Investigation of middle school students’ unit coordination levels in mathematics problems involving multiplicative relations

Abstract

This study aimed to identify Turkish middle school students’ unit coordination levels in mathematics problems involving multiplicative relations and investigate these unit coordination levels in each grade level. This study was designed as a qualitative case study in which a written instrument developed by Norton and his colleagues (2015) was implemented to 139 middle school students. The student responses were coded based on the rubric developed by Norton and his colleagues (2015), and the unit coordination stages of students at each grade level (5th, 6th, 7th, and 8th grades) were determined. The findings revealed that almost half of the middle school students operated at the lowest stage of unit coordination (Stage 1). While, at 5th, 6th, and 7th grades, the number of students operating at Stage 1 was higher than at other unit coordination stages, there were more students at Stage 2 in 8th grade. The number of students operating at Stage 3 was the lowest both at each grade level and in the whole group of 139 middle school students. Hence, very few of the middle school students could operate with three-level units as given and flexibly change between the three-level unit
structures. To sum up, the results showed that middle school students could hardly work with and coordinate more than one-level units in mathematics problems requiring multiplicative reasoning. Considering these findings, we suggest conducting more studies examining the unit coordination stages of students and the ways for increasing students’ unit coordination levels.