Elementary third and fourth grade students` modeling of mathematics word problems: Multiplication and division

Because mathematics consists of abstract concepts, it is difficult for manystudents who are developmentally in concrete operation period. In order to establisha sound foundation for these abstract concepts, students need concrete experiencesfor constructing meaningful concepts. For this reason, it is very imoprtant thatmathematical modeling must be used in teaching. Mathematical modeling is aprocess in that a complex phenomenon is described in mathematical terms, solvingthese mathematical descriptions and evaluating and interpreting results according tothe original situation. Research studies has shown that young children need suchexperiences from the very first year of schooling.This study has two main purposes. First is to determine what kind ofstrategies third and fourth graders use as they solve multiplication and division wordproblems. Second is to determine why they use these strategies. In order to serve theaims of the study two elementary schools were selected. From these schools onethird grade class and one fourth grade class were selected. A problem solving testwas administered to these classes. After the analysis of the strtaegies the studentsused in solving problems on the test, 8 students, 4 from each grade, were selectedfor the interviews.As a result of the analyses of the data collected, third graders were found tobe more successful than fourth graders in solving multiplication and division wordproblems. It was observed that students generally preferred to use symbolicoperations as a problem solving strategy, they only choose modeling the problemusing drawings when they had dificulty in understanding the problem or in choosingan operation. The reason for choosing symbolic operations to solve such problems,they stated that hey were not used to using modeling, it was difficult for them tomodel problem situations or it was easy and time saving to use operations. Inaddition, it was found that students chose an operation for solving a problemincluding fractional numbers without understanding. They also misinterpretfractional numbers (half and quarters), as a result, used incorrect operation.Key Words: Mathematics, problem solving, modeling, multiplicationand division word problems, half and quarter.