Mental arithmetic and strategy use with indirect number problems up to one hundred

Until recently mental arithmetic with two-digit numbers up to 100 has been a rather unexplored topic in research. Not only the units but even more the tens play a central role in this number domain, which results in two different computation procedures both widely in use: (1) decomposition or splitting off the tens and units in both numbers (1010), and (2) counting by tens up or down from the first unsplit number (N10). The purpose of this study is an exploration of these two different procedures, when used at a higher level of strategic problem solving. Third-graders were selected as consistent users of either 1010 or N10 procedures, and they were confronted with indirect number problems of the type 27 + … = 65. To achieve correct solutions one needs to engage in adaptation of computation procedure or in strategy change. In this context, five aspects of numerical restructuring and transformation could be discriminated. Results revealed two types of flexibility in strategy use: flexibility between strategies, especially strategy change from 1010 to N10, and b) flexibility within strategies, especially numerical adaptation within N10.