The number of traffic accidents has been continuously increasing in recent years worldwide. Many accidents are caused by distracted drivers, who take their attention away from driving. Motivated by the success of Convolutional Neural Networks (CNNs) in computer vision, many researchers developed CNN-based algorithms to recognize distracted driving from a dashcam and warn the driver against unsafe behaviors. However, current models have too many parameters, which is unfeasible for vehicle-mounted computing. This work proposes a novel knowledge-distillation-based framework to solve this problem. The proposed framework first constructs a high-performance teacher network by progressively strengthening the robustness to illumination changes from shallow to deep layers of a CNN. Then, the teacher network is used to guide the architecture searching process of a student network through knowledge distillation. After that, we use the teacher network again to transfer knowledge to the student network by knowledge distillation. Experimental results on the Statefarm Distracted Driver Detection Dataset and AUC Distracted Driver Dataset show that the proposed approach is highly effective for recognizing distracted driving behaviors from photos: (i) the teacher network's accuracy surpasses the previous best accuracy; (ii) the student network achieves very high accuracy with only 0.42M parameters (around 55% of the previous most lightweight model). Furthermore, the student network architecture can be extended to a spatial-temporal 3D CNN for recognizing distracted driving from video clips. The 3D student network largely surpasses the previous best accuracy with only 2.03M parameters on the Drive&Act Dataset.