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With the support of digital learning platforms, synchronous and collaborative learning has become a prominent learning paradigm in mathematics education. Computer-Supported Collaborative Learning (CSCL) has emerged as a valuable tool for enhancing mathematical discourse, problem solving, and ultimately learning outcomes. This paper presents an innovative examination of Graspable Math (GM), a dynamic mathematic notation and learning online platform, to enable synchronous, collaborative learning between pairs of students. Through analyzing students' online log data, we adopt a data-driven method to better understand the intricate dynamics of collaborative learning in mathematics as it happens. Specifically, we apply frequency distributions, cluster analysis to present students' dynamic interaction patterns and identify distinctive profiles of collaboration. Our findings reveal several collaboration profiles that emerge through these analyses. This research not only bridges the gap in current CSCL tools for mathematics, but also provides empirical insights into the effective design and implementation of such tools. The insights gained from this research offer implications for the design of digital learning tools that support effective and engaging collaborative learning experiences.