Exponentiation Is Not Repeated Multiplication: Developing Exponentiation as a Continuous Operation

The concept of exponents has been shown to be problematic for students, especially when expanding it from the domain of positive whole numbers to that of exponents that are negative and later rational. This paper presents a theoretical analysis of the concept of exponentiation as a continuous operat...

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Bibliographic Details
Published inNorth American Chapter of the International Group for the Psychology of Mathematics Education
Main Author Avitzur, Arnon
Format Report
LanguageEnglish
Published North American Chapter of the International Group for the Psychology of Mathematics Education 01.11.2012
Subjects
Algebra
Arithmetic
Fractions
Learning Activities
Mathematical Concepts
Mathematics Instruction
Multiplication
Numbers
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Summary:The concept of exponents has been shown to be problematic for students, especially when expanding it from the domain of positive whole numbers to that of exponents that are negative and later rational. This paper presents a theoretical analysis of the concept of exponentiation as a continuous operation and examines the deficiencies of existing approaches to teaching it. Two complementary theoretical frameworks are used to suggest an alternative definition for exponentiation and guiding principles for the development of a teaching trajectory, and then to analyze an example of the hypothetical learning of a student who goes through the first task in the trajectory. The paper concludes with some possible implications on curriculum and task design, as well as on the development of mathematical operations. [For the complete proceedings, see ED584829.]