Automatic analysis of students' collaborative interactions in physical settings is an emerging problem with a wide range of applications in education. However, this problem has been proven to be challenging due to the complex, interdependent and dynamic nature of student interactions in real-world contexts. In this paper, we propose a novel framework for the classification of student engagement in open-ended, face-to-face collaborative problem-solving (CPS) tasks purely from video data. Our framework i) estimates body pose from the recordings of student interactions; ii) combines face recognition with a Bayesian model to identify and track students with a high accuracy; and iii) classifies student engagement leveraging a Team Long Short-Term Memory (Team LSTM) neural network model. This novel approach allows the LSTMs to capture dependencies among individual students in their collaborative interactions. Our results show that the Team LSTM significantly improves the performance as compared to the baseline method that takes individual student trajectories into account independently. CCS CONCEPTS• Computing methodologies → Computer vision tasks; • Applied computing → Interactive learning environments.