Using a product-based teacher professional development workshop in the Just Do Math program as a case, this study investigated the discourse between teachers and teacher educators from three perspectives, namely focus, form, and flow, to see how the two cohorts communicated in the co-construction, whether the co-construction is feasible to produce innovative teaching materials, and what the feasible dialogical modes are for this co-construction. The participants included four experienced university-based mathematics teacher educators and 38 mathematics teachers. The discourse from the eight 3-hour sessions of the workshop was collected. The findings included that both teachers and teacher educators focused more on students' development of concepts than on learning motivation, even if learning motivation was one main problem to be solved. Feasible dialogical modes for co-construction in teacher professional development workshops in the context of East Asian educational cultures were revealed, which could be described as teacher educator-centred but teacher-focused.