Students’ Thinking of Direct, Inverse and Non-proportional Problems

The purpose of this study is to investigate students’ thinking of direct, inverse and non-proportional problems. Thity two seventh grade students from three different goverment schools participated in this study. To collect the data, the participants were asked to solve 9 open-ended problems, including 3 direct, 3 inverse and 3 non-proportional problems. Dual-process theory was used to analyze the data. The results showed that in direct proportional problems students’ answers were almost equally intuitive and analytical: in inverse and non-proportional problems their thinking was more intuitive, and with non-proportional problems, most intuitive and analytical answers were incorrect. In addition, the results showed that, in general, most students who provided incorrect answers to inverse proportional problems and especially non-proportional problems, had difficulty in distinguishing direct and inverse proportional problems and non-proportional problems because of using incorrect proportional strategies.