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  • 1.
    Hansson, Lena
    et al.
    Kristianstad University, Research environment Learning in Science and Mathematics (LISMA). Kristianstad University, School of Education and Environment, Avdelningen för Naturvetenskap.
    Hansson, Örjan
    Kristianstad University, Research environment Learning in Science and Mathematics (LISMA). Kristianstad University, School of Education and Environment, Avdelningen för Naturvetenskap.
    Juter, Kristina
    Kristianstad University, School of Education and Environment, Avdelningen för Naturvetenskap. Kristianstad University, Research environment Learning in Science and Mathematics (LISMA).
    Redfors, Andreas
    Kristianstad University, School of Education and Environment, Avdelningen för Naturvetenskap. Kristianstad University, Research environment Learning in Science and Mathematics (LISMA).
    Ett forskningsprojekt om matematikens roll i gymnasiefysiken2016In: NATDID:s skriftserie: Naturvetenskapernas och teknikens didaktik, no 1, p. 97-101Article in journal (Other (popular science, discussion, etc.))
    Abstract [sv]

    Matematik är ett viktigt verktyg för fysiken och matematiken sägs varafysikens språk. Tidigare forskning visar dock att elever ägnar mycket tid åt matematisk formelmanipulation medan mindre tid och kraft läggs på att relatera fysikens teoretiska modeller och begrepp till verk- ligheten. Syftet med forskningsprojektet vi beskriver här, är att för- djupa vår förståelse av matematikens roll i fysikundervisningen gene- rellt. Vi studerar därför matematikens roll i såväl problemlösningssitu- ationer som lärarledda genomgångar och laborativa moment. Pro- jektet kommer att ge förutsättningar för en ökad förståelse av matema- tikens roll i olika typer av fysikundervisning och för att identifiera i vilka situationer som kommunikationen visar på att matematiken ut- gör hinder eller möjligheter för fysiklärandet. Genom att identifiera så- dana tillfällen öppnas också möjligheten att arbeta för att bryta oöns- kade och stimulera önskade kommunikationsmönster och förstå hur matematiken kan användas på ett konstruktivt sätt i fysikundervis- ningen. Slutsatserna från projektet kommer därför att kunna användas i lärarutbildning, lärarfortbildning och av läromedelsförfattare, liksom av fysiklärare som vill arbeta för att utveckla sin undervisning.

  • 2.
    Hansson, Lena
    et al.
    Kristianstad University, Research environment Learning in Science and Mathematics (LISMA). Kristianstad University, School of Education and Environment, Avdelningen för Naturvetenskap.
    Hansson, Örjan
    Kristianstad University, School of Education and Environment, Avdelningen för Naturvetenskap. Kristianstad University, Research environment Learning in Science and Mathematics (LISMA).
    Juter, Kristina
    Kristianstad University, School of Education and Environment, Avdelningen för Naturvetenskap. Kristianstad University, Research environment Learning in Science and Mathematics (LISMA).
    Redfors, Andreas
    Kristianstad University, School of Education and Environment, Avdelningen för Naturvetenskap. Kristianstad University, Research environment Learning in Science and Mathematics (LISMA).
    Reality - theoretical models - mathematics: a ternary perspective on physics lessons in upper-secondary school2015In: Science & Education, ISSN 0926-7220, E-ISSN 1573-1901, Vol. 24, no 5-6, p. 615-644Article in journal (Refereed)
    Abstract [en]

    This article discusses the role of mathematics during physics lessons in upper-secondary school. Mathematics is an inherent part of theoretical models in physics and makes powerful predictions of natural phenomena possible. Ability to use both theoretical models and mathematics is central in physics. This paper takes as a starting point that the relations made during physics lessons between the three entities Reality, Theoretical models and Mathematics are of the outmost importance. A framework has been developed to sustain analyses of the communication during physics lessons. The study described in this article has explored the role of mathematics for physics teaching and learning in upper-secondary school during different kinds of physics lessons (lectures, problem solving and labwork). Observations are from three physics classes (in total 7 lessons) led by one teacher. The developed analytical framework is described together with results from the analysis of the 7 lessons. The results show that there are some relations made by students and teacher between theoretical models and reality, but the bulk of the discussion in the classroom is concerning the relation between theoretical models and mathematics. The results reported on here indicate that this also holds true for all the investigated organisational forms lectures, problem solving in groups and labwork.

  • 3.
    Hansson, Örjan
    Kristianstad University, School of Education and Environment, Avdelningen för Naturvetenskap. Kristianstad University, Forskningsmiljön Learning in Science and Mathematics (LISMA).
    Begreppskartor: ett verktyg i matematikdidaktisk forskning2008In: Dokumentation av Matematikbiennalen: Matematik - en huvudsak: Stockholm 2008, 31 januari - 1 februari, Stockholm: Stockholms universitet , 2008Conference paper (Other academic)
  • 4.
    Hansson, Örjan
    Kristianstad University, School of Education and Environment, Avdelningen för Naturvetenskap.
    Creating opportunities for prospective teachers to reflect on conceptual relations2011In: Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education / [ed] Ubuz, Behiye, Ankara, Turkey: IGPME , 2011, Vol. 1, p. 310-310Conference paper (Refereed)
  • 5.
    Hansson, Örjan
    Kristianstad University, School of Education and Environment, Avdelningen för Naturvetenskap. Kristianstad University, Forskningsmiljön Learning in Science and Mathematics (LISMA).
    Examining prospective teachers' reasoning of function: a feedback perspective2009In: Nordic research in mathematics education: Proceedings from NORMA 08 / [ed] C Winsölw, Rotterdam The Netherlands: Sense Publishers , 2009, p. 175-184Conference paper (Refereed)
  • 6.
    Hansson, Örjan
    Kristianstad University, School of Education and Environment, Avdelningen för Naturvetenskap. Kristianstad University, Forskningsmiljön Learning in Science and Mathematics (LISMA).
    Examining prospective teachers’ reasoning of functions in school mathematics2009In: Prooceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education / [ed] M. Tzekaki, M. Kaldrimidou, & H. Sakonidis (Eds.), Thessaloniki, 2009, p. 385-Conference paper (Refereed)
  • 7.
    Hansson, Örjan
    Kristianstad University, School of Education and Environment, Avdelningen för Naturvetenskap. Kristianstad University, Forskningsmiljön Learning in Science and Mathematics (LISMA).
    Lärarstudenters syn på funktioner2009In: Matematikdidaktiska frågor: resultat från en forskarskola / [ed] G Brandell, B Grevholm, K Wallby & H Wallin, Göteborg: NCM , 2009, p. 42-55Chapter in book (Other (popular science, discussion, etc.))
  • 8.
    Hansson, Örjan
    Kristianstad University, School of Education and Environment, Avdelningen för Naturvetenskap. Kristianstad University, Research environment Learning in Science and Mathematics (LISMA).
    Matematiska modeller2014Other (Other academic)
  • 9.
    Hansson, Örjan
    Kristianstad University, School of Education and Environment, Avdelningen för Naturvetenskap. Kristianstad University, Forskningsmiljön Learning in Science and Mathematics (LISMA).
    Matematiska modeller - vi studerar ett exempel2013Other (Other (popular science, discussion, etc.))
  • 10.
    Hansson, Örjan
    Kristianstad University, School of Education and Environment, Avdelningen för Naturvetenskap. Kristianstad University, Forskningsmiljön Learning in Science and Mathematics (LISMA).
    Matematiska modeller inom samband och förändring2013Other (Other (popular science, discussion, etc.))
  • 11.
    Hansson, Örjan
    Kristianstad University, School of Education and Environment, Avdelningen för Naturvetenskap.
    Preservice teacher's conceptions of the function concept and its significance in mathematics2007In: Relating practice and research in mathematics education: proocedings of NORMA 05, Fourth Nordic Conference on Mathematics Education / [ed] C Bergsten, B Grevholm, H Stromskag Måsoval & F Rönning, Trondheim: Tapir Academic Press , 2007, p. 271-285Conference paper (Refereed)
    Abstract [en]

    The purpose of this paper is to examine preservice teachers’ conceptions of the function concept as well as their conceptions of the significance of functions in mathematics. A further purpose is to study the effects of an intervention regarding the function concept. Two groups of preservice teachers who are specializing in mathematics and science are participating in the study. The findings indicate changes, firstly in the preservice teachers’ view on the function concept related to the intervention, and secondly with respect to different themes of relevance in their reasoning on the significance and presence of functions in various contexts.

  • 12.
    Hansson, Örjan
    Kristianstad University, Department of Mathematics and Science. Kristianstad University, Forskningsmiljön Learning in Science and Mathematics (LISMA).
    Preservice teachers' conceptions of the function concept, its significance in mathematics and presence in school mathematics2005In: Proceedings of NORMA 05, Fourth Nordic Conference on Mathematics Education / [ed] C. Bergsten, B. Grevholm, H. Strømskag Måsøval & F. Rønning, Trondheim, Norway: Tapir Academic Press , 2005, p. 271-285Conference paper (Refereed)
  • 13.
    Hansson, Örjan
    Kristianstad University, School of Education and Environment, Avdelningen för Naturvetenskap. Kristianstad University, Forskningsmiljön Learning in Science and Mathematics (LISMA).
    Preservice teachers' views of the presence of functions in school mathematics2010In: Proceedings of the 34th Conference of the. International Group for the Psychology of Mathematics Education: Mathematics in different settings / [ed] Pinto, M.M.F., Kawasaki, T.F., Belo Horizonte, Brazil, 2010, p. (vol 3) 49-56Conference paper (Refereed)
    Abstract [en]

    This paper examines preservice teacher's views on the function concept. It includes two groups of preservice teachers as they consider the presence of functions in school mathematics. The findings imply that preservice teachers will give issues related to the concept of function low priority in their teaching, and that they require additional support to develop their views on functions. The study illustrates that discussion about fundamental concepts should be an essential component in the preparation of preservice teachers. It also illustrates that reflection on the presence of functions impacts preservice teachers' reasoning, and serves as a starting point for valuable didactical discussions, which are related to subject matter knowledge, pedagogical content knowledge and curricular knowledge.

  • 14.
    Hansson, Örjan
    Kristianstad University, School of Education and Environment, Avdelningen för Naturvetenskap.
    Prospective teachers’ reasoning on linear and quadratic functions: a case study2011In: Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education / [ed] Ubuz, Behiye, Ankara, Turkey: IGPME , 2011, Vol. 3, p. 17-24Conference paper (Refereed)
  • 15.
    Hansson, Örjan
    Kristianstad University, School of Education and Environment, Avdelningen för Naturvetenskap. Kristianstad University, Forskningsmiljön Learning in Science and Mathematics (LISMA).
    Reflektionsverktyg - att utveckla modelleringsförmåga2013Other (Other (popular science, discussion, etc.))
  • 16.
    Hansson, Örjan
    Kristianstad University, School of Education and Environment, Avdelningen för Naturvetenskap. Kristianstad University, Research environment Learning in Science and Mathematics (LISMA).
    Resonemangsförmåga2014Other (Other (popular science, discussion, etc.))
  • 17.
    Hansson, Örjan
    Kristianstad University, School of Education and Environment, Avdelningen för Naturvetenskap. Kristianstad University, Forskningsmiljön Learning in Science and Mathematics (LISMA).
    Resonemangsförmåga2013Other (Other (popular science, discussion, etc.))
  • 18.
    Hansson, Örjan
    Kristianstad University, School of Education and Environment, Avdelningen för Naturvetenskap. Kristianstad University, Forskningsmiljön Learning in Science and Mathematics (LISMA).
    Samband och förändring2013Other (Other (popular science, discussion, etc.))
  • 19.
    Hansson, Örjan
    Kristianstad University, School of Education and Environment, Avdelningen för Naturvetenskap. Kristianstad University, Forskningsmiljön Learning in Science and Mathematics (LISMA).
    The significance of facilitating feedback of evoked concept images to the concept definition: a case study regarding the concept of function2007In: Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education: vol. 1 / [ed] Woo, J.H., Lew, H.C., Park, K.S. & D.Y., Seoul, South Korea, 2007, p. 224-Conference paper (Refereed)
  • 20.
    Hansson, Örjan
    Kristianstad University, School of Education and Environment, Avdelningen för Naturvetenskap.
    The significance of facilitating feedback of evoked concept images to the concept definition: a case study regarding the concept of function2007In: Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education / [ed] J H Woo, H C Lew, K S Park, & D Y Seo, Seoul, South Korea: Seoul National University , 2007, p. 224-Conference paper (Refereed)
    Abstract [en]

    This research examines one high achieving preservice teacher’s conceptions of the function concept and her line of reasoning as she after a calculus course tries to make clear what constitutes a function. A group of twenty-five preservice teachers specializing in mathematics and science participated in the study. One preservice teacher, called Emma, who completed the calculus course with “high pass” is the research subject for the case study in this presentation. The concepts of function and equation are closely linked for the preservice teacher in question. In the advancement of the preservice teacher’s reasoning on functions, feedback from evoked concept images to the concept definition is central, and leads her to a more developed understanding of what constitutes a function. The findings of the research call attention to one component of importance in the development of a concept image, namely, the feedback-process from evoked concept images to the concept definition. Based on the case study results, preservice teachers seemingly need to be exposed to problem formulations concerning the relationships of the function concept to other mathematical concepts (this conclusion is also supported by Hansson, 2006). It was made clear during the interview with Emma that she is not experienced in working with such problems. During an individual’s reasoning, the concept image will almost always be evoked, whereas the concept definition will remain inactive or even be forgotten (Tall & Vinner, 1981). The study indicates that one significant component in the development of preservice teachers’ understanding of the function concept could be to stimulate a feedback of evoked concept images to the concept definition in various contexts, as when Emma comes to a better understanding in the interview. The results of the study also support Vinner’s (1991, 1992) suggestion that this type of reconnection is primarily possible with problems that are not of the standard variety.

    References

    Hansson, Ö. (2006). Studying the views of preservice teachers on the concept of function(LTU doctoral thesis series No. 2006:22). Luleå: Luleå University of Technology. Tall, D., & Vinner, S. (1981). Concept images and concept definition in mathematics with particular reference to limits and continuity. Educational Studies in Mathematics, 12, 151-169.Vinner, S. (1991). The role of definitions in the teaching and learning of mathematics. In D.Tall (Ed.), Advanced mathematical thinking (pp. 65-81). Dordrecht: Kluwer.Vinner, S. (1992). The function concept as prototype for problems in mathematics. In G.Harel & E. Dubinsky (Eds.), The concept of function: Aspects of epistemology and pedagogy (pp. 195-213). Washington, DC: Mathematical Association of America.

  • 21.
    Hansson, Örjan
    Kristianstad University, School of Education and Environment, Avdelningen för Naturvetenskap. Kristianstad University, Forskningsmiljön Learning in Science and Mathematics (LISMA).
    Tillfällen att utveckla fördjupad förståelse - en bristvara?2013Other (Other (popular science, discussion, etc.))
  • 22.
    Hansson, Örjan
    et al.
    Kristianstad University, Research environment Learning in Science and Mathematics (LISMA). Kristianstad University, School of Education and Environment, Avdelningen för Naturvetenskap.
    Hansson, Lena
    Kristianstad University, Research environment Learning in Science and Mathematics (LISMA). Kristianstad University, School of Education and Environment, Avdelningen för Naturvetenskap.
    Juter, Kristina
    Kristianstad University, Research environment Learning in Science and Mathematics (LISMA). Kristianstad University, School of Education and Environment, Avdelningen för Naturvetenskap.
    Redfors, Andreas
    Kristianstad University, Research environment Learning in Science and Mathematics (LISMA). Kristianstad University, School of Education and Environment, Avdelningen för Naturvetenskap.
    An attempt to investigate the use of mathematics in physics classrooms2015In: Proceedings of the 39th Conference of the International Group for the Psychology of Mathematics Education / [ed] Kim Beswick, Tracey Muir, Jill Wells, 2015, Vol. 3, p. 25-32Conference paper (Refereed)
    Abstract [en]

    We outline a framework to study the use of mathematics in physics classrooms. The framework focuses on the relations made between Reality, Theoretical models and Mathematics. In this paper the analyses of one teacher and her 3rd year classes at secondary school are presented. The results show that phenomena in reality are often used as a short prelude to put focus on the relationship theoretical model and mathematics. Mathematics is generally used in an instrumental way to handle various formulas without further insight or discussion of the related models or their relation to reality. There is a lack of varied communication with a structural use of mathematics, i.e., mathematics used to support reasoning in relation to a theoretical model, highlighting the meaning of concepts and models in the studied classrooms. 

  • 23.
    Hansson, Örjan
    et al.
    Kristianstad University, School of Education and Environment, Avdelningen för Naturvetenskap.
    Holmberg, Inger
    Kristianstad University.
    Grevholm, Barbro
    Kristianstad University.
    Hur en innovativ lärandemiljö kan stödja  utvecklingen av lärarstuderandes kommunikationsförmåga i matematik2003In: / [ed] Ingrid Järnefelt, Lund: Lunds universitet , 2003, p. 45-48Conference paper (Refereed)
  • 24.
    Holmberg, Inger
    et al.
    Kristianstad University, School of Education and Environment.
    Grevholm, Barbro
    Kristianstad University, School of Education and Environment.
    Hansson, Örjan
    Kristianstad University, School of Education and Environment, Avdelningen för Naturvetenskap.
    Hur en innovativ lärandemiljö kan stödja utvecklingen av lärarstuderandes kommunikationsförmåga i matematik2004In: / [ed] Järnefelt, Ingrid, Lund: UCLU Lunds universitet , 2004, p. 45-48Conference paper (Refereed)
  • 25.
    Juter, Kristina
    et al.
    Kristianstad University, Faculty of Education, Research environment Learning in Science and Mathematics (LISMA). Kristianstad University, Faculty of Education, Avdelningen för matematik- och naturvetenskapernas didaktik.
    Hansson, Lena
    Kristianstad University, Faculty of Education, Avdelningen för matematik- och naturvetenskapernas didaktik. Kristianstad University, Faculty of Education, Research environment Learning in Science and Mathematics (LISMA).
    Hansson, Örjan
    Kristianstad University, Faculty of Education, Avdelningen för matematik- och naturvetenskapernas didaktik. Kristianstad University, Faculty of Education, Research environment Learning in Science and Mathematics (LISMA).
    Redfors, Andreas
    Kristianstad University, Faculty of Education, Research environment Learning in Science and Mathematics (LISMA). Kristianstad University, Faculty of Education, Avdelningen för matematik- och naturvetenskapernas didaktik.
    Upper secondary physics teachers’ views of mathematics2018In: Proceedings of Madif 11, 2018, p. 222-223Conference paper (Refereed)
    Abstract [en]

    Physics teachers at upper secondary school indirectly teach mathematics in their physics classes through their teaching strategies and preferred ways of using mathematics. Their views of physics and mathematics are important for the way they depict mathematics to the students. A web-questionnaire was administered to Swedish physics teachers. Part of the questions investigated views of mathematics, i.e. as a means for application, as a schema, as a formal construct or as processes. Mathematics as a means for application was the dominant opinion. Students’ lack of knowledge in mathematics was regarded as a problem to many of the teachers, and particularly problem solving and modelling. Students’ conceptual and relevance proficiencies in mathematics were less problematical.

  • 26.
    Redfors, Andreas
    et al.
    Kristianstad University, School of Education and Environment, Avdelningen för Naturvetenskap. Kristianstad University, Research environment Learning in Science and Mathematics (LISMA).
    Hansson, Lena
    Kristianstad University, School of Education and Environment, Avdelningen för Naturvetenskap. Kristianstad University, Research environment Learning in Science and Mathematics (LISMA).
    Hansson, Örjan
    Kristianstad University, School of Education and Environment, Avdelningen för Naturvetenskap. Kristianstad University, Research environment Learning in Science and Mathematics (LISMA).
    Juter, Kristina
    Kristianstad University, School of Education and Environment, Avdelningen för Naturvetenskap. Kristianstad University, Research environment Learning in Science and Mathematics (LISMA).
    A framework to explore the role of mathematics during physics lessons in upper-secondary school2016In: Insights from research in science teaching and learning: selected papers from the ESERA 2013 Conference / [ed] N. Papadouris, A. Hadjigeorgiou and C. Constantinou, Dordrecht: Springer Publishing Company, 2016, p. 139--151Chapter in book (Refereed)
    Abstract [en]

    This chapter discusses a framework for analysing the role of mathematics during physics lessons in upper-secondary school. It takes as a starting point that relations made during physics lessons between Reality, Theoretical models and Mathematics are of the outmost importance. The framework was developed to analyse the communication during physics lessons. It was developed during a pilot study exploring the role of mathematics for physics teaching and learning in upper-secondary school during different kinds of physics lessons (lectures, problem solving and labwork). In the overall project observations have been made in three physics classes (in total 7 lessons) led by one teacher. Here the developed analytical framework is described together with selected results from one class (3 lessons) showing how the framework could be used. This chapter describes and discusses the uses of the framework and shows how results on students and teachers usages of links between the three entities Reality, Theoretical models and Mathematics can be brought to the forefront in an analysis of complex physics teaching situations. And, how the framework can be used to analyse the different organisational forms: lectures, problem solving in groups and labwork.

  • 27.
    Redfors, Andreas
    et al.
    Kristianstad University, School of Education and Environment, Avdelningen för Naturvetenskap. Kristianstad University, Research environment Learning in Science and Mathematics (LISMA).
    Hansson, Lena
    Kristianstad University, School of Education and Environment, Avdelningen för Naturvetenskap. Kristianstad University, Research environment Learning in Science and Mathematics (LISMA).
    Hansson, Örjan
    Kristianstad University, School of Education and Environment, Avdelningen för Naturvetenskap. Kristianstad University, Research environment Learning in Science and Mathematics (LISMA).
    Juter, Kristina
    Kristianstad University, School of Education and Environment, Avdelningen för Naturvetenskap. Kristianstad University, Research environment Learning in Science and Mathematics (LISMA).
    Relating theoretical models, mathematical representations and the real world in upper-secondary physics2014Conference paper (Refereed)
  • 28.
    Redfors, Andreas
    et al.
    Kristianstad University, School of Education and Environment, Avdelningen för Naturvetenskap. Kristianstad University, Research environment Learning in Science and Mathematics (LISMA).
    Hansson, Lena
    Kristianstad University, School of Education and Environment, Avdelningen för Naturvetenskap. Kristianstad University, Research environment Learning in Science and Mathematics (LISMA).
    Hansson, Örjan
    Kristianstad University, School of Education and Environment, Avdelningen för Naturvetenskap. Kristianstad University, Research environment Learning in Science and Mathematics (LISMA).
    Juter, Kristina
    Kristianstad University, School of Education and Environment, Avdelningen för Naturvetenskap. Kristianstad University, Research environment Learning in Science and Mathematics (LISMA).
    The role of mathematics in the teaching and learning of physics2014In: Ebook proceedings of the ESERA 2013 conference, Nicosia, Cyprus: European Science Education Research Association , 2014, Part 2, p. 376-383Conference paper (Refereed)
    Abstract [en]

    This paper discusses the role of mathematics in physics teaching andlearning. The intention and strength of science is to describe what happens in the realworld by organizing explanations through theories and theoretical models. It has beenwidely suggested that learning in science is influenced by views about the nature ofscientific knowledge. Furthermore, mathematics is an inherent part of theories andmakes powerful predictions of natural phenomena possible. Ability to use mathematicsto argue and prove results is central in physics. Students have been found tostruggle with physics problems where they need to relate mathematically formulatedtheoretical models to the real world. This project has explored the role of mathematicsfor physics teaching and learning in upper-secondary school through investigations ofrelations made during physics lessons (lectures, problem solving and lab-work)between The real world – Theoretical models – Mathematics. A preliminary analysisindicate that there are some connections made by students and teacher betweentheories and the real world, but the bulk of the discussion in the classroom is concerningthe relation between theoretical models and mathematics, which is in linewith earlier research on problem solving. The preliminary results reported on hereindicate that this also holds true for all the investigated organisational forms lectures,problem solving in groups and lab-work. A finalized and extended analysis will bepublished elsewhere.

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