Recent advances in natural language processing (NLP) have the ability to transform how classroom learning takes place. Combined with the increasing integration of technology in today's classrooms, NLP systems leveraging question answering and dialog processing techniques can serve as private tutors or participants in classroom discussions to increase student engagement and learning. To progress towards this goal, we use the classroom discourse framework of academically productive talk (APT) to learn strategies that make for the best learning experience. In this paper, we introduce a new task, called future talk move prediction (FTMP): it consists of predicting the next talk move -- an utterance strategy from APT -- given a conversation history with its corresponding talk moves. We further introduce a neural network model for this task, which outperforms multiple baselines by a large margin. Finally, we compare our model's performance on FTMP to human performance and show several similarities between the two.