Investigation of middle school mathematics teachers' pedagogical preferences towards using models in the context of different fraction schemes

The purpose of this research is to examine middle school mathematics teachers' preferences and performances in using mathematical models in situations involving different fraction schemes and fraction operations. The study, utilizing the case study survey method, involves fifteen mathematics teachers currently working in the Altınordu district of Ordu Province. Purposeful sampling methods, including convenience sampling and criterion sampling, were employed in determining the participants of the study. Accordingly, the criteria for selecting teachers in the research were having a minimum of 10 years of professional experience, being stationed in the central district, and volunteering to participate in the study. In this research, the researchers employed the Model Usage Preferences Survey (MUPS), a data collection tool developed by the researchers to determine teachers' preferences for fraction schemas and fraction operations. The MUPS consists of 13 items rated on a 5-point Likert scale. Additionally, researchers created the Open-Ended Questions on Model Usage (OEQMU), consisting of 13 open-ended questions, and conducted semi-structured interviews to investigate the mathematical models used by participating teachers in various fraction schemas and operations. According to the research results, considering the fraction schemas, participants generally preferred the rectangle model, circle model, number line model, and finally the object model. For fraction operations, participants tended to prefer the rectangle model, number line model, circle model, and finally the object model. Consequently, it can be stated that teachers generally did not resort to discrete models and preferred continuous models in different fraction schemas and operations. When teachers' performance in using models in situations involving different fraction schemes and fraction operations was examined, it was seen that their performance levels were generally sufficient, except for situations involving iterative fraction schemes. It was observed that the participating teachers could only exhibit partially adequate performances in situations involving a iterative fraction scheme. When the performances regarding fraction operations were examined, it was seen that the teachers showed generally adequate performance except for multiplication and division operations. While teacher performances were partially adequate in multiplication, they were largely inadequate in division. Teachers generally used mathematical models not as a tool to support learning, but to complete the tasks given to them in the research process, and in most cases, they benefited from procedural knowledge to create the relevant model. In this context, it can be said that the models that teachers use in situations regarding different fraction schemes and fraction operations do not fully include the conceptual meanings and differences regarding the current situation. Keywords: Fraction Schemes, Using Mathematical Models, Middle School Mathematics Teachers, Pedagogical Preferences.