Investigating middle school inclusive students' learning process of basic fraction concepts with fraction models

The aim of this study is to investigate the middle school inclusive students' learning process of basic fraction concepts with fractional models. Phenomenology, one of the qualitative research methods, was used in the study. The study was conducted in the spring semester of the 2018-2019 academic year. The participants of the study consisted of 4 inclusive students (3 girls and 1 boy) studying in two different public middle schools in the Middle Black Sea Region. In order to determine the participants of the study, purposeful sampling method was used. Although the participants in the study were at different grade levels, the learning levels were close to each other. In this study, it is tried to teach the participants the basic concepts of fractions with fraction models for four weeks. The lecture process was recorded with a video-tape and an observation form was completed for each inclusive student during four weeks. The results were evaluated by using the Fractional Models Evaluation Scale developed by the researcher with the expert opinion. The items in the scale of evaluation include questions of area-region, length and set models in fractions and are in a mixed order. To analyze data qualitative analysis methods were used. The responses of the participants to the Fractional Models Assessment Scale, student observation notes and video recordings taken during the lecture process were examined together and the participants' level of understanding of the fractions was evaluated. As a result, it is seen that the use of models in teaching basic fraction concepts to inclusive students is positive in terms of facilitating their comprehension. Inclusive students gave correct answers to the questions about the regional model with the highest area among the three models. It is thought that the reason for this was the use of area model by teachers frequently. Although the area model is useful in terms of the part-whole relationship, it is thought that three models should be used together in order to comprehend all definitions of fractions while trying to form the concept of fraction. Inclusive students are thought to have difficulty in understanding length and set models due to their incomplete learning in the division. It was seen that the length model was correctly perceived by the inclusive students than the set model. In this sense, the set model was the most difficult model for students to comprehend. It was observed that the students were able to comprehend the set model more easily when supported while performing the division procedures required by the questions. Fraction is one of the main abstract concepts that students encounter. Inclusive students need more learning materials to construct the concept of fractions. In this study, it is thought that the concrete materials used for each model contributed positively to the conceptualization process of the fraction in their mind. In order to learn whole definitions of fraction correctly, it is recommended to use these three models together in instruction process. In addition, it was observed that some inclusion students made mistakes when comparing fraction values representing half and quarter. This mistake might be derived from not establishing a whole-piece relationship by students and comparing fractions according to the values of the numbers in their denominators. In order to identify and eliminate deficiencies, it is recommended that further research should be conducted on the mathematics education of inclusive students. As a result of these studies, the middle school mathematics curriculum should be revised to eliminate these deficiencies for the sake of inclusive students.