Supporting proportional reasoning in ratio and proportion through agricultural contexts: A local instructional theory

Abstract

Proportional reasoning constitutes a foundational competence in learning ratio and proportion. However, numerous junior high school students continue to exhibit reliance on additive reasoning rather than multiplicative reasoning when addressing proportional problems. This study aims to develop a Local Instructional Theory (LIT) that integrates agricultural activities to foster students’ proportional reasoning within the domain of ratio and proportion. Employing a design research methodology of the validation study type, the investigation comprised three interconnected phases: preparation for the experiment, design experiment, and retrospective analysis. The design experiment was conducted in two iterative cycles: a pilot experiment involving eight seventh-grade students and a subsequent teaching experiment involving 31 seventh-grade students from a junior high school in Belitang, Indonesia. Data were collected through student activity sheets, classroom observations, interviews, and assessments, and analyzed qualitatively using retrospective analysis. The findings reveal that agricultural practices—such as rice fertilization, plowing, rice field exploration via Google Earth, and rice planting row marking—serve as meaningful contextual anchors that support students in constructing conceptual understandings of ratio, rate, scale, and proportion. Engagement in these contextually grounded activities enabled students to compare quantities, identify unit rates, and represent proportional relationships through models such as ratio tables and double number lines. These learning trajectories facilitated a gradual shift from additive to multiplicative reasoning. The study underscores the pedagogical potential of authentic agrarian contexts to promote the progressive development of proportional reasoning and to provide a transferable framework for context-based mathematics instruction.