THE DEVELOPMENT OF LEARNING TRAJECTORY BASED ON SCIENTIFIC APPROACHES "PISA" ORIENTED PROBLEMS TO IMPROVE THE MATHEMATICAL REASONING ABILITIES OF EIGHT GRADE STUDENT OF JUNIOR HIGH SCHOOL

Abstract

This study is aimed at obtaining the learning trajectory of system of two variables linear equations generated from hypothetical learning trajectory which are designed through design research consists of three steps, those are preparing for the experiment, design experimental, and retrospective analysis. Learning trajectory is obtained by revising hypothetical learning trajectory obtained from trials and discussions with teachers of the subject. The research is focused on improving students mathematical reasoning abilities for handling mathematical problems. PISA like problems were used in this research. Learning activities are arranged based on scientific approches (Observing, Asking, Collecting Information, Processing Information, Communicating). Learning implementation was carried out  in eight grade class of PGRI 1 Junior High School Denpasar 2018/2019. Data related to the activities and strategies used by students in solving problems given during learning takes place, was collected through students' written answers on the worksheets, post-test results, interviews and observations. The collected data were analyzed descriptively. The learning trajectories of: (1) Creating mathematical models of two-variable linear equations and system of two-variable linear equation from everyday problems, (2) Defining two-variable linear equations and systems of two-variable linear equations, (3) Solve problems related to the system of two-variable linear equations with various methods.