An investigation of middle school students' tendency for additive and multiplicative reasoning according to different variables

The aim of this research is to examine middle school students' performances to distinguish proportional and non-proportional situations as well as their tendency for additive and multiplicative reasoning according to several variables (i.e., grade level, problem type and problem structure). Also, it was aimed to examine whether their performance in proportional and non-proportional problem situations differ in terms of these tendencies. For this purpose, causal comparison design was used. The participants are 5th, 6th, 7th and 8th grade students. The middle schools to be studied and the participants were selected according to the accessible sampling method. To collect data, two different tests were used as a word problem test and an open problem test. For data analysis, descriptive statistical methods, Brown-Forsythe Test Welch Test, dependent samples t Test and Kruskal Wallis H Test were used. As a result of the data analysis, it was found that the majority of the students had a high performance in distinguishing between proportional and non-proportional situations, they were more successful in missing value problems than in comparison problems, and they showed higher performance in problems with an integer relationship. It was observed that the performances increased as the grade level increased. It has been determined that more than half of the students have additive tendency and few students have multiplicative tendency. While there was no significant difference between the performances of those with additive, multiplicative or both additive and multiplicative tendencies in distinguishing between proportional and non-proportional situations, it was found that the difference between groups showing any tendency and not showing a tendency was significant.