Previous studies highlight the importance of investigate the construction in videorecorded learning situations. The aim of this study is to investigate how video-recordings can be used to enhance pre-service teachers' abilities to identify children's exploration of mathematics in preschools. Even if some previous studies have focused the use of video-recordings of learning situations to improve teaching, only a few of them focused how constructed videos enhance pre-service teachers' abilities to identify when children explore mathematics through learning-situations in preschool. The participants were pre-service teachers in a higher education course. Data consisted of pre-service teachers' written responses after viewing eleven edited video clips before, during, and after a compulsory mathematics teacher education course. The analysis is based on variation theory and show the impact of the construction of the video clips and how to design the clips to enhance the pre-service teachers' abilities to define mathematical components during the children's activities.

This study analyses teachers’ discernment of children’s mathematical knowledge development during preschool play activities and defines how children’s pre-knowledge supports or limits their learning possibilities. In total, two preschool teachers from different preschools participated in this research study. The data consists of two documentations of children’s activities, written notes, and reflections from these two participated preschool teachers. The teachers chose the samples and defined them as important examples of how to merge mathematical knowledge development in free play. Using variation theory, the focus was to define what aspects of children’s mathematical knowledge development were offered and how teachers discern children’s pre-knowledge. The results show how the preschool teachers discern children’s pre-mathematical knowledge in relation to development of abstract abilities, and the importance of identifying their participation in free play situations for promoting mathematical understanding. 

Den här avhandlingen studerar professionsutvecklande matematikundervisning i förskola och skola samt inom lärarutbildningen.

Det är utifrån ett behov av att utveckla kunskap om hur blivande och verksamma lärare kan utveckla sin kompetens att undervisa i matematik i de tidiga åren, som den här avhandlingens problemområde avgränsats, med intentionen att bidra till god matematikundervisning i förskola och skola genom att utveckla kunskap om lärares professionsutbildning. I denna avhandling är det både lärarutbildare och verksamma lärare som kollaborativt utvecklar sin förståelse för matematikundervisning och lärande i sina respektive verksamheter, genom kollaborativa insatser. I avhandlingen ingår fyra studier, och det som är gemensamt för samtliga ingående fyra studier är ett fokus på professionsutveckling för blivande och verksamma lärare som ska undervisa matematik i de yngre åren. Avhandlingens syfte är att bidra med kunskap om hur kollaborativ undervisningsutvecklande professionsutbildning kan utveckla blivande och verksamma lärares syn på och förståelse för yngre elevers/barns lärande i matematik och undervisningens betydelse för att stödja deras lärande. Kappans övergripande frågeställning är: Vilka inslag i professionsutveckling för blivande och verksamma lärare i matematik bidrar till att de utvecklar en förändrad syn på och förståelse för elevers kunnande och lärande genom matematikundervisning? Avhandlingens kunskapsbidrag utgörs av insikter i hur undervisning, kollaborativt planerad och iscensatt av lärarutbildare, i sin tur påverkar blivande och verksamma lärares syn på matematikundervisningens utformning samt barn och elevers matematikkunnande. För att se om det finns likheter och skillnader mellan olika utbildningskontexter har fyra studier valts ut, varav två lärarutbildningskontexter (förskollärar- och grundskollärarutbildning) och två kontexter för verksamma lärare (förskola och grundskola). Det teoretiska ramverk som använts som ansats, variationsteorin, bidrar till att lyfta fram det som haft betydelse för lärares förmåga att upptäcka och synliggöra aspekter som är avgörande för att iscensätta undervisning i relation till elevernas matematikkunnande. De kritiska aspekter som urskilts genom ett variationsteoretiskt perspektiv i syntetiseringen av de ingående fyra studierna är: För det första betydelsen av ämnesteoretiska innehållskunskaper. För det andra betydelsen av förståelse i hur innehållskunskapen behandlas och förstås i undervisningssammanhang. Såväl lärare som lärarstudenter i förskolan visade i större utsträckning svårigheter att identifiera barns informella kunskapsutveckling, samt svårighet att identifiera lärandets innehåll. Avseende lärarstudenter och lärare i grundskolans årskurs 4–6 hade de mindre svårigheter att identifiera innehållet, däremot fanns samma svårigheter med att identifiera barns och elevers förståelse av innehållet för lärarstudenterna. Det blir särskilt betydelsefullt inom lärarutbildning för blivande förskollärare eftersom det matematiska innehållet inte är lika framträdande inom denna kontext, och inte heller förståelsen för barns och elevers kunskapsutveckling i ämnet. Barns förmågor behöver både identifieras och utvecklas tidigt när de formellt inte räknar eller opererar med tal såsom CK (content knowledge) oftast presenteras inom matematikundervisning. Det innebär att MKT (Mathematical knowledge for teaching) utifrån den här studiens resultat behöver beaktas i större utsträckning inom olika utbildningssammanhang och mer specifikt inom lärarutbildningen mot de yngre åldrarna.

The aim of this study is to explore pre-service teachers’ procedural and conceptual understanding of pupils’ understanding of mean value, before and after an intervention. Participants are 66 pre-service teachers, and two teacher educators. The data consists of five video-recorded lessons and pre-service teachers’ pre- and post-test discussions. Based on variation theory, the analysis aimed to identify pre-service teachers’ expressed knowledge of procedural and conceptual understanding, focusing four categories of expressions: procedural (P), procedural didactics (PD), conceptual (C), and conceptual didactics (CD). The pre-service teachers’ expressed understanding of pupils’ knowledge developed differently in the five teacher student groups. A shift from procedural to conceptual focus occurred in two groups. The number of procedural related words expressed in the first group decreased from 104 (pre-test: 65 P and 39 PD) to 16 (post-test: 9 P and 7 PD), at the same time as the conceptual related words increased (pre 4 C and 0 CD and post 11 C and 16 CD). In the second group, 87 procedure-related words (36 P and 51 PD) identified during pre-test decreased after the intervention (3 P and 9 PD). Instead, concept-related words increased from 16 (12 C and 4 CD) to 29 (10 C and 19 CD). The changes occurred among participants who had got, except of theoretical instruction, challenging hands-on tasks about the Mathematical content in focus. The findings from this study contribute to understand how design of instruction for pre-service teacher contributes to enhance teacher students’ didactic perspective on pupils’ learning.

In this study, a total of 18 in-service teachers participated in one cycle of a learning study (Marton, 2015; Holmqvist, 2011) aiming to study development of academic literacy. The study was guided by variation theory (Marton 2015; Holmqvist, Gustavsson & Wernberg, 2008). The object of learning is academic literacy, a subject of importance for all teachers, as their professional work is supposed to be conducted on scientific based knowledge. The capability to read and understand scientific publications, and to judge the scientific value of different sources used by teachers, are crucial for the quality of teachers’ professional work. The study was designed following the steps of a learning study. This means collaborative discussions among the teachers, in this case the researchers who are the authors of this abstract, testing the participants’ knowledge before the teaching activity, by designing and implementing instruction offer the participants to discern the critical aspects of academic literacy to gain deeper knowledge, analysis of post-tests to describe the learning outcome, and to present the results. The lesson was focusing on the structure of, and differences between, scientific and popular scientific texts. Two texts were used presenting the same study and by the same author. By that, the in-service teachers were offered to see the same topics differently described based on the two different genre’s requirements. The results show how the participants in the pre-test focuses on the texts’ similarities, with an unawareness of genre differences. In the post-test, the differences in genre is described. A limitation of the study is that the two texts used in pre and post-tests are focusing slightly different topics, which is discerned and focused by the participants – an aspect not critical for developing academic literacy at a general level.

References

Holmqvist, M. (2011). Teachers’ learning in a learning study. Instructional science, 39(4), 497-511.

Holmqvist, M., Gustavsson, L. & Wernberg, A. (2008) Variation Theory – An Organizing Principle to 

Guide Design Research in Education. In Kelly, A.E., Lesh, R., &. Baek J. (eds) Handbook of design research methods in education, p 111-130. New York: Routledge. 

Marton, F. (2015). Necessary conditions of learning. London: Routledge.

Balli Lelinge och Christina Svensson, universitetsadjunkter och doktorander vid Malmö universitet, har haft förmånen att vägleda Karstorpskolans fritidshem praktikutvecklande forskningsprojekt läsåret 2019/2020: Learning study – att göra skillnad! . Detta pilotprojekt har präglats av gemensam respekt och tillit mellan de inblandade parterna.

Fritidslärarna på Karstorps fritidshem identifierade fyra olika kunskapsområden där elevernas förståelse och lärande behövde utvecklas. I alla fyra Learning studies har undervisningspraktiken varit i förgrunden. Detta har bland annat initialt (före lektionen) inneburit att mäta elevernas förkunskaper (förtest) av det aktuella lärandeobjektet som har följts upp med eftertest och senarelagda eftertest. Enligt fritidslärarna har denna skolutvecklingsmodell varit en ny pedagogisk upplevelse, och som har bidragit och utmanat deras tankar om undervisning och lärande. Fritidslärarna har prövat och utforskat delar av variationsteorin för att fördjupa sin förståelse för de villkor som är förknippade med förhållandet mellan undervisning och lärande.

Något kort om de fyra Learning studierna i antologin. Fritidshemmet Skeppet har gjort en studie som bidragit till att först. elevernas djupare förståelse för vad det innebär att säga Hej. Piratens fritidshem har i sin studie synliggjort elevernas kunskaper om hur känslor utan ord uppfattas av andra för att först. innebörden av kroppsspråket. Lärandeobjektet som Flottens fritidshem arbetat med bygger på vilken kunskap och förståelse eleverna har kring att redigera och klippa en bild på iPaden. Avslutningsvis har Kajutans fritidshem i sin studie studerat betydelsen av hur lektionsdesignen kan främja en ökad utveckling av elevers kreativa förmågor.

Antologin vill bidra till forskningsfältet praktikutvecklande skolforskning i fritidshem, där fokus är undervisningens kvalitet. En kombination av kollaborativa processer och undervisningsutveckling har genom skolutvecklingsmodellen Learning study prövats och utforskats i detta projekt.

Att skriva en antologi är en kollektiv kunskapsresa som leder till nya spännande kunskaper i verksamheterna. Den här antologin bygger på ett intresse av att utveckla sin undervisningspraktik och systematiskt ta reda på något man vill först.

Varje kapitel ansvaras av författarna och vid eventuella frågor kontaktas respektive författare och/eller rektor.  

Few research studies have been conducted in a primary school in early mathematical education about the teaching of geometry. This research aims to contribute with knowledge of how teachers' awareness and understanding of necessary conditions to enhance students' abilities to discern two- and three-dimensional shapes develop. In this research, qualitative methods were used to analyse data from a lesson study in grade 4 in the subject of mathematics. Data were primarily collected through audio-recorded conversations with teachers before and after the lesson, and the results of students' pre- and post-test. The results of this research showed increased awareness of using collaboration opportunities to apply professional classroom instructions and activities to enhance students' knowledge of two- and three-dimensional shapes. This research elucidates how the practice-based professional development approach emphasised the teachers' teaching targets for understanding students' content knowledge of geometric shapes. Additionally, the result highlighted teachers' awareness and understanding of the challenges students face in learning about three-dimensional shapes from two-dimensional representations. Future research should develop a more iterative and revised research lesson design to develop more powerful content knowledge and classroom activity in this topic area.

Föreliggande studie undersöker hur 61 pedagogers förståelse av Bishops matematiska aktiviteter Leka, Förklara, Designa, Lokalisera, Mäta och Räkna förändras under en kompetensutvecklingsinsats. Med stöd av vetenskapliga metoder inom sociokulturella teoribildningar, bidrar studien till att synliggöra historiska och kulturella motstånd som genom medierande handlingar producerats i verksamheten. Med inspiration från Engeströms kulturhistoriska aktivitetsteori och Wartofskys tre hieratiska nivåer av artefakter synliggörs i vilken utsträckning motstånden bidrar till förändring. Det empiriska materialet, som består av pedagogers skriftliga dokumentationer och reflektioner under kollegiala samtal, besvarar frågan: vilken typ av motstånd som synliggörs för en förändrad förståelse av Leka, Förklara och Designa som matematiska aktiviteter under insatsen. Det första motståndet för förändring är i kombination med deltagarnas uppfattning om att matematiska situationer uppstår så snart barn leker. Med stöd av Bishops begrepp för Leka leder insatsen till nya möjligheter för deltagarna att stödja både barns utveckling av lek som det matematiska tänkandet. Det andra motståndet som framkommer är för Förklara. Motståndet uppstår som ett resultat av hur barns handlingar i matematiska situationer synliggörs i dokumentationerna under de kollegiala samtalen. Deltagarna riktar uppmärksamheten på barnens verbala uttryck vilket leder till att insiktsfulla medierande handlingar i form av andra kreativa uttrycksformer förringas. Motståndet för förändrad förståelse av Designa uppstår utifrån deltagarnas tidigare tolkningar av matematik som ett icke kreativt ämne. Även i detta sista motstånd synliggörs hur andra kreativa uttrycksformer underskattas av deltagarna utgörande som matematiska situationer före insatsen. Under insatsen bidrar dock samtliga motstånd som framkommer med stöd av vetenskapliga teorier till nya insikter om matematiska situationer utgörande av Bishops matematiska aktiviteter i praktiken.

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.

In this paper, preschool teachers' documentation of their learning about playing as a mathematical activity are examined using Wartofsky's three levels of artefacts, primary, secondary and tertiary. Playing is one of Bishop's six mathematical activities and was a new consideration for most teachers and in contrast to how play is generally conceived as a tool for learning. Wartofsky's three levels of analysis provided insights into how the teachers were able to visualize and understand playing as a mathematical activity.