Att möta alla elevers behov i matematikundervisningen kan göras på olika sätt. En väg att gå är genom att använda sig av olika arbetssätt och uttrycksformer. För att få en djupare förståelse så är syftet med denna studie att öka kunskapen kring detta genom beskrivningar från lärare i förskoleklassen om deras matematikundervisning. Det har varit två frågeställningar till hjälp för att få svar på studiens syfte. Frågeställningarna är: - Hur beskriver lärarna deras användning av arbetssätt och uttrycksformer i matematikundervisningen, samt -Vilka möjligheter beskriver lärarna att arbetssätt och uttrycksformer kan ha för lärande. Studiens syfte och frågeställningar har besvarats genom kvalitativa intervjuer med fem verksamma lärare i förskoleklass. Den teoretiska utgångspunkt studien har är den sociokulturella teorin där socialt samspel, medierande redskap och språk är i fokus. Studiens resultat visar på hur lärarna använder olika arbetssätt och uttrycksformer i matematiken. Det visar även vilka möjligheter lärarna ser att dessa har för lärandet. Slutligen framkommer det möjliga hinder med användningen av dessa arbetssätt och uttrycksformer. Resultatavsnittet följs av diskussionsavsnittet där både studiens metod och resultat diskuteras. / To meet all students needs in mathematics, teaching can be done in different ways. One way to do this is by using different working methods and different forms of expressions. The aim of this study is to increase the knowledge about this through the descriptions from teachers in preschool class about their mathematics teaching. Two questions help to answer the aim of the study. The questions are how the teachers describe their use of working methods and different forms of expression in mathematics teaching, and what possibilities the teachers describe that different working methods and different forms of expression can have for students’ learning. The study is based on qualitative interviews with five active teachers in Swedish preschool class (6 years old students). The theoretical starting point of the study is the socio-cultural theory where social interaction, mediating tools and language are in focus. The study illustrates how the teachers use different working methods and forms of expression in mathematics. It also gives examples of what opportunities the teachers see that these have for students’ learning. Finally, in the data, some possible obstacles to the use of these working methods and forms of expression also emerges.

Följande examensarbete är en interventions-studie med utgångspunkt i aritmetik-undervis-ning och tals del-helhetsrelationer. Vissa fors-kare menar att del-helhetsrelationer är en grund för vidare aritmetikkunskaper, medan andra forskare menar att det är viktigare att elever utvecklar räkneförmågor. Syftet med denna studie är att undersöka hur undervis-ning om tals del-helhetsrelationer i addition och subtraktion kan utformas ur ett variat-ionsteoretiskt perspektiv. Lärandeobjektet för undervisningssekvensen är att identifiera ett okänt tal i en del-helhetsrelation inom talom-rådet 0-10. Undersökningen gjordes med 13 elever i för-skoleklass genom ett förtest, en undervis-ningssekvens om tre lektioner samt ett efter-test. Undervisningssekvensen och testerna vi-deoinspelades för att utgöra underlag för ana-lys. Lektionerna gjordes för att visa olika vari-ationsmönster som kontrast, separation, gene-ralisering och fusion för att eleverna skulle kunna urskilja kritiska aspekter. Exempelvis användes ”part-whole bars” och kommutati-vitet i undervisningen för att synliggöra de kri-tiska aspekterna. De kritiska aspekterna som kom fram i resultatet var att urskilja att de två delarna ryms i och tillsammans är lika mycket som helheten, kunna ta hjälp av två tal i en relation mellan helhet och delar för att finna det tredje talet, kunna ta hjälp av helheten och en del för att hitta den andra delen och att kunna ta hjälp av kunskaper om tidi-gare del-helhetsrelationer för att hitta okända tal i nya del-helhetsrelationer. / The following thesis is an intervention study based on arithmetic teaching and part-whole relationships of numbers. Some researchers argue that part-whole relationships are a basis for further arithmetic skills, while other re-searchers believe that it is more important that students develop counting abilities. The pur-pose of this study is to investigate how teach-ing of part-whole relationships in addition and subtraction can be designed from a variation theory perspective. The object of learning for the teaching sequence is to identify an un-known number of a part-whole relationship, in the number range 0-10. The study was conducted with 13 students in preschool class through a pre-test, a teaching sequence of three lessons and a post-test. The teaching sequence and the tests were vide-otaped to provide a basis for analysis. The les-sons were designed to show different patterns of variation such as contrast, separation, gen-eralization and fusion so that the students would be able to discern critical aspects. For example, "Part-whole bars" and commuta-tivity were used in the lessons, in order to highlight the critical aspects. The critical as-pects that emerged in the result were to discern that the two parts fit in and together is as much as the whole, be able to use two numbers in a relation between the whole and the parts to find the third number, be able to use the whole and one part to find the second part and to be able to use knowledge about previous part-whole relationships to find the unknown number in new part-whole relationships.

The development of language, writing and reading is crucial for pupils’ knowledge development in school. Interactive book reading has positive effects on pupils’ linguistic development and furthers their learning in school. Our study aims to find out how some teachers perceive their work with interactive book reading in preschool class and grade 3. The questions asked proceed from the didactic questions what, how and why. To achieve our aim and answer our questions, six interviews were held, three with teachers in preschool class and three with teachers in grade 3. Based on the interviews, categories were distinguished for each research question and similarities and differences between the two grades. The teachers describe interactive book reading as active participants and reflecting readers. In grade 3 the teachers work with established methods, while the majority of the teachers in preschool class work with models they have devised on their own. All the teachers state different reasons why they work with interactive book reading, but similar categories are revealed after analysis. The conclusion is that more training is needed in interactive book reading for teachers in preschool class.

The aim is to provide knowledge about educators ' views on physical activity in the transition between preschool and school. The selection consisted of pre-school teachers, teachers, and teachers specializing in sport. In total, six individual interviews were conducted and a focus group with four people. The results of the study show that transitions can be a challenge for both preschool teachers, teachers and children. If there is major change too fast between school forms and unstructured, it can contribute to a precariousness in the transition for children. There may be a risk of a decrease in physical activity without a structured interaction where the staff have an interaction between each other and their respective activities, therefore this study be important for pre-school and school activities in Transitions. Preschool teachers and teachers see synergy as an opportunity to maintain play and physics activity in transitions. It was considered important to take part of each other's experiences and competencies from the different educational contexts. One conclusion in the study is that it can be a challenge to create a sustainable transition structure for children to be able to maintain physical activity with an increased age.

The transition from preschool to primary school is considered by many researchers as being one of the most challenging transitions that children can experience in their educational development. In 1998, in an effort by the Swedish government to facilitate this transition, preschool class was introduced as a voluntary bridge year between preschool and primary school.  Changes in school legislation in 2018 made attendance to preschool class compulsory. Despite the introduction of preschool class in the Swedish system, a lack of knowledge and research about the policies and practices in preschool classes for successful supporting this transition has been observed. The aim of the present qualitative study was to characterize preschool, preschool class, and primary school teachers’ understandings of the transition from preschool to primary school as reflected in their teaching practices. Semi-structured interviews were conducted with preschool, preschool class and primary school teachers at one school and affiliated preschool in a town in the South of Sweden. Observations of the preschool class were also conducted. Theories of transition were applied to analyze the teachers’ understandings of the transition from preschool to primary school.  All of the participating teachers considered the change to compulsory attendance in preschool class to be beneficial for a successful transition for the children from preschool to primary school. Two key factors were identified that appeared to be consequential for how the teachers understood and worked with children’s transitions: (a) the organizational structures in place to support the teachers’ work, related to the teachers’ ability to coordinate with each other and have access to information relevant to prepare the children for the transition; and (b) the lack of a common pedagogical framework across the preschool and school.

Abstract The purpose of this work is to contribute knowledge about the transition of children from preschool to preschool classes. The experiences of pedagogical staff, parents and children are described, based on four deepening questions. The questions are about what the actors experience as positive and what the difficulties were in the transition process, and they also cover the differences of children and collaboration between actors. The method consists of qualitative interviews with parents, children, and pedagogical staff. The interviews concern the experiences of transition from the different actors. The results show the importance of a solid transition plan, the emphasis on good first contact between pedagogical staff and children, and a good parent-teacher relationship. Meetings concerning the handover between parents and pedagogical staff, and the opportunity for children to visit their new school before the school start, are also important factors for a good transition. What is seen as problematic is the lack of time for teachers to visit the children in preschool and preschool classes, difficulties to find suitable times for teacher meetings between preschool and preschool classes and the responsibility of the meetings concerning the handover. Children are different, and adapting the handover to each individual is important. The teachers responsible for the preschool classes need to get information regarding the children from preschool teachers and parents. The conclusions are that work regarding transition is important for parents and children’s security, and that a close cooperation between parents, children, and pedagogical staff is central. This way, experiences, perspectives, and knowledge of the individual child can be shared. Key words: differences of children, preparative work, collaboration, transition from preschool to preschool class. / Sammanfattning Examensarbetets syfte är att bidra med kunskap om processen vid barns övergång från förskola till förskoleklass. Arbetet beskriver erfarenheter hos pedagogisk personal, föräldrar och barn. Fyra frågeställningar har formulerats för att fördjupa syftet. Frågorna handlar om vad aktörerna ser som positivt och problematiskt i övergången, samt barns olikheter och samverkan mellan aktörerna. Metoden i den här studien är kvalitativa intervjuer med föräldrar, barn och pedagogisk personal. Intervjuerna berör de olika aktörernas tankar och erfarenheter av övergången. Resultatet visar att det som är positivt i övergången är en tydlig övergångsplan, bra första kontakt mellan pedagogisk personal och barn samt en trygg föräldra- och lärarrelation. Överlämningssamtal mellan pedagogisk personal och föräldrar och att barnen i förväg får besöka den nya skolan är också viktiga moment i övergången. Det som ses som problematiskt är lärarnas tidsbrist för att besöka barnen i förskola och förskoleklass, mötestider mellan lärare inom förskola och förskoleklass samt ansvaret för överlämningssamtalet. Barn är olika och att anpassa övergången efter individen är viktigt. Lärarna för förskoleklasserna måste få information om barnen från förskola och föräldrar. Slutsatserna är att arbetet i övergången är viktigt för föräldrar och barns trygghet samt att samarbete mellan föräldrar, barn och pedagogisk personal är betydelsefullt. Detta för att lära av varandras verksamheter, erfarenheter, synsätt och framförallt få kunskap om det enskilda barnet. Nyckelord: barns olikheter, förberedande arbete, samverkan, övergången förskola till förskoleklass.

En god taluppfattning är grundläggande för förståelse i matematik. Forskning (Lundberg & Sterner, 2009; Sayers, Andrews & Björklund Boistrup, 2016) visar på hur viktig barns tidiga matematiska kunnande är för goda skolframgångar i matematik i grundskolan samt att tidiga insatser i matematikundervisningen verkar främjande för elevers matematiska utveckling. Med utgångspunkt i detta har denna studie undersökt i vilken mån förskoleklasselever, med påvisad bristfällig taluppfattning, kan utveckla förståelse av antal och talraden. Detta med en tidsbegränsad och strukturerad undervisningsinsats med fokus på dessa två delar inom taluppfattningen. Som kartläggningsmaterial för att undersöka elevernas kunskap i taluppfattning användes Elevintervju vid skolstarten (McIntosh, 2008). Utformandet av undervisningen i interventionen tog sin utgångspunkt dels från resultatet av kartläggningen, dels från boken Tänka, resonera och räkna i förskoleklass (Sterner, Helenius & Wallby, 2014) och genomsyrades av ett sociokulturellt perspektiv på lärande där det är i det matematiska samtalet i gruppen som elevernas förmågor och kunskaper utvecklas. Under interventionen användes olika representationer för tal, exempelvis konkret och visuellt material för att stödja elevernas matematiska förståelse. Resultatet av studien visar på att en strukturerad undervisningsinsats gav positiv utveckling för den aktuella elevgruppen i denna studie, vilket är i linje med tidigare forskningsresultat (Sterner, 2015; Vennberg, 2015). / A strong number sense is foundational for mathematical understanding. Research (Lundberg & Sterner, 2009; Sayers, Andrews & Björklund Boistrup, 2016) has shown strong evidence of the relationship between student’s mathematical abilities when starting school entry and their later performance in mathematics. An early intervention in mathematics has significant positive effects on the student’s mathematical development through elementary school. As a continuation from this prior research the present study examined how preschool-students, with inadequate number sense, can develop an understanding of quantity and number sequence using the support of a structured and time specific intervention with focus on those two parts within number sense. Student interview at school entry (McIntosh, 2008) was the basis for examining the student’s number sense. The structure of the intervention lessons was based on the results from the survey and from the pedagogical literature Tänka, resonera och räkna i förskoleklass (Sterner, Helenius & Wallby, 2014). A sociocultural perspective pervaded where it is assumed the students’ abilities and knowledge develop from mathematical collective reasoning. During the intervention different representations where used, for example concrete and visual material to support the students mathematical understanding. The result demonstrated that a structured intervention in this study had significant effect on the group of preschool-students, which supports research (Sterner, 2015; Vennberg, 2015).

The study seeks to investigate four preschool teachers’ views of making literacy learning a pleasurable experience in preschool class and to identify any differences in their views. The study is based on interviews with four teachers with at least ten years’ experience of work in preschool class. The teachers work in three different municipalities. The result shows that making literacy learning pleasurable is a complex concept, which means that a varied way of working is necessary so that as many pupils as possible will find learning to read a pleasurable experience. Above all, the teachers make learning to read a pleasure through shared activities, in which play, reading aloud and linguistic awareness are important elements in the teaching. The Bornholm model is a common denominator in the work of learning to read for the four preschool teachers, as a consequence of which the teachers’ views of making literacy learning pleasurable are relatively similar.

Mathematics is a subject that contains many different concepts that are ultimately important for students to have knowledge of in order to cope with the subject, but also everyday situations. The teaching of mathematics often means that the students get to meet mathematics by working through the mathematics textbook, where an alternative could be to let the students meet mathematics and its concepts through play. Play is especially important as a teaching method in preschool class, because preschool class is expected to use the playful pedagogy from preschool to prepare students for the school years to come. The purpose of this study is therefore to gain more knowledge in how preschool class teachers can promote students´ concept development in mathematics, by using play as a teaching method. The following research questions are addressed:  ·       What kinds of games are presented by teachers on social media to develop students´ mathematical conceptual ability in mathematics?  ·       What aspects of the teacher´s role are displayed on social media when it comes to students´ mathematical concept development through play? Posts on social media were collected, to see how active teachers in preschool class work with play in the subject of mathematics. The prevailing pandemic that took place at the time the work was written, influenced the choice of method. Social media is a collective name for a number of different platforms and for this work, 4 different platforms were selected to see how teachers use play in their mathematics lessons. To help analyzing the various posts, an analysis protocol was developed with various aspects around, among other things, the teacher´s role in the play. The results show that play in many posts is used in concept development. The results also show that teachers let their students work with different pedagogically materials and play to attach many of all the concepts of mathematics.

Matematisk problemlösning är för elever ett utmanande område som är beroende av att lärare har en genomtänkt plan för hur undervisningen ska struktureras. De olika syner som visat sig finnas på problemlösning har vidare inspirerat till den här studiens syfte, vilket är att synliggöra olika uppfattningar av vad problemlösning i förskoleklass och årskurs 1–3 innebär. För att svara mot syftet för studien har en fenomenografisk ansats använts och frågeställningarna ”På vilka kvalitativt skilda sätt uppfattar lärare problemlösning i de lägre årskurserna?” och ”På vilka kvalitativt skilda sätt uppfattar lärare syftet med att undervisa i problemlösning i de lägre årskurserna?” har formulerats. Genom semistrukturerade intervjuer med fyra lärare har data samlats in och analyserats. Resultatet visar på fem olika uppfattningar av problemlösning vilka handlar om att se problemlösning som en textuppgift, en utmanande process, en procedur, ett gemensamt arbete eller ett kreativt tänkande. Därefter presenteras fyra uppfattningar av vad syftet med undervisning i problemlösning är. Syftet uppfattas handla om att följa läroplan och förbereda inför nationella prov, att ge eleverna förberedande verktyg, att skapa en förståelse för problemlösning och att testa elevernas kunskaper. Avslutningsvis diskuteras studiens metodval följt av en diskussion kring resultatet i relation till tidigare forskning och yrkesverksamheten. / Mathematical problem solving is a challenging area for younger students that relies on teachers having a well-thought-out plan for how the teaching should be structured. The different views that have been identified regarding problem solving have further inspired the purpose of this study. The purpose is to highlight different ways of experiencing what problem solving in preschool and grades 1–3 entails. With regards to the purpose of the study, a phenomenographic approach has been used, and the research questions "In what qualitatively different ways do teachers experience problem solving in the lower grades?" and "In what qualitatively different ways do teachers experience the purpose of teaching problem solving in the lower grades?" has been formulated. Data has been collected and analyzed through semi-structured interviews with four teachers. The results reveal five different understandings of problem solving, which involve seeing problem solving as a word problem, a challenging process, a procedure, a collaborative work, or a creative thinking. Furthermore, four different ways of experiencing the purpose of teaching problem solving are presented. The purpose is experienced to be about following the curriculum and preparing for national tests, providing preparatory tools for students, fostering an understanding of problem solving, and testing students' knowledge. Finally, the study's choice of method is discussed, followed by a discussion of the results in relation to previous research and professional practice.