Students' Reasoning Behavior on Generalization of Figural Pattern

Abstract

Pattern generalization is a core area in mathematics that is recognized by a community of researchers as an approach to develop student's algebraic reasoning. Examining students' generalization strategies of patterns becomes very important in term of learning advanced algebra. This study applied qualitative descriptive methods and was to investigate of students' reasoning behavior to generalize some algebraic patterns. The sample were the 8 th grade students of SMPN 2 Jatirejo Mojokerto. Two volunteer students (first and second) were selected as research subjetcs and based on the existing of students reasoning behaviors. The semi-structured interview were individually conducted to reveal students reasoning behaviors in constructing generalize patterns while they solved the given problem. The obtained data was classified through the generalization strategies in the existing literatures. According to the results of the task performed by the first subject, she performed figural reasoning based on the figural pattern task. The second subject categorized numerical reasoning based on the figural pattern task. The result of this study emphasized that students mainly utilized a recursive strategy to achieve immediate and near generalization. Two of subjects used functional strategy to reach the far generalization but had not yet received the correct answer. The expected implications of this study are as consideration for designing the learning on the generalization of patterns in accordance with the students' reasoning behavior.