Development of the Process Conception of Function

• Published in: Educational studies in mathematics 1992-06, Vol.23 (3), p.247-285
• Main Authors: Breidenbach, Daniel, Dubinsky, Ed, Hawks, Julie, Nichols, Devilyna
• Format: Article
• Language: English
• Subjects: Algebra; Boolean data; Cognitive Development; Cognitive Measurement; College Mathematics; Computer Assisted Instruction; Computers in education; Concept Formation; Epistemology; Functions (Mathematics); Higher Education; Integers; ISETL Programing Language; Knowledge Level; Mathematical expressions; Mathematical functions; Mathematical objects; Mathematical sets; Mathematics Achievement; Mathematics Education; Mathematics Instruction; Secondary Education
• ISSN: 0013-1954; 1573-0816
• DOI: 10.1007/BF02309532

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.