The Project ‘Concepts in Secondary Mathematics and Science'(CSMS) based at Chelsea College, University of London has two research teams, one for mathematics and one for science. The aim of the mathematics team is to draw up a hierarchy of understanding in secondary school mathematics, in order to give information to teachers and developers of curriculum. To meet this purpose the team has tested ten thousend British children (age 11-16) on various mathematical topics. The testing was on a series of items in particular topics which appear in the secondary school mathematics curriculum (whole numbers, fractions, decimals; graphs, algorithms). The emphasis was on word problems and computational techniques only, were on the whole avoided. Firstly about thirty children were interviewed, using the problems as a basis; the children were asked how they would solve the problem. Methods of solution, both correct and incorrect were found from these interviews. Secondly some two hundred children were tested using a written test and finally the test was given to a large sample of children.