Collaborative Problem Solving (CPS) is a core skill in education, where the process of peer interaction is highly important. However, existing educational dialogue datasets mostly focus on classroom instruction or tutoring (i.e., teacher/tutor-student interaction), yet datasets centering small-group, student-student interaction are limited. This thus leaves research with limited resources for studying how students interact, coordinate, and solve problems together in real educational settings. To address this, we introduce PeerMathDial, the first dataset of peer CPS dialogues collected from authentic middle school math classrooms. It contains 55 dialogues from 27 students, totaling 6,406 turns. To facilitate research on CPS discourse analysis, we further build a corpus-grounded dialogue act taxonomy assisted by LLMs. Using the dataset and the dialogue act taxonomy, we demonstrate the practical applications of PeerMathDial across three use cases. First, we track how dialogues evolve over time and measure the impact of teacher interventions. Second, we align dialogue actions with student surveys to reveal the connection between students' traits (e.g., confidence, leadership) and their actual behaviors. Third, by evaluating LLMs on dialogue act prediction, we glimpse at the potential of LLMs for student simulation in educational applications. Our dataset and source code will be released to the community.

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