STUDENTS' UNDERSTANDING OF ALGEBRAIC NOTATION: 11–15
STUDENTS' UNDERSTANDING OF ALGEBRAIC NOTATION: 11–15
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学生对代数符号的理解：11–15
DOI：
10.1023/a:1002970913563
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发表时间：
1997
影响因子：
3.2
通讯作者：
K. Stacey
中科院分区：
文献类型：
--
作者：
M. MacGregor;K. Stacey
研究发现，大多数 15 岁以下的学生似乎无法将代数字母解释为广义数字，甚至无法将其解释为特定的未知数。相反，他们会忽略这些字母，用数值替换它们，或者将它们视为速记名称。文献中给出的主要解释是与认知发展水平的一般联系。在本文中，我们提出了文献中被忽视的误解的具体起源的证据，这些证据可能与认知水平有关，也可能无关。这些起源是：对新符号的直观假设和实用推理、与熟悉的符号系统的类比、数学新学习的干扰以及误导性教材的影响。认识到这些误解的根源对于改进代数教学是必要的。
Research studies have found that the majority of students up to age 15 seem unable to interpret algebraic letters as generalised numbers or even as specific unknowns. Instead, they ignore the letters, replace them with numerical values, or regard them as shorthand names. The principal explanation given in the literature has been a general link to levels of cognitive development. In this paper we present evidence for specific origins of misinterpretation that have been overlooked in the literature, and which may or may not be associated with cognitive level. These origins are: intuitive assumptions and pragmatic reasoning about a new notation, analogies with familiar symbol systems, interference from new learning in mathematics, and the effects of misleading teaching materials. Recognition of these origins of misunderstanding is necessary for improving the teaching of algebra.