DESIGN-BASED RESEARCH IN MATHEMATICS EDUCATION

This paper sketches the approach of design-based research in mathematics education with results oftwo innovation-oriented projects. The projects investigated how students can be involved in thedevelopment of mathematical concepts and skills by using design tools related to guided reinventionand emergent modelling. Both studies combine design-based research with a prominent role for thehypothetical learning trajectory as a research instrument in the three phases of design research (design,teaching experiment, retrospective analysis). Each of the phases of the research cycles is addressed: thepreliminary phase in which a hypothetical learning trajectory and instructional activities are designed,the teaching experiment phase and the phase of the retrospective analysis. We conclude with areflection on design-based research as an approach to study innovative teaching approaches that offersresearchers to take into account contextual factors and that create opportunities for others to adapt theresults to their research or teaching practice