The results of an exploratory study into measurement of elementary mathematics ability are presented. The focus is on the abilities involved in solving standard computation problems on the one hand and problems presented in a realistic context on the other. The objectives were to assess to what extent these abilities are shared or distinct, and the extent to which students' language level plays a differential role in these abilities. Data from a sample of over 2,000 students from first, second, and third grade in the Netherlands were analyzed in a multidimensional item response theory (IRT) framework. The latent correlation between the two ability dimensions (computational skills and applied mathematics problem solving) ranged from 0.81 in grade 1 to 0.87 in grade 3, indicating that the ability dimensions are highly correlated but still distinct. Moreover, students' language level had differential effects on the two mathematical abilities: Effects were larger on applied problem solving than on computational skills. The implications of these findings for measurement practices in the field of elementary mathematics are discussed.