Abstract:

The aim of this study was to investigate seventh grade students’ use of solution strategies needed to solve proportional reasoning problems. A private middle school and two public middle schools of a city located in the inner region of Turkey were selected as the sample of the study. In total, 278 students (157 boys and 121 girls) took part in the study. Survey methodology was used to describe seventh grade students’ proportional reasoning strategies. Proportional Reasoning Test (PRT) consisting of five open ended problems was developed by the researchers to determine students’ solution strategies. Student responses to each problem were graded by the help of a rubric. Besides, the correct solution strategies used by the students were coded by considering pre-existing proportional reasoning strategies in the mathematics education literature. Analysis of students’ correct responses showed eight different solution strategies including cross product algorithm, factor of change, building up, equivalent fractions unit rate, part-to-part reasoning, ratio tables and part-to-whole reasoning. The number of strategies used in each problem ranged between two and five. As a whole, the most frequent strategies used by the students were cross product algorithm, factor of change strategy and part-to-part reasoning strategy. However, cross product algorithm was the most frequent strategy among all strategies. This strategy has no physical referent and lacks meaning for students. Therefore, cross product algorithm should not be introduced to students until they have many experiences with intuitive and conceptual strategies such as factor of change strategy, build-up strategy or unit rate strategy

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