Middle school students’ quantitative reasoning in pictorial, symbolic and iconographic problems

Uyguç, Ayşenur
The aim of this study was to examine middle school students’ (5th–8th grade) quantitative reasoning in early algebra problems given in pictorial, symbolic, and iconographic forms and involved single-unit and multiple-unit substitutions. The study was carried out with a total of 60 students studying in two public middle schools in the town of Şarkışla, Sivas, in October of the 2021-2022 academic year. Participants were determined by the purposeful and convenience sampling method. In this study, a multiple case research design was used, and a total of seven problems were used in pictorial, symbolic, and iconographic forms. The collected data were analyzed with the content analysis method to explore middle grade students’ quantitative reasoning. The results of the study showed that forms of the problems were not determinative in the students’ quantitative reasoning. Instead, it was concluded that the students’ quantitative reasoning differed according to the level of complexity of the relationship such as single unit substitution and multiple unit substitution within each form. Finally, the reasons behind students' explanations were generally similar at each grade level (5th-8th grade) so, there were no distinct differences between students’ quantitative reasoning at different grade levels in the problems addressing pictographic, iconographic, and symbolic forms. Thus, this study concluded that middle school students, even 8th graders, did not demonstrate sufficient quantitative reasoning, especially in multiple-unit substitution problems in each of the three forms. In this sense, this study informs teachers and teacher educators about the forms of the problems used in early algebra teaching as well as the complexity of the relationship (i.e., single-unit vs multiple-unit substitutions) involved in the problem.
Citation Formats
A. Uyguç, “Middle school students’ quantitative reasoning in pictorial, symbolic and iconographic problems,” M.S. - Master of Science, Middle East Technical University, 2023.