<![CDATA[Mathematical thinking is a fundamental component required to solve mathematical problems, both routine and non-routine. Appropriate thinking processes and solutions form mathematical thinking trajectories, either through complex thinking skills or through the use of heuristic strategies; therefore, both require greater attention. This study aims to investigate prospective mathematics teachers’ mathematical thinking trajectories in number patterns and to identify their learning obstacles. The study adopted a qualitative method using a case study design, enabling an in-depth analysis. We used a test and interviews to collect the data from 28 participants in the Mathematical Thinking course. The findings indicate that students’ mathematical thinking trajectories in solving number-pattern problems vary depending on the type of problem. In Problem 1, four trajectories were identified: (a) conjecturing and clarifying, (b) starting from the most certain information and then moving to statements with lower certainty, (c) synthesising all statements simultaneously and carrying out verification, and (d) identifying the constituent digits first and then determining their positions through verification. In Problem 2, five trajectories were identified: (a) reasoning from specific cases to obtain a generalisation, (b) decomposing the pattern by counting the number of squares and branch segments, (c) recursive reasoning, (d) using diagrams, and (e) guessing a quadratic formula. In addition, two main obstacles were identified in students’ mathematical thinking: (a) students lacked the skills to determine relationships between patterns, and (b) students were not yet able to generalise relationships between patterns.]]>
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