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 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.

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 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.

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.

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.

I denna del ska du och dina kollegor att arbeta med att utveckla elevers förmåga att kommunicera kring en statistisk undersökning. Ni kommer att få ta del av några olika aspekter av hur yngre elever kan kommunicera kring ett statistiskt material.

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.