Does computing the answer to an arithmetic problem yourself help you to more fluently recall that answer? For example, if you are asked to find the answer to 8 x 6 by adding eight six times, do you remember that answer better than if you are simply told that 8 x 6 = 48 and directed to memorize it? Across four studies I pit learning artificial arithmetic facts (e.g., a # b = 10(a +b) + ab) via flash-card like rote memorization against learning those same facts by actually computing the answer. I found that, on a speeded, cued-recall test given immediately after practice, participants who practiced flashcard-like memorization consistently outperformed those who computed the answers themselves. This advantage persisted even after learning a second, interfering, set of facts. However, my third and fourth studies demonstrate that despite this initial advantage of memorization practice, computing the answer yourself may still result in better long term fluency, via a mechanism that I term “self-re-presentation”. Essentially, the idea is that if you know how to compute a fact, then you can always recompute it when you cannot recall it, and, most importantly, that re-exposure to the correct answer will boost your subsequent ability to recall that answer. An additional layer of complexity is introduced by Study 2, which suggests that memorization alone can lead to robust long term memory provided that practice occurs with enough frequency that little forgetting occurs between practice sessions. This nuanced answer provides practical guidance for educators, clarifies why prior studies comparing self-computation to rote memorization have produced mixed results, and contributes to the human memory literature, describing an important learning mechanism (self-re-presentation) that has not figured prominently in prior discussions of memory.