Innovative Pedagogies in Realistic Mathematics Education: What, Why and How of Design-Based Classroom Research

Abstract

Developing a mathematical mindset involves understanding the underlying cognitive processes. Mathematization, a key in realistic mathematics education (RME), is an activity of organizing a subject from reality or a mathematical subject. This literature-based paper intends to provide guiding principles for conducting design research in mathematics classrooms as guided by RME. Guided re-invention of mathematics and didactical phenomenology are two key philosophical underpinnings of RME. The activity, reality, level, intertwinement, interactivity, and guidance principles are central to how RME fosters mathematical understanding and problem-solving skills. The innovative plans in design-based research are developed by using design heuristics that follow the framework of the theory of realistic mathematics education. The main methodological intention of design-based research (DBR) is to actively influence and improve educational situations through designed interventions. Interventionist, theory-generative, prospective, and reflective analysis, iterative, and ecologically valid and practice-oriented are the key five characteristics of DBR. DBR is a process-oriented investigation focusing on how learning occurs, consisting of three successive, flexible, and iterative phases: Preliminary design, the teaching experiment, and retrospective analysis. Designing an innovation in mathematics education and finalizing for better learning can follow the sequence of RME principles to DBR phases.