Investigating 5th grade students' reasoning skills on the topic of fractions

In today's education system, it is widely recognized that students experience various challenges with mathematics. One of the main reasons for this situation is that students' reasoning skills are weak. Students' mathematical reasoning skills can be developed in an environment where students can easily discuss, express ideas, develop new strategies, encounter non-routine problem types and challenge each other's ideas. For this reason, in this study, it is aimed to examine how 5th grade students' reasoning skills develop in a classroom environment in which discussing, explaining and developing various ideas and strategies are the main focus. This study is designed as an action research study, one of the qualitative research methodologies. Four middle school 5th grade students, who are studying at a public school in a central village of Tokat province, participated in the study. The topic of fractions, which has been well established in the literature that students struggle and have various misconceptions about, was selected as the focus of the study. Although eight students participated in the study, four students were selected as a focus group based on various criteria such as willingness to participate to the study, mathematical achievements, gender, or communication skills. Firstly, "Reasoning Skill Assessment Form", which was prepared by the researcher, was used to determine the reasoning skills of the participants before the implementation of the designed unit. Then, semi-structured individual interviews with four students in the focus group were conducted and more detailed information regarding to their reasoning skills was obtained. After the interviews, an implementation of a designed fraction unit during 20 hours was carried out and then "Reasoning Skill Assessment Form" was administered again. Semi-structured individual interviews with four students were conducted again. The data sources for this study were consisted of assessment forms, worksheets, individual interview records, student diaries, researcher diaries and instruction videos. The findings of the study revealed that students generally used rule based reasoning strategies in their first choices before the implementation of the unit. In the case of students encountering an erroneous reasoning strategy, it was observed that the students who participated in the study were mostly able to recognize the errors, but remained focused on the results without concentrating on the error of the given strategy. In the problem-writing skills, it was determined that the students did not succeed and made various mistakes while constructing problems. In the post-implementation data, it was seen that the students were able to propose different solutions apart from the rule based reasoning strategy. In their statements about their solutions, it was determined that they were used more generalizable expressions than before. The students who encountered with an erroneous strategy were able to explain the errors made in the strategy more easily and focus on the errors of the strategy rather than faulty results. Regarding to the problem-writing skills, it was observed that the students improved their problem writing skills compared to the pre-implementation. The findings of the study showed that the students' reasoning skills in the fractions unit showed a significant improvement compared to the pre- and post-implementation data. In this respect, it is suggested that mathematics teachers can more often use activities that aim to develop students' reasoning skills, which in return result in more conceptual understanding in their instructions. It has been revealed in the study that students' reasoning skills can be developed in a classroom environment such as the one implemented in the study. Keywords: Fractions, Mathematical Reasoning, Mathematics Education, Proof, Reasoning.