Learning Trajectory in Problem-Based Mathematics Learning with Literacy and Numeracy Reinforcement: An Implementation of Lesson Study at Junior High School

Abstract

This study aims to explore the learning trajectory of problem-based learning with literacy and numeracy reinforcement. This study was conducted at Junior High School and involved 32 subjects from class VIII. This study employed Gravemeijer and Cobb's design research comprising three stages: preparing the experiment of hypothetical learning trajectory (HLT), designing the experiment by implementing the designed HLT-based learning, and conducting retrospective analysis by comparing HLT with the implemented learning. The learning trajectory in this study consisted of three components: learning objectives, a series of tasks and learning activities, and students' techniques to think and learn. This research was conducted based on lesson study activities to create a lesson study for the learning community. Design research stages corresponded to lesson study stages and included studying curriculum, formulating goals and plans, conducting research lessons, and reflecting the lesson. This study has revealed that students' actual learning trajectory has four levels of modeling: situational, referential, general, and formal levels. At the situational level, non-mathematical literacy becomes the initial reference for students to collaborate and communicate with others; thus, mathematical concepts are created. The referential level leads students to represent real problems in real mathematical concepts. The representation process aims to understand the concept in different situations. Finally, the students analogize the acquired understanding and bring it to the formal level to get a full understanding of the concept of one point position to another in Cartesian coordinates.