Cross-sectional and incremental age effects on cognitive processes that underlie individual differences in components of working memory (WM; phonological loop, visual-spatial sketchpad, executive processing) and mathematical problem-solving accuracy were examined in elementary school children. A battery of tests was administered that assessed problem solving, achievement, memory, and cognitive processing (inhibition, speed, phonological coding) in children in Grades 1, 2, and 3 (Wave 1) and 1 year later (Wave 2). The results showed that: (1) 31% of the explainable within-person changes across testing waves and 42% of the age-related differences in word problem-solving accuracy were related to executive processing; and (2) executive processing and reading performance in Year 1 were the only variables that contributed unique variance to Year 2 problem-solving performance. The results support the notion that growth in the executive system is an important predictor of children's problem solving abilities beyond the contribution of reading and calculation skills and that growth in executive processing can operate independently of individual differences in phonological processing, inhibition, and processing speed. [Abstract altered to comply with ERIC guidelines.]