Online education and e-learning have vigorously sprung up and produced massive educational data in a streaming way. It is very challenging to acquire the appropriate learning resources and the suitable learning partners from the streaming-updated educational big data. This article aims to provide sustainable smart educational services including precise personalized recommendation and adaptive clustering under different contexts by correlatively analyzing the global educational data from multiple dimensions via incremental tensor decomposition. First, a tensor-based recommendation and service framework for the streaming educational big data is developed. Then three local tensors concerning learners, resources, and learning records are constructed and further fused to an integrated global learner-resource tensor. Afterward, we present an incremental tensor-based correlative analysis and personalized recommendation (ITCA-PR) algorithm to recommend appropriate resources under various contexts. Besides, we also propose an incremental tensor-based adaptive clustering and community recommendation (ITAC-CR) algorithm to recommend suitable learning partners under various contexts and accordingly construct adaptive learning communities. Extensive experimental results demonstrate that the ITCA-PR algorithm outperforms state-of-the-art improved collaborative filtering algorithms by F-score measurement and the ITAC-CR algorithm has a better clustering performance by DVI measurement. These precise educational services will promote the development of sustainable smart education.