Explaining new ideas to oneself can promote transfer, but how and when such self-explanation is effective is unclear. This study evaluated whether self-explanation leads to lasting improvements in transfer success and whether it is more effective in combination with direct instruction or invention. Third- through fifth-grade children (ages 8-11; n=85) learned about mathematical equivalence under one of four conditions varying in (a) instruction on versus invention of a procedure and (b) self-explanation versus no explanation. Both self-explanation and instruction helped children learn and remember a correct procedure, and self-explanation promoted transfer regardless of instructional condition. Neither manipulation promoted greater improvements on an independent measure of conceptual knowledge. Microgenetic analyses provided insights into potential mechanisms underlying these effects.