Keywords
SPLDV
Pirie-Kieren’s Theory
layers of student's mathematical understanding
How to Cite
Abstract
This research aims to uncover layers of students' mathematical understanding and provide scaffolding to achieve all layers of Pirie-Kieren's mathematical understanding. This study is qualitative research with a multiple case study design. The research subjects are categorized into three types: (1) S1A and S1B are students who write structured problem-solving steps and their answers are correct, (2) S2A and S2B are students who write structured problem-solving steps but make mistakes in some steps resulting incorrect answers, and (3) S3A and S3B are students who write unstructured problem-solving steps but their answers are correct. Two subjects are chosen from each category to generate saturated data. The results of this research indicate that (1) S1A and S1B experience folding back to the inner layers, then systematically reach all layers of mathematical understanding after scaffolding, (2) S2A and S2B reach certain outer layers of mathematical understanding after scaffolding, (3) S3A and S3B reach certain inner layers of mathematical understanding after scaffolding. This research found that each subject reaches all layers of Pirie-Kieren's mathematical understanding after scaffolding through three methods: (1) providing prompting questions, (2) providing problem-solving examples, and (3) providing constructive feedback on subject answers. The teacher’s understanding of students' Pirie-Kieren mathematical understanding layers can be used to improve learning.
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