Accurate and automatic production of the basic number combinations is a major objective of elementary mathematics education. Typically, it is not an objective that is easily and quickly attained. Indeed, teachers regularly lament about how difficult it is to get their students to master the basic "number facts." This problem may be due, in part, to educators' misconceptions of how children learn basic number combinations and how number combinations are represented in adult long-term memory. This paper first outlines the historical debate on how number combinations are learned or internalized and then critically reviews the empirical evidence for and conceptual adequacy of current models of how number combinations are represented in and efficiently produced from long-term memory. An alternative view is offered that argues that, while adults may retrieve some number combinations from associative memory (a "reproductive" process), many combinations can be accurately and automatically produced from stored rules, algorithms, or principles (efficient "reconstructive" processes). (JN)