A problem-centered alternative to formalistic teaching

Increased attention has been given in recent times to the teacher-centered and formalistic nature of mathematics teaching in schools, and well-founded proposals have been made to change this tradition toward a problem-centered direction which takes into account pupils' previous learning experiences and out-of-school practices. After a historical scrutiny and the criticism of the current formalistic tradition - 'first theory, then practice' - , the article outlines an alternative teaching strategy which provides at least in theory better opportunities for discussive and meaningful teaching-learning processes in school mathematics. Finally, some main results from one of the teaching experiments of the project "Contextual Ap- proach to the Teaching and Learning of Mathematics" are examined. The teaching experiment focused on developing proportional reasoning and ratio concept in the eighth grade of the comprehensive school. Although numerous problems were encountered in the implementation of the "contextual program" designed on the basis of the ideas of Freudenthal's didactical phenomenology and the ideas of the "Vygotskian school" of psychology, the learning results achieved by means of the contextual program were at least equally good and partly better than those achieved in groups taught by the textbook.