Effects of Graphing Calculators and a Model for Conceptual Change on Community College Algebra Students' Concept of Function

Abstract:
Three treatment groups and a control group were compared on two dependent variables regarding their understanding of the concept of function.
During the unit of study for the concept, Treatment Group I students used graphing calculators and participated in a conceptual change assignment.
Treatment Group II students used graphing calculators only during study of the unit. Treatment Group III students participated in the conceptual change assignment only during the unit. Treatment Group IV served as a control group.
Regarding students' understanding and application of the function concepts, domain and range, and their understanding of the concept of scale, the results of the covariate analysis revealed a significant treatment interaction effect. The least square means procedure indicated differences between Treatment Groups I and II, between Treatment Groups I and III, and between Treatment Groups III and IV. The group mean for students who used calculators only was significantly higher than the group mean for students who used calculators and participated in the assignment. The group mean for students who participated in the assignment only was significantly higher that the group means for a) students who used graphing calculators and participated in the assignment and b) students in the control group.
Regarding students' ability to identify, construct, and define function, the results of the covariate analyses revealed a significant effect regarding the factor of conceptual change assignment. The group mean for students who participated in the assignment was significantly lower than the group mean for students who did not participate in the assignment.
Exploratory analyses revealed that the students' definitions of the concept of function were dominated by the ordered pair representation of the concept. This point-wise view of functions was further emphasized through the students' images of the concept of function.
Classroom observations of the treatment and control groups revealed additional information regarding the effect of the graphing calculator on classroom discourse.
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