Making use of search systems to foster learning is an emerging research trend known assearch as learning. Earlier works identified result diversification as a useful technique to support learning-oriented search, since diversification ensures a comprehensive coverage of various aspects of the queried topic in the result list. Inspired by this finding, first we define a new research problem, multidimensional result diversification, in the context of educational search. We argue that in a search engine for the education domain, it is necessary to diversify results across multiple dimensions, that is, not only for the topical aspects covered by the retrieved documents, but also for other dimensions, such as the type of the document (e.g., text, video, etc.) or its intellectual level (say, for beginners/experts). Second, we propose a framework that extends the probabilistic and supervised diversification methods to take into account the coverage of such multiple dimensions. We demonstrate its effectiveness upon a newly developed test collection based on a real-life educational search engine. Thorough experiments based on gathered relevance annotations reveal that the proposed framework outperforms the baseline by up to 2.4%. An alternative evaluation utilizing user clicks also yields improvements of up to 2% w.r.t. various metrics.