Design research: Looking into the heart of mathematics education

Design research can be characterized as a research approach in which the design of educational materials is interwoven with the development of theory. Design research aims at educational innovation and it has a cyclic character: development and prediction, teaching experiments and reflection and revision form an iterative process. In design hypotheses, as in other research approaches, hypotheses are formulated preliminary to the data collection. However, in design research these hypotheses are continually tested and revised during the teaching experiment. Design research cycles typically consist of three phases: preparation and design phase, teaching experiment and retrospective analysis. The results of the retrospective analysis normally lead to new designs and a follow-up cycle. The hypothetical learning trajectory is an essential instrument during each phase of a design study, though plays a different role in each phase. Design research is not an easy approach but valuable as it offers a unique opportunity for learning to understand students’ thinking and learning

A model for a widespread implementation of inquiry-based learning

Innovative teaching practices such as inquirybased learning (IBL) have long been topics of discussion amongst mathematics and science educators. However, it is not easy to change day-to-day teaching on a large scale. The relevant question of how to promote a widespread uptake of IBL in day-to-day teaching therefore needs more consideration. In order to ensure such uptake of IBL in a variety of different contexts, a model including dissemination and implementation strategies needs to be designed. In this paper, we present the design of a focused and flexible model for dissemination and implementation as developed within the international project PRIMAS, funded by the EU under Framework 7. The design of this model is rooted in design research. We will outline and explain the complexity of the model, including its theoretical basis, its iterative approach for evaluation and refinement, and its intended contributions to research

What counts as evidence for the long-term realisation of whole-class scaffolding?

To promote whole-class scaffolding of mathematical language, a teacher was encouraged to employ a repertoire of seven strategies (e.g., reformulating) in a multilingual primary classroom (22 pupils; aged 10–12). This paper investigates whether the enactment of these strategies has led to long-term whole-class scaffolding as identifiable by its key characteristics: diagnosis, responsiveness and handover. Comparison of pupils' pre- and post-test scores on three linguistic key elements all yielded statistically significant differences with large effect sizes, thus confirmed handover. A statistically significant shift from high-support to low-support strategies revealed responsiveness to pupils’ levels over nine lessons. A qualitative analysis showed interrelatedness of performed strategies and scaffolding characteristics (e.g., diagnosis). The results provide empirical evidence of the long-term realisation of whole-class scaffolding

Using the computer in space geometry

First some changes in the space geometry curriculum in The Netherlands are sketched. A part of the changes in the lower grades of secondary education and almost the complete change of the space geometry in the higher grades. During this sketch the need for the use of a computer will raise. In the second part of this paper it will be shown how computertools assist this new space geometry curriculum

Using the computer in space geometry

First some changes in the space geometry curriculum in The Netherlands are sketched. A part of the changes in the lower grades of secondary education and almost the complete change of the space geometry in the higher grades. During this sketch the need for the use of a computer will raise. In the second part of this paper it will be shown how computertools assist this new space geometry curriculum

One episode, two lenses : a reflective analysis of student learning with computer algebra from instrumental and onto-semiotic perspectives

A deep understanding of students’ learning processes is one of the core challenges of research in mathematics education. To achieve this, different theoretical lenses are available. The question is how these different lenses compare and contrast, and how they can be coordinated and combined to provide a more comprehensive view on the topic of study. To investigate this, one single episode is analyzed with two theoretical lenses, the instrumental genesis perspective and the onto-semiotic approach. The results from this joint analysis provide a rich view on the observed phenomena and help to identify the affordances and constraints of each of the two theoretical approaches and to articulate them. This way, the networking of theories proves to affect theoretical advancements

Improving work processes by making the invisible visible

There is a growing movement for industrial companies to modify their production practices according to methodologies collectively known as process improvement. After World War II, Japanese companies such as Toyota developed new manufacturing paradigms (e.g., lean manufacturing) under the guidance of American experts, particularly W.E. Deming. Since the 1980s, the Japanese methodologies have been spreading to the West in a major way, in the form of programmes such as Total Quality Management (TQM) and Total Productive Maintenance (TPM) (Deming, 1986; Nakajima, 1988)