The mathematics curriculum and pupils' thinking processes : learning to solve algebraic problems in year 7 and year 8 in England and Thailand
Previous studies of pupils' learning of algebra have been inclined to study errors in given answers. The present study attempts to investigate pupils' thinking processes in the early stages of learning algebra by examining and comparing responses made by English and Thai pupils to the researcher's algebra test. The research was conducted among pupils during their "normal" lessons in secondary school algebra. Pupil participants were in the first two years of secondary education. Data collection included lesson observations, interviews, and the researcher's algebra test. The thinking processes were first categorised from the interview data to provide a framework for analysing pupils' written responses to the researcher's test. Later, a codebook was kept in which pupils' responses to the researcher’s test were coded. The study goes on to analyse the outcomes from this coding procedure. The research indicates that the differences in the way pupils think appear to be closely related to the teaching and curriculum provided. In both countries, success in algebra is dependent on having good arithmetic skills. Also the reluctance of pupils to use algebra to solve easy problems results in algebraic skills being inadequately developed to solve more difficult problems. An implication for practice is that the Thai school should consider the bearing which the understanding of simplification of like terms has upon a pupil's ability to solve linear equations. Both schools could consider ways of making effective use of patterns and sequences to develop algebraic thinking. The codebook developed in this research could serve as a tool for mathematics teachers in helping them to understand the complexity of their pupils thinking processes in solving algebraic problems. An investigation involving more schools in other settings could follow this.