Teaching plays a fundamental role in human learning. Typically, a human teaching strategy would involve assessing a student's knowledge progress for tailoring the teaching materials in a way that enhances the learning progress. A human teacher would achieve this by tracing a student's knowledge over important learning concepts in a task. Albeit, such teaching strategy is not well exploited yet in machine learning as current machine teaching methods tend to directly assess the progress on individual training samples without paying attention to the underlying learning concepts in a learning task. In this paper, we propose a novel method, called Knowledge Augmented Data Teaching (KADT), which can optimize a data teaching strategy for a student model by tracing its knowledge progress over multiple learning concepts in a learning task. Specifically, the KADT method incorporates a knowledge tracing model to dynamically capture the knowledge progress of a student model in terms of latent learning concepts. Then we develop an attention pooling mechanism to distill knowledge representations of a student model with respect to class labels, which enables to develop a data teaching strategy on critical training samples. We have evaluated the performance of the KADT method on four different machine learning tasks including knowledge tracing, sentiment analysis, movie recommendation, and image classification. The results comparing to the state-of-the-art methods empirically validate that KADT consistently outperforms others on all tasks.