Creativity, Mathematizing, and Didactizing: Leen Streefland's work continues

This reaction to the papers in this PME Special Issue of Educational Studies in Mathematics draws a wider perspective on the issues addressed and some of the constructs used in research in Realistic Mathematics Education (RME). In particular, it tries to show that while the problems addressed existed within the world-wide arena of mathematics education and were not unique to the Dutch educational system, the methods used at the Freudenthal Institute to address them were uniquely adapted to that system yet foreshadowed developments in the wider field of mathematics education. The predictive aspects of mathematizing, didactizing, and guided reinvention, in which models-of become models-for on various levels, resonate with trends in mathematics education in recent years, including those promoted by the National Council of Teachers of Mathematics in the USA. Research methodologies, too, have broadened to include more humanistic qualitative methods. Developmental research as epitomized in the RME tradition makes the distinction between quantitative and qualitative research obsolete, because there is no restriction on research methods that may be useful in investigating how to improve the teaching and learning of mathematics, and in the designing of mathematics curricula. Thus some aspects of this research resonate with what have come to be known as multitiered teaching experiments. However, in RME there is also a special content-oriented didactical approach that harmonizes with an emphasis on didactics (rather than pedagogy)in several other European countries. Some implications are drawn for future research directions. This revised version was published online in August 2006 with corrections to the Cover Date.