Kunskapsområdet matematik blir alltmer fokuserat även i förskolan, med mål av vilket kunnande barnen förväntas utveckla. Därav finns det behov av att förstå vad barn faktiskt erbjuds lära och vad de utvecklar för förmågor innan de börjar skolan. Studiens övergripande syfte är att beskriva på vilket sätt förskollärare utvecklar och iscensätter aktiviteter om tal och räknande, och vilket kunnande som blir möjligt för barnen att utveckla. Studien har fokuserat på förskollärarnas lärande samt iscensättande av aktiviteter med matematiskt innehåll (aritmetik, taluppfattning och räknefärdigheter). Den första delstudien beskriver processen kring förskollärares kollektiva lärande. Genom att reflektera och diskutera egna dokumentationer utvecklas de i sin profession avseende lärandet av tal och räknande i aktiviteter med barn. Den andra delstudien beskriver hur förskollärare planerar och iscensätter en aktivitet med fokus tal och räknande, och hur detta påverkade barnens möjligheter till lärande. Studien utgår från ett variationsteoriskt perspektiv (Marton, 2015) samt Chi’s (2009) taxonomi, avseende i vilken form aktiviteterna iscensätts (aktiv - konstruktiv - interaktiv). Studiens resultat visar att förskollärarnas lärande om ämnesinnehåll är en komplex process, där förskollärarnas delade erfarenheter gör det möjligt för dem att över tid urskilja nya aspekter av tal och räknande och därmed också hantera innehållet i aktiviteter på ett förändrat sätt. Studiens resultat visar även skillnader mellan hur lärarna valde att iscensätta aktiviteterna och att detta resulterade i olika möjligheter för barnen att lära.

This study analysed how preschool teachers differently enacted the same mathematical activity for preschool children to discern numbers, and how this affected the children's learning opportunities during the activity. The analysis was based on variation theory and Chi's taxonomy of learning activities. Two Swedish preschool teachers' enactment of the same mathematical activity for 27 children aged 4-6 years was studied. Video recordings of what the children were offered to discern were used in the analysis. The results indicate that variations in how the teachers chose to enact the activity produced two different learning opportunities for the children. Differences in what aspects were made discernible were closely linked to the characteristics of the activity implemented. The enactments differed even if the same game was chosen and the same amount of time was used in the play-based activity. In one preschool group, there were few opportunities to discern more than the nominal form of numbers; the other preschool group had an activity focused on all number forms simultaneously. In addition, in the latter group, the children had the opportunity to develop equinumerosity. The results suggest that the activity with limited variation was more appropriate for learning with undeveloped knowledge; the children with more developed understanding required a more varied design. This study contributes to the knowledge of how the design of an activity affects children's learning differently, which is important when planning learning-based preschool activities.

The aim of this study is to describe in what way preschool activities contribute to the development of children's knowledge of different forms of numbers; symbols, ordinal and cardinal. Video -recordings from three different groups of preschool children age d 3 to 5 years old have been analyzed based on variation theory (Marton, 2015) to describe the children’s discernment of numbers. The activities were planned and enacted by preschool teachers. The teachers’ intentions were to teach the children numerosity (Hannula - Sormunen et.al., 2016). The activities offered learning possibilities during the activities, e.g. to sort digits by magnitude, value or just to match symbols. The video -recordings were analyzed to capture what as- pects of the numbers the children were offered to discern, and what aspects were not offered to discern during the different activities. Simultaneous discernment of numbers in different forms are important for children’s future mathematical performance (Hannul- Sormunen et.al., 2015). The fi ndings unveil the teachers’ challenges to design preschool activities offering children simultaneously discernment of num- bers’ different forms. The activities mainly make the children discern numbers as symbols to match or as magnitude, while the cardinal form occurred only to a limited extent.

This article reports a study of educators differentiating aspects of mathematical knowledge for teaching in preschool as part of a further-education programme. Eight Swedish preschool educators participated in focus group discussions about documentations from their own practice during a school year, to enhance their awareness of their mathematics education practice. The object of learning for the participants is more specifically how numbers and counting are made content for learning in preschool practice. The educators' authentic documentations are reflected upon in focus group meetings and further analysed by the researchers to find out what aspects the educators differentiate during the programme. Results show that educators' learning about content for children's learning in preschool is a complex process. This process involves several aspects necessary to discern for a professional development to occur, but the collaborative approach seems prosperous in that new aspects are brought to the fore, influencing their reflective practice.