Educational taxonomies organize educational content, such as exercise problems, into concepts, which are also called skills or knowledge components. These taxonomies define learning objectives in educational applications such as intelligent tutoring systems. Developed through human expertise and iterative refinement, they also provide fundamental structure for curricula, assessment, and models of student learning. Recent advances in semantic text embeddings make it possible to construct alternative educational taxonomies computationally from the content itself. In this paper, we investigate this possibility by clustering embeddings of math questions to construct embedding-based educational taxonomies. We compare these taxonomies with the existing Common Core State Standards (CCSS)-based knowledge-component taxonomies in two ASSISTments datasets and evaluate their utility in Deep Knowledge Tracing, a downstream task that relies on taxonomic mappings of questions to knowledge components. The embedding-based taxonomies exhibit substantial but incomplete correspondence with the existing taxonomies, revealing both preserved and alternative organizations of educational content. When used for knowledge tracing, they improve predictive performance by approximately 3–5 AUC percentage points. These results demonstrate the potential of semantic embeddings for automatically constructing educational taxonomies that both recover structure present in human-developed taxonomies and provide useful alternative representations for downstream educational modeling.