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  • 1.
    Bartolini Bussi, M G
    et al.
    Universita' di Modena e Reggio Emilia, Modena, Itlay.
    Gade, Sharada
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    Janvier, M
    Kahane, J-P
    Matsko, V
    Maschietto, M
    Ouvrier-Buffet, C
    Saul, M
    Mathematics in context: focusing on students2009In: Challenging Mathematics In and Beyond the Classroom – The 16th ICMI Study / [ed] E. J. Barbeau and P. J. Taylor, New York: Springer Science+Business Media B.V., 2009, p. 171-203Chapter in book (Refereed)
    Abstract [en]

    This chapter presents nine case studies in which school students engage in challenging mathematics outside their immediate classroom environment. In each case, students are encouraged to collaborate in investigations that go beyond the standard curriculum and creatively use the ingredients of the particular context. In Italy, students visit a mathematical laboratory to understand and utilize mathematical machines. Morning assembly at an Indian school brings students from many classes together in the solution of mathematical problems. Four of the projects are from France: students analyze the configuration of a heap of sand, pursue astronomical investigations with software, obtain a flavor of research by having secondary school teams investigate interesting problems, and are presented at all levels with open-ended research problems. There are three programs from the United States, the first, an advanced geometry sequence for secondary students completing the regular syllabus early, the second, activities arising from exhibits in an art museum, and the third, using the school lawn to deepen student understanding of geometric constructions. All such activities need to be evaluated for their effectiveness, so that they move from just being initiatives of dynamic individuals to serve as the foundation for systemic improvements in the way in which students learn, understand and use mathematics. In the early part of this chapter, we briefly mention how research into such activities might be approached.

  • 2.
    Bergqvist, Ewa
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    A verbal factor in the PISA 2003 mathematics items: Tentative analyses2009In: Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education: In Search for Theories in Mathematics Education, Thessaloniki, Greece: PME , 2009, p. 145-152Conference paper (Refereed)
    Abstract [en]

    This study uses a statistical method to identify verbal items among mathematical items from PISA 2003. The verbal items are preliminary analysed and compared to the non-verbal items concerning number of text lines, response types, cognitive level, and competences measured. The results show that the verbal items, to a higher percentage than the non-verbal items, measures the reproduction competency, are straigh­t­forward, and of open constructed-response type. These results and proposed further analyses are discussed.

  • 3.
    Bergqvist, Ewa
    et al.
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    Dyrvold, Anneli
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Österholm, Magnus
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    Relating vocabulary in mathematical tasks to aspects of reading and solving2012In: Evaluation and comparison of mathematical achievement: Dimensions and perspectives. Proceedings of MADIF 8, The Eighth Mathematics Education Research Seminar, Umeå, January 24-25, 2012 / [ed] Christer Bergsten, Eva Jablonka & Manya Raman, Linköping: SMDF , 2012, p. 61-70Conference paper (Refereed)
    Abstract [en]

    This paper focuses on relationships between vocabulary in mathematical tasks and aspects of reading and solving these tasks. The paper contains a framework that highlights a number of different aspects of word difficulty as well as many issues to consider when planning and implementing empirical studies concerning vocabulary in tasks, where the aspect of common/uncommon words is one important part. The paper also presents an empirical method where corpora are used to investigate issues of vocabulary in mathematical tasks. The results from the empirical study show that there are connections between different types of vocabulary and task difficulty, but that they seem to be mainly an effect of the total number of words in a task.

  • 4.
    Bergqvist, Ewa
    et al.
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    Theens, Frithjof
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    Österholm, Magnus
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    Relations between linguistic features and difficulty of PISA tasks in different languages2016In: Proceedings of the 40th Conference of the International Group for the Psychology of Mathematics Education / [ed] Csíkos, C., Rausch, A., & Szitányi, J., Szeged, Hungary: PME , 2016, Vol. 1, p. 125-125Conference paper (Refereed)
  • 5.
    Bergqvist, Ewa
    et al.
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Österholm, Magnus
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    A theoretical model of the connection between the process of reading and the process of solving mathematical tasks2010In: Mathematics and mathematics education: Cultural and social dimensions. Proceedings of MADIF 7 / [ed] C. Bergsten, E. Jablonka & T. Wedege, Linköping, Sweden: Svensk förening för matematikdidaktisk forskning, SMDF , 2010, p. 47-57Conference paper (Refereed)
    Abstract [en]

    In this paper we suggest a theoretical model of the connection between the process of reading and the process of solving mathematical tasks. The model takes into consideration different types of previous research about the relationship between reading and solving mathematical tasks, including research about traits of mathematical tasks (a linguistic perspective), about the reading process (a psychological perspective), and about behavior and reasoning when solving tasks (a mathematics education perspective). In contrast to other models, our model is not linear but cyclic, and considers behavior such as re-reading the task.

  • 6.
    Bergqvist, Ewa
    et al.
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    Österholm, Magnus
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. Monash University, Australia.
    Communicating mathematics or mathematical communication?: An analysis of competence frameworks2012In: Proceedings of the 36th Conference of the International Group for the Psychology of Mathematics Education: Vol. 2: opportunities to learn in mathematics education / [ed] Tai-Yih Tso, 2012, p. 67-74Conference paper (Refereed)
    Abstract [en]

    In this study we analyse the communication competence included in two different frameworks of mathematical knowledge. The main purpose is to find out if mathematical communication is primarily described as communication of or about mathematics or if it is (also) described as a special type of communication. The results show that aspects of mathematics are mostly included as the content of communication in the frameworks but the use of different forms of representation is highlighted both in the frameworks and also in prior research as a potential cause for characterising mathematical communication differently than "ordinary" communication.

  • 7.
    Bergqvist, Ewa
    et al.
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    Österholm, Magnus
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    Språkbrukets roll i matematikundervisningen2014In: Nämnaren : tidskrift för matematikundervisning, ISSN 0348-2723, Vol. 2014, no 1, p. 27-31Article in journal (Other (popular science, discussion, etc.))
    Abstract [sv]

    Det språk vi använder oss av i matematikklassrummet kan fokuseras på många olika sätt. Språket är också nödvändigt att förhålla sig till vid utvecklingen av sitt matematiska tänkande. Författarna diskuterar här relationer mellan språk och lärande.

  • 8.
    Birky, Geoffrey
    et al.
    Georgetown University.
    Campbell, Connie M
    Millsaps College, USA.
    Raman, Manya
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    Sandefur, James
    Georgetown University.
    Somers, Kay
    Moravian College, USA.
    One problem, nine student-produced proofs2011In: The College Mathematics Journal, ISSN 0746-8342, E-ISSN 1931-1346, Vol. 42, no 5, p. 355-360Article in journal (Refereed)
    Abstract [en]

    The context of this paper is a project aimed at meeting the challenges of teaching an introduction-to-proof course at our own institutions. These courses are typically taken by second year students intending to major in mathematics or computer science and are taught in sections of 15 to 24 students. These students benefit from being given the freedom to explore different methods of proof without the presumption that they will use a certain method.  This is the story of how what could have been a routine, closed problem became an open one.

  • 9.
    Blanck, Andreas
    Umeå University, Faculty of Science and Technology, Department of Physics.
    American Option Price Approximation for Real-Time Clearing2018Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    American-style options are contracts traded on financial markets. These are derivatives of some underlying security or securities that in contrast to European-style options allow their holders to exercise at any point before the contracts expire. However, this advantage aggravates the mathematical formulation of an option's value considerably, explaining why essentially no exact closed-formed pricing formulas exist. Numerous price approximation methods are although available, but their possible areas of application as well as performance, measured by speed and accuracy, differ. A clearing house offering real-time solutions are especially dependent on fast pricing methods to calculate portfolio risk, where accuracy is assumed to be an important factor to guarantee low-discrepancy estimations. Conversely, overly biased risk estimates may worsen a clearing house's ability to manage great losses, endangering the stability of a financial market it operates.

    The purpose of this project was to find methods with optimal performance and to investigate if price approximation errors induce biases in option portfolios' risk estimates. Regarding performance, a Quasi-Monte Carlo least squares method was found suitable for at least one type of exotic option. Yet none of the analyzed closed-form approximation methods could be assessed as optimal because of their varying strengths, where although the Binomial Tree model performed most consistently. Moreover, the answer to which method entails the best risk estimates remains inconclusive since only one set of parameters was used due to heavy calculations. A larger study involving a broader range of parameter values must therefore be performed in order to answer this reliably. However, it was revealed that large errors in risk estimates are avoided only if American standard options are priced with any of the analyzed methods and not when a faster European formula is employed. Furthermore, those that were analyzed can yield rather different risk estimates, implying that relatively large errors may arise if an inadequate method is applied.

  • 10.
    Blomqvist, Charlotta
    et al.
    Berghemsskolan, Umeå.
    Gade, Sharada
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    Att kommunicera om likamedtecknet2013In: Nämnaren : tidskrift för matematikundervisning, ISSN 0348-2723, no 4, p. 39-42Article in journal (Other (popular science, discussion, etc.))
    Abstract [sv]

    I denna artikel beskriver en lärare och en forskare sitt arbete med att utveckla den muntliga kommunikationsförmågan inom matematik i en fjärdeklass. Aktionsforskning utgör bakgrunden för arbetet och likamedtecknet står i fokus när eleverna utmanas i sitt matematiska tänkande med hjälp av lappar.

  • 11.
    Bodin, Kenneth
    et al.
    Umeå University, Faculty of Science and Technology, High Performance Computing Center North (HPC2N).
    Lacoursière, Claude
    Umeå University, Faculty of Science and Technology, High Performance Computing Center North (HPC2N).
    Nilsson, Martin
    Servin, Martin
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Constraint based particle fluids on GPGPU2011Conference paper (Other academic)
    Abstract [en]

    We present a fluid simulation method adapted for stream parallelism on general purpose graphics processingunits (GPGPU). In this method the equations of Navier and Stokes are discretized using particles and kernelfunctions as in Smoothed Particle Hydrodynamics (SPH), but rather than using penalty methods or solving for a divergence free velocity field, incompressibility is enforced using holonomic kinematic constraints [1]. We useone constraint for each smoothed particle stating that the local density should be kept constant. Other constraintsare used for boundary conditions and multiphysics coupling. We also present a viscosity model in which theshear rate at each pseudo particle is constrained to satisfy a given constitutive law. The computation of theconstraint forces, namely, the pressure and the stresses, requires the solution system of linear equations whichhave a sparse, saddle point structure. These are solved using the Uzawa method of preconditioned conjugate gradients (CG) applied directly to the symmetric indefinite matrix. The overall simulation method has its rootsin a discrete variational principle and the SPOOK time stepping scheme for constrained mechanical systems [2].The SPOOK method is second order accurate on the positions and constraints violations, and is stable at largetime-steps, thus often allowing several orders of magnitude larger timesteps in our method compared to intraditional SPH methods. The numerical implementation on GPGPU that is the main result of this paper consistsof the following components: particle neighbour searches based on spatial decomposition; summation of kernel densities; construction of Jacobians representing the constraints on the density, boundary conditions, viscosityand multiphysics couplings; a Uzawa CG solver for the system of linear equations; and finally, discrete timestepping of velocities and positions. The CG solver is particularly suitable for stream computing since it is basedon matrix-vector multiplications. The sparse system data is stored in a compressed matrix format and the algorithms operating on this data on GPGPU are implemented in CUDA and OpenCL. Our simulation resultsinclude performance measurements, and validation of the method for benchmark problems. We achieve up totwo orders of magnitude speed-up from the GPGPU over traditional processors and together with the increased timestep efficiency of our method we arrive at interactive performance for systems with up to two million fluidparticles representing an incompressible fluid.

  • 12.
    Brännström, Åke
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Carlsson, Linus
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Rossberg, Axel
    School of Biological Sciences, Queen’s University Belfast, Belfast, BT9 7BL UK.
    Rigorous conditions for food-web intervality in high-dimensional trophic niche spaces2011In: Journal of Mathematical Biology, ISSN 0303-6812, E-ISSN 1432-1416, Vol. 63, no 3, p. 575-592Article in journal (Refereed)
    Abstract [en]

    Food webs represent trophic (feeding) interactions in ecosystems. Since the late 1970s, it has been recognized that food-webs have a surprisingly close relationship to interval graphs. One interpretation of food-web intervality is that trophic niche space is low-dimensional, meaning that the trophic character of a species can be expressed by a single or at most a few quantitative traits. In a companion paper we demonstrated, by simulating a minimal food-web model, that food webs are also expected to be interval when niche-space is high-dimensional. Here we characterize the fundamental mechanisms underlying this phenomenon by proving a set of rigorous conditions for food-web intervality in high-dimensional niche spaces. Our results apply to a large class of food-web models, including the special case previously studied numerically.

  • 13.
    Brännström, Åke
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Gross, Thilo
    Max-Planck-Institute for Physics of Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany.
    Blasius, Bernd
    Institute for Chemistry and Biology of Marine Environment, Oldenburg University, 26111 Oldenburg, Germany.
    Dieckmann, Ulf
    Evolution and Ecology Program, International Institute for Applied Systems Analysis (IIASA), Schlossplatz 1, 2361 Laxenburg, Austria.
    Consequences of fluctuating group size for the evolution of cooperation2011In: Journal of Mathematical Biology, ISSN 0303-6812, E-ISSN 1432-1416, Vol. 63, no 2, p. 263-281Article in journal (Refereed)
    Abstract [en]

    Studies of cooperation have traditionally focused on discrete games such as the well-known prisoner’s dilemma, in which players choose between two pure strategies: cooperation and defection. Increasingly, however, cooperation is being studied in continuous games that feature a continuum of strategies determining the level of cooperative investment. For the continuous snowdrift game, it has been shown that a gradually evolving monomorphic population may undergo evolutionary branching, resulting in the emergence of a defector strategy that coexists with a cooperator strategy. This phenomenon has been dubbed the ‘tragedy of the commune’. Here we study the effects of fluctuating group size on the tragedy of the commune and derive analytical conditions for evolutionary branching. Our results show that the effects of fluctuating group size on evolutionary dynamics critically depend on the structure of payoff functions. For games with additively separable benefits and costs, fluctuations in group size make evolutionary branching less likely, and sufficiently large fluctuations in group size can always turn an evolutionary branching point into a locally evolutionarily stable strategy. For games with multiplicatively separable benefits and costs, fluctuations in group size can either prevent or induce the tragedy of the commune. For games with general interactions between benefits and costs, we derive a general classification scheme based on second derivatives of the payoff function, to elucidate when fluctuations in group size help or hinder cooperation.

  • 14.
    Brännström, Åke
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Johansson, Jacob
    Lund University.
    von Festenberg, Niels
    The Hitchhiker’s Guide to Adaptive Dynamics2013In: Games, ISSN 2073-4336, E-ISSN 2073-4336, no 4, p. 304-328Article in journal (Refereed)
    Abstract [en]

    Adaptive dynamics is a mathematical framework for studying evolution. It extends evolutionary game theory to account for more realistic ecological dynamics and it can incorporate both frequency- and density-dependent selection. This is a practical guide to adaptive dynamics that aims to illustrate how the methodology can be applied to the study of specific systems. The theory is presented in detail for a single, monomorphic, asexually reproducing population. We explain the necessary terminology to understand the basic arguments in models based on adaptive dynamics, including invasion fitness, the selection gradient, pairwise invasibility plots (PIP), evolutionarily singular strategies, and the canonical equation. The presentation is supported with a worked-out example of evolution of arrival times in migratory birds. We show how the adaptive dynamics methodology can be extended to study evolution in polymorphic populations using trait evolution plots (TEPs). We give an overview of literature that generalises adaptive dynamics techniques to other scenarios, such as sexual, diploid populations, and spatially-structured populations. We conclude by discussing how adaptive dynamics relates to evolutionary game theory and how adaptive-dynamics techniques can be used in speciation research.

  • 15. Cornforth, Daniel M
    et al.
    Sumpter, David J T
    Brown, Sam P
    Brännström, Åke
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Synergy and group size in microbial cooperation2012In: American Naturalist, ISSN 0003-0147, E-ISSN 1537-5323, Vol. 180, no 3, p. 296-305Article in journal (Refereed)
    Abstract [en]

    Abstract Microbes produce many molecules that are important for their growth and development, and the exploitation of these secretions by nonproducers has recently become an important paradigm in microbial social evolution. Although the production of these public-goods molecules has been studied intensely, little is known of how the benefits accrued and the costs incurred depend on the quantity of public-goods molecules produced. We focus here on the relationship between the shape of the benefit curve and cellular density, using a model assuming three types of benefit functions: diminishing, accelerating, and sigmoidal (accelerating and then diminishing). We classify the latter two as being synergistic and argue that sigmoidal curves are common in microbial systems. Synergistic benefit curves interact with group sizes to give very different expected evolutionary dynamics. In particular, we show that whether and to what extent microbes evolve to produce public goods depends strongly on group size. We show that synergy can create an "evolutionary trap" that can stymie the establishment and maintenance of cooperation. By allowing density-dependent regulation of production (quorum sensing), we show how this trap may be avoided. We discuss the implications of our results on experimental design.

  • 16.
    Dejby, Jesper
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Larsson, Josef
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Optimizing production line sequence to minimize waste: A paint shop problem2016Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    In the competitive automobile manufacturing industry only the most efficient and profitable companies will survive. Companies search for ways to cut costs and increase production without lower their standards of quality. In the field of optimization research such problems can be formulated as combinatorial optimization problems. The Car Sequencing problem (CSP) tries to find the optimal production sequence which increases the number of produced units. Parrello et al. (1986) where the first one to formulate the problem with respect to an assembly line in a automobile factory. Volvo GTO in Umeå desires to minimize their paint consumption in the paint shop. By formulating paint process in the top coat, which is the last part of the paint shop, as a Integer Linear Program the number of color changes can be minimized. Hence the paint consumption is reduced which leads to lower costs. Using a greedy approach while simulating the process the number of color changes can be reduced based on historical data. This result is based on a somewhat simplified model of a real life problem. The number of parameters in the model can be increased to reflect the complexity of the paint shop. The purpose of this thesis is to present a way to decrease the paint consumption

  • 17.
    Dyrvold, Anneli
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Which textual features are difficult when reading and solving mathematics tasks?2017In: Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education: CERME 10, Dublin: Dublin City University , 2017Conference paper (Refereed)
    Abstract [en]

    Despite the digital revolution much of the mathematics practiced in schools is still tightly bound to two-dimensional texts. This emphasis on text is neither surprising, nor inadequate, since mathematics has developed through a long history with the use of written text, consisting of natural language, mathematical notation and images. Natural language is our native language consisting of letters and words (see e.g., www.oed.com). Different features of the mathematics text are also important in written tests, since reading the text is part of the assessment. If the text is hard to read, that difficulty can be relevant as part of assessing the communicative competence in mathematics. Crucial is, however, whether potentially difficult textual features are part of what the assessment aims at. This issue is investigated in the current study, using a synthesis of statistical results and qualitative analyses of task text.

  • 18.
    Dyrvold, Anneli
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    Bergqvist, Ewa
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    Österholm, Magnus
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    Uncommon vocabulary in mathematical tasks in relation to demand of reading ability and solution frequency2015In: Nordisk matematikkdidaktikk, ISSN 1104-2176, Vol. 20, no 1, p. 5-31Article in journal (Refereed)
    Abstract [en]

    This study reports on the relation between commonness of the vocabulary used in mathematics tasks and aspects of students’ reading and solving of the tasks. The vocabulary in PISA tasks is analyzed according to how common the words are in a mathematical and an everyday context. The study examines correlations between different aspects of task difficulty and the presence of different types of uncommon vocabulary. The results show that the amount of words that are uncommon in both contexts are most important in relation to the reading and solving of the tasks. These words are not connected to the solution frequency of the task but to the demand of reading ability when solving the task.

  • 19.
    Edmonds-Wathen, Cris
    Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    Indigenous language speaking students learning mathematics in English: Expectations of and for teachers2015In: Australian Journal of Indigenous Education, ISSN 1326-0111, E-ISSN 2049-7784, Vol. 44, no 1, p. 48-58Article in journal (Refereed)
    Abstract [en]

    Effective mathematics teaching for Indigenous language speaking students needs to be based on fair expectations of both students and teachers. Concepts of ‘age-appropriate learning’ and ‘school readiness’ structure assessment expectations that entire cohorts of Indigenous language speaking students are unable to meet. This institutionalises both student and teacher failure, as both are exhorted to meet unachievable expectations. The voices of teachers teaching in a very remote school provide insight into teachers’ responses to the mismatch between the system expectations and the teaching context. Teacher interviews in a small Northern Territory school, conducted within an ethnographic study, showed that teachers’ decisions regarding the level of mathematics curriculum taught were informed by students’ prior learning and by the language dynamic in their classrooms. The need and pressure to teach Standard Australian English also affected how mathematics was taught. This leads to a reformulation of the concept of school readiness to ask how schools can be more ready for their Indigenous language speaking students in terms of preparing and supporting teachers.

  • 20.
    Forsberg, Tomas
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Swaption pricing and isolating volatility exposure2011Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    Starting from basic financial mathematics, we cover the mathematics of pricing swaptions, options on interest rate swaps. We then continue to the topic of obtaining an approximately pure volatility exposure. This exposure to volatility, which in practice enables us to trade volatility according to our perceptions of the market, is obtained by buying or selling swaptions and appropriate amounts of the underlying interest rate swap contract. Taking offsetting positions in the underlying contract is called hedging and is covered in depth. We note that hedging can primarily be done in two ways, and discuss the advantages and disadvantages of each of them. After deriving the value formulas for such a swaption strategy aimed at isolating volatility exposure we end with a discussion on the transition from theory to practice.We find that this way of trading volatility is conceptually simple, but that pre-trade profitability analysis is difficult due to the sometimes poor availability of the sophisticated data needed to simulate such a swaption strategy. Despite the possible limitations in the data necessary to translate this theory into an experimental setup, this thesis serves as a good basis for further research on the profitability of a volatility trading strategy using interest rate swaptions.

  • 21.
    Gade, Sharada
    Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    Activity settings and pedagogical categories2015In: Research in Mathematics Education, ISSN 1479-4802, E-ISSN 1754-0178, Vol. 17, no 2, p. 148-149Article in journal (Refereed)
    Abstract [en]

    This report discusses analysis of data collected as participant observer during doctoral work (Gade, 2006), examined more recently with Engeström’s version of activity theory (Gade, 2014). The empirical data under consideration refer to two particular group tasks conducted by two experienced teachers at the commencement of the academic term, with all students assembled into small groups. I consider the conduct of these tasks as an Activity setting (Tharp & Gallimore, 1988), in realising which teachers exemplified the pedagogical category of Joint productive activity (Dalton & Tharp, 2002). These two constructs draw on cultural historical activity theory (CHAT) perspectives which explain how human consciousness and personality develop in goal-directed activities.

  • 22.
    Gade, Sharada
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. Homi Bhaba Centre for Sciecne Education (HBCSE), Tata Institute of Fundamental Research (TIFR), Mumbai, India.
    Analysing appropriation in a mathematics classroom: The case of a textbook and a mnemonic2008Conference paper (Refereed)
    Abstract [en]

    The appropriation of cultural resources in any social environment is of theoretical interest in order to understand Vygotsky's contention of how skills that are interpsychological become intrapsychological, allowing the individual to direct attention to elements that are necessary to carry out a particular task at hand. The analysis of appropriation is of methodological interest to be able to obtain explanatory power and understand as Rogoff argues how students comprehend their roles, transform practice through appropriation and relate their participation from one activity to another. Combining a theoretical and methodological interest, this paper discusses two instances of appropriation by students who utilise a textbook and a mnemonic in meeting instructional goals in the classroom teaching-learning of mathematics. Leont'ev distinguished the process of appropriation as unique to human ontogenetic development, one that takes place in an objective world of cultural resources. In analysing embedded goals, mastery of cultural resources and transformation of practice, an understanding is sought of the complex, collaborative and situated conditions that facilitate the process of appropriation and the cultural nature of human development.

  • 23.
    Gade, Sharada
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. University of Oxford.
    Analysing two group-tasks and a collaborative classroom practice with Engeström’s activity theory2014In: Proceedings of the British Society for Research into Learning Mathematics (BSRLM) Volume 34 Number 1 / [ed] Patrick Barmby, 2014, p. 43-48Conference paper (Refereed)
    Abstract [en]

    Two teachers, Olaf and Knut, conducted two group-tasks in succession, early in the academic year at a gymnasium or upper secondary school in Norway. In doing so they steered classroom practice away from traditional instruction, with Olaf alone as teacher, to cooperative learning in small groups with guidance from both. While the first group-task titled When Together initiated cooperative learning by students in small groups, the second titled How Heavy initiated student groups to build upon group cooperation and work with other groups in a collaborative classroom practice. It was Olaf and Knut’s intention to have their students cooperate in small groups at all times and collaborate with students from other groups on occasion. A few months into the year, Olaf and Knut’s students’ groups had opportunity to discuss rules of cooperation whereupon their collaborative classroom practice became the norm. Using examples of students’ attempts at both group-tasks, I portray Olaf and Knut’s initiation of such a practice. Using Engeström’s activity model I shed light on how students' participation was transformed to meet with their intentions.

  • 24.
    Gade, Sharada
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. Høgskolen i Agder, Kristiansand, Norway.
    Artefact mediated classroom practice2007In: Relating practice and research in mathematics education - Proceedings of Norma05 / [ed] C. Bergsten, B. Grevholm, H. S. Måsøval and F. Rønning, Trondheim: Tapir Academic Press , 2007, p. 257-269Conference paper (Refereed)
    Abstract [en]

    This paper reports on a classroom study of meaning being made by students working in small groups in a mathematics classroom at an upper secondary school. A naturalistic study, it observes student activities within the classroom from a socio-cultural-historical perspective. It addresses the artefact mediated classroom practice, wherein student participation and meaning making is guided and apprenticed by the teachers. Mediated by artefacts within intentional practices, the mathematics classroom constitutes a culture which is also the medium for meaning making.

  • 25.
    Gade, Sharada
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    Close-to-practice classroom research by way of Vygotskian units of analysis2012In: Proceedings of the 12th International Congress on Mathematics Education (ICME), 8-15 July 2012, Seoul, Korea, 2012, p. 4312-4321Conference paper (Refereed)
    Abstract [en]

    This paper discusses the potential of Vygotskian units in researching classroom practices. Adopting a close-to-practice approach and action research where possible, an attempt is made to shed light on ongoing practices across grades 4-6, 7-9 and the gymnaisum. The theory/practice approach adopted keeps alive the relationship between theory-which-informs and theory-being-built, as well as existing-practice and steered-practice in these studies. The potential to inform researcher reflexivity and guide educational action along with the ability of units to grasp complexity, from as many perspectives as possible, and ascend to the concrete is brought forward. Such a strategy is deliberate, geared towards informing practitioner inquiry in ongoing classrooms. 

  • 26.
    Gade, Sharada
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    Cooperation and collaboration as zones of proximal development within the mathematics classroom2010In: Nordic Studies in Mathematics Education, ISSN 1104-2176, Vol. 15, no 2, p. 49-68Article in journal (Refereed)
    Abstract [en]

    Beyond understanding the Vygotskian construct of zone of proximal development or ZPD with reference to an individual student, this paper explores the formation of ZPD within the pedagogical constructs of cooperation, wherein students cooperate with each other within their groups; as well as collaboration, wherein students from different groups that constitute the classroom collaborate with each other. Identified on the basis of functions that are in the process of maturing, the formation of either ZPD is exemplified from a socio-cultural-historical study at an upper secondary mathematics classroom in Norway. An emphasis on what distinguishes events in instruction that are educational from those that are not is also explored, before illustrating what nature of ZPD is established. The role of guidance received, imitation and cultural resources in the development of higher mental functions is understood as these ZPD are formed, enabling students to act independently within the classroom teaching-learning of mathematics. 

  • 27.
    Gade, Sharada
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    Oneself in practitioner research, with Vygotsky and Bakhtin2016In: Reflective Practice, ISSN 1462-3943, E-ISSN 1470-1103, Vol. 17, no 4, p. 403-414Article in journal (Refereed)
    Abstract [en]

    Practitioner action and reflection are understood as central to practitioner research in this paper. While Vygotskian based premise highlight instructional practices and intervention as central to practitioner understanding, Bakhtin based dialogical premise draw on relational constructs and attend to practitioner being, answerability and authorship. Vygotskian and Bakhtinain units of analysis used are viewed as means with which to conceive practitioner action/reflection and build a community of practitioners. Taken together practitioner knowing is found inextricable with practitioner ontology, making practitioner research of ongoing instructional practices more human in line with Dewey.

  • 28.
    Gade, Sharada
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    Practitioner collaboration at a Grade four mathematics classroom: by way of relational knowing and relational agency2014In: Promoting change through action research / [ed] Franz Rauch, Angela Schuster, Thomas Stern, Maria Pribila and Andrew Townsend, Rotterdam: Sense Publishers, 2014, p. 35-47Chapter in book (Refereed)
    Abstract [en]

    Drawing on narrative inquiry as well as activity theory perspectives, in this chapter I examine three aspects in relation to research conducted with a mathematics teacher Lotta, as Charlotta is known, at a Grade 4-6 school in Sweden. First, the nature of relational knowing which, born of practitioner narratives, led us to collaborate and take action (Hollingsworth, Dybdahl & Minarik, 1993).

  • 29.
    Gade, Sharada
    Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. Oxford University, UK.
    Praxis and phronesis as units of analysis: realising a social science that matters in practitioner inquiry2014In: Reflective Practice, ISSN 1462-3943, E-ISSN 1470-1103, Vol. 15, no 6, p. 718-728Article in journal (Refereed)
    Abstract [en]

    The notions of praxis, or practical action, and phronesis, or practical wisdom, are engaged with from two perspectives in this paper – with examples from author's classroom studies across various Grade schools in Sweden on one hand and the theoretical exposition of these notions across a selection of existing literature on the other. A persuasive case is made for having praxis and phronesis be regarded as units of analysis suitable for grasping as well as furthering practitioner inquiry. The results of such research, conducted as a practice, are aimed at informing the vicarious and the experiential, upon which any reader can in turn base actions. In their ability to examine the practical, particular and local, the pursuit of such a social science is argued as being one that matters to the practitioners themselves.

  • 30.
    Gade, Sharada
    Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    School change and educational reform: how activity theory could respond to Sarason's insights2016In: Da Investigação às Práticas, ISSN 2182-1372, Vol. 6, no 2, p. 25-38Article in journal (Refereed)
    Abstract [en]

    Three perspectives are brought together in this paper, towards recognising the centrality of participant agency in school change and educational reform. First, observations made by Sarason in relation to school change and educational reform. Second, Engeström's activity theory based interventionist methodology, which seeks recognition of agency in the conduct of local interventions. Finally an empirical case of teacher-researcher collaboration and project based intervention at a Grade four mathematics classroom in Sweden. Herein lies the possibility of viewing school change and educational reform in terms of students' interests and teacher agency within classroom interventions.

  • 31.
    Gade, Sharada
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    Students' meaning making in a collaborative classroom practice as initiated by two teachers2011In: Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education, vol. 2: Developing Mathematical Thinking / [ed] Behiye Ubuz, Ankara, 2011, p. 2-361-2-368Conference paper (Refereed)
    Abstract [en]

    This paper reports the nature of classroom practice that afforded students' meaning making at an upper secondary mathematics classroom in Norway. The participation of both teachers and students in the collaborative classroom practice they jointly establish is outlined. A longitudinal and person-in-practice view sheds light not only on the meaning producing foreground that was initiated, but also the nature of its growth. An artefact of instructional practice of two teachers Olaf and Knut is thus evidenced. In this there is opportunity to appreciate mathematical content, pedagogy and students' thinking in an integrated manner – making such knowledge useful and usable by practising as well as prospective teachers of mathematics.

  • 32.
    Gade, Sharada
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. University of Oxford.
    Surface area to volume ratio and metabolism: analysing small group-task as Vygotskian activity2013In: Proceedings of the British Society for Research into Learning Mathematics (BSRLM) Volume 33 Number 3 / [ed] C Smith, London, 2013, p. 25-30Conference paper (Other academic)
    Abstract [en]

    Three students Dan, Levi and Thor, attempt a group-task containing worksheets A and B. While worksheet A asks students to calculate and compare surface area to volume ratio of a sphere for six successive units, worksheet B asks them to consider the metabolism of living cells and the bearing the ratio has on their functioning and size. While Levi and Thor own the group-task, follow its instructions and deliberate on its questions, Dan declares his intention of observing Levi and Thor and takes a free ride. Based on students inscriptions and transcript of audio-recordings, I show how Levi and Thor work through calculations required in worksheet A with ease, even coming up with conjectures. In attempting worksheet B they are able to correlate better metabolism in cells with a smaller radius, yet question if that model is indeed borne out in reality. The concept of activity in Vygostkian theory is used to study students attempts at the group-task. Three constructs from cultural historical activity theory and/or CHAT namely leading activity, germ cell of activity and learning activity are utilised to shed light on attempts by Dan, Levi and Thor at their group-task. 

  • 33.
    Gade, Sharada
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    Teacher-researcher collaboration as Formative Intervention and Expansive Learning Activity2015In: CERME9: Proceedings of the Ninth Congress of the European Society for Research in Mathematics Education / [ed] Konrad Krainer and Naďa Vondrová, Prague: Charles University, Faculty of Education and ERME , 2015, p. 3029-3035Conference paper (Refereed)
    Abstract [en]

    Extended teacher-researcher collaboration is reported in this paper, by drawing upon cultural historical activity theory (CHAT) perspectives. Teaching is herein conceived as dialectical practice in which teachers are both shaped by and shape instructional practices. Three instructional interventions conducted at a Grade four mathematics classroom in Sweden constitute and exemplify the construct of Formative Intervention. Teacher-researcher collaboration which paralleled such conduct next exemplifies the construct of Expansive learning activity. Such transformation and change sheds light on how mid-level taken for granted phenomena in schools can be worked with and around, besides contributing to the motivational sphere of students and teachers.

  • 34.
    Gade, Sharada
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    Teacher-researcher collaboration as transformation – A case study2014In: Abstract of papers of the International Society of Cultural and Activity Research (ISCAR) International Conference, 29 September - 3 October 2014, Sydney, Australia, 2014, p. 18-18Conference paper (Refereed)
    Abstract [en]

    This paper details researcher collaboration with Lotta, a mathematics teacher at a Grade 4-6 school. This began with a six month study during which I observed Lotta's classroom teaching at Grade six. My pursuit of narrative perspectives in this study, created room for intersubjectivity and endeared Lotta and me to collaborate thereafter. Lotta's application for project funding from national school authorities, then paved way for researcher intervention in Lotta's teaching, at her now Grade four. Our conceiving teaching-learning in Vygotskian terms allowed for two kinds of interventions. Talk based interventions geared towards correlating mathematics and communication as part of Lotta's project and specific interventions relating to say mathematical problem posing and students' use of the mathematical = sign. In Lotta next being employed by national school authorities themselves, our collaboration shifted to reflecting and reporting on our interventions by means of co-authorship. The trajectory from participant observation to co-authorship in our collaboration thus corresponds to my reference to Lotta as Lea in my first study, to her theorising and facing up to public scrutiny as herself. Lotta is since Rektor of a school at which we intend to widen our collaboration. 

    While recognising agentive understanding as teacher and researcher to be a result of intervening in Lotta's instructional practice, it is purpose, goals and outcomes of teacher-researcher collaboration that is of interest. With its transformative manner as backdrop and in line with writings led by Anna Stetsenko I examine three specific aspects. First, in what way did our collaboration qualify as leading activity, enabling research to capture our selves as evolving in our interventions. Second, how did our actions exemplify a transformative activist stance that promoted human knowing and becoming, rooted in the ideals of social justice. Finally, how did our attempts at collaborative purposeful transformation stem out of social practice, through social practice and for social practice we set out to change. In line with a practical-theoretical endeavor, such analysis sheds light on a transformatory vision of human development in terms of a dialectical, non-reductionist, non-dualist, non-additive relational ontology as played out in our case of teacher-researcher collaboration. 

  • 35.
    Gade, Sharada
    Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    Teacher-researcher collaboration in a Grade Four mathematics classroom: Restoring equality to students usage of the '=' sign2012In: Educational action research, ISSN 0965-0792, E-ISSN 1747-5074, Vol. 20, no 4, p. 553-570Article in journal (Refereed)
    Abstract [en]

    This article portrays action research conducted in relation to students’ faulty use of the equality sign at a Grade four mathematics classroom in Sweden. Substantial background on teacher-researcher collaboration that prepares ground for the action research is offered. Drawing on CHAT perspectives the conduct of activities mediated by diagrammatic objects (lappar) as cultural artefacts and students' inscriptions in these is also provided. As semiotic activity the action research cycle allows students to reflect on signs, meanings and their interrelationships while working with knowledgeable others. A three stage conclusion discusses relevant research in mathematics education, the nature of practical theory realised, and actionable knowledge thereby possible in terms of trustworthiness.

  • 36.
    Gade, Sharada
    Faculty of Mathematics and Sciences, University of Agder, Kristiansand, Norway.
    The micro-culture of a mathematics classroom: artefacts and activity in meaning making and problem solving2006Doctoral thesis, monograph (Other academic)
  • 37.
    Gade, Sharada
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    Theory in service of the concrete: Cultural studies, schooling and critical mathematics education2012Conference paper (Refereed)
    Abstract [en]

    As different from building theory from research the ability of theorising for action research at two Grade eight classrooms is discussed, by deploying cultural studies and problematising how students and teachers are (dis)empowered by cultural, political, global and economic forces. Moving beyond adoption of a neutral outlook to schooling and mathematics, the practice of mathematics education research necessitates careful and critical thinking through of content, context and agency. An attempt is made to narrate a better story of what could transpire within four walls of a mathematics classroom - situated as classroom and school themselves are in wider societal contexts. 

  • 38.
    Gade, Sharada
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    Two small stories about self and world at grades four and five: informing close-to-practice research of mathematics classrooms2012In: Responsible Research: Papers from the Fourth Qualitative Research Conference / [ed] Petri Salo, Åbo: Åbo Akademi University, The Faculty of Education , 2012, p. 34-44Conference paper (Refereed)
    Abstract [en]

    This paper deliberates upon two small stories offered by Sara and Eva at a grade 4-6 Swedish school. The two narratives allow research to examine the notion of students' subjectivity within teaching-learning of mathematics and schooling more broadly. Offered as talk-in-interaction these are analysed with respect to what Sara and Eva did with their talk, as well as the nature of self that either was able to accomplish. There is opportunity to examine the role played by these stories in mediating the lived world and told world that either experienced. While Sara examined writing in story books, Eva examined babysitting her siblings. The positioning of either as social beings in their contextual tellings, informs agency and actions of either in their respective lives. Such analysis informs research about students' identity or their who in addition to the how of their participation, vital to initiating any educational action.

  • 39.
    Gade, Sharada
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. City University of New York, Oxford University.
    Unpacking teacher-researcher collaboration with three theoretical frameworks: a case of expansive learning activity?2015In: Cultural Studies of Science Education, ISSN 1871-1502, E-ISSN 1871-1510, Vol. 10, no 3, p. 603-619Article in journal (Refereed)
    Abstract [en]

    Long association with a mathematics teacher at a Grade 4-6 school in Sweden, is basis for reporting a case of teacher-researcher collaboration. Three theoretical frameworks used to study its development over time are relational knowing, relational agency and cogenerative dialogue. While relational knowing uses narrative perspectives to explore the experiential and relational nature of collaboration; relational agency, draws on activity theory perspectives and identifies the change in the purpose of collaboration, from initially conducting classroom interventions to co-authoring research. Finally, cogenerative dialogue, deploys hermeneutic-phenomenological perspectives and investigates the dialogue that transpired between Lotta and the author, as they co-authored their research report. Such analysis sheds invaluable light on a case of expansive learning activity. 

  • 40.
    Gade, Sharada
    et al.
    Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. The Graduate Centre, City University of New York, New York, NY, USA.
    Blomqvist, Charlotta
    Berghemskolan, Umeå.
    From problem posing to posing problems via explicit mediation in Grades 4 and 52015In: Mathematical problem posing: from research to effective practice / [ed] Florence Mihaela Singer, Nerida F. Ellerton, Jinfa Cai, New York: Springer Science+Business Media B.V., 2015, p. 195-213Chapter in book (Refereed)
    Abstract [en]

    Drawing upon cultural historical activity theory (CHAT) perspectives,in this chapter we portray a classroom practice of problem posing that evolved with a cohort of students across Grades 4 and 5 in Sweden. In line with a language and literacy pedagogy, the classroom practice in which students utilised textbook vocabulary handed out on slips of paper (lappar in Swedish) advanced through three distinct stages namely: formulating written questions, problem posing as dyads and actively posing problems to one another. Mediated explicitly by lappar, such a practice provided social and public opportunities for students to attribute personal meaning and make conscious use of words in semiotic activity, as well as appropriate cultural meaning and valid norms of use. The increasing gain and display of agency by students in this practice, informed by student(s)-acting-with-lappar-as-mediational-means as unit of analysis, was indicative of their self-regulation, volition and independence. Developmental in approach, such classroom practice was born through teacher–researcher collaboration.

  • 41.
    Gade, Sharada
    et al.
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    Blomqvist, Charlotta
    Grisbacka Primary School, Umeå.
    Investigating everyday measures through exploratory talk: whole class plenary intervention and landscape study at grade four2018In: Cultural Studies of Science Education, ISSN 1871-1502, E-ISSN 1871-1510, Vol. 13, no 1, p. 235-252Article in journal (Refereed)
    Abstract [en]

    We report an exploratory talk based, whole class plenary intervention, in relation to students' understanding of everyday measures and measurement, in a grade four classroom at a grade 4-6 school in Sweden. Extended, project related, teacher-researcher collaboration forms basis for such cultural historical activity theory or CHAT based efforts. As formative intervention, the conduct of the plenary is not pre-determined but embedded in ongoing curricular realities, with the agency of students and teacher promoted, pedagogical ideas reutilised and the role of researcher viewed as supporting design and growth of the intervention. Under Charlotta's guidance as teacher, the plenary is opportunity for her students to examine improbable scenarios such as, Can Eva and Anton measure the length of Sweden on foot, Can Lars and Iris measure their age in decimeters. A zone of proximal development is created, in which students make the transition from spontaneous to scientific concepts and learn how various units of measurement are objects-that-can-be-used-for-certain-purposes. With opportunity for critical and reflective inquiry, in a plenary designed to lead development, Charlotta's students look beyond the making of rote measurements and articulate a theory of measure in nascent terms. Such a landscape of teaching-learning is finally understood in terms of the nature of talk that was facilitated, the manner of pedagogy utilised, the style of teaching exercised and the kind of learning that was demanded of her students.

  • 42.
    Gade, Sharada
    et al.
    Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    Blomqvist, Charlotta
    Grisbacka Primary School, Umeå, Sweden.
    Shared object and stakeholdership in teacher-researcher expansive learning activity2016In: Proceedings of the 40th Conference of the International Group for the Psychology of Mathematics Education: volume 2: research reports / [ed] Csaba Csíkos, Attila Rausch and Judit Szitányi, Szeged, Hungary: PME , 2016, p. 267-274Conference paper (Refereed)
    Abstract [en]

    Cultural historical activity theory (CHAT) perspectives are used to shed light on an extended teacher-researcher collaboration, at a Grade 4-6 school in Sweden. Beginning with participant observation and emerging forms of engagement like co-authorship of research reports, the collaboration is understood as expansive learning activity. Treating the practices of teaching and research as distinct yet collaborating activity systems within this, provides an opportunity to analyse the manner in which joint conduct of project related instructional interventions became shared object. This also enabled teacher and researcher to become active stakeholders in each other's practice. Dialectical realisation of stakeholdership and shared object led to reconceptualisation and transformation of the very horizons of our work.

  • 43.
    Garpebring, Anders
    et al.
    Umeå University, Faculty of Medicine, Department of Radiation Sciences, Radiation Physics.
    Brynolfsson, Patrik
    Umeå University, Faculty of Medicine, Department of Radiation Sciences, Radiation Physics.
    Kuess, Peter
    Department of Radiotherapy, Medical University of Vienna, Vienna, Austria; Christian Doppler Laboratory for Medical Radiation Research for Radiation Oncology, Vienna, Austria.
    Georg, Dietmar
    Department of Radiotherapy, Medical University of Vienna, Vienna, Austria; Christian Doppler Laboratory for Medical Radiation Research for Radiation Oncology, Vienna, Austria.
    Helbich, Thomas H.
    Department of Biomedical Imaging and Image-Guided Therapy, Medical University of Vienna, Vienna, Austria; Christian Doppler Laboratory for Medical Radiation Research for Radiation Oncology, Vienna, Austria.
    Nyholm, Tufve
    Umeå University, Faculty of Medicine, Department of Radiation Sciences, Radiation Physics.
    Löfstedt, Tommy
    Umeå University, Faculty of Medicine, Department of Radiation Sciences, Radiation Physics.
    Density Estimation of Grey-Level Co-Occurrence Matrices for Image Texture Analysis2018In: Physics in Medicine and Biology, ISSN 0031-9155, E-ISSN 1361-6560, Vol. 63, no 19Article in journal (Refereed)
    Abstract [en]

    The Haralick texture features are common in the image analysis literature, partly because of their simplicity and because their values can be interpreted. It was recently observed that the Haralick texture features are very sensitive to the size of the GLCM that was used to compute them, which led to a new formulation that is invariant to the GLCM size. However, these new features still depend on the sample size used to compute the GLCM, i.e. the size of the input image region-of-interest (ROI).

    The purpose of this work was to investigate the performance of density estimation methods for approximating the GLCM and subsequently the corresponding invariant features.

    Three density estimation methods were evaluated, namely a piece-wise constant distribution, the Parzen-windows method, and the Gaussian mixture model. The methods were evaluated on 29 different image textures and 20 invariant Haralick texture features as well as a wide range of different ROI sizes.

    The results indicate that there are two types of features: those that have a clear minimum error for a particular GLCM size for each ROI size, and those whose error decreases monotonically with increased GLCM size. For the first type of features, the Gaussian mixture model gave the smallest errors, and in particular for small ROI sizes (less than about 20×20).

    In conclusion, the Gaussian mixture model is the preferred method for the first type of features (in particular for small ROIs). For the second type of features, simply using a large GLCM size is preferred.

  • 44.
    Grenholm, Robin
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    A Comparison of Factors in Phenotype Classification using Microarray Data2017Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
  • 45.
    Grenholm, Robin
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Market Making in High Speed Space2016Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
  • 46.
    Hållberg, Moa
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Calculating sensitivities in the SABR/LIBOR market model for European swaptions2012Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    This article presents a new approach for calculating sensitivities of European swaptions. The sensitivities are found by applying an adjoint method to a stochastic volatility model, namely the SABR/LIBOR market model. This market model predicts the volatility smile and follows the market fluctuations more accurately than earlier used deterministic volatility market models for complex derivatives. The new adjoint method involves not only sensitivity calculations, it also presents a way of estimating the time discretization error using an a posteriori approach. The error calculation is described in this document but not investigated further.

    The first step in order to calculate the sensitivities is to calibrate the SABR/LIBOR market model to some market data. In our calculations we used data from June 15 2011 with 6 month intervals between the maturity times. When this calibration is complete all of the parameters in the SABR/LIBOR market model are specified and we can continue with the sensitivity calculations using the new adjoint method. The results from these calculations show that the method is a good choice for estimating sensitivities if we consider a complex financial derivative like the European swaption. The method is quite computational so we recommend that it is only used on a small number of securities with respect to a large number of parameters. The method provides more market-driven price and sensitivity estimations than earlier used methods and can benefit hedging of portfolios.

  • 47.
    Leijon, Rasmus
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    The Einstein Field Equations: on semi-Riemannian manifolds, and the Schwarzschild solution2012Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    Semi-Riemannian manifolds is a subject popular in physics, with applications particularly to modern gravitational theory and electrodynamics. Semi-Riemannian geometry is a branch of differential geometry, similar to Riemannian geometry. In fact, Riemannian geometry is a special case of semi-Riemannian geometry where the scalar product of nonzero vectors is only allowed to be positive. This essay approaches the subject from a mathematical perspective, proving some of the main theorems of semi-Riemannian geometry such as the existence and uniqueness of the covariant derivative of Levi-Civita connection, and some properties of the curvature tensor. Finally, this essay aims to deal with the physical applications of semi-Riemannian geometry. In it, two key theorems are proven - the equivalenceof the Einstein field equations, the foundation of modern gravitational physics, and the Schwarzschild solution to the Einstein field equations. Examples of applications of these theorems are presented.

  • 48.
    Lithner, Johan
    Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
    Principles for designing mathematical tasks that enhance imitative and creative reasoning2017In: ZDM - the International Journal on Mathematics Education, ISSN 1863-9690, E-ISSN 1863-9704, Vol. 49, no 6, p. 937-949Article in journal (Refereed)
    Abstract [en]

    The design research programme Learning by Imitative and Creative Reasoning (LICR) studies whether, how and why tasks and teaching that enhance creative reasoning lead to a more productive struggle and more efficient learning than the common but inefficient task designs based on imitating given solution procedures. The purpose of this paper is to synthesise the research outcomes determined to date by providing the following: a conceptual framework for key concepts and relationships among teaching, tasks, student activities and learning; a theoretical basis for analyses of causal effects between task/teaching design and learning outcomes; a design research methodology for transforming initial design ideas, through cycles of evaluation and revision, into firmer design principles; and an application of this theory and methodology to empirical studies carried out to date, in order to propose task-design principles related to imitative and creative reasoning.

  • 49.
    Lundgren, Christina
    Umeå University, Faculty of Science and Technology, Department of Mathematics Technology and Science Education. Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    Lust till matematik - en rättighet eller bara några få förunnat?2010Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesis
    Abstract [sv]

    Denna studie är genomfört som ett undervisningsförsök, där formativ bedömning har imple­menterats i matematikundervisning. Syftet med studien var att studera om det var möjligt att förändra undervisningen på denna korta tid samt om eleverna blev mer motiverade och om de upplevde mer lust till ämnet genom denna undervisningsstrategi. Ett särskilt fokus riktades på elever i matematiksvårigheter.

     

    Studien genomfördes i en årskurs 7:a, under höstterminen 2009, med inspiration Wiliam, (2007) Five ”Key Strategies” for Effective Assessmentutifrån och Black et al. (2003), Assess­ment for Learning – Putting it into practice. De förändringar som gjordes genomfördes av den ordinarie matematikläraren med stöd av mig som handledare under hela försöksperioden.

     

    För metodinsamling valdes, enkät, observation och intervju för att därigenom kunna göra en triangulerad ansats. Både enkät och intervju gjordes som för- och eftermätning och riktades mot eleverna. Observationer gjordes även de före försöket i avseende på att studera lärarens undervisning och de utvalda elevernas beteende och effektiva arbetstid i klassrummet. Däref­ter gjordes fortlöpande observationer under hela försökets gång. Av klassens 15 elever valde 14 att ställa upp i undersökningen.

     

    Förändringar tar tid, vilket medför att resultatet inte blev häpnadsväckande men visade ändå på tendenser till att elevernas motivation och lust till matematiken ökade genom implemente­ring av formativ bedömning i undervisningen.

  • 50.
    Mannelqvist, Katarina
    Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.
    Intensivmatematik2014Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    The purpose of the study was to evaluate a specific student case in a mathematics project about one to one tuition. I wanted to explore/examine the experience of this one to one tuition for a student in special education need. The experiences examined were students, guardians, intense teacher, and math teacher. They were then compared with the experience of previous projects that have been studied through literature studies.

    The method used was qualitative and the empirical material was collected through Semi-structured interviews. The study involved five respondents. The empirical results found also consisted literary studies based on two projects at the international level, three projects at the national level and one project at a local level. The result was analyzed by qualitative analysis. There was also a reading from a narrative analysis. When each of the respondents’ interviews was read with focus on each individual interview.

    The results showed that all the respondents in this particular case were in favor of the intervention results. This proved to be consistent with past experience in the international and national as well as the local project. A clear parental involvement emerged as an important factor for the insert effect, but other factors have an impact on the operation of positive effect

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