Effective question classification is crucial for AI-driven educational tools, enabling adaptive learning systems to categorize questions by skill area, difficulty level, and competence. This classification not only supports educational diagnostics and analytics but also enhances complex tasks like information retrieval and question answering by associating questions with relevant categories. Traditional methods, often based on word embeddings and conventional classifiers, struggle to capture the nuanced relationships in natural language, leading to suboptimal performance. To address this, we propose a novel approach leveraging graph convolutional networks (GCNs), named Phrase Question-Graph Convolutional Network (PQ-GCN) to better model the inherent structure of questions. By representing questions as graphs -- where nodes signify words or phrases and edges denote syntactic or semantic relationships -- our method allows GCNs to learn from the interconnected nature of language more effectively. Additionally, we explore the incorporation of phrase-based features to enhance classification accuracy, especially in low-resource settings. Our findings demonstrate that GCNs, augmented with these features, offer a promising solution for more accurate and context-aware question classification, bridging the gap between graph neural network research and practical educational applications.