Advances in understanding the brain have led researchers in mathematics education to call for an end to "textbook" style teaching and problem setting in schools and colleges.
Speaking at a conference at the University of Ulster, Susan Lamon of the mathematics department at Marquette University, Wisconsin, said that maths education has traditionally relied on the "telling model" of teaching and on tests requiring true/false answers.
But recent work by scientists on the neurological functioning of the brain, together with new theories and research results on thinking, learning and problem-solving from cognitive psychology and information processing suggests that this approach is deeply flawed.
Professor Lamon says that the central argument behind the new thinking is that people construct their own knowledge. New knowledge is best accommodated and most deeply understood when it is assimilated into the framework of past experiences. But since experience is highly individual, there should be much more recognition of the richness and complexity of the experience students bring into class.
"The biggest problem is how to package mathematics in a way that best preserves the integrity of the powerful, logical structure of the subject and conveys our beliefs about what it means to do mathematics while taking into account the cognitive reality of human beings," she says.
Teachers should encourage students to take responsibility for learning. And in exams, Professor Lamon says: "There should be fewer questions requiring deeper understanding and more emphasis on how and why and the conclusions that can be drawn from these answers."