A local instructional theory for learning the concept of arithmetic sequence through pocah piring game

The nth-term formula is an arithmetic sequence subtopic that contributes significantly to explaining the fundamental concept of an arithmetic sequence. This study aimed to design a Local Instructional Theory (LIT) based on Realistic Mathematics Education (RME) to find the nth-term formula in an arithmetic sequence through the Pocah Piring game. This study was conducted on eighth-grade students in Palembang, Indonesia. This study used educational design research with a validation study, starting with a preliminary design, design experiments, and retrospective analysis. The learning trajectory in this study begins with rich circumstances that require mathematical reasoning rather than abstraction or exact definitions. Three structured learning activities integrating the Pocah Piring game were applied to help the students explore the concept of an arithmetic sequence. To effectively teach arithmetic sequences, instruction should progress from concrete representations, such as physical manipulatives and visual patterns that help students recognise sequential structures, to more abstract forms, including symbolic expressions and general formulas. The developed LIT accurately predicted students’ thinking throughout the learning process, supporting their progression toward the intended learning objectives. Teachers are encouraged to use the LIT derived from this study to guide instruction and design alternative learning pathways when teaching arithmetic sequences.