Modes of Description and the Problem of Representation in Linear Algebra
Modes of Description and the Problem of Representation in Linear Algebra
复制标题
线性代数中的描述模式和表示问题
DOI：
10.1007/0-306-47224-4_7
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发表时间：
2000
影响因子：
1.5
通讯作者：
J. Hillel
中科院分区：
文献类型：
--
作者：
J. Hillel
本章从向量和算子的不同描述方式的角度探讨了线性代数的教学和学习。我们确定了课堂实践中使用的不同模式及其相关语言，并讨论了从一种模式转换为另一种模式的机制。然后，我们更具体地关注向量和运算符相对于基的表示，以说明线性代数学生面临的一些困难。大学水平的线性代数教学几乎普遍被认为对教师和学生来说都是令人沮丧的经历。许多教授这样一门课程的人已经接受了这样一个事实：这只是“野兽的本性”，而且没有什么办法可以改变现状。这种态度也许可以解释为什么直到最近，线性代数学习的研究工作还很少。与已被广泛研究的微积分概念不同，大多数关于线性代数学习和教学的研究都是相对较新的。从 Harel (1985) 的工作开始，Robert 和 Robinet (1989)、Rogalski (1990)、Dorier (1990)、Pavlopoulou (1993)、Sierpinska (1995)、Dreyfus 和 Hillel (1998)、Sierpinska、Dreyfus 和 Hillel (1999) 等人也做出了其他贡献。
This chapter1 examines the teaching and learning of linear algebra from the perspective of the different modes of description of vectors and operators. We identify the different modes and their associated language, as used in classroom practice, as well as discuss the mechanisms of translating from one mode to the another. We then focus more specifically on the representation ofa vector and an operator relative to a basis in order to illustrate some of the difficulties faced by students of linear algebra.The teaching of linear algebra at a university level is almost universally regarded as a frustrating experience for instructors and students alike. Many among those who teach such a course have resigned themselves to the fact that this is simply ‘the nature of the beast’and that not much can be done to change things. This attitude might explain the reason why, until recently, there was a paucity of research work on the learning of linear algebra. Unlike the notions of calculus, which have been researched extensively, most of the research on learning and teaching linear algebra is relatively recent. Starting with the work of Harel (1985), other contributions have been made by, eg, Robert and Robinet (1989), Rogalski (1990), Dorier (1990), Pavlopoulou (1993), Sierpinska (1995), Dreyfus and Hillel (1998), Sierpinska, Dreyfus and Hillel (1999).