Research into the development of mathematical cognition has accelerated in recent times. In this literature review, findings from different approaches to studying simple addition performance are reviewed. A review of findings from studies incorporating observation, self-report or both revealed the complex process of change associated with developing retrieval strategies for simple addition. These findings are synthesized using a model of change labelled the Moving-On Process to represent the wave-like transitional pattern of strategy use preceding retrieval. A review of findings from studies based on the analysis of reaction times revealed a robust finding known as "the problem-size effect." Different explanations of the problem-size effect, incorporating different theoretical accounts of the nature of retrieval, exact answers, and strategy choice, are compared and contrasted. A review of findings based on a combination of both approaches uncovered important methodological considerations associated with analyzing reaction times and offers direction for future research aimed at unravelling the convoluted construct Of automaticity.