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- Bergqvist, Tomas, 1962-
(författare)
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To explore and verify in mathematics
- 2001
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This dissertation consists of four articles and a summary. The main focus of the studies is students' explorations in upper secondary school mathematics. In the first study the central research question was to find out if the students could learn something difficult by using the graphing calculator. The students were working with questions connected to factorisation of quadratic polynomials, and the factor theorem. The results indicate that the students got a better understanding for the factor theorem, and for the connection between graphical and algebraical representations. The second study focused on a the last part of an investigation, the verification of an idea or a conjecture. Students were given three conjectures and asked to decide if they were true or false, and also to explain why the conjectures were true or false. In this study I found that the students wanted to use rather abstract mathematics in order to verify the conjectures. Since the results from the second study disagreed with other research in similar situations, I wanted to see what Swedish teachers had to say of the students' ways to verify the conjectures. The third study is an interview study where some teachers were asked what expectations they had on students who were supposed to verify the three conjectures from the second study. The teachers were also confronted with examples from my second study, and asked to comment on how the students performed. The results indicate that teachers tend to underestimate students' mathematical reasoning. A central focus to all my three studies is explorations in mathematics. My fourth study, a revised version of a pilot study performed 1998, concerns exactly that: how students in upper secondary school explore a mathematical concept. The results indicate that the students are able to perform explorations in mathematics, and that the graphing calculator has a potential as a pedagogical aid, it can be a support for the students' mathematical reasoning.
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- Bjerneby Häll, Maria
(författare)
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Varför undervisning i matematik? : argument för matematik i grundskolan - i läroplaner, läroplansdebatt och hos blivande lärare
- 2002
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The aim of this study is to investigate, describe and analyse the justification and the goals of mathematics education in compulsory school in Sweden. The focus here is on student teachers and their conceptions of why mathematics should be taught in school.A qualitative approach has been used and data (short texts) have been collected from five cohorts of student teachers during their first and second year of education respectively. The data were interpreted on a conceptual level, in the descriptions of arguments for mathematics. A study of curriculum texts and debates has served the purpose as background and context related to the arguments presented by the student teachers.The outcome of the analysis of the student teachers' texts resulted in ten basic arguments for school mathematics. The main arguments are of either functional or formal character.
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- Cronquist, Eva, 1959-
(författare)
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Spelet kan börja : Om vad en bildlärarutbildning på samtidskonstens grund kan erbjuda av transformativt lärande
- 2015
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- To enter higher education means making new experiences and develop newunderstanding within a knowledge field. The situation could also entail, for thestudent, an entirely different self-understanding. This licentiate thesis deals withthis kind of learning process.The overall aim of this licentiate thesis is to analyze what an art teachers education,founded on contemporary conceptual art, can offer in terms of transformativelearning. The point of departure is adults learning processes as renegotiations ofprevious interpretations which can be transformed to new understanding. The studyanalyzes what aspects of transformative learning are reflected in students' texts andimages, produced as part of the studied course. The licentiate thesis also discussespossibilities and constraints of this learning process. The study was conducted as acase study based on a hermeneutic approach. Material was collected from thecourse blog which consisted of students' texts and images.The study results show a transformative learning process which students experiencedas emotionally tumultuous because their self-image, as future art teachers, isrenegotiated. The situation contains a dimension of learning which I call "twistingand turning" in which new understanding is being formed. This situation requires aself-reflexive creative approach. The result generates questions about therelationship between the content of the education (what) and the learner (who) in anart teachers education founded on a non-traditional base. This applies above all ineducations that challenge students' prior understanding of a field. One could alsoask how adult learning is staged as relearning in higher education. The studydevelops a concept of reflexive creativity which contains a more abstract level thanjust problem solving. The idea of reflexive turn in art education, based onconceptually contemporary art, is also discussed.
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- Gadde, Erland
(författare)
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Stable iterated function systems
- 1992
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The purpose of this thesis is to generalize the growing theory of iterated function systems (IFSs). Earlier, hyperbolic IFSs with finitely many functions have been studied extensively. Also, hyperbolic IFSs with infinitely many functions have been studied. In this thesis, more general IFSs are studied.The Hausdorff pseudometric is studied. This is a generalization of the Hausdorff metric. Wide and narrow limit sets are studied. These are two types of limits of sequences of sets in a complete pseudometric space.Stable Iterated Function Systems, a kind of generalization of hyperbolic IFSs, are defined. Some different, but closely related, types of stability for the IFSs are considered. It is proved that the IFSs with the most general type of stability have unique attractors. Also, invariant sets, addressing, and periodic points for stable IFSs are studied.Hutchinson’s metric (also called Vaserhstein’s metric) is generalized from being defined on a space of probability measures, into a class of norms, the £-norms, on a space of real measures (on certain metric spaces). Under rather general conditions, it is proved that these norms, when they are restricted to positive measures, give rise to complete metric spaces with the metric topology coinciding with the weak*-topology.Then, IFSs with probabilities (IFSPs) are studied, in particular, stable IFSPs. The £-norm-results are used to prove that, as in the case of hyperbolic IFSPs, IFSPs with the most general kind of stability have unique invariant measures. These measures are ”attractive”. Also, an invariant measure is constructed by first ”lifting” the IFSP to the code space. Finally, it is proved that the Random Iteration Algorithm in a sense will ”work” for some stable IFSPs.
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- Rodhe, Staffan, 1946-
(författare)
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Matematikens utveckling i Sverige fram till 1731
- 2002
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis contains two parts:In the first papers I consider the development of mathematics up till around 1720. I have done a special study of the period between 1710 and 1720, when you could find three Swedes writing about contemporary mathematics, Christopher Polhem, Emanuel Swedenborg and Anders Gabriel Duhre. Especially Duhre has been of interest in his writings about series.The second part of the thesis deals with the first Swedish internationally well-known mathematician Samuel Klingenstierna. The study of his life and mathematics finishes with his arrival back to Sweden after his long travel to the centers of science in Europe. There are lots of new facts added to his biography during that period. Klingenstierna was involved in the actual mathematical discussions between Johann and Nicholaus Bernoulli, Fontenelle, Clairaut, Cramer and Stirling. I present the contents of some of Klingenstierna's manuscripts, which he wrote in Basel, Paris and London, for instance a problem of calculus of variation, a formula of the circumference of an ellipse and a formula to get a good approximation for the number π.
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