Abstract
The purpose of this study was to investigate middle school students’ solution strategies in solving different types of proportional (i.e., missing value, numerical comparison and qualitative reasoning problems) and non-proportional problems and to compare if differences existed between sixth and eighth grades students’ solution strategies. Data were collected from 101 sixth grade (n=44) and eighth grade (n=57) students from three different public middle schools. The students were asked to solve ten open-ended items that included seven proportional problems and three non-proportional problems. Descriptive data analysis methods were used to analyze data. The results revealed that the students’ solution strategies differed based on problem type and grade level. The eighth grade students used cross-multiplication as a leading strategy whereas the sixth grade students used factor of change strategy. Moreover, the results showed that students commonly used incorrect proportional strategies to solve non-proportional problems.
Highlights
Ratio and proportion are two concepts that fall under the general umbrella of proportional reasoning
Proportional reasoning comprises a network of understandings and relationships, and it plays an important role in solving ratio and proportion problems
The results of the study revealed that the sixth grade students mostly preferred to use strategies highlighting multiplicative relationships such as factor of change, unit rate
Summary
Ratio and proportion are two concepts that fall under the general umbrella of proportional reasoning. Research showed that students’ proportional reasoning abilities were generally problematic (Ayan & Işıksal-Bostan, 2018, 2019; Atabaş & Öner, 2016; BenChaim, Keret, & Ilany, 2012; Behr, Lesh, Post, & Silver, 1983; Cramer & Post, 1993; Cramer, Post, & Behr, 1989; Hart, 1988; Lamon, 2007; Özgün-Koca & Kayhan-Altay, 2009; Toluk-Uçar & Bozkuş, 2018). Students frequently used limited number of strategies and mostly formal strategies, which do not highlight multiplicative relationships, to set up and solve proportional problems (Ayan & Işıksal-Bostan, 2019; BenChaim et al, 2012; Cramer & Post, 1993; Özgün-Koca & Kayhan-Altay, 2009; Toluk-Uçar & Bozkuş, 2018). Middle school students (grades 5-8 in Turkey), are critical stakeholders whose conceptions of ratio and proportion need to be studied
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