In recent years the theory known as constructivism has attracted considerable attention from researchers and document writers in particular. Implementation of constructivist principles inside the classroom is still problematic, however. Different reasons for this are explored in the paper. An overview of previously - and in some cases still - popular theories of learning and teaching precedes a detailed discussion of constructivism: its sources, definitions, advocates, and critics. A number of classroom experiments designed and executed within a constructivist paradigm are reported in considerable detail. The roles of both learner and teacher are described. Throughout, the discussion is confined to mathematics, mathematics education, and the mathematics classroom. However, the main arguments presented are applicable as well to other disciplines.