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Reflections on the Importance of Reference for Understanding Thinking

Year 2015, Volume: 2 Issue: 1, 54 - 60, 21.01.2015

Abstract

An intentional form of the semantics of algebraic expressions in the tradition starting with Frege is popular in mathematics education. On the other hand, mathematical logic including predicate calculus and lambda calculus is dominated for more than 50 years by referential semantics. A third field of investigation is the semantics of mathematics as realized in programming languages and computer algebra systems. The paper explores the tension between these approaches and tries to clarify the role of reference both in he developed mathematics as well as in the learning process. Referential semantics simplifies theories but requires mental objects to be constructed to be useful. This links the topic to reification theory. A small collection of observations of learners’ behavior adds support to the claim that reference is of some importance in the learning process.

Year 2015, Volume: 2 Issue: 1, 54 - 60, 21.01.2015

Abstract

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Details

Primary Language English
Journal Section Articles
Authors

Reinhard Oldenburg

Publication Date January 21, 2015
Published in Issue Year 2015 Volume: 2 Issue: 1

Cite

APA Oldenburg, R. (2015). Reflections on the Importance of Reference for Understanding Thinking. International Journal of Contemporary Educational Research, 2(1), 54-60.

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IJCER (International Journal of Contemporary Educational Research) ISSN: 2148-3868