Based on an enactivist perspective on learning mathematics, we articulate three key processes of designing mathematics-grounding activities (MGAs) where students’ mathematical thinking can be motivated and shaped with the interactions between their enactments and the evolving tasks in the activities. Then, evaluation criteria and design steps will be derived in terms of the key processes. The key processes of designing MGAs, the criteria for evaluating quality MGAs and the design steps also emerged from the reciprocal relationships between theories and practices in the context of the Just Do Math (JDM) program. The processes and steps of designing MGAs suggested in this article can benefit researchers and educators to develop original activities for advancing the learning of mathematics in line with the enactivist perspective. Additionally, the key processes can be further referred to for explanations of how metaphorical grounds of mathematics can emerge under systemic interactions between learners, tasks and social contexts, and how learners’ motivation is integrated into the evolving tasks. Criteria could be applied for not only evaluating the potential of MGAs but also for identifying the weaknesses needed to be modified.
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