Joint Mission or Mission Impossible? : Exploring Conditions for Itinerant Early Childhood Special Education Teachers’ Work

This thesis aims to examine what conditions enable or constrain itinerant early childhood special education teachers (ECSETs) work with providing support for children with special educational needs in Finnish early childhood education and care (ECEC) in settings where Swedish is the medium of instruction in Finland. An itinerant ECSET provides support to several different ECEC settings in a municipality. This means that itinerant ECSETs, compared to ECSETs working in a group, face different challenges due to their working conditions. These working conditions were explored in this thesis by focusing on what frames and constitutes the work and role for itinerant ECSETs, what kind of support is offered to children in ECEC and what views and strategies ECSETs use during consultation. The phenomenon studied is complex and difficult to untangle. To grasp all aspects intertwined, the frame factor theory, in combination with the theory of professions, is used. The frame factor theory constitutes the basis for studying conditions at different levels that might affect the work of ECSETs. Furthermore, the frame factor theory needs to be completed with the system of professions for being able to study the profession itself since frame factor theory does not provide the possibility to do so. Itinerant ECSETs are in focus in three of the included articles, and in one article, personnel working in ECEC are in focus. Data were collected through questionnaires and interviews. The study is a mixed-methods study with an explanatory sequential design, meaning that quantitative data collection is followed by a phase of qualitative data collection. The data are comprehensive, and several methods are used to analyse the data. The methods used in Study 1 and Study 2 comprise predominantly descriptive statistics, with an additional qualitatively oriented content analysis in Study 2. Studies 3 and 4 are characterised by a qualitative approach, where Study 3 comprises thematic analysis and Study 4 uses crosscase analysis. The results compiled from the present study show that conditions for ECSETs are challenging in various ways and on different levels. On a legal level, the foundation for ECEC and children’s right to support is emphasised; there is a unified support system for children in need of special educational support participating in ECEC. The foundation might be there on a legal level, but the present study indicates that there are many challenges for ECSETs on an organisational level; the premises for doing their work do not always align with the vision on the legal level. In the synthesis of the results, inhibitors and facilitators for the provision of support are discussed in relation to ECSET jurisdiction, namely how ECSETs claim legitimacy for, or control of, their work. The results show that there are inhibitors in the work environment that complicate ECSETs’ work and weaken their jurisdiction. Inhibitors in the present study are ECSETs’ diminished work role, insufficient resources and nonengaged personnel. In contrast to these inhibitors, there are also facilitators that support ECSETs in implementing support in ECEC. The facilitators for support provision are collaboration, supportive leaders and environment, and autonomy and flexibility. When these circumstances coincide, support provision for children with special educational needs becomes a joint mission.Denna avhandling syftar till att undersöka vilka villkor som möjliggör eller begränsar ambulerande speciallärares möjligheter att erbjuda stöd till barn i behov av stöd som deltar i småbarnspedagogik eller i förskoleundervisning i finlandssvensk kontext. Ambulerande speciallärare inom småbarnspedagogik ansvarar för att barn inom småbarnspedagogik eller i förskoleundervisning i en kommun får det stöd som de har rätt till. Ambulerande speciallärare ställs på grund av deras arbetsförhållande inför andra utmaningar än de speciallärare som arbetar i en grupp. Möjliggörande och begränsande faktorer relaterade till ambulerande speciallärares arbetsförutsättningar samt hur dessa påverkar deras befogenhet att genomföra sitt arbete undersöks via följande forskningsfrågor: Vad ramar in och utgör arbetet och rollen för ambulerande speciallärare inom småbarnspedagogik? Vilken typ av stöd erbjuds barn med språkliga utmaningar och vilka strategier använder ambulerande speciallärare sig av under konsultation? Fenomenet som studeras är komplext och består av flera aspekter som är sammanflätade eller beroende av varandra. För att försöka få grepp om både yttre och inre aspekter som påverkar arbetet används ramfaktorteorin. Som komplement till ramfaktorteorin används professionsteorin för att studera speciallärarnas grad av befogenhet att genomföra arbetet. Ambulerande speciallärare är i fokus i tre av de inkluderade artiklarna, medan det är personalen som arbetar inom småbarnspedagogik eller i förskoleundervisning som står i fokus i den fjärde artikeln. Data till de fyra studierna har samlats in genom frågeformulär och intervjuer. Denna studie är en mixed-methods studie där de första kvantitativa datainsamlingarna efterföljts av en fas av kvalitativ datainsamling. Data är till sin karaktär omfattande och flera metoder används för att analysera data. Metoderna som används i Studie 1 och Studie 2 omfattar övervägande deskriptiv statistik, men delar av data för Studie 2 analyseras med en kvalitativt orienterad innehållsanalys. Studie 3 och Studie 4 kännetecknas av ett kvalitativt angreppssätt, där Studie 3 är en tematisk analys medan Studie 4 är en jämförande fallstudie. Resultaten från denna studie visar att förutsättningarna för speciallärare är utmanande på olika sätt och på olika nivåer. På en juridisk nivå betonas grunden för småbarnspedagogik och barns rätt till stöd. Det finns numera ett enhetligt stödsystem för barn i behov av specialpedagogiskt stöd. Trots att grunden för arbetet finns på en juridisk nivå, visar den föreliggande studien att det finns många utmaningar för speciallärare på en organisatorisk nivå. Premisserna för att speciallärarna ska kunna utföra sitt arbete överensstämmer inte alltid med visionen på det juridiska planet. I syntesen av resultaten diskuteras begränsande och möjliggörande aspekter i speciallärarens arbete. Denna diskussion kopplas till speciallärarnas jurisdiktion, det vill säga vilken befogenhet och kontroll de har över sitt arbetsområde. Resultatet visar att det finns begränsande faktorer i arbetsmiljön som komplicerar speciallärares arbete och försvagar deras jurisdiktion. Barriärer som framkommer i denna studie är speciallärares förminskade arbetsroll, otillräckliga resurser och icke-engagerad personal. I motsats till hinder finns det också möjliggörare som stödjer speciallärare att implementera stöd inom småbarnspedagogiken. Möjliggörare för tillhandahållande av stöd är samarbete, stödjande ledare och omgivning samt autonomi och flexibilitet. När dessa omständigheter sammanfaller blir stöd till barn med särskilda utbildningsbehov ett gemensamt uppdrag

On a nonconvolution Volterra resolvent

AbstractUnder fairly weak assumptions, the solutions of the system of Volterra equations x(t) = ∝0ta(t, s) x(s) ds + f(t), t > 0, can be written in the form x(t) = f(t) + ∝0tr(t, s) f(s) ds, t > 0, where r is the resolvent of a, i.e., the solution of the equation r(t, s) = a(t, s) + ∝0ta(t, v) r(v, s)dv, 0 < s < t. Conditions on a are given which imply that the resolvent operator f ∝0t r(t, s) f(s) ds maps a weighted L1 space continuously into another weighted L1 space, and a weighted L∞ space into another weighted L∞ space. Our main theorem is used to study the asymptotic behavior of two differential delay equations

A bound on the solutions of a nonlinear volterra equation

AbstractWe study the scalar, nonlinear Volterra integrodifferential equation (∗), x′(t) + ∫[0,t] g(x(t − s)) dμ(s) = f(t) (t ⩾ 0). We let g be continuous, μ positive definite, and f integrable over (0, ∞). The standard assumption on g which yields boundedness of the solutions of (∗) prevents g(x) from growing faster than an exponential as x → ∞. Here we present a weaker condition on g, which does not restrict the growth rate of g(x) as x → ∞, but which still implies that the solutions of (∗) are bounded. In particular, when g is nondecreasing and either nonnegative or odd, we get bounds which are independent of g

De Branges-Rovnyak realizations of operator-valued Schur functions on the complex right half-plane

We give a controllable energy-preserving and an observable co-energy-preserving de Branges-Rovnyak functional model realization of an arbitrary given operator Schur function defined on the complex right-half plane. We work the theory out fully in the right-half plane, without using results for the disk case, in order to expose the technical details of continuous-time systems theory. At the end of the article, we make explicit the connection to the corresponding classical de Branges-Rovnyak realizations for Schur functions on the complex unit disk.Comment: 68 pages: General polishing; no essential change

Mission impossible? Finnish itinerant early childhood special education teachers’ views of their work and working conditions

ABSTRACT: Providing support to children in their younger years is prominent in Finnish early childhood education and care (ECEC), as most children need some form of support for learning and development during this stage. Itinerant early childhood special education teachers (ECSETs) are important resources in providing support to children with special educational needs (SEN). Previous research in Finland addresses areas where itinerant ECSETs predominantly work in contexts where Finnish is the medium of instruction. Therefore, it is of interest to examine itinerant ECSETs' views of elements affecting their work with supporting children with SEN in Swedish-medium ECEC settings. This research is explorative to its character and data was collected through a questionnaire sent to all itinerant ECSETs working in Swedish-speaking regions of Finland. Descriptive statistics were used to depict the work conditions for ECSETs'. The results show that ECSETs own professional ambition and children’s support needs affect the work the most. Furthermore, inequality in ECSETs working conditions have direct consequences for practice. This study concludes with a discussion of how ECSETs' working conditions influence the support that children receive and areas that should be addressed to ensure equal and efficient learning for all children

Spectral Decomposition and Invariant Manifolds for Some Functional Partial Differential Equations

AbstractWe study the integrodifferential convolution equationddt(x+μ∗x)−Ax−ν∗x=fon [0, +∞),x=φon (−∞, 0],as well as a nonlinear perturbation of the corresponding homogeneous equation. HereAis the generator of an analytic semigroup on a Hilbert spaceH, andμandνare operator-valued dominated measures with values inL(H) andL(D(A), H) respectively. Under the assumption that the operator given by the Laplace transform of the left-hand side of the equation is boundedly invertible on some right half-plane and on a line in the left half-plane, parallel to the imaginary axis, we decompose the solutions into components with different exponential growth rates. We construct projectors onto the stable and unstable subspaces, which are then used for the construction of stable and unstable manifolds for the nonlinear equation, which can have a fully nonlinear character. The results are applied to two equations of parabolic type. Moreover, the spectrum of the generator of the translation semigroup in various weighted spaces is determined, including the stable and unstable subspaces of our problem

Weak admissibility does not imply admissibility for analytic semigroups

Two conjectures on admissible control operators by George Weiss are disproved in this paper. One conjecture says that an operator $B$ defined on an infinite-dimensional Hilbert space $U$ is an admissible control operator if for every element $u \in U$ the vector $Bu$ defines an admissible control operator. The other conjecture says that $B$ is an admissible control operator if a certain resolvent estimate is satisfied. The examples given in this paper show that even for analytic semigroups the conjectures do not hold. In the last section we construct a semigroup example showing that the first estimate in the Hille-Yosida theorem is not sufficient to conclude boundedness of the semigroup

Coprime factorization and optimal control on the doubly infinite discrete time axis

We study the problem of strongly coprime factorization over H-infinity of the unit disc. We give a necessary and sufficient condition for the existence of such a coprime factorization in terms of an optimal control problem over the doubly infinite discrete-time axis. In particular, we show that an equivalent condition for the existence of such a coprime factorization is that both the control and filter algebraic Riccati equation (of an arbitrary realization) have a solution (in general unbounded and even non densely defined) and that a coupling condition involving these solutions is satisfied