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 paper, a methodology is proposed for gaining insights into preservice teachers’ understandings about young children’s mathematics learning. Using data from a Swedish and Norwegian pilot study, it is possible to see how a set of questions about a stimulus photo of children playing with some glass jars provided insights into the preservice teachers’ mathematical and pedagogical understandings. Although the preservice teachers seemed to be able to recognise a range of mathematical activities and respond to children engaging in them, they often gave only implicit, general information. This raises questions about teacher educators’ expectations about whether preservice teachers, at the end of their courses, should be able to provide more explicit descriptions of what children are doing and suggestions for how to develop their mathematical understandings. Information of this kind can inform teacher educators about what could be improved in future mathematics education courses in early years programmes.

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.

In many countries around the world, young children use different kinds of information and communication technologies (ICT) on a daily basis. In this chapter, the use of games or apps on these technologies is explored in relationship to children’s learning of mathematical thinking. The work of Biesta on education and socialisation is combined with that of Radford on subjectification and objectification to theorise young children’s learning of mathematical thinking. Two Swedish preschool children’s interactions with a balance game on an Interactive Table are analysed to consider the value of this theory and what it says about the affordances of the game.

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.

This article investigates a map-drawing activity in a Swedish preschool from the perspective of how children are positioned as being or becoming mathematicians by the children themselves, the teacher and the researcher. The children positioned themselves as being mathematicians, who were capable of expressing and using their own experiences and skills. The researcher also focused on the children’s expertise and so positioned them as being mathematicians. Nevertheless, there were times when the children acknowledged their need for more skills and knowledge to solve a problem and thus positioned themselves as becoming mathematicians. Similarly, some of the teacher’s questions also focussed on developing children’s mathematics skills, which thus emphasized children’s incompleteness or state as becoming mathematicians. By contrasting the teacher’s role with those of the children and the researcher, it is possible to identify how the teacher affects children’s socialisation and learning through her questioning.

New norms and values introduced into preschools through curricula changes require teachers to adapt their teaching. However, in making adjustments in order to increase children’s agency, teachers can loose sight of how they wield their own power. In this project, a professional development facilitator worked with five Swedish teachers. Although the preschool teachers considered their primary role to be carers who resisted interfering in children’s explorations, the initial analysis suggests that they were wielding considerable power in their interpretations of what was occurring. Consequently, it has become important for the professional development facilitator to unpack with teachers the power that they wield in order to develop their teaching. This project description discusses initial ideas for doing this.