Center for Education Research Seventy kindergarten children who had spent the year solving a variety of basic word problems were individually interviewed as they solved addition, subtraction, multiplication, division, multistep, and nonroutine word problems. Thirty-two children used a valid strategy for all nine problems and 44 correctly answered seven or more problems. Only 5 children were not able to answer any problems correctly. The results suggest that children can solve a wide range of problems, including problems involving multiplication and division situations, much earlier than generally has been presumed. With only a few exceptions, children's strategies could be characterized as representing or modeling the action or relationships described in the problems. The conception of problem solving as modeling could provide a unifying framework for thinking about problem solving in the primary grades. Modeling offers a parsimonious and coherent way of thinking about children's mathematical problem solving that is relatively straightforward and is accessible to teachers and students alike.

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This study determines the relative difficulty and associated strategy use of arithmetic (addition and subtraction) story problems when presented in American Sign Language to primary level (K-3) deaf and hard-of-hearing students. Results showed that deaf and hard-of-hearing students may consider and respond to arithmetic story problems differently than their hearing peers, with the critical dimension in problem difficulty being based on the operation typically used to solve the problem, not the story within the problem. The types of strategies used by the students supported the order of problem difficulty. The visual-spatial nature of the problem presentation appeared not to assist the deaf and hard-of-hearing students in solving the problems. Factors that may have contributed to this pattern of problem difficulty are discussed so that educators can better align mathematics instruction to the thinking of the deaf child.

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