Proportional Reasoning of Junior High School Students in Solving Geometric Similarity Problems Based on Mathematical Disposition

Abstract

Proportional reasoning is the foundation of mathematical abilities, including algebra, geometry, and statistics, and is influenced by students' mathematical dispositions. The transition from additive to multiplicative reasoning plays a crucial role in problem-solving. This study explores junior high school students' strategies in understanding geometric similarity through a qualitative case study involving three students in Surabaya selected through purposive sampling based on high, medium, and low mathematical dispositions This study uses a qualitative approach with a case study method.  The subjects of the study consisted of three eighth-grade students purposively selected to represent high, medium, and low mathematical disposition, allowing an in-depth examination of how different dispositions influence proportional reasoning. The instruments used were similarity problem worksheets and semi-structured interview guidelines. Data were collected through student answers and interviews, then analysed through data reduction, data presentation, and drawing conclusions. The results showed differences in proportional reasoning strategies according to mathematical disposition: S1 at level 3 (Formal Reasoning), S2 at level 2 (Quantitative Reasoning), and S3 at level 0 (Non-Proportional Reasoning). Proportional reasoning develops when quantity coordination and multiplicative strategies are used in an integrated manner, in line with each student's mathematical disposition. Student with high disposition consistently use ratio-based multiplicative strategies, student with medium disposition use multiplicative strategies, while student with low disposition tend to use additive rules or random approaches. These findings are exploratory and can serve as a basis for studying misconceptions and developing proportional learning.