Function Concept: Learning from History

Authors

Ruthmae Sears, University of South Florida
Dung Tran, North Carolina State University
Seoung Woo Lee, Gifted School in South Korea
Amanda Thomas, University of Nebraska

Abstract

The importance of functions in school mathematics has grown tremendously within the past century. Functions have progressed from being scantly represented in school mathematics to being a core mathematical topic. C.B. Boyer (1946) acknowledged “The development of the function concept has revolutionized mathematics in much the same way as did the nearly simultaneous rise of non-Euclidean geometry. It has transformed mathematics from a pure natural science- the queen of the sciences- into something vastly large. It has established mathematics as the basis of all rigorous thinking – the logic of all possible relations” (Markovits, Eylor, & Bruckheimer, 1986, p. 18).

Historical speeches and documents, such as Klein’s 1893 Evanston Colloquium, Moore’s 1902 presidential address to the American Mathematical Society, The Reorganization of Mathematics in Secondary Education Report (1923), and The Report of Progressive Education and Joint Committee (1940), advocated that functions and “relational thinking” be a core concept in school mathematics. In fact, Felix Klein considered functions to be the “soul of mathematics”, and advocated that teachers teach functional concepts.

Fortunately, the recommendations made decades ago pertaining to the importance of functions, and the needs to readily integrate the function concept into school mathematics by researchers were not ignored. The recommendations made regarding functions decades ago are evident in today’s curriculum standards. Standards for mathematics require students to be able to define functions, describe functions, identify functions, analyze functions, and recognize patterns in function (NCTM, 2000; Common Core State Standards 2010). Most notably, The Common Core State Standards (2010) has functions as one of five conceptual categories in high school mathematics.

Considering the increased emphasis placed on functions in school mathematics within the past century, we sought to describe how the function concept was presented in secondary mathematics textbooks prior to the “New Math” era.

First Page

14

Last Page

23

Recommended Citation

Sears, Ruthmae; Tran, Dung; Lee, Seoung Woo; and Thomas, Amanda (2016) "Function Concept: Learning from History," Transformations: Vol. 1: Iss. 1, Article 2.
Available at: https://nsuworks.nova.edu/transformations/vol1/iss1/2