Learning from social-media conversations has gained significant attention recently because of its applications in areas like rumor detection. In this research, we propose a new way to represent social-media conversations as binarized constituency trees that allows comparing features in source-posts and their replies effectively. Moreover, we propose to use convolution units in Tree LSTMs that are better at learning patterns in features obtained from the source and reply posts. Our Tree LSTM models employ multi-task (stance + rumor) learning and propagate the useful stance signal up in the tree for rumor classification at the root node. The proposed models achieve state-of-the-art performance, outperforming the current best model by 12% and 15% on F1-macro for rumor-veracity classification and stance classification tasks respectively.