Confrey & Smith (1995)

Splitting, Covariation, and Their Role in the Development of Exponential Functions

• Authors: Jere Confrey and Erick Smith
• Journal: Journal for Research in Mathematics Education
• Year: 1995
• Source: http://www.jstor.org/stable/749228

Abstract

Exponential and logarithmic functions are typically presented as formulas with which students learn to associate the rules for exponents/logarithms, a particular algebraic form, and routine algorithms. We present a theoretical argument for an approach to exponentials more closely related to students' constructions. This approach is based on a primitive multiplicative operation labeled "splitting" that is not repeated addition. Whereas educators traditionally rely on counting structures to build a number system, we suggest that students need the opportunity to build a number system from splitting structures and their geometric forms. We advocate a "covariation" approach to functions that supports a construction of the exponential function based on an isomorphism between splitting and counting structures.

Corrolary

APA

Confrey, J., & Smith, E. (1995). Splitting, covariation, and their role in the development of exponential functions. Journal for Research in Mathematics Education, 26(1), 66–86. http://doi.org/10.2307/749228

BibTeX

@article{Confrey1995,
author = {Confrey, Jere and Smith, Erick},
doi = {10.2307/749228},
journal = {Journal for Research in Mathematics Education},
number = {1},
pages = {66--86},
title = {{Splitting, covariation, and their role in the development of exponential functions}},
url = {http://www.jstor.org/stable/749228},
volume = {26},
year = {1995}
}