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  • 1.
    Brunström, Mats
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Matematiska resonemang i en lärandemiljö med dynamiska matematikprogram2015Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    The overall problem that formed the basis for this thesis is that students get limited opportunity to develop their mathematical reasoning ability while, at the same time, there are dynamic mathematics software available which can be used to foster this ability. The aim of this thesis is to contribute to knowledge in this area by focusing on task design in a dynamic software environment and by studying the reasoning that emerges when students work on tasks in such an environment. To analyze students’ mathematical reasoning, a new analytical tool was developed in the form of an expanded version of Toulmin’s model.

    Results from one of the studies in this thesis show that exploratory tasks in a dynamic software environment can promote mathematical reasoning in which claims are formulated, examined and refined in a cyclic process. However, this reasoning often displayed a lack of the more conceptual, analytic and explanatory reasoning normally associated with mathematics. This result was partly confirmed by another of the studies. Hence, one key question in the thesis has been how to design tasks that promote conceptual and explanatory reasoning. Two articles in the thesis deal with task design. One of them suggests a model for task design with a focus on exploration, explanation, and generalization. This model aims, first, to promote semantic proof production and then, after the proof has been constructed, to encourage further generalizations. The other article dealing with task design concerns the design of prediction tasks to foster student reasoning about exponential functions. The research process pinpointed key didactical variables that proved crucial in designing these tasks.

  • 2.
    Brunström, Mats
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Students’ Mathematical Reasoning in a Dynamic Software EnvironmentManuscript (preprint) (Other academic)
    Abstract [en]

    Mathematical reasoning has been identified as one of the key competencies needed to master mathematics. It is also well documented that dynamic mathematics software can be utilized to provide students with opportunities to practice different aspects of mathematical reasoning. In this study an expanded version of Toulmin’s model of argumentation was used to analyze the reasoning that emerged when three student pairs used GeoGebra to explore how the different parameters influence the graph of the function y = A sin (Bx + C) + D. Several characteristic features, both promising and cautionary, were discerned in the students’ reasoning.

  • 3.
    Brunström, Mats
    et al.
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Fahlgren, Maria
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Designing Prediction Tasks in a Mathematics Software Environment2015In: The International Journal for Technology in Mathematics Education, ISSN 1744-2710, E-ISSN 2045-2519, Vol. 22, no 1, p. 3-18Article in journal (Refereed)
    Abstract [en]

    There is a recognized need in mathematics teaching for new kinds of task which exploit the affordances provided by new technology. This paper focuses on the design of prediction tasks to foster student reasoning about exponential functions in a mathematics software environment. It draws on the first iteration of a design based research study conducted by the authors in collaboration with four upper secondary school teachers. A task sequence was trailed with four 10th grade classes, involving a total of 85 students. The research process pinpointed key didactical variables that proved crucial in designing these tasks. As well as being useful in the task design process, the didactical variables were found to be valuable in the processes of analysis and revision. While the didactical variables identified a priori were informed by the research literature concerning reasoning and functions, those identified a posteriori deal mainly with scaffolding issues that emerged.  

  • 4.
    Brunström, Mats
    et al.
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Fahlgren, Maria
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    GeoGebra - A Tool to Create Favorable Learning Situations with Emphasize on Logical Reasoning and Communication2009Conference paper (Other (popular science, discussion, etc.))
    Abstract [en]

    Logic reasoning and communication are general competencies, important in all areas of mathematics. We think that one of the major advantages of GeoGebra is the possibility to create favorable learning situations for these competencies. We would like to investigate these possibilities. Our main interest is to find out how students use logic reasoning and how they communicate when they work in pairs with GeoGebra. We think that investigating the validity of certain geometrical statements is a kind of task appropriate for this purpose

  • 5.
    Brunström, Mats
    et al.
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Fahlgren, Maria
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Orchestration of mathematical discussions drawing on students’ computer-based work2017In: ICT in mathematics education: the future and the realities: Proceedings of MADIF 10 The tenth research seminar of the Swedish Society for Research in Mathematics Education / [ed] Johan Häggström, Eva Norén, Jorryt van Bommel, Judy Sayers, Ola Helenius, Yvonne Liljekvist, Göteborg: Svensk förening för MatematikDidaktisk Forskning - SMDF, 2017, p. 77-87Conference paper (Refereed)
    Abstract [en]

    Research points out the importance of following up students’ work on computerbasedtasks with whole-class discussions in which students play a central role.However, at the same time, research highlights the challenge for teachers in orchestratingsuch follow-up discussions. This paper examines whether an establishedmodel developed as guidance for teachers to orchestrate mathematical whole-classdiscussions (Stein, Engle, Smith & Hughes, 2008) could be useful in this educationalsetting. Students’ written responses to two different tasks are the main data used toexamine the model. The results indicate that the model has great potential to guidethese follow-up discussions

  • 6.
    Brunström, Mats
    et al.
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Mossberg, Eva
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Vinerean-Bernhoff, Mirela
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    An exploratory approach to engineering mathematics using GeoGebra2016Conference paper (Other academic)
  • 7.
    Fahlgren, Maria
    et al.
    Karlstad University, Faculty of Health, Science and Technology (starting 2013).
    Brunström, Mats
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    A Model for Task Design with Focus on Exploration,Explanation, and Generalization in a Dynamic GeometryEnvironment2014In: Technology, Knowledge and Learning, ISSN 2211-1662, E-ISSN 2211-1670, Vol. 19, no 3, p. 287-315Article in journal (Refereed)
    Abstract [en]

    The increasing availability of new technologies in schools provides new possibilities

    for the integration of technology in mathematics education. However, research

    has shown that there is a need for new kinds of task that utilize the affordances provided by

    new technology. Numerous studies have demonstrated that dynamic geometry environments

    provide opportunities for students to engage in mathematical activities such as

    exploration, conjecturing, explanation, and generalization. This paper presents a model for

    design of tasks that promote these kinds of mathematical activity, especially tasks that

    foster students to make generalizations. This model has been primarily developed to suit

    the use of dynamic environments in tackling geometrical locus problems. The model was

    initially constructed in the light of previous literature. This initial model was used to design

    a concrete example of such a task situation which was tested in action through a case study

    with two doctoral students. Findings from this case study were used to guide revision of the

    initial model.

  • 8.
    Fahlgren, Maria
    et al.
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Brunström, Mats
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Geometriska begrepp och metoder i historien: Exemplen area och klassiska konstruktioner2019Report (Refereed)
  • 9.
    Fahlgren, Maria
    et al.
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Brunström, Mats
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    How the word 'mathematical' influences students’ responses to explanation tasks in a dynamic mathematics software environment2018In: Proceedings of the Fifth ERME Topic Conference (ETC 5) on Mathematics Education in the Digital Age (MEDA) / [ed] Hans-Georg Weigand, Alison Clark-Wilson, Ana Donevska-Todorova, Eleonora Faggiano, Niels Grønbæk, Jana Trgalova, Copenhagen, Denmark: University of Copenhagen , 2018, p. 83-90Conference paper (Refereed)
    Abstract [en]

    Task design is a central issue in mathematics education, not least in relation to digital technology. This paper reports how a smal lbut significant change in wording affects students’ explanatory responses. The study is comparative and involves 229 10th grade students working on tasks designed for a dynamic mathematics software environment. The findings indicate that inclusion of the word ‘mathematical’ prompted students to use algebraic symbols and algebraic arguments, to a higher degree.

  • 10.
    Fahlgren, Maria
    et al.
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Brunström, Mats
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Using slider tools to explore and validate2015In: CERME9 Proceedings of the Ninth Congress of the European Society for Research in Mathematics Education, 2015Conference paper (Refereed)
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