Abstract
This study was designed to investigate issues connected with the teaching of subtraction during the primary school years of education in the United Kingdom. The central aim of the research was to show how problems associated with the setting out and solving of subtraction algorithms, together with the use of mathematical language, and the pupils’ capacity for memory were key issues and contributing factors to pupils’ consistent difficulties with subtraction. The research was based on one central question that of: “Why are our pupils failing to understand subtractions, and what factors contribute to this failing?” The study was conducted over a period of five years. The main subjects of the study were a group of 22 mixed ability pupils, who remained in the same school for that period, who were initially set the question 36-15, in the 1995, UK Mathematics achievement tests for 7 year olds. They reflected pupils from the 7-11 year age range (Years 2-6) within the primary phase of education. As this group of children progressed through the school their work became more complex and this thesis extended its scope into the question of subtraction performance. The passage of time also saw a change in the classroom numbers and, where possible, new school entrants were included in the research. The data collected consisted of: pupil observation, pupil interviews, examination results from national standardised tests, algorithms formulated for this research and school reports. The data gathered by the study acknowledges that during their formative years of education, pupils lack the linguistic and conceptual knowledge necessary to understand the manipulation of the symbols in subtraction problems. The research highlights and contributes new knowledge to the issues of subtraction by identifying three significant elements, that of: 1. ‘Concrete apparatus’ to assist in learning subtraction. 2. The underpinning use of mathematical language in subtraction. 3. The mechanism of ‘Proactive Inhibition’ in the pupil’s ability to perform subtraction. In so doing, some of the problems and influences on the learning and teaching of subtraction with young pupils has been explored and used to show some of the factors that contribute to the continued underachievement of young primary school pupils in understanding subtraction.