Solving challenging math problems often invites a child to ride an "emotional roller-coaster" and experience a complex mixture of emotions including confusion, frustration, joy, and surprise. Early exposure to this type of "hard fun" may stimulate child's interest and curiosity of mathematics and nurture life long skills such as resilience and perseverance. However, without optimal support, it may also turn off child prematurely due to unresolved frustration. An ideal teacher is able to pick up child's subtle emotional signals in real time and respond optimally to offer cognitive and emotional support. In order to design an intelligent tutor specifically designed for this purpose, it is necessary to understand at fine-grained level the child's emotion experience and its interplay with the inter-personal communication dynamics between child and his/her teacher. In this study, we made such an attempt by analyzing a series of video recordings of problem solving sessions by a young student and his mom, the ideal teacher. We demonstrate a multimodal analysis framework to characterize several aspects of the child-mom interaction patterns within the emotional context at a granular level. We then build machine learning models to predict teacher's response using extracted multimodal features. In addition, we validate the performance of automatic detector of affect, intent-to-connect behavior, and voice activity, using annotated data, which provides evidence of the potential utility of the presented tools in scaling up analysis of this type to large number of subjects and in implementing tools to guide teachers towards optimal interactions in real time. [For the full proceedings, see ED592609.]