Evaluation of Teachers’ Problem Solving Strategies Impressionability by the Semantic Types of proportional problems

 In a cognitive sense, the concept of proportionality and the requirement for the development of proportional thinking are complex and teaching them needs concept-based approaches. Studying the perceptional quality in teachers amounts to how learners develop conceptual structures.. The goal of this study was to consider the teachers’ and prospective teachers selected strategies in teaching proportional problems solving activity and the impressionability of 4 semantic problems types. Convenient sampling was used to select three independent groups of subjects, including 180 elementary school teachers, middle school math teachers, and prospective teachers who participated in the study voluntarily. The research tools included one author-made test, contained 12 tasks including direct proportional word problems (missing value and comparison). The content validity of the test was approved by professors of "mathematics education" and "test construction". The results showed significant differences between 3 independent groups in applying the strategies leading to correct solving among the semantic problem types. In addition, the rate of using proportional reasoning strategies among these semantic types didn’t follow similar patterns. In order for the development of future teachers, attention to the consequences of delayed emergence of students' proportional thinking should be employed in the design of educational curriculum.