Design research on how IT may support the development of symbols and meaning in mathematics education

This paper sketches the methodology and some results of three studies that were part of a comprehensive research project called “IT and mathematics education”. With the theory of Realistic Mathematics Education as a background, the project investigated the contribution of IT tools for the guided reinvention of mathematical concepts and the influence of IT use on the students’ process of symbolising. Each of the studies focussed on a different mathematical topic and used different types of technological tools. The three studies that are discussed in this paper combine the methodology of design research with a prominent role for the Hypothetical Learning Trajectory as a research instrument in all phases of design research (design, teaching experiment, retrospective analysis). In the first section we state the overarching research question. In section 2 we describe the research methodology. 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. In section 3 we address each of the three studies subsequently and present some exemplary results. Section 4 contains a discussion, and section 5 states common conclusions from the three studies.

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