A Analisis Penalaran Aljabar Siswa SMA Melalui Soal Pola Bilangan Aritmatika Berbasis Representasi Visual

Abstract

Background:Mathematics, especially algebraic reasoning, plays a crucial role in developing logical and systematic thinking skills. However, students often struggle to translate concrete patterns into abstract algebraic forms, indicating a gap between visual understanding and symbolic expression. The use of visual media in arithmetic sequence problems has proven effective in strengthening the connection between concrete and abstract concepts. This observation aims to examine students' thought processes in constructing reasoning from observed patterns and their ability to express them in algebraic symbols.Objectif :  This study aims to explore students' thought processes in understanding and solving visual pattern-based mathematics problems, specifically in observing patterns, constructing reasoning, and expressing mathematical ideas into algebraic forms.Methods :The observation was conducted at SMA Negeri 1 Sugihwaras from June 10-16, 2025. The subjects were two students (Muhammad Fahmi Saputra and Anna Althofun Nisa’). Data were collected through visual pattern problem sheets (arithmetic sequence dot patterns), observation guidelines, and interview guidelines. Data were analyzed qualitatively, focusing on pattern generalization, logical argumentation, and symbolic expression. Results:Both students demonstrated good pattern generalization abilities, identifying the pattern of adding 4 dots and recognizing it as an arithmetic sequence. They also showed sufficient logical reasoning, explaining the steps and reasons for using the formula, and performing trials. However, both students still faced difficulties in formal expression, such as the inconsistent and not entirely accurate symbolic writing of the formula Un​=a+(n−1) × b. Conclusion: Students' generalization and logical reasoning abilities are well-developed, but formal expression in algebraic symbols remains a challenge. Visual learning is helpful, but it needs to be balanced with practice in writing formal formulas to enhance overall algebraic reasoning.