Immigrant parents' views about mathematics education are rarely investigated, yet these are likely to affect their relationship to early childhood education and care (ECEC) and potentially their adopted country. In this study, Polish parents, who had immigrated to Norway, were surveyed about their views about mathematics education for young children, including what was made available in ECEC institutions in Poland and in Norway. We investigated whether the responses showed that parents' views about what is mathematics in early childhood and how it should be taught or learnt could be related to parents' considerations of the power and authority linked to their position as immigrants. The results have implications for multicultural ECEC and policy makers.

In this chapter, an adapted version of Dowling's distributive strategies is used to show how two children, Klara and Teo, are provided with differential enhancement in the mathematical learning opportunities that they are offered. The analysis shows that the use of everyday settings of mathematics problem, including expectations about the social relationship in those settings, can cause children to collude in the kind of enhancement that they experience. Expectations about the social relationships, within the problems being solved and between the participants, contributed to the two children using strategies which channeled them towards operating in different domains.

In this chapter, we introduce the conference from which the chapters in this book originated. Then we discuss some of the background issues in order to describe the need for discussing issues to do with construction and instruction in early childhood mathematics. In particular, we discuss the evidence to do with whether children can learn mathematics through play and the role of the teacher in this discussion. Finally, we discuss the chapters in relation to the "dance of construction with instruction".

This book presents chapters based on papers presented at the second POEM conference on early mathematics learning. These chapters broaden the discussion about mathematics education in early childhood, by exploring the debate about construction versus instruction. Specific sections investigate the teaching and learning of mathematical processes and mathematical content, early childhood teacher development, transitions for young children between home and preschool, between home and school and between preschool and school. The chapters use a range of innovative theoretical and methodological approaches which will form an interesting basis for future research in this area.

The informal character of preschool mathematics, engaged in during children's play, places complex requirements on preschool teachers. It also leads to challenges in developing appropriate analytical tools for researching teacher work. In this paper a framework, the "didaktic space", is described and used to analyse interactions between preschool teachers and children in relationship to mathematical learning situations. An interaction between a preschool teacher and a group of children about how to compare their temperatures is analysed, using this framework. The analysis focuses on how the teacher's contributions as well as those of the children changed as the role of the mathematics changed. The paper discusses how the didaktic space offers a nuanced understanding of preschool mathematical situations, both to researchers and to teachers.

One of Bishop's six mathematical activities is playing which includes modelling, hypothetical thinking and abstraction. These can be in young children's play, but do they by their presence make this play mathematical? In this chapter, we explore this question by first defining play and then comparing its features with what is known about mathematicians' academic play and how mathematics education researchers have described young children's play. From this theoretical discussion, we discuss the features of play, which can enable it to be described as mathematical. We use these features to analyse a small episode of children playing to discuss if and how their play could be considered to be mathematical.

In this paper, the distinction between Bernstein's horizontal and vertical discourse is used to show how two children are restricted in their possibilities to learn mathematics. The social relationships set up within contexts, both of the problems being solved, and between participants, contributed to the horizontal or vertical discourse being employed. In a circular motion, these discourses then reinforced the social relationships that could come into play. It is argued that mathematical exclusion can occur when social relationships, not only within problem contexts but also within interactions, miscue the kind of discourse which is foregrounded. Children can become confused over the sort of discourse that contributes to mathematics learning.

Problem solving can involve using mathematics to solve everyday problems. In this study, we examine an interaction between a teacher and a class of six-year olds in Sweden around an open-ended problem, from an everyday context. Using Bernstein's ideas about vertical and horizontal discourse, a mixture of everyday and mathematics understandings is identified in the interaction. This mixture seems to result in confusion for both the teacher and the children over what should be the focus. This paper raises issues about how the connection to the everyday in problem solving could reduce children's opportunities to learn mathematics.