Investigation of students' mathematical reasoning ability in solving open-ended problems

The aim of this study was to analyse the reasoning ability in solving open-ended mathematics problems in the area of circle material. Reasoning ability is an important component of education as it necessary for understanding mathematics in particular and presents an important means of developing ideas. The importance of reasoning ability presented in solving open-ended mathematics problems that is a problem that has multiple solutions and alternatives or settlement. The study was conducted in April at the 2015/2016 academic year. Subjects in this study were 8th-grade students of SMP Negeri 1 Singaraja. The study used a case study with qualitative research techniques to investigate how students' reasoning ability in solving open-ended mathematics problems. The data was collected through an essay test, interview, observation, and documentation. The study was use reasoning aspect that described by Trends in International Mathematics and Science Study (TIMSS) 2008. From the data obtained, it was identified that the students lacked of reasoning ability, specifically in aspect of think mathematically and describe a new the results obtained through problem solving and expand on these solutions, provide evidence for the validity of an action or the truth of a mathematical expression, illustrating an appropriate geometric figure, and identifying and use interrelations between variables in mathematical situations. However, students also demonstrate a creative thinking ability when solving the problems using their knowledge in a real life situation to present a unique solution that the author never predicted before.