Development of the Process Conception of Function

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, usi...

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Bibliographic Details
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
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Summary: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.
ISSN:0013-1954
1573-0816
DOI:10.1007/BF02309532