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Children’s multiplicative thinking as the recognition of equal group structures and the enumeration of the composite units was the subject of this research. In this paper, we provide an overview of the Multiplication and Division Investigations project. The results were obtained from a small sample of Australian children (n = 21) in their first year of school (mean age 5 years 6 months) who participated in a teaching experiment of five lessons taught by their classroom teacher. The tasks introduced children to the “equal groups” aspect of multiplication. A theoretical framework of constructivist learning, together with research literature underpinning early multiplicative thinking, tasks, and children’s thinking, was used to design the research. Our findings indicate that young children could imagine equal group structures and, in doing so, recognise and enumerate composite units. As the children came to these tasks without any prior formal instruction, it seemed that they had intuitive understandings of equal group structures based on their life experiences. We argue that the implications for teaching include creating learning provocations that elicit children’s early ideas of multiplication, visualisation, and abstraction. The research has also shown the importance of observing children, listening to their explanations of their thinking, and using insights provided by their drawings.

This chapter presents a critical review and celebration of the most significant Australasian early childhood mathematics education research that has been published over the period 2016–2019. We utilise the internationally-accepted definition of ‘early childhood’ as the age range birth to eight years, encompassing prior to school settings, school settings, as well as home and community contexts. Eminent scholars in the field have undertaken the research presented in this chapter in conjunction with a range of stakeholders in early childhood mathematics education, including teachers, families and children. This chapter is structured according to six key themes which emerged from the preliminary analysis and categorisation of the current research across the Australasian region; namely: Mathematics content; Curriculum, policy and assessment; Aspects of teaching and learning; Home and prior to school contexts; Australian and New Zealand Indigenous education; and Emerging areas of research. Indeed, this review highlights several very promising new areas of research, for example: mathematics education for children aged birth to two years; and innovative research methodologies such as ‘camera glasses’ and ‘trolley cams’ utilised in everyday context. The new areas discussed in this chapter highlight the growing interest in, and opportunities for, research in the early years space. However, with the emergence of new areas of research there has been a decline in other areas such as pattern and algebra, geometry, and length measurement. From the synthesis of the research literature the following findings are evident. First, young children are often capable of mathematical thinking from a very early age, which suggests a mismatch between the intended curriculum and children’s capabilities when they start school. Second, the current education policies within Australia and New Zealand have yet to bridge the mathematical transition from early childhood settings to school. Third, the contrast between a holistic appreciation of the mathematics surrounding children in prior to school settings is in stark contrast to school settings where mathematics is formalised and segmented and less richly experiential. The chapter concludes with a discussion of recommendations for future research in this field.

Children’s multiplicative thinking as the visualization of equal group structures and the enumeration the composite units was the subject of this study. The results were obtained from a small sample of Australian children (n = 18) in their first year of school (mean age 5 years 6 months) who participated in a lesson taught by their classroom teacher. The 12 Little Ducks problem stimulated children to visualize and to draw different ways of making equal groups. Fifteen children (83 %) could identify and create equal groups; eight of these children (44 %) could also quantify the number of groups they formed. These findings show that some young children understand early multiplicative ideas and can visualize equal group situations and communicate about these through their drawings and talk. The study emphasises the value of encouraging mathematical visualization from an early age; using open thought-provoking problems to reveal children’s thinking; and promoting drawing as a form of mathematical communication.

This chapter presents the stories of classrooms and the children in them to illustrate some of the practices of highly effective teachers of mathematics. The vignettes of classrooms will be drawn from a research project that was designed to closely examine the practices of "highly effective" teachers of mathematics with young children. The teachers were first identified as highly effective based on the measurable improvements in children's mathematical learning over two consecutive years of the Early Numeracy Research Project (ENRP). During the final year of the project a case study was undertaken to identify the characteristics of effective teachers. Teacher behaviours that promoted classroom interactions that stimulated mathematical thinking and reflection in the context of high teacher expectations were at the heart of the study. Four elements of the research literature that underpins the study are briefly described: the characteristics of effective teachers of mathematics, questioning, listening, and a perspective of young learners.

Children begin to form mathematical concepts at an early age and many of these concepts are linked to measurement experiences. Often mathematics education in pre-school and at the beginning of school is focused on numbers. In order to acknowledge children’s mathematical concepts and to build on them, a mathematics intervention program that focused on measurement replaced the usual mathematics curriculum for 40 children entering their first year of school in Australia. This chapter presents the results of the children’s performance on a one-to-one task-based interview that tested their number knowledge at the beginning and end of the school year. In addition, two case studies and some classroom stories from the intervention are described. Findings indicate that a measurement-based curriculum can stimulate the development of children’s number knowledge and their number sense.

As part of the Victorian Early Numeracy Research Project, over 1400 Victorian children in the first (Preparatory) year of school were assessed in mathematics by their classroom teachers. Using a task-based, one-to-one interview, administered during the first and last month of the school year, a picture emerged of the mathematical knowledge and understanding that young children bring to school, and the changes in this knowledge and understanding during the first year of school. A major feature of this research was that high quality, robust information on young children’s mathematical understanding was collected for so many children. An important finding was that much of what has traditionally formed the mathematics curriculum for the first year of school was already understood clearly by many children on arrival at school. In this article, data on children’s understanding are shared, and some implications for classroom practice are discussed.