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  • Public defence: 2020-01-23 09:15 Weber, Växjö
    Ebbelind, Andreas
    Linnaeus University, Faculty of Technology, Department of Mathematics. Linnaeus University.
    Becoming recognised as mathematically proficient: The role of a primary school teacher education programme2020Doctoral thesis, monograph (Other academic)
    Abstract [en]

    This study focuses on upper primary prospective teachers in their first years of a teacher education programme in Sweden, in particular, a 20-week mathematics education course. It aims to contribute with insight into how, or even if, experience from a teacher education programme and other relevant past and present social practices and figured worlds plays a role in prospective generalist teachers’ imaginings of themselves as primary mathematics teachers-to-be and potentially shapes their identity. The theoretical perspective, Patterns of Participation, guides the logic and the research process and is used to interpret the construct of professional identity development. Ethnographic methods were crucial during the research process, which starts by taking a wide perspective on relevant social practices and then focuses exclusively on the everyday lives of prospective teachers.

    This study adds to the understanding of how the similarities in the discursive patterns of two prospective teachers, Evie and Lisa, frame their processes as teachers-to-be by staying committed to their prior positive experiences of mathematics. The figured world of performative mathematics is a significant aspect of Evie’s and Lisa’s experience, which involves being recognised for mathematical ability. Evie’s identity development is framed in relation to how her degree of certainty changes during her teacher education experience. She became recognised as someone who helps others in mathematics and found a way of performing this role during the teacher education programme. Lisa’s identity development is framed in relation to her commitment to the figured world of performative mathematics. She became recognised as a winner of competitions and for quickly completing the textbook exercises – experiences that proved formative during her teacher education programme.

    In this study, I conclude that the teacher education programme has an impact regarding prospective teachers’ professional development, but perhaps not in the way teacher educators expect or want. Thus, the teacher educators’ intention for the education programme differs from the result. An important aspect is that prospective teachers are not challenged first and foremost by encountering the theoretical perspectives involved in teaching mathematics. Instead, their prior experience is confirmed when used as a key source in determining what teaching mathematics means in terms of identity.

  • Public defence: 2020-01-31 13:15 Sal Myrdal, Växjö
    Muhr, Anneli
    Linnaeus University, Faculty of Social Sciences, Department of Social Work.
    Andra generationens unga företagare med utländsk bakgrund: En förståelse av det egna företagandet utifrån social position2020Doctoral thesis, monograph (Other academic)
    Abstract [en]

    This dissertation is about young second-generation immigrants who choose to become entrepreneurs. In a qualitative interview study, 22 young individuals’ choices and trajectories as entrepreneurs were examined. The aim of the dissertation was to understand how these young entrepreneurs, based on their social position, motivated their choices and trajectories into working life as business owners. The results of the study show how the young entrepreneurs act based on their social position, in which both structural and intergenerational factors have significance for their choices. Furthermore, variations are clarified in the individuals’ motives and trajectories as young entrepreneurs, which can be understood against the backdrop of various social positions. Three patterns have crystallised from the young entrepreneurs’ stories: the “follower” – the early entrepreneur with a strong tradition of business in their family, the “climber” – the later and strategic young entrepreneur who also has a strong tradition of business, and finally the “stopover” – who does not have a tradition of business in their family. But the most prominent pattern is the “early and horizontal business trajectory”. This trajectory does not represent the typical highly educated springboard examples, which are normally highlighted in previous research. Instead it represents a “new category” which includes young people who come from less highly educated business environments, and who largely follow in the footsteps of their parents and relatives and continues to work in typical trade- and service branches. For this category, it is more likely the individuals’ lack of education, rather than strong education, that drives them to become entrepreneurs. The young people in this category leave school early and start their own businesses. Central to this is how the young people continue to work in the increasingly uncertain and informal labour market, in which relatively strenuous living patterns are passed on through generations, and where the young people partially fall outside the public welfare systems.

  • Public defence: 2020-02-06 14:00 Weber, Växjö
    Nordqvist, Jonas
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Residue fixed point index and wildly ramified power series2020Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    This thesis concerns discrete dynamical systems. These are systems where the dynamics is modeled by iterated functions. There are several applications of discrete dynamical system e.g. in biology, pseudo random number generation and statistical mechanics. In this thesis we are interested in discrete dynamical systems described by iterations of a power series f fixing the origin, where it is tangent to the identity. In particular, the coefficients of f are given in a field of positive characteristic p. We are interested in the so-called lower ramification numbers of such series. The lower ramification numbers encodes the multiplicity of the origin as a fixed point of f under p-power iterates. In particular this thesis contains four papers all related to the topic of lower ramification numbers of such power series.

    In Paper I we consider so-called 2-ramified power series and give a characterization of such in terms of its first significant terms. This is further extended in Paper II, where we geometrically locate the periodic points of 2-ramified power series in the open unit disk. In doing, so we provide a self-contained proof of the main result of the first paper.

    In Paper III, we consider power series with a fixed point at the origin of small multiplicity, i.e. the multiplicity of the fixed point is less than that of the characteristic of the ground field. We provide a characterization of all such power series having the smallest possible lower ramification numbers, in terms of its first significant terms, and in terms of the nonvanishing of the so-called iterative residue. In doing so, we also provide a formula for the residue fixed point index for the case of a multiple fixed point. We further extend the results of Paper II by locating geometrically the periodic points in the open unit disk of convergent power series with small multiplicity.

    In Paper IV we consider power series of large multiplicity, and introduce an invariant in positive characteristic closely related to the residue fixed point index. We provide a characterization of these power series having the smallest possible lower ramification numbers in terms of the nonvanishing of this invariant. As a by-product we obtain results about the dimension of the moduli space of formal classification of wildly ramified power series.