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Students' Understanding of Real, Rational, and Irrational Numbers

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Students' Understanding of Real, Rational, and Irrational Numbers

Arbour, Deidre (2012) Students' Understanding of Real, Rational, and Irrational Numbers. Masters thesis, Concordia University.

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Abstract

This thesis presents a study of the understanding of real, rational, and irrational numbers by 30 fourth semester college science students in the Montreal region. The written answers to a set of seven questions were analyzed to determine the students’ interpretations of mathematical signs according to C. S. Peirce’s classifications and to describe their modes of thought according to Vygotsky’s theory of concept development. From these interpretations, we are able to reconstruct a facsimile of what the students’ concept images are as they pertain to the sets in question. Finding the concept images to be idiosyncratic and rarely in agreement with what conventional mathematics holds to be true, we examine the way the number systems are approached in school and in the field of mathematics and use this, along with the analyses, to make pedagogical recommendations.

Divisions:Concordia University > Faculty of Arts and Science > Mathematics and Statistics
Item Type:Thesis (Masters)
Authors:Arbour, Deidre
Institution:Concordia University
Degree Name:M.T.M.
Program:Teaching of Mathematics
Date:March 2012
Thesis Supervisor(s):Sierpinska, Anna
ID Code:973825
Deposited By:DEIDRE ARBOUR
Deposited On:20 Jun 2012 11:47
Last Modified:20 Jun 2012 11:47
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