Realistic Mathematics Education By Marja

Marja van den Heuvel-Panhuizen

Realistic Mathematics Education

This lecture addresses several “progress” issues related to the Dutch approach to mathematics education, called “Realistic Mathematics Education” (RME). The most important of these issues is the way in which RME facilitates the progress of children’s understanding in mathematics. This topic forms the heart of the lecture. Attention is paid to both the micro-didactic and the macro-didactic perspective of the students’ growth. Progress in achievements, as the result of this learning, is the next progress issue to be dealt with. Finally, the spotlights are turned towards the developments within RME itself. The general focus in the lecture is on primary school mathematics education.

RME in brief Realistic Mathematics Education, or RME, is the Dutch answer to the need, felt worldwide, to reform the teaching of mathematics. The roots of the Dutch reform movement go back to the beginning of the seventies, when the first ideas for RME were conceptualized. It was a reaction to both the American “New Math” movement, which was likely to flood our country in those days, and the then prevailing Dutch approach to mathematics education, which often is labeled as “mechanistic mathematics education.”

Since the early days of RME much design work connected to developmental research (or design research) has been carried out. If anything is to be learned from the Dutch history of the reform of mathematics education, it is that such a reform takes time. It looks a superfluous statement, but it is not. Again and again, too optimistic thoughts are heard about educational innovations. Our experience is that reforms in education take time. The development of RME is thirty years old now, and we still consider it as “work under construction.”Marja van den Heuvel-Panhuizen That we see it in this way, however, has not only to do with the fact that until now the struggle against the mechanistic approach to mathematics education has not been conquered completely — especially in classroom practice much work still has to be done in this respect. More determining for the continuing development of RME is its own character. Inherent to RME, with its founding idea of mathematics as a human activity, is that it can never be considered a fixed and finished theory of mathematics education. “Progress” issues to be dealt with This self-renewing feature of RME was an important reason for choosing “work in progress” as the title for this lecture. But there were more reasons for this choice. The title also refers to another significant characteristic of RME, namely its focusing on the growth of the children’s knowledge a nd understanding of mathematics.

The way in which RME continually works on the progress of children is the first progress issue to be dealt with in this lecture. This progress work is distinguished in two levels of working on the mathematical development. Attention is paid to both the micro-didactic perspective and the macro-didactic perspective of

the students’ growth. The micro-didactic perspective clarifies how within the context of one or two lessons shifts in comprehension and abilities can happen. In this process, models which originate from context situations and which function as bridges to higher levels of understanding have a key role. The macro-didactic perspective deals with the progress in understanding over a longer period of time. The focus here is on learning-teaching trajectories – including the attainment targets to be reached at the end of primary school and the landmarks along the route – that serve as a longitudinal framework for teaching mathematics. The coherence between the various levels of mathematical understanding that is made apparent in this trajectory description plays a key role in stimulating students’ growth. A following progress issue has to do with the students’ achievements in mathematics. The question is whether RME brought Dutch primary students to the top level of mathematics achievements. Although the TIMSS results and results from other comparative studies are suggesting this, there are also arguments against.

Finally, the lecture deals with the progress in the RME approach to mathematics education. Although this approach is already some thirty years old it is still “under construction.”