Levels of understanding in mathematics and their application to an algebra test

Summary

The Concepts in Secondary Mathematics and Science Project isolated four ‘levels’ of understanding in algebra. These were derived from a national study. The research reported here set out to assess how realistic it was to apply the notion of ‘level’ to individual schools. Two contrasting schools were investigated, and it was found that the nature and operation of the levels established by the CSMS Project were robust enough to withstand marked departures from normality in their populations. Hence it was suggested that the levels of understanding in algebra offer firm evidence for teachers and others for the appropriate sequencing of pupils’ work in this area. In the light of the Cockcroft Report this would appear to have considerable practical implications for teaching.