This study investigated the strategy characteristics and development of children with mathematical disabilities (MD) in the domain of simple addition and subtraction, in terms of Lemaire and Siegler's model of strategic change, using the choice/no-choice method and the combined chronological-age (CA)/ability-level (AL)-match design. Four groups of children, matched on either CA or mathematical AL, solved a series of 36 problems with the bridge over 10 in four conditions. In the choice condition, children could choose between retrieval, decomposition to 10, and counting on to solve each problem. In the retrieval, decomposition, and counting conditions, they had to answer the same 36 problems using retrieval, decomposition to 10, and counting on, respectively. The results revealed clear differences in the frequency, efficiency, and adaptiveness with which the CA-matched children applied the available strategies. In contrast, we observed no differences in strategy frequency, efficiency, and adaptiveness between the AL-matched children. These results support the hypothesis that the strategy development of children with MD is marked by a delay rather than a specific deficit. Moreover, this study further documents the value of the methodology used to study children's strategy use and development in the domain of simple arithmetic.