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标题：Semiotic Objectifications of the Compensation Strategy: En Route to the Reification of Integers
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作者：Andreas Koukkoufis ; Julian Williams
期刊名称：Revista Latinoamericana de Investigación en Matemática Educativa
印刷版ISSN：1665-2436
电子版ISSN：2007-6819
出版年度：2006
期号：Esp
页码：157-175
出版社：Comité Latinoamericano de Matemática Educativa
摘要：We report an analysis of data from an experimental replication of Object-Process Linking and Embedding (OPLE) in the case of integer arithmetic instruction originally developed by Linchevski and Williams (1999) in the realistic mathematics education (RME) tradition. Our analysis applies Radfords theory of semiotic objectification to reveal new insights into how reification is achieved. In particular the method of analysis shows how the factual generalization of the so-called compensation strategy encapsulates the notion that adding to one side is the same as subtracting from the other side: a vital grounding for symbolic integer operations later. Other aspects of objectification are discussed that are considered likely to be important to the semiotic chaining that students achieve in the OPLE sequence that can lead to an intuitive grounding of integer operations. We argue that semiotic theory needs to be elaborated to understand the vital role of models and modelling in leveraging reifications in RME.
关键词：Integers; Semiotics; Theories of Learning. Enteros; semiótica; teorías del aprendizaje. Inteiros; Semióticos; Teoria de Aprendizagem. Entiers; sémiotique; th...