WHEN DO CHILDREN BEGIN TO LEARN MATHEMATICS? VIEWS OF PRESCHOOL PRACTITIONERS IN REGIONAL AND RURAL AUSTRALIA

ABSTRACT Preschool directors, teachers, and assistants from regional and rural eastern Australia were interviewed in the autumn of 2008 to discover their knowledge and beliefs concerning whether young children had the capacity to solve mathematical problems, when young children begin to think mathematically, and their observations of children's mathematics learning. Respondents overwhelmingly agreed that preschool children were capable of mathematical activity and thought. Fifty eight (88%) respondents believed that children had begun to exhibit mathematical thinking by age 3; 30 (46%) by their first birthday. Practitioners interviewed were able to provide examples of both incidental and planned mathematical activities across a breadth of content, including number and operations, measurement, geometry, and fundamental classifying and ordering activities. The practitioners also demonstrated a creditable awareness of children who seemed to have a good grasp of mathematics. Many practitioners realized that mathematical proclivity could be shown in the processes children use as they engaged in mathematical activity and solved mathematical problems. Keywords: Mathematical thinking, preschool mathematics, practitioner knowledge YOUNG CHILDREN AND MATHEMATICS Mathematics is a core component of cognition, and 'robust mathematical learning by all young children is a necessary base for later learning' (Clements, Sarama, and DiBiase, 2003, p. 105). Many researchers have recognised that children bring to school powerful mathematical knowledge, skills and dispositions (e.g., The project Mathematical Thinking of Preschool Children in Rural and Regional Australia: Research and Practice has been introduced earlier RESULTS Four questions sought to elicit Early Childhood practitioners' views on young children's mathematics learning, seeking information about whether very young children are capable of working on mathematical problems or activities, when children begin to think mathematically, examples of mathematics learning observed recently, and the actions of a child considered to have a good grasp of mathematical knowledge. Capacity of preschool children to work on mathematical problems or engage in mathematical activities Responses were of three kinds-unconditionally positive, conditional or equivocal, and negative. Typical responses of the first kind, together with the number of practitioners that broadly fitted each category, include: Yes I think so (1) Without a doubt (1) We underestimate children's thinking and learning capacity (1) Yes, absolutely, definitely. We have children capable of subtraction and multiplication (1) It permeates informal activities (6) No limit (1) Natural problem solvers (1) It is in everything we do (2) From nursery point of view, yes (1) Even in the babies' room (1) Children are capable of quantitative judgments as toddlers (1), and Capable of deep thinking, prediction, and problem solving (1). Typical responses of the second kind included: In summary, the practitioners were overwhelmingly in agreement that pre-school children are capable of engaging in mathematical activity and thought. When children begin to think mathematically Responses were grouped into three broad categories: those who thought children start to think mathematically at less than 12 months, between 12 and 24 months, and older than 2 years. In the <12 month category (n=30), 6 practitioners believed mathematical thinking began from birth, and 13 believed preschool children's mathematical thinking is evident in babies. A practitioner said: We don't have mathematics as such. They learn to recognise numbers but counting and sums are for the school. Overall, a total of the 58 practitioners (88%) thought that mathematical thinking starts before the age of 3, and many identified mathematical activity in babies and toddlers. Such a finding is surprising, considering that evidence of infant and toddler mathematical thinking is not usually incorporated well in the preparation of certified practitioners or the meagre in-service opportunities available in Australia. Hopefully the task of providing a theoretical rationale for the mathematical development of preschool children will be made easier due to these positive attitudes and the fund of personal experience and observations that we now know early childhood practitioners can draw upon