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The concept of variation and misconceptions in cartesian graphing


Authors: 
Clement, J.
Category: 
Volume: 
11(2)
Pages: 
77-87
Year: 
1989
Publisher: 
Focus on Learning Problems in Mathematics
Abstract: 

In this paper I propose some basic elements of a model of knowledge structures used in comprehending and generating graphs, with emphasis on the concept of covariation and on the analogical character of graphical representation. I then use this competence model to attempt to organize and interpret some of the existing literature on misconceptions in graphing. Two types of common misconceptions, treating the graph as a picture, and slope-height confusions, will be discussed, as will the earliest recorded use of graphs in the work of Oresme in 1361. One of the motives for studying concepts used in graphing is that it may help us understand the nature of the more general concepts of variable and function and the role that analogue spatial models play in representation.