situations that might give insight into students’ notion of the sequence of partial sums.