More on the History of Functions, with Remarks on Teaching

  • Israel Kleiner


The notion of function is central in both mathematics and mathematics education. Textbook definitions or descriptions of function have varied with time, context, and level of presentation. A function has been viewed as a formula, a rule, a correspondence, a relation between variables, a table of values, a graph, a mapping, a transformation, an operation, a set of ordered pairs (see, e.g., Math Teacher 61:575–579, 1968; Int Jour Math Educ Sci Technol 11:489–492, 1980; Learn Math 62(2):18–24, 28, 1986). These ideas reflect the historical evolution of the function concept. We will briefly trace some aspects of this evolutionary process, and following the historical account in each section (except for the first and last), draw some pedagogical morals.


Nineteenth Century Power Series Fourier Series Eighteenth Century Function Concept 
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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsYork UniversityTorontoCanada

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