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In a mixed-design study involving 28 teachers, this research assessed the quality of mathematics learning tasks produced through teacher-GenAI collaboration and then explored who was responsible for each dimension of quality. When tasks were designed for instruction, the tasks were typically of high quality in terms of requests for explanation, cognitive demand, real-world context, and collaboration, but of lower quality in terms of connections across content and differentiation. For practice tasks, requests for explanation remained high, but quality on other dimensions was low. Instructional task quality was generally attributable to GenAI, whereas practice task quality depended upon teacher support. This study suggests that future improvements are needed on both the GenAI and teacher sides in creating high-quality practice tasks.