Developing a Hypothetical Learning Trajectory for Linear Functions Through Collaborative Mathematical Modeling

Abstract

Students still encounter difficulties in understanding linear functions, particularly when they are required to connect contextual situations with mathematical forms and to understand variables, constant change, and symbolic representations. This study aims to develop and describe students' learning trajectory in learning linear functions through a collaborative mathematical modeling approach using the context of a leaking faucet. This study employed a design research method consisting of three stages: preparing for the experiment, conducting the design experiment, and performing retrospective analysis. The participants were eighth-grade junior high school students grouped heterogeneously according to their mathematical ability. The learning design was structured based on six stages of mathematical modeling. The results indicate that the leaking-faucet context helped students understand the relationship between time and water volume as a linear function. Students were able to identify the problem, formulate assumptions, conduct experiments, construct a model, evaluate the model, and apply it to estimate losses caused by water leakage. Therefore, a learning trajectory based on collaborative mathematical modeling can support students' understanding of linear functions.