An investigation into children's understanding of the order of operations

This thesis reports on the findings of an international study into the way in which children approach calculations which involve the order of operations. The study involved 203 pupils aged between 12 to 14 years from four different countries: England, The USA (New York State), Japan and The Netherlands. Many pupils in England are taught to use mnemonics such as BODMAS or BIDMAS to remember the correct order of operations, and in the USA pupils are often taught to use PEMDAS. However in Japan and The Netherlands these methods are not used, and the approach to teaching mathematics differs considerably across the countries. In this study pupils from classes in these four countries have been given calculations to perform and their work has been analysed for misconceptions. The analysis of their work has involved use of the Key Recorder software as a data collection tool, in which the pupils’ calculator keystrokes have been recorded and played back to give a unique insight into their thinking. Analysis of the children’s work has resulted in the categorisation of the misconceptions that were observed, and suggests that the nature of the mathematics curriculum and the teaching methods employed may have a significant effect on the way in which children approach calculations of this sort.