ABSTRACT
Instructional research is reviewed where teaching failures have produced students who are less able to use learning skills or had less access to knowledge than before they were taught. Higher anxiety students profited from the greater structure provided by a teacher-centred approach while lower anxiety students profited more from a student-centred approach. Teachers should take into account the different levels of knowledge and skills of individual students when teaching. Students with little prior knowledge benefit from small concrete steps, while pupils with a lot of prior knowledge actually thrive in a setting in which they can use this knowledge. They must be given the opportunity to use their strategies and automated knowledge. The theory of mathemathantic activities clearly shows why differentiation is also important for the more gifted pupils; after all, the students have something to lose, their existing knowledge.
