Analyzing Mathematical Problem-Solving Abilities in Set Theory: A Case Study of Seventh-Grade Students

Abstract

This study aims to analyze and describe the mathematical problem-solving abilities of students in set theory, specifically within a seventh-grade class at a private school in Bandung. The research employed a qualitative case study approach, collecting data through tests and documentation. A diagnostic test served as the primary instrument for evaluating students' problem-solving skills. The findings reveal distinct patterns in how students approach mathematical problems, correlating with their achievement levels. High-achieving students consistently followed Polya's four stages of problem-solving: understanding the problem, devising a plan, carrying out the plan, and looking back to reflect on their solution. In contrast, moderate-achieving students generally adhered to the first two stages, namely understanding the problem and carrying out the plan, often omitting the reflective stage. Low-achieving students predominantly focused on the initial stage of understanding the problem, struggling to advance beyond this point. The study highlights that the ability to understand the problem is the most developed skill among students, as it is the step where most students succeeded. However, devising a plan was identified as the most challenging aspect, with the fewest students able to correctly formulate a strategy for solving the problems. These findings suggest that while understanding is a common strength, there is a need for targeted interventions to improve students' abilities to plan and execute problem-solving strategies effectively