DESIGN-BASED RESEARCH IN MATHEMATICS EDUCATION

Abstract

This paper sketches the approach of design-based research in mathematics education with results of
two innovation-oriented projects. The projects investigated how students can be involved in the
development of mathematical concepts and skills by using design tools related to guided reinvention
and emergent modelling. Both studies combine design-based research with a prominent role for the
hypothetical 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: the
preliminary 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 a
reflection on design-based research as an approach to study innovative teaching approaches that offers
researchers to take into account contextual factors and that create opportunities for others to adapt the
results to their research or teaching practice.