A Folding Back Analysis on Elementary Students' Growth in Mathematical Understanding

Abstract

The purpose of this study is to analyze folding back characteristics on elementary students' growth in mathematical understanding with relational and instrumental understanding. This research used a qualitative approach with case study. The growth in mathematical understanding is analyzed in layers of Pirie-Kieren model, namely primitive knowing, image making, image having, property noticing, formalizing, observing, structuring, and inventizing. The results of this study are folding back on students with relational understanding, from property noticing stage to image making stage. In addition, there was also a folding back from image making stage to primitive knowing stage. Folding back that occurs in students with relational understanding has a trajectory to observing stage. In students with instrumental understanding, there is a folding back from property noticing stage to image making stage, and has a path to formalizing stage. The conclusion of this research is that there is a two folding back on students with relational understanding and one folding back on students with instrumental understanding. In addition, students with relational understanding have a folding back trajectory that is longer than students with instrumental understanding.

Keywords

• Folding back
• Pirie-Kieren
• understanding
• instrumental
• relational

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