ASSESSING THE EFFECTS OF TEACHING ON THREE TENTH-GRADE STUDENTS’ CONCEPT IMAGES OF QUADRATIC FUNCTIONS

ASSESSING THE EFFECTS OF TEACHING ON THREE TENTH-GRADE STUDENTS’ CONCEPT IMAGES OF QUADRATIC FUNCTIONS

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ASSESSING THE EFFECTS OF TEACHING ON THREE TENTH-GRADE STUDENTS' CONCEPT IMAGES OF QUADRATIC FUNCTIONS

This paper explores the effects of teaching on the concept images, with respect to quadratic functions, of three tenth-grade students –, one high-performing, one medium-performing, and one lowperforming.Pre- and post-teaching interview data, focusing on the students', verbal, symbolic, tabular and graphical representations of quadratic functions, and on their affective responses to those representations, are summarized. At the post-teaching stage, after a sequence of 10 lessons onelementary algebraic functions, the high-performing interviewee enjoyed grappling with quadratic function tasks. During lessons he incorporated symbolic representations of quadratic functions into his thinking, and his mode of reasoning began to change from inductive to deductive. The medium performing interviewee liked solving only those quadratic function questions that she thought she could answer correctly. Her concept image continued to rely almost exclusively on reading coordinates from a given graph and was not connected to more symbolic ways of thinking about quadratic functions. The low-performing interviewee did not like questions concerning quadratic functions, and did not think he could answer them correctly. Nevertheless, his concept image with ,respect to quadratic functions began to feature more accurate and richer cognitive connections.

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