To say there is no such thing as "problem-solving" is to fly in the face of 50 years of research in psychology, education and cognitive science. Nobel Prize winners Newell and Simon wrote decisively about human problem-solving 25 years ago. Were they talking nonsense? One of the aims of mathematics teaching has always been to prepare students to solve problems, and this is still the case. Thank goodness it is part of the national curriculum, as Using and Applying Maths.
To claim that "discovery learning" requires children to "reinvent mathematics, which took us hundreds of thousands of years to invent" is simply false. Actually, mathematics is 5,000 years old. Modern psychology tells us that children have to construct their own meanings to understand fully. But this is a mental process and is best achieved by teachers teaching as well as children doing exercises and discussing and solving problems. Trying to rediscover mathematics would be laughable, and no one advocates it.
The real issue is that Mr Deuchar's Campaign for Real Education is a moral crusade to turn back the clock 100 years and to restore Victorian values. But the copperplate writing and simple sums that were all a Victorian clerk needed will not do today. School-leavers also need to solve more complex problems and to use information technology skills, if they are to get on and contribute to the prosperity of Britain in the 21st century.
DR PAUL ERNEST Reader in mathematics education School of Education University of Exeter