Number sense in secondary school pupils : a thesis presented in partial fulfilment of the requirements for the degree of Master of Educational Studies (Mathematics) at Massey University

Abstract

Number sense refers to a quantitative appreciation of numbers and an ability to perform calculations in creative and original ways. A pupil with number sense will not be bound by learnt procedures when calculating, instead he/she will be able to create self-made solutions that reflect a good understanding of numbers and flexible ways of using operations on them. Number sense development is now recognised as an integral component in the syllabi of many western countries and is promoted as an appropriate and productive way of teaching mathematics. Much of number sense revolves around computational mathematics, at which New Zealand pupils, on a comparative international basis, do not rate highly. This study examines the number sense of a range of New Zealand secondary school-aged pupils by means of a questionnaire, and the processes that pupils use when performing calculations by a series of interviews. Affective factors that have influenced a pupil's mathematical development have also been studied. The qualitative and quantitative data generated enables judgements to be made about the development of number sense and what factors affect this development. Results suggest that many pupils have had little experience with some of the computational aspects of number sense (estimation and mental arithmetic), only partly appreciate the potential of the distributive principle in numerical calculations and are too locked into algorithmic type solutions. By contrast, pupils with well developed number sense demonstrate good number operation knowledge which they employ in a variety of creative ways when solving problems. Indications are that the foundations for this expertise are put in place at an early age by examining the properties of numbers, performing number drill exercises and validating the processes so that a sense making aspect is built into mathematics education.