This paper outlines a theoretical perspective for studying student understandings of the concept of addition. The notion of operational sense is defined as a way to describe the notion of addition as a mathematical object, paving the way for an application of the theory of reification at this level. Previous frameworks relative to problem solving…

After a year of instruction, 70 kindergarten children were individually interviewed as they solved basic, multistep, and nonroutine word problems. Thirty-two used a valid strategy for all 9 problems, and 44 correctly answered 7 or more problems. Modeling provided a unifying framework for thinking about problem solving. (Author/MDH)