In this paper we describe stories of mathematics learning in play that are often neglected in this era of schoolification and discussions of what counts as learning in early childhood. Drawing on theories of early childhood teaching and learning that emphasize the importance of teachers' (a) content knowledge, pedagogical content knowledge, and knowledge of children's development, (b) action competencies, and (c) attitudes and beliefs, we explore three stories of child-teacher interaction in play. We found that, despite different political and public perceptions of what counts as learning in three countries, preschool teachers evidenced competencies in similar ways - each illustrating s neglected story of children's mathematical learning.

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.

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.

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.

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 order to better understand the mathematics that preschool children engage in, we categorised the activities made available in one Swedish preschool. Although using Bishop’s 6 categories of mathematical activities and Walkerdine’s distinction between instrumental and pedagogical activities overcame some of our categorisation issues, they did not solve all of them. Some activities could be included in several categories which brought us back to a discussion about who was making what kinds of distinctions and for what purposes

This paper investigates how three children provided mathematical explanations whilst playing with a set of glass jars in a Swedish preschool. Using the idea of semiotic bundles combined with the work on multimodal interactions, the different semiotic resources used individually and in combinations by the children are described. Given that the children were developing their verbal fluency, it was not surprising to find that they also included physical arrangements of the jars and actions to support their explanations. Hence, to produce their explanations of different attributes such as thin and sameness, the children drew on each other’s gestures and actions with the jars. This research has implications for how the relationship between verbal language and gestures can be viewed in regard to young children’s explanations.

Currently there is much discussion internationally about what and how mathematics should be integrated into preschool programs. In Swedish preschools, there is a strong tradition of children’s play. Using video data, we identify how one teacher in a Swedish preschool recognises and builds on mathematical teaching moments that arise from children’s play. The role of respectful listening and asking challenging questions is important in the development of children’s mathematical curiosity. We use this data to explore whether using teaching moments is an appropriate teaching practice in preschools for ensuring that children have good mathematical knowledge to begin school with.

Internationally there is much discussion about what and how mathematics should be integrated into preschool programmes. In Swedish preschools, there is a strong tradition of valorising children’s play. Using video data, we identify how one teacher in a Swedish preschool recognises and builds on mathematical teaching moments that arise from children’s play. We use these data to discuss how the guided play context facilitates some teacher actions while constraining others. Respectful listening and asking challenging questions seem to stimulate the development of children’s mathematical curiosity. However, the teacher is not able to insist that her suggestions for activities are taken up by the children.

Recently, attention has been focussed on the mathematics learnt in preschools and how this contributes to children’s subsequent learning in schools. This paper explores the dilemma of trying to increase preschool children’s learning of mathematics, whilst allowing their play to guide that learning. In Sweden, the revised curriculum for preschools specifies more mathematics to be covered. Yet, like other countries, Sweden traditionally has seen preschools as places where learning arises from children’s play. We suggest two avenues for further research that would contribute information to increasing the likelihood of play supporting mathematics learning.

In the Swedish preschool curriculum, it is stated that children’s learning should happen through play. There is also an expectation that children will engage with ICT and be provided with situations that require them to engage with mathematical concepts. Consequently, the object of this research project is to evaluate mathematical games designed for interactive tables in regard to children’s needs and intersts. Four mathematical games are analysed to determine whether they utilise the affordances of the interactive tables in ways that were likely to support preschool children’s possibilities for learning mathematical concepts and language as well as how to interact with each other. This investigation provides information about how the affordances of interactive tables can be utlised to best meet the needs of young children for future design projects.

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This paper explores tensions between the teacher's intention and the students' interpretation of a reformed classroom practice. Focus for this paper is particular on the social and socio-mathematical norms. The example presented in the paper is connected to the use of resources, such as manipulatives, to catch both explicit and implicit tensions between the students' perceptions of existing norms and teacher ' s intention of supporting norms. These tensions could form and cause a barrier to students' opportunities to learn. Reform teaching is likely to fail if students do not share a similar understanding to that of their teacher in regards to their contribution to mathematics learning.