The influence of cognitive growth in working memory (WM) on mathematical problem solution accuracy was examined in elementary school children (N = 353) at risk and not at risk for serious math problem solving difficulties. A battery of tests was administered that assessed problem solving, achievement, and cognitive processing (WM, inhibition, naming speed, phonological coding) in children in 1st, 2nd, and 3rd grade across 3 testing waves. The results were that (a) children identified as at risk for serious math problem solving difficulties in Wave 1 showed less growth rate and lower levels of performance on cognitive measures than did children not at risk; (b) fluid intelligence and 2 components of WM (central executive, visual-spatial sketchpad) in Wave 1 (Year 1) predicted Wave 3 word problem solving solution accuracy; and (c) growth in the central executive and phonological storage component of WM was related to growth in solution accuracy. The results support the notion that growth in WM is an important predictor of children's problem solving beyond the contribution of reading, calculation skills, and individual differences in phonological processing, inhibition, and processing speed. (Contains 10 tables, 1 figure and 2 footnotes.)