Asking students to to self-explain while studying is another way in which new learning becomes integrated with prior knowledge. With my colleague, Dr. Shanta Hattikudur, and my advisor, Dr. Martha Alibali, I investigated the interplay between asking students to self-explain examples of both well-understood (whole number division) and more difficult (fraction division) concepts and giving students opportunities to compare the examples. We found that self-explanation improved conceptual learning of fraction division, but opportunities to compare alone (without prompts to explain the comparison) did not.

**Sidney, P.G.**, Hattikudur, S., & Alibali, M.W. (2015). How do contrasting cases and self-explanation promote learning? Evidence from fraction division*. Learning and Instruction, 40,* 29-38. DOI: 10.1016/j.learninstruc.2015.07.006

Often, students invent informal strategies for problem solving in addition to more formal strategies that are learned during instruction. Dr. Shanta Hattikudur, Dr. Martha Alibali, and I examined whether *bridging* these formal and informal strategies through comparison instruction supports conceptual understanding better than learning about formal and informal strategies separately. We found that comparison instruction was most helpful for those students who reported disliking mathematics. Students who liked mathematics learned equally well with and without support for comparison.

Hattikudur, S., **Sidney, P. G.**, & Alibali, M. W. (2016). Does comparing informal and formal procedures promote mathematics learning? The benefits of bridging depend on attitudes towards mathematics. *Journal of Problem Solving, 9*(1), Article 2. DOI: 10.7771/1932-6246.1180