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Intelligent education systems have enabled personalized learning (PL). In PL, students are presented with educational contents that are consistent with their personal knowledge states (KS), and the critical task is accurately estimating these states through data. Knowledge tracing (KT) infers KS (latent) through historical student interactions (observed) with the knowledge components (KCs). A wide variety of KT techniques have been developed, from Bayesian Knowledge Tracing (BKT) to Deep Knowledge Tracing (DKT). However, in most of these methods, the KCs are represented as stand-alone entities, and the effect of representing KCs using contexts such as learning-related factors has been under-investigated. Also, KT needs to generate personalized results to facilitate tasks such as exercise recommendation. In this paper, we propose two approaches that use a contextualized representation of KCs, one with a content-based approach and another with a Long Short Term Memory (LSTM) network plus a personalization mechanism. By performing extensive experiments on two real-world datasets, results show not only a tangible improvement in prediction accuracy in the KT task compared to existing methods, but also its effectiveness in improving the recommendation precision. [ABSTRACT FROM AUTHOR]