Understanding the number line: conception and practice

This study investigates the relationship between teacher’s presentation and children’s understanding of the number line within an English primary school that follows the curricular guidance presented within the National Numeracy Strategy (DfEE, 1999a). Following an exploratory study, which guided the development of a questionnaire, the preparation of a pilot study, and the initial investigation with the trainee teachers, the study was re-conceptualised to consider the way in which teachers within each year group of a primary school used the number line and the ways in which their children conceptualized and interpreted it. Using a mixed methodology, the theoretical framework of the study draws upon methods associated with case study, action research and ethnography and involved the use of questionnaires, teacher observations and interviews with selected children. Analysis of the questionnaire data is mainly through the use of descriptive statistics that lead to discussion on children’s embodiments of the number line, their interpretations of what it is and their accuracy in estimating magnitudes. The results of the study suggest that conceptualising the number line as a continuous rather than discrete representation of the number system that evolves for the notion of a repeated unit was less important than carrying out actions on the number line. It is suggested that this emphasis caused ambiguity in the way teachers referred to the number line and restricted understanding amongst the children that focused upon the ordering of numbers and the actions that could be associated with this ordering. The results also suggest that children’s conceptions of magnitude on a segmented 0 to 100 number line neither meet objectives specified within the National Numeracy Strategy nor confirm hypothesised models that suggest a linear or logarithmic pattern of accuracy. The number line is seen to be a tool but its use as a tool becomes limited because teachers, and consequently children, display little if any awareness of its underlying structure and its strength as a representation of the number system.