This paper focuses on kindergarten teachers' interactions with young children during mathematical learning activities involving the use of digital tools. We aim to characterise the teachers' roles and actions in these activities and extend considerations of teachers' orchestrations current in the research literature with regard to agency and mediation. Our analysis of teacher-children-digital tool interaction reveals that the kindergarten teachers took three roles in their work with young children, which we call Assistant, Mediator and Teacher roles. These roles were used interchangeably and purposefully by the kindergarten teachers. With regard to agency and mediation, we argue that agency is distributed over the human and non-human agents in the activity and that agency and mediation are interrelated.

This study tests an intervention that introduces a structured curriculum for five-year-olds into the universal preschool context of Norway, where the business as usual is an unstructured curriculum. We conduct a field experiment with 691 five-year-olds in 71 preschools and measure treatment impacts on children's development in mathematics, language, and executive functioning. The nine-month intervention has effects on child development at post-intervention and the effects persist one year following the end of the treatment. The effects are mainly driven by the preschools identified as low-quality at baseline, indicating that a structured curriculum can reduce inequality in early childhood learning environments.

The aim of this article is to illustrate how students, through collaborative smallgroup problem solving, appropriate the concept of geometric series. Student appropriation of cultural tools is dependent on five sociocultural aspects: involvement in joint activity, shared focus of attention, shared meanings for utterances, transforming actions and utterances and use of pre-existing cultural knowledge from the classroom in small-group problem solving. As an analytical point of departure, four mathematical theoretical components are identified when appropriating the cultural tool of geometric series: (1) estimating of parameters, (2) establishing of the general term, (3) composing of the sum and (4) deciding on convergence. Analyses of five excerpts focused on the students' social processes of knowledge objectification and the corresponding semiotic means, i.e., lecture notes, linguistic devices, gestures, head movements and gaze, to obtain shared foci and meanings. The investigation of these processes unveils the manner in which the students established links to pre-existing mathematical knowledge in the classroom and how they simultaneously combined the various mathematical theoretical components that go into appropriating the cultural tool of geometric series. From the excerpts, it is evident that the students' participation changes throughout their involvement in the problem-solving process. The students are gaining mathematical knowing through a process of transforming and by establishing shared meanings for the concept and its theoretical components.

In this study we investigated qualities of the mathematical discourse in four kindergarten classes in which kindergarten teachers and 5-year-old children engaged in mathematical learning activities. We analysed differences in the mathematical discourses in two experimental kindergarten classes and two control kindergarten classes, in a research and development project. The overarching research question guiding our study was as follows: what characterises the mathematical discourse unfolding in kindergarten classes? In our study we drew on the theoretical framework Mathematical Discourse in Instruction coined by Adler and Ronda, as we quantified the collected qualitative data. Our analyses identified significant characteristics of mathematical discourse with respect to the children's opportunities to contribute with ideas and arguments. The discourse in the kindergartens differed both with respect to the extent and nature of verbal utterances among the participants, as well as the mathematical engagement nurtured amongst the children. Moreover, the mathematical discourse within the experimental kindergarten classes, to a greater extent than that in the control kindergarten classes, initiated opportunities for the participating children's mathematical learning.

This study explores kindergarten teachers' accounts of their developing mathematical practice in the context of their participation in a developmental research project. Observations and interviews were analysed to elaborate the accounts as regards orchestrating mathematical activities in the kindergarten. A co-learning agreement was established as collaboration between the kindergarten teachers and researchers. The study reveals that the kindergarten teachers argue that they have been empowered in developing an inquiry stance towards mathematics and mathematical activities. Taking an inquiry stance, they claim, has increased their awareness of the mathematics involved in activities, and enabled them to be more explicit when communicating mathematical ideas to children. An adjusted didactic triangle within the kindergarten setting is proposed based on these results.