Lek som matematisk aktivitet : hur matematiska aktiviteter konstitueras i förskola och förskoleklass och hur de förändras under en kompetensutvecklingsinsats

Sammanfattning: Previous research has examined the relationship between successful professional development and certain changes within the teaching of mathematics. These changes are not only in regard to the understanding of mathematics but also in regard to the teaching of mathematics. However, teachers’ potential resistance to change has not been studied to the same extent. Therefore, with the support of methods within sociocultural theory, this study aims to investigate how academic discussions may contribute to change. This study examines how, during professional development, 61 preschool teachers comprehend the mathematical activities which make up preschool mathematics education. Few studies have been conducted which focus on professional development courses for preschool teachers working with younger children within the research field of mathematics education (Tirosh,Tsamir & Levenson, 2011). Existing research suggests that preschool teachers only perceive mathematics to be about counting and measuring (Clements & Sarama, 2007). More broadly, an argument has been made in favour of encouraging preschool children to think about and make a series of mental relationships rather than teaching them specific subject content. Counting, measuring, patterns and geometry are considered to be mathematical content and do not necessarily include the expectation of mathematical thinking, such as when playing (Bishop, 1988b). This is in contrast to the Swedish preschool curriculum which emphasises mathematical thinking. In a background document to the Swedish curriculum (Utbildningsdepartementet, 2010), mathematics in preschool is discussed on the basis of Bishop’s (1988) six mathematical activities: Counting, Measuring, Locating, Designing, Playing and Explaining. Playing is the mathematical activity which deals with aspects of mathematical thinking. Bishop (1988) considered playing to be an activity characterised by three components: thinking hypothetically (imagining a potential action to make in a game – the beginning of abstract thought); modelling (abstracting something for reality); and abstracting (identifying the relevant features to focus on within a situation which includes guessing, estimating, assuming or adopting). In Sweden, the role of playing in education is a major concern of early childhood educators. Playing has a long history in the Swedish preschool curriculum which could mean that the preschool teachers are unlikely to naturally connect it with mathematical thinking. Previous studies have suggested that when children play, they learn; however, it may be that Swedish preschool teachers have difficulty comprehending the activity of playing as a mathematical activity given that playing has always had a large role in Swedish preschool education. All teachers have different ideas about what teaching methods in use in different situations and therefore respond differently to professional development. Taking inspiration from Engeström’s (2008) CHAT (Cultural-Historical Activity Theory) and Wartofsky’s three levels of artefacts, this study investigates the extent to which resistance towards change transpired in a preschool setting. In addition, this study investigates, through collegial conversations among the teachers, to what extent this resistance contributed to changing the preschool teachers’ views of how mathematical activities are implemented in the preschool. The empirical material consists of the teachers completing written documentation wherein they all answered the question: what kind of resistance was evident during the changed understanding that Playing, Explaining and Designing can be seen as mathematical activities? In combination with the perception that mathematical situations occur as soon as children play, cultural and historical aspects were also shown to be the main reasons behind any resistance towards playing. This is based on the knowledge that playing consists of traditions in creative forms of expressions which children are assigned when solely playing. Further, this revealed itself through several documented observations that were made of playing initiated by the children whereby the preschool teachers did not want to interfere. In addition, other documented observations show that some playing initiated by the children did include material that was thought to be mathematical and resulted in the children counting. Nevertheless, the teachers’ resistance when viewing playing was foremost noticed when observing the mathematical aspects in children’s play situations. However, when Bishop (1988b) introduced the concept of ‘playing’, the resistance shown by the teachers led to a discussion and the bringing up of new aspects of children’s ways of playing. Furthermore, three more instances of resistance towards technology, explanations and design were identified. One case of the resistance towards technology was observed at the beginning of the course as a result of the participants not having access to certain technical devices that were needed in order to carry out the documentation.A second case of resistance towards explanation also emerged. This was a result of the intention of the programme to support the participants by applying the theory in practice (Karmiloff-Smith & Inhelder, 1975), as it was thought that observing the children’s actions would allow the teachers to gain certain knowledge. In addition, it was thought the teachers would benefit from taking note of how the children explain concepts and then basing them on different theories. However, the teachers’ resistance made it clear that they simply perceived the concept of ‘explaining’ through asking why-questions to the children and them understanding the children’s explanations. However, instead, asking why-questions meant that the preschool teachers missed the children’s actions because they were solely focused on the children’s verbal expressions. This showed the teachers that their resistance to change contributes to more expressions of how children investigate mathematics in preschool. The resistance towards design which arose in the process was because the participants did not perceive mathematics to be a creative subject. Nevertheless, this resistance contributed to a new development in how more mathematical activities can be observed in practice. With the support of scientific methods in sociocultural theory, this study contributes by making historical and cultural resistance visible. Rather than disregard these instances of resistance and be stunned each time there is no result, these four identified cases of resistance have contributed in showing meaningful change. During professional development, these changes reflect the teachers’ changed understanding of how mathematical activities constitute learning in the preschool and preschool class.