Teaching style plays an influential role in helping students to achieve academic success. In this paper, we explore a new problem of effectively understanding teachers' teaching styles. Specifically, we study 1) how to quantitatively characterize various teachers' teaching styles for various teachers and 2) how to model the subtle relationship between cross-media teaching related data (speech, facial expressions and body motions, content et al.) and teaching styles. Using the adjectives selected from more than 10,000 feedback questionnaires provided by an educational enterprise, a novel concept called Teaching Style Semantic Space (TSSS) is developed based on the pleasure-arousal dimensional theory to describe teaching styles quantitatively and comprehensively. Then a multi-task deep learning based model, Attention-based Multi-path Multi-task Deep Neural Network (AMMDNN), is proposed to accurately and robustly capture the internal correlations between cross-media features and TSSS. Based on the benchmark dataset, we further develop a comprehensive data set including 4,541 full-annotated cross-modality teaching classes. Our experimental results demonstrate that the proposed AMMDNN outperforms (+0.0842% in terms of the concordance correlation coefficient (CCC) on average) baseline methods. To further demonstrate the advantages of the proposed TSSS and our model, several interesting case studies are carried out, such as teaching styles comparison among different teachers and courses, and leveraging the proposed method for teaching quality analysis.