Recognizing student behaviors in classroom videos remains challenging due to complex backgrounds, frequent occlusions, subtle inter-class motion differences, and temporal jitter in frame-wise predictions. To address these issues, this paper proposes a hybrid student behavior recognition framework that integrates a Multi-branch Spatiotemporal Attention Network (MSTA-Net) with a Behavior State Kalman Filter (BSKF). At the perceptual level, MSTA-Net employs decoupled channel, spatial, and short-term temporal attention branches to enhance discriminative behavioral features while suppressing irrelevant background information. At the cognitive level, BSKF reformulates behavior recognition as a continuous state estimation problem in a high-dimensional probability space, where behavioral inertia is exploited to smooth noisy observations and improve temporal consistency. Experimental results on the SCB-Dataset and real-world classroom video sequences demonstrate that the proposed method achieves an accuracy of 94.7% and a real-time inference speed of 33 FPS. Compared with purely deep learning-based models, the proposed framework reduces the Action Category Switching (ACS) rate by 50%, indicating substantially improved robustness in long-term behavior recognition. These results suggest that coupling attention-based perception with Kalman-based state estimation provides an effective and efficient solution for reliable student behavior analysis in intelligent classroom environments.