| Sumario: | Background: Empirical studies have revealed students' development of computational thinking (CT) and mathematical thinking (MT) during programming‐based mathematical problem‐solving, highlighting specific CT concepts or practices that serve as learning goals or outcomes. However, implementing programming‐based mathematics instruction requires teachers to have sufficient knowledge about learners' thinking processes in such a context, while very little is known about multifaceted solution development from a learner‐centred perspective. Objectives: Viewing CT and MT as processes that go beyond specific skills or concepts, we conducted a qualitative study to investigate how participants develop computational solutions to mathematical problems and construct meaningful understandings of these solutions. Methods: We adopted an interpretive approach to participants' solution pathways to reveal their diverse thinking processes underlying solution development. A constant comparative analysis approach was undertaken to guide the data analysis. Results and Conclusions: We identified multiple solution pathways in developing programming‐based mathematical solutions (PMS) and characterised four significant pathways comprising seven distinct sub‐situations: (1) transition between personal MT and invalid PMS, (2) evolution from invalid PMS to valid PMS, (3) construction from non‐meaningful PMS to meaningful PMS and (4) revision from suboptimal PMS to optimal PMS. The findings contribute to a deeper understanding of problem solvers' learning in programming‐based mathematical problem‐solving and offer implications for theory and practice in programming‐rich mathematics education.
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