Fostering Conceptual Understanding of Exponential Functions Through Collaborative Learning in a High School Mathematics Class

Abstract

  The present study defines “deepening understanding” as “reconstructing knowledge”, and examines how collaborative learning in a high school mathematics class facilitates individuals’ understanding.  Eleventh graders (N=66) solved mathematical problems about exponential functions in 3 stages : pre-test, during the lesson (2 conditions : collaborative learning and explanation of the answers by the teacher), and post-test.  The results indicated that making their own ideas clear, elaborating their own ideas by linking prior knowledge and others’ ideas with their own in order to resolve cognitive conflicts, and producing new ideas facilitated students’ knowledge reconstruction at the post-test.  This suggests that when organizing collaborative learning, the following points are important for proper knowledge reconstruction : the teacher should (a) prepare problems that students can use their prior knowledge to solve and give them adequate time to solve them, (b) prompt students to point out any weaknesses in others’ ideas and to clarify the basis of others’ ideas, and (c) prepare problems that can be solved in various ways and encourage students to express their ideas.