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Although children's use of a variety of strategies to solve arithmetic problems has been well documented, there is no agreed on standardized and validated method for assessing this mix. We examined the convergent validity of typically achieving (TA, N = 39) and low achieving (LA, N = 20) second and third grade children's strategy choices in simple addition using three different methods: child self-report, observer-report, and response time (RT). The high concordance between child and observer reports (Kappa = .948) in both groups suggests that the participants were aware of, and could accurately report, the strategies they used. The Receiver-Operator Characteristic (ROC) analysis showed that RT accurately differentiated between retrieval and counting (AUC = 82%). The specificity and sensitivity of the ROC profiles were significantly greater for the TA group than for LA group, even though the groups did not differ in the overall strategy mix. Our findings suggest that ROC analysis is more sensitive to group differences in the mechanisms governing strategy choice than observation or child report. Children's use of retrieval strategies as well as accuracy during both retrieval and counting trials were all related to the central executive, but not the phonological and visuospatial sketchpad, component of working memory. We discuss the implication of these findings for early mathematical learning.