Development of the process conception of function

Abstract

Our goal in this paper is to make two points. First, college students, even those who have taken a fair number of mathematics courses, do not have much of an understanding of the function concept; and second, an epistemological theory we have been developing points to an instructional treatment, using computers, that results in substantial improvements for many students. They seem to develop a process conception of function and are able to use it to do mathematics. After an introductory section we outline, in Section 2, our theoretical epistemology in general and indicate how it applies to the function concept in particular. In Sections 3; 4, and 5 we provide specific details on this study and describe the development of the function concept that appeared to take place in the students that we are considering. In Section 6 we interpret the results and draw some conclusions.

DNR-Based Curricula: The Case of Complex Numbers

“…This, of course, is due to students' weak understanding of the concept of function, as has been widely documented (see, for example, [1,29]). …”

“…(3) Cubic equations without the second term are reducible to system (1) through the same identity, which, by (1), is reducible to a quadratic equation. And finally, (4) Any general cubic equation is reducible to a cubic equation without the second term through Change of Variable, which, by (3), is reducible to a cubic equation.…”

Covariation between variables in a modelling process: The ACODESA (collaborative learning, scientific debate and self-reflection) method

“…Bloch, 2003;Breidenbach et al, 1992;Carlson, 1998;Harel & Dubinsky, 1992;Hitt, 1994;Mesa, 2004;Trigueros & Martínez-Planell, 2010),…”

Applying Covariational Reasoning While Modeling Dynamic Events: A Framework and a Study

“…Research into students' developing function conception has revealed that a view of function as a process that accepts input and produces output (Breidenbach, Dubinsky, Hawks & Nichols, 1992) is essential for the development of a mature image of function. This view has also been shown to be foundational for coordinating images of two variables changing in tandem with each other (Thompson, 1994a;Carlson, 1998).…”