Investigating the Possibility of Performing Algebraic Generalization Based on the Analysis of Problem Solving on Near/Far Generalization of 6th Graders

Abstract

Students who have learned arithmetic in elementary mathematics would learn algebra in middle schools in earnest. So, the transition from arithmetical thinking to algebraic thinking is an important success factor for algebra learning. Therefore, in this study, 64 sixth graders solved the problems of near generalization and far generalization concerning the generalization of some figure patterns. Subsequently we analyzed their problem solving. As a result of the analysis, several cases of students having difficulties in performing algebraic generalization were identified. Through the discussion of the research results, several pedagogical implications were drawn to support the transition from arithmetical thinking to algebraic thinking in elementary school students.

Keywords

• arithmetical generalization
• algebraic generalization
• near generalization
• far generalization
• early algebra