Divergent thinking (DT), which involves finding new possibilities and seeing the familiar from a new perspective, has been stressed in mathematical creativity education. However, convergent thinking (CT), which involves searching for a correct single answer, has been relatively understudied in relation to developing mathematical creativity. Moreover, how to relate the two thinking modes when facilitating mathematical creativity in daily teaching has rarely been studied. In this study, we propose a framework of dynamic interplay between DT and CT, which we call DT/CT "dynamics," that characterizes the creative learning process in the classroom, and to provide an example we analyze research results from two classes from our 3-year longitudinal study with an experienced teacher, in order to demonstrate the framework. Findings indicate that there were significant differences between the two classes in how DT/CT dynamics worked with respect to three aspects, namely, authority distribution, micro-level transition, and macro-level goals. This paper provides a new integrative framework that combines extant work on the psychology of DT/CT with ongoing research in mathematics education, which offers a meaningful lens to capture the way mathematical creativity is pursued effectively in everyday mathematics classrooms. In particular, the study provides a reinterpretation of the theoretical perspectives of Tan and Sriraman (2017) on creativity and provides an analytical tool that enables an understanding of creative learning processes in everyday mathematics classrooms in relation to DT/CT dynamics.