# Strategies Employed by 7th and 8th Graders for Quantitative Proportional Reasoning Problems

## Abstract

In mathematics education, reasoning is noted a crucial skill for understanding various mathematical concepts. Proportional reasoning, in turn, is also important as the mathematics curricula introduces the concept “ratio” in the 6th grade and the concepts “ratio and proportion” in the 7th grade. In this context, the aim of this study is to analyse the strategies used by 7th and 8th graders while solving quantitative proportional reasoning problems. In this endeavour, descriptive case study method was employed. The study group consisted of 28 7th grade and 28 8th grade students who were studying at two secondary schools during 2015-2016 academic year. For the purpose of the study, a proportional reasoning test of 10 open-ended questions was applied. In analyzing the data, descriptive analysis, which is a qualitative data analysis method, was used. In conclusion it was found that 8th graders were able to come up with a greater variety of strategies compared to 7th graders, while their most frequently employed strategy was a crossing algorithm. In contrast, 7th graders often resorted to the unit rate strategy for solving the problems. In addition, 8th graders were found to be more accurate compared to 7th graders, in terms of choosing the correct strategy. In conclusion, it can be forcefully argued that increased emphasis on various types of problems can help with the development of the students’ proportional reasoning skills.

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