\Tip in three blops of milk....\" : an ethnographic study of the development of mathematical concepts and language in Early Childhood Education"

It is becoming increasingly obvious that many students taught according to traditional methods do not develop a thorough understanding of the concepts of mathematics. Much of what they can do is mechanically learnt with no links to a body of interrelated concepts, to the web of meanings which lie at the heart of a quantitative view of the world. It would seem that what is lacking in the teaching of mathematics is the teaching of its language. A language is truly learnt when it can be used to communicate ideas to others and can provide a medium for further thought. The aim of this study was to take elements from the theory of language and of mathematics education and apply them in a classroom setting. The study employed ethnographic methods to record the interactions and the outcomes of the curriculum. This dissertation explores the way the curriculum worked for a group of low achieving students, and attempts to make further suggestions for improving practice. Eleven six and seven year old children, pupils of a country primary school in Tasmania, were selected by their teachers to participate in this study. They were judged to be poor performers in both language and mathematics. These children were taught as a small group for five weeks, one hour each school day by the researcher. All the mathematical activities were presented in a narrative context, they all had reference to the children's lives, and the work itself was carried out using concrete materials. The classroom climate and general teaching approach was very much like that described by Bickmore-Brand (1993) whose teaching in mathematics followed the language teaching advocated by Cambourne. Children were given practice at speaking about mathematics by frequent audio taping at the conclusion of sessions. The information collection methods employed were those required of ethnographic studies, including the participant observer, her diary of reflections, children's taped language, children's work and the remarks of their teachers. Individual testing sessions were conducted during the sixth week of the study. The results showed, that compared with three control children, the participating children had learnt many new concepts, and could apply them in similar as well as in challenging new situations. Their taped language improved markedly, as did the children's ability to express themselves mathematically and to understand directions concerning mathematical problems. The happy atmosphere of the sessions, the good relationships which developed, and the increased competence of the children in both mathematics and language, confirm the choice of the teaching methodology. The problems encountered, the children whose behaviour was at times negative, have provided ideas for further developments.