This study employed the technological pedagogical content knowledge (TPACK) framework to guide the collaborative design process between preservice and practicing teachers. The teams designed technological pedagogical mathematics tools (TPMTs) for inquiry-based learning based on the syllabi for secondary mathematics. The content of the chat messages of preservice and practicing teachers was coded with different dimensions of TPACK to unpack the process of how the teams arrived at critical design

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... decisions. The TPMTs were further evaluated by 30 practicing mathematics teachers, with respect to three criteria: (1) technology tools and curriculum goals, (2) technology tools and teaching activities, and (3) the fit between pedagogy and technology. The content analysis revealed that the collaborative design process involved three clear stages, demarcated by the different versions of the TMPTs: replacement, enhancement, and transformation. Practicing teachers' pedagogical content knowledge played a crucial role in the design of pedagogically sound tools, and for refining the initial TPACK of preservice teachers. The subsequent evaluations supported the positive pedagogical values of the TPMTs. Overall, this study contributes to TPACK research with a case where the collaborative design process with distributed expert knowledge can be synthesised to create pedagogically sound technological tools for mathematics.