Students’ Mathematical Thinking in Solving KenKen Puzzles Based on Stacey’s theory

Mathematical thinking in non-routine problem solving involves more than obtaining correct answers; it also concerns how students select starting points, relate mathematical information, consider possibilities, and justify their decisions. This study examined how Grade 8 students’ mathematical thinking processes appeared while solving KenKen puzzles using Stacey’s framework of specialization, generalization, conjecturing, and convincing. A qualitative descriptive design was used with eight students selected from one Grade 8 class based on contrasting response patterns in an introductory KenKen task. Data were collected from students’ written solutions to four KenKen puzzles and task-based retrospective interviews and were analyzed deductively using operational definitions of the four processes. The findings show that the four processes were interrelated and varied across the initial performance profiles. Students in the higher profile more consistently coordinated puzzle constraints, generated and checked possible combinations, and provided mathematical justifications. Students in the intermediate profile demonstrated similar processes but with more revisions, particularly on the 4×4 tasks. Students in the lower profile experienced greater difficulty coordinating permissible numbers, cage conditions, and row–column restrictions. The study contributes qualitative evidence of how Stacey’s four mathematical thinking processes become visible when students solve a puzzle requiring simultaneous coordination of multiple constraints. The findings also suggest that KenKen can provide teachers with a structured context for observing students’ reasoning and identifying areas where instructional support is needed.