Radical Constructivism in Mathematics Education

All too frequently the present methods of teaching mathematics generate in the student a lasting aversion to numbers, rather than an understanding of the useful and sometimes enchanting things one can do with them. Parents, teachers, and researchers in the field of education are well aware of this dismal situation, but their views about what causes the widespread failure and what steps should be taken to correct it have so far not come anywhere near a practicable consensus.
The authors of this book have all had extensive experience in teaching as well as in educational research. They approach the problems they have isolated from their own individual pespectives. Yet they share both an overall goal and a specific fundamental conviction that characterizes the efforts about which they write. The common goal is to find a better way to teach mathematics. The common conviction is that knowledge cannot simply be transferred ready-made from parent to child or from teacher to student, but has to be actively built up by each learner in his or her own mind. The purpose of the book is not to make yet another move to theoretical philosophical debate about constructivism. Rather, the book clarifies how the didactic attitude changes when the constructivist theory of knowing is put into practice, and what results have been attained when this is done. Rather than forecasts of what might be achieved in the future, the papers assembled here report on experiments and implementations that have actually been carried out.