Explaining new ideas to oneself can promote learning and transfer, but questions remain about how to maximize the pedagogical value of self-explanations. This study investigated how type of instruction affected self-explanation quality and subsequent learning outcomes for second- through fifth-grade children learning to solve mathematical equivalence problems (e.g., 7+3+9=7+_). Experiment 1 varied whether instruction was conceptual or procedural in nature (n=40), and Experiment 2 varied whether children were prompted to self-explain after conceptual instruction (n=48). Conceptual instruction led to higher quality explanations, greater conceptual knowledge, and similar procedural knowledge compared with procedural instruction. No effect was found for self-explanation prompts. Conceptual instruction can be more efficient than procedural instruction and may make self-explanation prompts unnecessary. (Contains 3 tables and 4 figures.)