Interactive Learning: Unpacking the Influence of Computer Simulations on Students’ Mathematical Modeling Processes

Abstract

Mathematical modeling and use of technology have been recognized as powerful vehicles for advancing mathematical thinking. The use of technology to aid students to gain understanding about real-world mathematical problems has long been a subject of inquiry. Using the extended Blum’s modeling cycle as the theoretical framework, this study explores how computer simulations influence fifth-grade students’ mathematical modeling processes. We investigated interpretations and perceptions of students regarding a situation model, and how these interpretations and perceptions changed as a result of exposure to the simulation. Observing students as they worked with three interactive computer simulations during task-based interviews, we found that animated graphics of the simulations helped the participants to visualize the problem and learn about the effect of different variables and their interactions on the outcomes of the simulations. Students explored simulation environments, ran simulations to observe outcomes of specific settings, and formed conjectures to describe the effect of simulation variables on the outcomes. Analyzing participants’ activities and movements along the extended Blum modeling cycle, we propose a three-stage learning model composed of “exploration and discovery”, “structured inquiry”, and “synthesizing”.

Keywords

• mathematics education
• mathematical modeling
• interactive simulation
• technology