Dr Jo Boaler, a lecturer and researcher in mathematics at King's College, London, monitored 300 pupils from two London state schools for three years, from the age of 13 until they had taken their GCSEs.
In the traditional school, pupils were taught using whole class teaching, text books and frequent tests - the kind of methods being encouraged by Chris Woodhead, the Chief Inspector of Schools, the Secretary of State for Education Gillian Shephard, and leading right-wing educationists. There were high standards of discipline, pupils were motivated and worked hard, and they were in sets of similar ability pupils.
By comparison, at the "progressive" school, pupils worked on open-ended projects in mixed ability groups in every maths lesson. There was very little whole class teaching and discipline was "extremely relaxed".
At the start of the three years there were no differences between the two sets of pupils in terms of mathematical attainment, gender, ethnic origin or class. Both schools had good maths teachers. But at the end of the three years pupils in the project-based school attained significantly higher grades, not because they knew more maths but because they had developed a more effective way of using it.
At the textbook school, many of the pupils were unable to use maths in day-to-day situations because they could not adapt their formal textbook procedures to anything other than textbook questions.
Dr Boaler argues that international maths tests in which British children have a poor showing assess knowledge that has little educational value and which is increasingly incompatible with the demands of the modern world.
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