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.