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The aim of this paper is to present fixed point result of mappings satisfying a generalized rational contractive condition in the setup of multiplicative metric spaces. As an application, we obtain a common fixed point of a pair of weakly compatible mappings. Some common fixed point results of pair of rational contractive types mappings involved in cocyclic representation of a nonempty subset of a multiplicative metric space are also obtained. Some examples are presented to support the results proved herein. Our results generalize and extend various results in the existing literature.

The aim of this paper is to present coincidence and common fixed point results of set-valued mappings satisfying certain generalized graphic F-contractive conditions on a family of sets endowed with a graph. It is worth mentioning that these results are obtained without appealing to any form of continuity of mappings involved herein. Some examples are presented to support the results proved in this paper. Our results unify, generalize and extend various comparable results in the existing literature. © 2016, Springer International Publishing.

The aim of this paper is to present common fixed point results of set-valued graphic F-contraction mappings on a family of sets endowed with a graph. Some examples are presented to support the results proved herein. Our results unify, generalize and extend various results in the existing literature.

This paper aims at an accurate and efficient computation of effective quantities, e.g., the homogenized coefficients for approximating the solutions to partial differential equations with oscillatory coefficients. Typical multiscale methods are based on a micro-macro coupling, where the macromodel describes the coarse scale behaviour, and the micro model is solved only locally to upscale the effective quantities, which are missing in the macro model. The fact that the micro problems are solved over small domains within the entire macroscopic domain, implies imposing artificial boundary conditions on the boundary of the microscopic domains. A naive treatment of these artificial boundary conditions leads to a first order error in ε/δ, where ε < δ represents the characteristic length ofthe small scale oscillations and δ^d is the size of micro domain. This error dominates all other errors originating from the discretization of the macro and the micro problems, and its reduction is a main issue in today’s engineering multiscale computations. The objective of the present work is to analyse a parabolic approach, first announced in [A. Abdulle,D. Arjmand, E. Paganoni, C. R. Acad. Sci. Paris, Ser. I, 2019], for computing the homogenized coefficients with arbitrarily high convergence rates in ε/δ. The analysis covers the setting of periodic microstructure,and numerical simulations are provided to verify the theoretical findings for more general settings, e.g. non-periodic micro structures.

This thesis brings together three thematic topics, PageRank of evolving tree graphs, stopping criteria for ranks and perturbed Markov chains with damping component. The commonality in these topics is their focus on ranking problems in information networks. In the fields of science and engineering, information networks are interesting from both practical and theoretical perspectives. The fascinating property of networks is their applicability in analysing broad spectrum of problems and well established mathematical objects. One of the most common algorithms in networks' analysis is PageRank. It was developed for web pages’ ranking and now serves as a tool for identifying important vertices as well as studying characteristics of real-world systems in several areas of applications. Despite numerous successes of the algorithm in real life, the analysis of information networks is still challenging. Specifically, when the system experiences changes in vertices /edges or it is not strongly connected or when a damping stochastic matrix and a damping factor are added to an information matrix. For these reasons, extending existing or developing methods to understand such complex networks is necessary.

Chapter 2 of this thesis focuses on information networks with no bidirectional interaction. They are commonly encountered in ecological systems, number theory and security systems. We consider certain specific changes in a network and describe how the corresponding information matrix can be updated as well as PageRank scores. Specifically, we consider the graph partitioned into levels of vertices and describe how PageRank is updated as the network evolves.

In Chapter 3, we review different stopping criteria used in solving a linear system of equations and investigate each stopping criterion against some classical iterative methods. Also, we explore whether clustering algorithms may be used as stopping criteria.

Chapter 4 focuses on perturbed Markov chains commonly used for the description of information networks. In such models, the transition matrix of an information Markov chain is usually regularised and approximated by a stochastic (Google type) matrix. Stationary distribution of the stochastic matrix is equivalent to PageRank, which is very important for ranking of vertices in information networks. Determining stationary probabilities and related characteristics of singularly perturbed Markov chains is complicated; leave alone the choice of regularisation parameter. We use the procedure of artificial regeneration for the perturbed Markov chain with the matrix of transition probabilities and coupling methods. We obtain ergodic theorems, in the form of asymptotic relations. We also derive explicit upper bounds for the rate of convergence in ergodic relations. Finally, we illustrate these results with numerical examples.

PageRank update refers to the process of computing new PageRank values after change(s) (addition or removal of links/vertices) has occurred in real life networks. The purpose of the updating is to avoid recalculating the values from scratch. To efficiently carry out the update, we consider PageRank as the expected number of visits to target vertex if multiple random walks are performed, starting at each vertex once and weighing each of these walks by a weight value. Hence, it might be looked at as updating non-normalised PageRank. In the proposed approach, a scaled adjacency matrix is sequentially updated after every change and the levels of the vertices being updated as well. This enables sets of internal and sink vertices dependent on their roots or parents, thus vector-vector product can be performed sequentially since there are no infinite steps from one vertex to the other.

A PageRank update refers to the process of computing new PageRank valuesafter a change(s) (addition or removal of links/vertices) has occurred in real-lifenetworks. The purpose of updating is to avoid re-calculating the values from scratch.To efficiently carry out the update, we consider PageRank to be the expected numberof visits to a target vertex if multiple random walks are performed, starting at eachvertex once and weighing each of these walks by a weight value. Hence, it mightbe looked at as updating a non-normalized PageRank. We focus on networks of treegraphs and propose an approach to sequentially update a scaled adjacency matrix afterevery change, as well as the levels of the vertices. In this way, we can update thePageRank of affected vertices by their corresponding levels.

In this article, we study how PageRank can be updated in an evolving tree graph. We are interested in finding how ranks of the graph can be updated simultaneously and effectively using previous ranks without resorting to iterative methods such as the Jacobi or Power method. We demonstrate and discuss how PageRank can be updated when a leaf is added to a tree, at least one leaf is added to a vertex with at least one outgoing edge, an edge added to vertices at the same level and forward edge is added in a tree graph. The results of this paper provide new insights and applications of standard partitioning of vertices of the graph into levels using breadth-first search algorithm. Then, one determines PageRanks as the expected numbers of random walk starting from any vertex in the graph. We noted that time complexity of the proposed method is linear, which is quite good. Also, it is important to point out that the types of vertex play essential role in updating of PageRank.

Summary Updating PageRank refers to a process of computing new PageRank values after changes have occurred in a graph. The main goal of the updating is to avoid recalculating the values from scratch. This chapter focuses on updating PageRank of an evolving tree graph when a vertex and an edge are added sequentially. It describes how to maintain level structures when a cycle is created and investigates the practical and theoretical efficiency to update PageRanks for an evolving graph with many cycles. The chapter discusses the convergence of the power method applied to stochastic complement of Google matrix when a feedback vertex set is used. It also demonstrates that the partition by feedback vertex set improves asymptotic convergence of power method in updating PageRank in a network with cyclic components.

Bioinformatics, internet search engines (web pages) and social networks are some of the examples with large and high sparsity matrices. For some of these systems, only the actual ranks of the solution vector is interesting rather than the vector itself. In this case, it is desirable that the stopping criterion reflects the error in ranks rather than the residual vector that might have a lower convergence. This chapter evaluates stopping criteria on Jacobi, successive over relaxation (SOR) and power series iterative schemes. Numerical experiments were performed and results show that Kendall's correlation coefficient gives good stopping criterion of ranks for linear system of equations. The chapter focuses on the termination criterion as means of obtaining good ranks. It outlines some studies carried out on stopping criteria in solving the linear system.

The paper is devoted to studies of perturbed Markov chains commonly used for description of information networks. In such models, the matrix of transition probabilities for the corresponding Markov chain is usually regularised by adding  a special damping matrix multiplied by a small damping (perturbation) parameter ε. In this paper, we present results of the detailed perturbation analysis of Markov chains with damping component and numerical experiments supporting and illustrating the results of this perturbation analysis.

This chapter is devoted to studies of perturbed Markov chains, commonly used for the description of information networks. In such models, the matrix of transition probabilities for the corresponding Markov chain is usually regularized by adding aspecial damping matrix, multiplied by a small damping (perturbation) parameter ε. In this chapter, we present the results of detailed perturbation analysis of Markov chains with damping component and numerical experiments supporting and illustrating the results of this perturbation analysis.

The driving forces of conducting the two studies presented in this thesis are: the strong position of curriculum resources in the mathematics classroom in general; teachers’ faith in curriculum resources to convey the intentions and goals of mathematics education; and the expected benefits to mathematics education through expanding the knowledge base of research in the area of curriculum resources in general, and teacher guides in particular. This thesis builds upon two studies conducted in Sweden. The first is a study on how teachers use teacher guides. The results of this study could be seen as one piece in the building of a theoretical understanding of how teachers use their tools in planning and enacting teaching. The data for Study I were collected through semi-structured interviews with five early-years mathematics teachers. In advance, the teachers were asked to copy the pages from the teacher guide they had used the week before the interview. The analysis of the interviews shows that less experienced teachers desire a wider scope of content in their teacher guide. More experienced teachers desire support from teaching activities, in the design of teaching in classroom practice. Another interesting result was that all teachers in our study, regardless of prior experience, knowledge, beliefs, etc., want the teacher guide to offer connections between theory and practice. The second study investigates what content is represented in Swedish textbooks. The results of this study map the terrain over how the most commonly used textbooks in Sweden construct the topic of proportion and proportional reasoning. My choice of textbooks is based on a questionnaire among all compulsory school mathematics teachers in the sixth largest municipality in Sweden, revealing that two curriculum resources together covered 97% of the classrooms in Grades 7-9. The study provides insights into the strengths and weaknesses in the presented structure regarding proportional reasoning in the most commonly used textbooks in Swedish lower secondary school. Teachers could use these insights when making decisions about how to use their textbooks, and to possibly reconsider how to organize the enactment of the national curriculum in order to develop deep understanding. The analyses could provide authors of teacher guides and textbooks with valuable information to consider regarding structure and design.

This poster presents a study on the voice of two Swedish mathematics teacher guides. We have made a content analysis of teacher guides to the two most commonly used mathematics textbooks in Swedish lower secondary school Grades 7 to 9. Our theoretical stance is that curriculum resources can support teachers pedagogical design capacity. Our analysis shows that the voice of both guides speaks through the teacher with narratives and scripted instructions, instead of making visible the strengths and weaknesses with different teaching design considerations. The results could be used to further elaborate on how the teacher guides can be designed to support the pedagogical design capacity for a range of different teachers.

In this paper we report on how two Swedish mathematics teacher guides communicate with teachers. We have analysed the guides from the theoretical stance that curriculum resources can support teachers’ pedagogical design capacity, i.e. support them to find productive ways to adapt curriculum resources. To investigate the guides we studied the “voice” by the use of language, focusing on personal pronouns and imperatives. Our analysis shows that both guides often speak “through” the teacher with narratives and scripted instructions, rather than “to” the teacher about strengths and weaknesses with different teaching design considerations. The results also show that in addition to speaking “to” or “through” guides can speak “past” the teacher, positioning her as an observer of the interaction between students and textbooks. This language construction is unexpected and may thus be seen as expanding the framework for investigating the “voice” of teacher guides. 

In this study we investigate how teachers talk about their use of mathematics teacher guides for support and inspiration, with the aim of broadening the knowledge of how teachers use these guides in and for teaching. Our second aim is to test whether guidelines for designing educative curriculum material can serve as an analytical tool. The results show that less experienced teachers use a wider scope of content in the teacher guide whereas more experienced teachers use teaching activities1 and support for the design of teaching. Common for all teachers, despite level of experience, is that they want the teacher guide to provide connections between theory and practice. The analytical tool served well for analysing interviews, helping us pay attention to the features of the content discussed.

The double-mean-reverting model by Gatheral [1] is motivated by empirical dynamics of the variance of the stock price. No closed-form solution for European option exists in the above model. We study the behaviour of the implied volatility with respect to the logarithmic strike price and maturity near expiry and at-the- money. Using the method by Pagliarani and Pascucci [6], we calculate explicitly the first few terms of the asymptotic expansion of the implied volatility within a parabolic region.

The double-mean-reverting model by Gatheral is motivated by empirical dynamics of the variance of the stock price. No closed-form solution for European option exists in the above model. We study the behaviour of the implied volatility with respect to the logarithmic strike price and maturity near expiry and at-the-money. Using the method by Pagliarani and Pascucci, we calculate explicitly the first few terms of the asymptotic expansion of the implied volatility within a parabolic region.

The global solution of a fuzzy linear system contains the crisp vector solution of a real linear system. So discussion about the global solution of a  fuzzy linear system  with a fuzzy number vector  in the right hand side and crisp a coefficient matrix  is considered. The advantage of the paper is developing a new algorithm to find the solution of such system by considering a global solution based upon the concept of a convex fuzzy numbers. At first the existence and uniqueness of the solution are introduced and then the related theorems and properties about the solution are proved in details. Finally the method is illustrated by solving some numerical examples.

Time variation of constants of nature is still a question of debate among astronomers, physicists, geologists, and palaeontologists. But are the fundamental physical constants really varying in space or time and how changing these parameters may occur?. Paul Dirac was interested in this question in the large number hypothesis (LNH). He arrived by coincidence at the revolutionary hypothesis that the gravitational constant G should be varied inversely with the cosmic time t. LNH sparked off many ideas and arguments about the possibility of time or space variations of the fundamental constants of nature. In this work, we review details and arguments regarding the time and space variation of dimensional and dimensionless constants based on a detailed comparison for the recorded literature over about one and a half-century. 

Skolans nationella målsättning är att erbjuda alla elever en inkluderande skolgång med likvärdiga förutsättningar att uppnå målen för utbildningen och att utvecklas så långt som möjligt. Trots strävan efter en inkluderande skola kategoriserar och särskiljer det svenska utbildningssystemet elever med intellektuell funktionsnedsättning (IF). För elever som har IF finns en alternativ skolform: grundsärskola, som har en egen läroplan och kursplaner. Elever som har diagnosen lindrig IF (LIF) erbjuds möjlighet att påverka om de vill få sin utbildning i grundsärskolan eller i grundskolan. Det kan vara en utmaning för lärare att planera sin undervisning utifrån två olika läroplaner, läroplanen för grundsärskolan och läroplanen för grundskolan

Syftet med denna studie var att utforska undervisningssituationen för elever som har LIF i åldern 9-15 år, genom perspektivet från lärare i grundsärskolan och lärare i grundskolan.

Tjugotvå lärare (11 specialskollärare och 11 grundskollärare) intervjuades om deras erfarenheter och uppfattningar om undervisningssituationen i skolan för elever med LIF. Tematisk analys användes för att induktivt analysera data.

Resultatet i den här studien bygger på ett tidigare avhandlingsarbete, som fokuserade på undervisningssituationen för elever som har LIF. Lärare i grundsärskolan och lärare i grundskolan hade gemensamma och skilda erfarenheter och uppfattningar om hinder och möjligheter i undervisningen för elever med IF. Masterteman som sammanfattade kluster handlade om styrdokumentens krav och elevers förutsättningar, lärares val av innehåll och representationsformer och lärares arbete med sociala dimensioner.

According to the Salamanca declaration and framework (UNESCO, 1994) each country should strive to establish an inclusive school where all children can be together in the same school system, in regular classrooms with a customized education in community with others. Despite all children's right to a meaningful and equivalent teaching, categorizations of children with disabilities still occur and in Sweden there is a low degree of inclusion in regular school for pupils with intellectual disabilities (Education, 2012). For these reasons, it is of importance to increase knowledge about and investigate how classroom environments can be inclusive and provide a challenging and meaningful education for all. This chapter discusses inclusive education for children with mild intellectual disability (MID) and how teachers can work to enable learning for all pupils in their classroom. Examples will be given from field notes of different teaching sessions in lower secondary school in Sweden.

Barn som har intellektuell funktionsnedsättning kan få sin undervisning i grundskolan, men läsa enligt grundsärskolans läroplan. Hur är det att göra övergångar mellan olika skolformer och olika skolor för barn som har intellektuell funktionsnedsättning? Hur kan det se ut för dessa barn i förskola och skolan innan utredning inför mottagande i särskola, under utredning och efter utredning? Detta kapitel diskuterar just dessa frågor och presenterar tre föräldraberättelser om sina barns skoltid.

I denna rapport redovisas resultatet från en följeforskning av ett kompe­tensutvecklingsprojekt inom vård- och omsorgssektorn, kallat KIVO. Det övergripande målet med projektet har varit att det ska bidra till att arbets­platser upplevs som mer kvalitetsmedvetna och attraktiva. Tidsperioden för genomförandet av projektet har pågått under två år med avslut i janu­ari 2013. Konkret har projektet inneburit att cirka 300 medarbetare från olika femton olika arbetsplatser i Västmanland har getts möjlighet att delta i ett utbildningsprogram.

Utvärderingens roll har varit att granska hur deltagarna omsätter erfaren­heter och kunskaper utifrån utbildningsinsatser gällande friskfaktorer, lärande och samarbetsformer.

I denna rapport redovisas resultatet från en utvärdering av ett kommunprojekt inom förskola, grundskola och gymnasium inom Flens kommun, kallat Skolprojektet. Det övergripande målet med projektet har varit att det ska bidra till att alla elever i kommunen successivt nu och i framtiden ska klara godkända resultat i skolan. Tidsperioden för genomförandet av projektet har varit tre år med avslut mars 2015. Konkret har projektet inneburit att främst förskolor, grundskolor, gymnasium och fritidshem och egentligen alla samhällsmedborgare ska involveras i detta projekt, allt för att stödja alla elever till att uppnå måluppfyllelsen.

With assistance from the European Social Fund, Mälardalen University started the JämBredd project to offer an education in equality and diversity issues. Part of this project has been education in Process Leadership. The aim was to design a skills enhancement Leadership course for creating processes of change in a multicultural working life. Schools, district courts, various municipal health care institutions, housing associations and universities have all requested knowledge about equality and diversity issues, in order to be able to create a better exchange of ideas both internally within organizations and externally in customer contacts. All participants have some form of leadership in their various activities. The professional roles of the 33 participants at the start of the education course were headmasters to preschool or school managers in various municipal administrations, personnel officers, gender instructors, lecturers, counselors, and administrators in various municipalities, counties and District Court. Process Leadership education was offered in nine so-called education modules over one year. The teaching methods varied with different approaches to in equality and diversity issues by researchers. Education modules were organized as full-day educational activities and located outside the university.

The overall aim of the study is to identify learning and change processes related to equality and diversity issues among participants in the Process Leadership Education. Another aim is to develop an education model which can be used for skills enhancement in the areas of equality and diversity for different occupations? The questions are: How has participation in the education led to increased knowledge of equality and diversity issues? How has the education given participants increased knowledge that has contributed to a process of change regarding equality and diversity issues? What factors can be seen as important in the change process regarding equality and diversity issues? What conclusions can be drawn from the evaluation to contribute to the future development of process management training?

The research strategy of this study has been Action research. The Action researcher has followed the learning process throughout a year and evaluated the program through observations, visual method, interviews and questionnaires. The results showed an understanding among the participants that they had attained increased knowledge about diversity that was mainly due to two factors: One reason was that the lecturers were knowledgeable researchers in various diversity issues and shared their own knowledge with the participants. The second reason was that there was plenty of time for reflection, reference reading and networking since the educational program spanned the entire year. The final result also indicated a training model that might be used to create a better understanding of diversity issues within various occupations. The result show consistent responses from the participants of the education, as described above, and can thus be said to be relevant to further education in equality and diversity issues. Through this education in process management, participants’ attained increased knowledge on the one hand and also on the other hand tools to drive processes that in turn can lead to employees with increasing knowledge about diversity issues.

Keywords: process

We study universality properties of the Epstein zeta function En(L,s) for lattices L of large dimension n and suitable regions of complex numbers s . Our main result is that, as n→∞ , En(L,s) is universal in the right half of the critical strip as L varies over all n -dimensional lattices L . The proof uses an approximation result for Dirichlet polynomials together with a recent result on the distribution of lengths of lattice vectors in a random lattice of large dimension and a strong uniform estimate for the error term in the generalized circle problem. Using the same basic approach we also prove that, as n→∞ , En(L1,s)−En(L2,s) is universal in the full half-plane to the right of the critical line as (L1,L2) varies over all pairs of n -dimensional lattices. Finally, we prove a more classical universality result for En(L,s) in the s -variable valid for almost all lattices L of dimension n . As part of the proof we obtain a strong bound of En(L,s) on the critical line that is subconvex for n≥5 and almost all n -dimensional lattices L.

Under några år har min handledning av kandidatuppsatser på distans ökat. Det jag kommer att utveckla i min presentation är hur jag har använt teknik för att ge respons på uppsatsutkast och inlämningsuppgifter. Upprinnelsen till teknikanvändningen är att fler studenter väljer handledning via e-post när de skriver sin kandidatuppsats. Den återkoppling jag tidigare har gett har varit i form av infogade skriftliga kommentarer, både övergripande och detaljerade i inskickat dokument. Ibland har den skriftliga återkopplingen kompletteras med telefonsamtal. För några studenter fungerade detta, för andra inte. Uteblivna möten i realtid mellan studenter och handledare resulterar i att handledningen blir en utmaning, för båda parter. Tid, eller brist på tid, var den utlösande faktorn som tvingade mig att anamma en ny metod för återkoppling, med hjälp av teknik. Från att enbart ha infogat skriftliga kommentarer i studenternas dokument, till att även lägga till färgmarkeringar i text har jag nu provat att använda Kaltura Video för återkoppling. Denna arbetsmetod startade jag med våren -17, som ett pilotprojekt. Mitt tillvägagångssätt är att först läsa texten och göra anteckningar. Sedan skriver jag in några korta kommentarer i studenternas text. Därefter startar jag videoinspelningen som spelar in min röst samtidigt med att deras text visas i bild. Min erfarenhet är att denna form av återkoppling tar mindre tid i anspråk än att ge skriftliga kommentarer, en tidseffektivisering av handledningstiden. De studenter som ingick i pilotprojektet och som fått ta del av denna handledning, under ht-17 är positiva till denna form av återkoppling. Studenterna upplever att mina kommentarer blev tydligare. Det blev enklare att förstå vad och hur de kunde utveckla sin text samt att de förstod mitt resonemang bättre. Återkoppling med ljud och bild vill de att jag fortsätter med. Metoden kommer jag att fortsätta använda, både vad det gäller respons på kandidatuppsatstexter samt på inlämningsuppgifter i andra kurser.

Lärare inom högre utbildning förväntas ha studenters lärande i fokus. Hur studenter lär, vad som stimulerar deras lärande och kunskapande är frågor som lärare bör och ska ställa sig. Andra förväntningar som finns är att utveckla och utvärdera kurser och program, och att lärare själva ska lära sig. Den fråga som ställs i denna studie är vilka möjligheter som finns att lära i arbetet, sett ur lärares perspektiv. En annan fråga som också ställs är hur eller om lärare i högre utbildning kan eller har möjlighet att utveckla sin praktiska klokhet, praxis i Aristotelisk mening. Samtal med kollegor inom högre utbildning som undervisar i olika ämnen i lärarprogram, utgör empiri. Resultaten visar att frågor som prioriteras är hur studenter ska stöttas, stimuleras och erbjudas varierad undervisning. Studenternas lärande är i fokus. Resultatet visar också att få undervisande lärare förstår frågan om hur de lär i arbetet. Att de lär i arbetet framkommer dock i deras berättelser om vad som influerar dem att utveckla undervisning, uppgifter eller kurser. En preliminär analys är att det behövs tid för att medvetandegöra varför man gör som man gör. Metoder för att lära i arbete är bland andra att få diskutera med och att få frågor av kollegor. En tidig slutsats som kan dras är att fokus på studenter bidrar till att medvetenhet om det egna lärandet hamnar i skymundan.

Lärare inom högre utbildning förväntas ha studenters lärande i fokus. Hur studenter lär, vad som stimulerar deras lärande och kunskapande är frågor som lärare bör och ska ställa sig. Andra förväntningar som finns är att utveckla och utvärdera kurser och program, och att lärare själva ska lära sig. Den fråga som ställs i denna studie är vilka möjligheter som finns att lära i arbetet, sett ur lärares perspektiv. En annan fråga som också ställs är hur eller om lärare i högre utbildning kan eller har möjlighet att utveckla sin praktiska klokhet, praxis. Samtal med kollegor inom högre utbildning som undervisar i olika ämnen i lärarprogram, utgör empiri. Resultaten visar att frågor som prioriteras är hur studenter ska stöttas, stimuleras och erbjudas varierad undervisning. Studenternas lärande är i fokus. Resultatet visar också att få undervisande lärare förstår frågan om hur de lär i arbetet. Att de lär i arbetet framkommer dock i deras berättelser om vad som influerar dem att utveckla undervisning, uppgifter eller kurser. I analysen används Aristoteles begrepp praxis (Gustavsson, 2000) samt de delar som Kemmis och Smith (2008) menar stöttar sociala, kulturella och materiella villkor så att det är möjligt för individen att agera. En preliminär analys är att det behövs tid för att medvetandegöra varför man gör som man gör. Metoder för att lära i arbete är bland andra att få diskutera med och att få frågor av kollegor. En tidig slutsats som kan dras är att fokus på studenter bidrar till att medvetenhet om det egna lärandet hamnar i skymundan.

Referenser

Gustavsson, B. (2000). Kunskapsfilosofi. Tre former i historisk belysning. Stockholm: Wahlström & Wistrand.

Kemmis, S., & Smith, T. (2008). Enabeling praxis. Challenges för Education. Rotterdam: Sense Publications.

Distanshandledning av kandidatuppsatser har ökat. Från att enbart ha infogat kommentarer i dokumentet till att lägga till färgmarkeringar har jag provat att använda Kaltura Video för återkoppling. Mina erfarenheter av denna nya arbetsmetod är bland andra tidsbesparing och studenter upplever en tydligare återkoppling, med mindre risk för missförstånd.

Den här presentationen handlar om reflektion och lärande i universitetslärares arbete, med fokus på relationen mellan vad vi som universitetslärares tänker och planerar och vad vi sedan faktiskt gör. Med detta vill vi dels teoretisera den egna erfarenheten, dels utveckla vår praktik, som ett led i ett professionellt förhållningssätt som universitetslärare. Vi vill också bidra till en kollegial diskussion kring vårt arbete som universitetslärare.

Vi är båda lärare och forskare i ämnet pedagogik och har omfattande kunskaper om lärande och om vad som krävs för att skapa goda lärmiljöer. Vi har dock en misstanke om att vi inte alltid efterlever våra kunskaper och ideal i handling i mötet med studenter. En del av syftet med presentationen är att analysera våra egna, ofta omedvetna, ideal och förgivettaganden som lärare i högre utbildning samt att reflektera över på vilka sätt det påverkar oss som lärare, inspirerade av ex Gibson (1998) och Leitch & Day (2000).

Det empiriska materialet består av exempel hämtade från vår egen erfarenhet. De belysande exempel vi valt att använda oss av i den här texten har vi bearbetat med en form av aktionsforskning som kan kallas introspektiv reflektion. Metoden går i korthet ut på att använda sina egna erfarenheter som empiri, och behandla det genom teoretisk reflektion för att skapa ny kunskap. Genom att hantera den introspektiva reflektionen gemensamt och analysera med begrepp som lyfter från det individuella, ägnar vi oss inte bara åt subjektiv reflektion utan också kollegial reflektion.

För att analysera våra erfarenheter använder vi teorierna om den reflekterande praktikern samt om transformativt lärande. Den reflekterande praktikern (Schön, 1983) har under flera årtionden använts inom aktionsforskning kring lärares arbete i skolan. Avsikten är att skapa nya former av kunskap och utveckling av praktiken, genom att lyfta reflektion som ett professionellt redskap (se t ex Goodson & Hargreaves, 1996; Meierdirk, 2016; Brookfield, 2017). Centrala begrepp är reflektion-i-handling och reflektion-över-handling. Det transformativa lärandet handlar om de processer i vilka en person skiftar perspektiv och på så vis ändrar sitt handlande, sina förgivettaganden och föreställningar om sig själv och världen (Mezirow, 2000; Wilhelmson, 1998). Ett transformativt lärande innebär att kritiskt granska både inåt och utåt. En inre kritisk granskning är att få fatt de i de egna föreställningar och yttre kritisk granskning är att vara kritisk till de ämnesspecifika kunskaperna som ska förmedlas i undervisning (Wilhelmson, 1998).

Att tänka nytt kring den egna praktiken, att göra nytt, reflektera i handling på nya sätt ser vi som professionella redskap. Vi vill också lyfta vikten av reflektion-över-handling tillsammans med kollegor. Kollektivet behövs för både inre och yttre kritisk reflektion, så att lärande som transformation möjliggörs. Slutligen menar vi att det här angreppssättet kan vara ett redskap för att tillämpa ett vetenskapligt förhållningssätt i den egna praktiken.

Referenser

Brookfield, Stephen (2017). Becoming a critically reflective teacher. San Francisco: Jossey-Bass Inc.

Gibson, Linda S. (1998). Teaching as an encounter with the self: Unraveling the mix of personal beliefs, education ideologies, and pedagogical practices. Anthropology & education quarterly, 29 (3), pp 360-371.

Goodson, Ivor & Hargreaves, Andy (1996). Teachers’ Professional Lives. London: Falmer Press.

Leitch, Ruth, & Day, Christopher (2000). Action research and reflective practice: Towards a holistic view. Educational Action Research, 8 (1), pp 179-193.

Meierdirk, Charlotte (2016). Is reflective practice an essential component of becoming a professional teacher?. Reflective Practice, 17 (3), pp 369-378.

Mezirow, Jack (2000). Learning as transformation. Critical perspectives on a theory in progress. San Francisco: Jossey-Bass Inc.

Schön, Donald (1983). The reflective practitioner. How professionals think in action. New York: Basic Books.

Wilhelmson, Lena (1998). Lärande dialog. Samtalsmönster, perspektivförändring och lärande i gruppsamtal. Arbete och hälsa, vetenskaplig skriftserie, 1998:16.

Syftet med den här artikeln är att rikta ljuset mot vår egen praktik som universitetslärare, att analysera våra egna, ofta omedvetetna, idela och förgivettaganden samt att reflketera över på vilka sätt det påverkar undervisningssituationen. Vi vill också bidra med kunskap till det högskolepedagogiska fältet. Empirin består av exempel från vår egen undervisningserfarenhet, och vi analyserar dem med hjälp av begreppen reflektion-i-handling och reflektion-över-handling, samt transformativt lärande. 

The primary focus of this presentation is to gain a deeper understanding of teachers’ perspectives on how to promote children’s writing development in the Swedish preschool class. The research questions are: According to teachers, in which contexts during day-to-day teaching activities are children stimulated and challenged to write? How do teachers describe their support of children’s writing development?

Since the introduction in 1998 of the preschool class, its lack of equivalence in teaching, its lack of clear guidelines on the teaching purpose, its content and its status as a voluntary school form has been discussed and criticized both in research and in politics (Sandberg, 2012). I July 2016 new sections were introduced in the curriculum for preschool class and from July, 1st 2018 it is mandatory for all six-year-olds to attend preschool class.

The theoretical approach is based on Vygotsky’s (1978) sociocultural perspective about learning and development. Centrally within the sociocultural perspective is that human beings acquire knowledge by participating in various activities in interaction with others. Together with a more competent person the child can solve a task and complete a skill that it is not yet capable of its own. According to Wood, Bruner and Ross (1976), scaffolding can be described as a temporary support structure for a child’s learning process that with time becomes unnecessary.

The study is based on a qualitative approach through interviews with twelve teachers working in preschool class in seven different municipalities in Sweden. These semi-structured interviews were characterised by being based on a number of predetermined themes: background questions, writing activities during the week, artefacts in the learning environment, documented in an interview guide. The transcribed interviews were thematically analysed (Braun & Clark, 2006). The data were organised into two themes; Writing and Support.

The result shows mainly two different views of how to develop children´s writing. One approach places great weight on working to develop creative and functional writing. The other approach is primarily characterised by working on technical skills and developing the child’s phonological awareness. Teachers utilise various support strategies to develop children’s writing skills which can be divided into high-level and low-level skills (Bingham, Quinn and Gerde, 2017). But there are teachers that do not have awareness of how to support children and how to develop their writing through different writing activities; this can be explained by a lack of knowledge regarding how literacy develops.

The results of this study contributes to reflection and discussion regarding approaches and didactic strategies that need to be developed in preschool class to support children’s early writing.

Bingham, G. E., Quinn, M. F., & Gerde, H. K. (2017). Examining early childhood teacher’s writing practices: Associations between pedagogical supports and children´s writing skills. Early Childhood Research Quarterly, 39, 35-46.

Braun, V., & Clark, V. (2006). Using thematic analysis in psychology. Qualitative Research in Psychology, 3(2), 77-101.

Sandberg, G. (2012). På väg in i skolan om villkor för olika barns delaktighet och skriftspråkslärande. Diss Uppsala: Uppsala University.

Vygotsky, L. S. (1978). Mind in society. The development of higher psychological processes. London: Harvard University Press.

Syftet med kapitlet är att fördjupa förståelsen av lärares perspektiv på barns skriftspråksutveckling i förskoleklass. Studiens teoretiska utgångspunkter är inspirerade av Vygotsky och Bruners tankar kring lärande och dess betydelse för barns läs- och skrivutvecklingen. Studien är kvalitativ med en latent innehållsanalys av fokusgruppsamtal som genomförts med 18 lärare som arbetar i förskoleklass och grundskolans tidiga år. Resultaten visar att det förekommer fyra temaområden; introduktion av formellt skriftspråk; läsaktiviteter; skrivaktiviteter och kartläggning vad gäller det pedagogiska innehållet och i vilka sammanhang barn får erfara olika skriftspråksaktiviteter.