Analisis Kemampuan Abstraksi Matematis Peserta Didik Berdasarkan Tingkat Resiliensi Matematis di SMP

Abstract

This study addresses the urgent issue of students’ difficulties in developing mathematical abstraction skills, which are essential for understanding, applying, and generalizing mathematical concepts at the secondary education level. Recognizing that mathematical resilience—defined as the capacity to persevere and adapt when facing mathematical challenges—is a key psychological factor influencing abstraction, this research aims to describe the mathematical abstraction abilities of students based on their level of mathematical resilience. Employing a qualitative descriptive approach, the study was conducted at a junior high school in Indonesia with participants selected purposively from three resilience categories: high, moderate, and low, as determined by an academic resilience scale. Data were collected through resilience questionnaires, written abstraction tests on the Pythagorean theorem, and in-depth interviews. The analysis focused on empirical and theoretical abstraction indicators, including the identification of object characteristics, symbolic representation, idealization, conceptual application, inter-conceptual relationships, manipulation of abstract concepts, and generalization. The findings reveal a significant relationship between resilience and abstraction ability: students with high mathematical resilience demonstrated optimal achievement across all abstraction indicators, showing reflective and systematic thinking. Those with moderate resilience met only basic indicators and required further guidance for complex abstraction, while students with low resilience exhibited limited abilities, especially in generalization and complex problem solving. The results emphasize that mathematical resilience is a crucial supporting factor in the development of abstract thinking and problem-solving skills. The study suggests that integrating the enhancement of both cognitive (abstraction) and affective (resilience) aspects is essential for improving mathematics learning outcomes in secondary education.