Understanding student behavior in the classroom is essential to improve both pedagogical quality and student engagement. Existing methods for predicting student engagement typically require substantial annotated data to model the diversity of student behaviors, yet privacy concerns often restrict researchers to their own proprietary datasets. Moreover, the classroom context, represented in peers' actions, is ignored. To address the aforementioned limitation, we propose a novel three-stage framework for video-based student engagement measurement. First, we explore the few-shot adaptation of the vision-language model for student action recognition, which is fine-tuned to distinguish among action categories with a few training samples. Second, to handle continuous and unpredictable student actions, we utilize the sliding temporal window technique to divide each student's 2-minute-long video into non-overlapping segments. Each segment is assigned an action category via the fine-tuned VLM model, generating a sequence of action predictions. Finally, we leverage the large language model to classify this entire sequence of actions, together with the classroom context, as belonging to an engaged or disengaged student. The experimental results demonstrate the effectiveness of the proposed approach in identifying student engagement. The source code will be available at https://github.com/ahmed-nady/context_aware_student_engagement.