The study of children's mathematical behaviour goes back many years. Piaget in the 1930s used clinical interviews to unearth children's ideas about number. Earlier than this, Brueckner had used tests that measured ability in computation and solving verbal problems, and tests that sampled various combinations of a particular skill (such as the addition of fractions). In a short time the picture emerged that mathematics was an extremely difficult subject for many children to master. Some people, however, claimed that it was mathematics education that was failing. To investigate the problems, large scale surveys, such as the National Assessment of Educational Progress (NAEP) in the United States of America, have been used. The latest NAEP assessments sampled 45,000 students. In Britain the Concepts in Secondary Mathematics and Science (CSMS) research programme assessed 10,000 students. Likewise, the International Association for the Evaluation of Educational Achievement (lEA) survey in mathematics used in New Zealand a sample of 5177 for the 'core test' as part of a study of secondary school mathematics in 23 countries.