Improving Students’ Mathematical Connections in Linear Programming through a GeoGebra-Supported Local Learning Design Based on Realistic Mathematics Education

Introduction: Students often struggle to develop mathematical connection abilities in linear programming due to its abstract nature and procedural teaching methods. While Realistic Mathematics Education (RME) and Local Instructional Theory (LIT) offer structured learning trajectories, and GeoGebra provides dynamic visualization, their integration into a cohesive learning design for linear programming remains underexplored.Objective: This study aimed to develop and evaluate a GeoGebra-supported local learning design grounded in RME to improve students' mathematical connection abilities in linear programming.Method: A design-based research methodology was employed, involving iterative development and testing. A quasi-experimental pretest-posttest control group design was used to assess effectiveness with 68 undergraduate mathematics education students. The experimental group (n=34) received instruction via the developed learning design, while the control group (n=34) received conventional instruction. Data were collected using a Mathematical Connection Ability Test (MCAT), observations, and questionnaires.Results: The expert validation showed high scores for content validity (M=4.64), construct validity (M=4.51), and practicality (M=4.17). Quantitatively, the experimental group significantly outperformed the control group in post-test scores (t(66)=5.94, p<.001) with a large effect size (Cohen's d=1.45), demonstrating a greater improvement in connecting concepts to real-world contexts and within problem-solving processes. Qualitatively, students valued the contextualized approach and GeoGebra's interactivity for facilitating deeper understanding.Conclusions: The GeoGebra-assisted LIT based on RME significantly enhanced students' mathematical connection abilities. The study proposes an effective, integrated instructional design for linear programming and recommends future research to optimize time allocation and extend the model to other mathematical topics.Key Words: Mathematical Connection Abilities; Realistic Mathematics Education; Local Instructional Theory; GeoGebra; Blended Learning.