Models of Problem Solving: A Study of Kindergarten Children's Problem-Solving Processes

Abstract

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. The construction of a model or representation of a problem situation is one of the most fundamental problem-solving processes. Many problems can be solved by representing directly the critical features of the problem situation with an equation, a computer program, or a physical or pictorial representation. Modeling also turns out to be a relatively natural problemsolving process for young children. There is an extensive body of research documenting that even before they receive formal instruction in arithmetic, young children can solve a variety of different types of addition and subtraction word problems by directly modeling with counters the different action and relationships described in the problems (Carpenter, 1985;