Student attention is an indispensable input for uncovering their goals, intentions, and interests, which prove to be invaluable for a multitude of research areas, ranging from psychology to interactive systems. However, most existing methods to classify attention fail to model its complex nature. To bridge this gap, we propose AttentioNet, a novel Convolutional Neural Network-based approach that utilizes Electroencephalography (EEG) data to classify attention into five states: Selective, Sustained, Divided, Alternating, and relaxed state. We collected a dataset of 20 subjects through standard neuropsychological tasks to elicit different attentional states. The average across-student accuracy of our proposed model at this configuration is 92.3% (SD=3.04), which is well-suited for end-user applications. Our transfer learning-based approach for personalizing the model to individual subjects effectively addresses the issue of individual variability in EEG signals, resulting in improved performance and adaptability of the model for real-world applications. This represents a significant advancement in the field of EEG-based classification. Experimental results demonstrate that AttentioNet outperforms a popular EEGnet baseline (p-value < 0.05) in both subject-independent and subject-dependent settings, confirming the effectiveness of our proposed approach despite the limitations of our dataset. These results highlight the promising potential of AttentioNet for attention classification using EEG data.