1Third Misconceptions Seminar Proceedings (1993) Paper Title: How, How Often, and Under What Conditions Misconceptions are Developed: The case of Linear Graphs

Abstract: The purpose of the present study was threefold: (a) to examine misconceptions related to the construction of linear graphs; (b) to analyze the cognitive processes underlying the development of the different kinds of misconceptions; and (c) to investigate the effects of a metacognitive intervention on students ’ sense of graphs. The intervention was derived from current theories in the areas of social cognition and metacognition, and from systematic observations of adolescents solving complex mathematical problems. Participants were seventh grade students randomly selected from two Israeli schools (four classes). Intact classes were randomly assigned into either an experimental or a control group. Results indicated that overall students encountered serious difficulties in constructing (and interpreting) linear graphs. Five kinds of misconceptions were identified: constructing an entire graph as a single, one point; misunderstanding the notion of covariation; conserving the form of an increasing function under al