Signs and meanings in students' emergent algebraic thinking: A semiotic analysis
Signs and meanings in students' emergent algebraic thinking: A semiotic analysis
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学生新兴代数思维中的符号和意义：符号学分析
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发表时间：
2000
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通讯作者：
L. Radford
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文献类型：
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作者：
L. Radford
本文是一项关于学生代数符号化的纵向课堂研究的一部分，其目的有两个：(1)调查学生使用符号的方式，并在他们第一次遇到模式的代数泛化时赋予他们意义；(2)提供关于学生涌现的代数思维的说明。该研究一方面借鉴了维果茨基的历史文化心理学学派，另一方面借鉴了巴赫金和沃洛希诺夫的话语理论，并以符号文化理论框架为基础，在该框架中，代数思维被认为是一种符号介导的认知实践。在这一理论框架内，学生的代数活动是在个体主体性和符号对象化的社会手段的相互作用下进行研究的。民族志定性方法论，在历史认识论研究的支持下，确保了一系列教学活动的设计和解释。本文的重点是由一小群学生进行的讨论，其中提供了解释性的，情境语篇分析。结果揭示了学生的生产（口头和书面）符号和他们的意义，因为他们从事数学一般性表达的构建和他们的紧急代数思维的社会性质。
The purpose of this article, which is part of a longitudinal classroom research about students' algebraic symbolizations, is twofold: (1) to investigate the way students use signs and endow them with meaning in their very first encounter with the algebraic generalization of patterns and(2) to provide accounts about the students' emergent algebraic thinking. The research draws from Vygotsky's historical-cultural school of psychology, on the one hand, and from Bakhtin and Voloshinov's theory of discourse on the other, and is grounded in a semiotic-cultural theoretical framework in which algebraic thinking is considered as a sign-mediated cognitive praxis. Within this theoretical framework, the students' algebraic activity is investigated in the interaction of the individual's subjectivity and the social means of semiotic objectification. An ethnographic qualitative methodology, supported by historic, epistemological research, ensured the design and interpretation of a set of teaching activities. The paper focuses on the discussion held by a small group of students of which an interpretative, situated discourse analysis is provided. The results shed some light on the students' production of (oral and written) signs and their meanings as they engage in the construction of expressions of mathematical generality and on the social nature of their emergent algebraic thinking.