The strategy choice model (SCM) is a highly influential theory of human problem-solving. One strength of this theory is the allowance for both item and person variance to contribute to problem-solving outcomes, but this central tenet of the model has not been empirically tested. Explanatory item response theory (EIRT) provides an ideal approach to testing this core feature of SCM, as it allows for simultaneous estimation of both item and person effects on problem-solving outcomes. We used EIRT to test and confirm this central tenet of the SCM for adolescents' (n = 376) solving of addition problems. The approach also allowed us to identify the strategy choices of adolescents who still struggle with basic arithmetic. The synthesis of SCM theory and EIRT modeling has implications for more fully investigating the sources of individual differences in students' problem solving, and for identifying problem-solving patterns associated with poor academic achievement. [This is the online version of an article published in "Journal of Educational Psychology."]