Investigation of secondary school mathematics teachers 'and teacher candidates' success in distinguishing proportional and non-proportional relationships

Proportional reasoning is a concept that is frequently met in daily life and is necessary for understanding many topics in mathematics. One of the basic requirements for the acquisition of proportional reasoning skill is the ability to distinguish proportional and non-proportional situations. In this sense, this study aims to examine the successes of middle school mathematics teachers and prospective teachers knowing and distinguishing proportional and non-proportional situations. The research was carried out with survey method. The participants consisted of prospective middle school mathematics teachers at the final year of a teacher education program at a state university located in the Black Sea Region and in-service mathematics teachers working in the same region. Two different identification tests developed by the researcher were applied as the data collection tool. In the first stage of the tests; sixproblems including different relationships are given in various contexts: direct and inverse proportional, additive, constant, linear and parabolic. In the second stage, by giving different representations of the relationship types, they were expected to recognize the different types of relationships between variables, explain and pose a problem suitable for the related relationship. In the data analysis, t-test, chi-square test and descriptive statistics methods were used. Findings from the second stage indicated that context variable affects both preservice and in-service teachers'achievement in solving proportional and non-proportional problems. Findings obtained in the second stagealso showed that the they had inadequate knowledge about the representation of non-proportional situations and that they were more successful in the representation of proportionality with equations than with the graphical representation. In cases that teachers and preservice teachers were compared, in-service teachers were more successful in both stages.