From complex to simple: Analyzing prospective teachers' analogy reasoning in creating accessible geometry problems - Rosyidi, Abdul Haris; Sa'dijah, Cholis; Purnomo, Heri; Abdullah, Abdul Halim (KALAMATIKA Jurnal Pendidikan Matematika, 2025)
Students often struggle to identify relevant analog problems when solving new tasks, highlighting the need for teachers to design simple analog problems that serve as scaffolding. This study aims to analyze prospective teachers’ analogical reasoning processes in simplifying complex geometry problems using the Analogical Reasoning in Mathematics (ARM) framework. This qualitative research involved 34 prospective mathematics teachers from a public university in Surabaya, Indonesia. Participants were selected through purposive sampling based on their academic performance and prior coursework in geometry and problem solving. Data were collected through task-based interviews, written work, and observations during problem-simplification activities. The collected data were analyzed thematically, guided by the components of the ARM framework. The results indicate that prospective teachers with varying ability levels employed different analogical reasoning strategies to simplify complex problems through ARM activities. High-ability prospective teachers identified a broader range of student difficulties and adapted the problems into two-step analog problems featuring variations in visual representations, number of circles, and geometric shapes. Conversely, low-ability prospective teachers focused on difficulties related to verbal representation and the need for concrete numerical information, adapting the problems into single, highly simplified analog problems with specific images and numbers. Overall, prospective teachers actively utilized analogical reasoning to design analog problems that addressed student difficulties. Differences in ability were associated with the complexity of adaptation strategies and the depth of difficulty identification, underscoring the importance of training prospective teachers to integrate both approaches to effectively support student understanding.