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  • 1.
    Hansson, Lena
    et al.
    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, Research environment Learning in Science and Mathematics (LISMA). Kristianstad University, School of Education and Environment, Avdelningen för Naturvetenskap.
    Juter, Kristina
    Kristianstad University, Faculty of Education, Research environment Learning in Science and Mathematics (LISMA). Kristianstad University, Faculty of Education, Avdelningen för matematik- och naturvetenskapernas didaktik.
    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.
    A case study of the role of mathematics in physics textbooks and in associated lessons2019In: Mathematics in physics education / [ed] G. Pospiech, M. Michelini, & B. Eylon, Dordrecht: Springer, 2019, p. 293-316Chapter in book (Refereed)
    Abstract [en]

    This chapter describes a case study of the role of mathematics in physics textbooks and in associated teacher led lessons. The theoretical framework (Hansson et al. 2015) used in the analysis focuses on relations communicated between three entities: Theoretical models, Mathematics, and Reality. Previously the framework has been used for analysing classroom situations. In this chapter, the framework is further developed and refined, and for the first time used to analyse physics textbooks. The case study described here is a synchronised analysis of a physics textbook and associated classroom communication during teacher led lessons, and contributes with an in-depth description of relations made between Theoretical modelsMathematicsand Reality. With the starting point in this case we discuss future uses of the analysis framework. We also raise questions for further research concerning how physics textbooks support and not support a meaningful physics teaching with respect to the role of mathematics and how relations between Theoretical modelsMathematics, and Reality are communicated.

  • 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, 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.

  • 3.
    Hansson, Lena
    et al.
    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, Research environment Learning in Science and Mathematics (LISMA). Kristianstad University, School of Education and Environment, Avdelningen för Naturvetenskap.
    Juter, Kristina
    Kristianstad University, Faculty of Education, Research environment Learning in Science and Mathematics (LISMA). Kristianstad University, Faculty of Education, Avdelningen för matematik- och naturvetenskapernas didaktik.
    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.
    The notion of projectile motion: a case study2018In: Proceedings of the 42nd Conference of theInternational Group for the Psychology of Mathematics Education / [ed] E. Bergqvist, M. Österholm, C. Granberg & L. Sumpter, 2018, Vol. 5, p. 243-Conference paper (Other academic)
    Abstract [en]

    This study adds to research on the use of mathematics in physics classrooms at upper secondary school. The aim is to look closer into what types of transfer do the teacher and textbook set up for the pupils with respect to ways of reasoning from other physics contexts as well as from mathematics. The frame for analysis is an analytical model based on relations made between Reality, Theoretical models and Mathematics (Redfors, Hansson, Hansson & Juter, 2016). Horizontal and vertical transfer is defined as mappings of new information to an activated known structure and as the creation of a new structure in the learner’s mind, respectively (Rebello, Cui, Benett, Zollman & Ozimek, 2007). Transfer occurs within mathematics and physics and also between the topics.We will focus on a physics lecture (40 min, video recorded) in a 3rd year class. When reasoning movement of charged particles in electric fields the teacher stresses hori- zontal transfer from mechanics and projectile motion. The procedure used is focused on analysing movement in “x direction” and “y direction” separately, not explicitly relating movement to the field direction. Whereas the argumentation in the textbook is based on movement in relation to the existence of a field direction. When considering velocity, the main focus is in both cases on a framework where the components of velocity is central.The tangent of a curve is a notion the students in the present study are quite familiar with from their courses in mathematics, which makes an opportunity for transfer from a mathematics context to help understanding physics. However, the notion of tangent is not used in the textbook or by the teacher in relation to velocity. Using the vector concept in this way would require students and teachers to perform a vertical transfer. This has been shown hard for both students and teachers. However, introducing this way of reasoning had made use of an opportunity for structural use of mathematics – an opportunity overlooked by both teacher and textbook.

  • 4.
    Hansson, Örjan
    Kristianstad University, Faculty of Education, Research environment Learning in Science and Mathematics (LISMA). Kristianstad University, School of Education and Environment, Avdelningen för Naturvetenskap.
    Samband och förändring: en översikt med exempel på uppgifter2015Other (Other academic)
  • 5.
    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. 

  • 6.
    Hansson, Örjan
    et al.
    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, 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).
    Juter, Kristina
    Kristianstad University, Faculty of Education, Research environment Learning in Science and Mathematics (LISMA). Kristianstad University, Faculty of Education, Avdelningen för matematik- och naturvetenskapernas didaktik.
    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.
    The notion of projectile motion: a case study2018Conference paper (Refereed)
    Abstract [en]

    This study adds to research on the use of mathematics in physics classrooms at upper secondary school. The aim is to look closer into what types of transfer do the teacher and textbook set up for the pupils with respect to ways of reasoning from other physics contexts as well as from mathematics. The frame for analysis is an analytical model based on relations made between Reality, Theoretical models and Mathematics (Redfors, Hansson, Hansson & Juter, 2016). Horizontal and vertical transfer is defined as mappings of new information to an activated known structure and as the creation of a new structure in the learner’s mind, respectively (Rebello, Cui, Benett, Zollman & Ozimek, 2007). Transfer occurs within mathematics and physics and also between the topics.We will focus on a physics lecture (40 min, video recorded) in a 3rd year class. When reasoning movement of charged particles in electric fields the teacher stresses hori- zontal transfer from mechanics and projectile motion. The procedure used is focused on analysing movement in “x direction” and “y direction” separately, not explicitly relating movement to the field direction. Whereas the argumentation in the textbook is based on movement in relation to the existence of a field direction. When considering velocity, the main focus is in both cases on a framework where the components of velocity is central.The tangent of a curve is a notion the students in the present study are quite familiar with from their courses in mathematics, which makes an opportunity for transfer from a mathematics context to help understanding physics. However, the notion of tangent is not used in the textbook or by the teacher in relation to velocity. Using the vector concept in this way would require students and teachers to perform a vertical transfer. This has been shown hard for both students and teachers. However, introducing this way of reasoning had made use of an opportunity for structural use of mathematics – anopportunity overlooked by both teacher and textbook.

  • 7.
    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)
  • 8.
    Hansson, Örjan
    et al.
    Kristianstad University, Faculty of Education, Research environment Learning in Science and Mathematics (LISMA). Kristianstad University, School of Education and Environment, Avdelningen för Naturvetenskap.
    Juter, Kristina
    Kristianstad University, Faculty of Education, Research environment Learning in Science and Mathematics (LISMA). Kristianstad University, Faculty of Education, Avdelningen för matematik- och naturvetenskapernas didaktik.
    Drug calculations in nursing education: is mathematics a problem2018In: Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education, Umeå, 2018, Vol. 5, p. 244-244Conference paper (Refereed)
    Abstract [en]

    This study concerns the teaching of drug calculations in nursing education. It is part of a larger study and focuses on the first year of a three-year nursing program when the students are introduced to drug calculations. The students who attended the first year on the program was divided into smaller groups. We followed one group where the lecture and problem-solving session was video recorded.It is well known that drug calculations are a critical component in nursing practice. Nurses need to do drug calculations correctly and as part of their nursing education must take a drug calculation test obtaining no errors in the results. However, in spite of drug calculation tests many adverse events occur in nursing practice (e.g., Røykenes & Larsen, 2010). Studies of nursing practice show that mathematics enters practices in a rich variety of ways and that it is not advisable to avoid the complexity of a situation by only using standard methods to capture its visible arithmetic and teach it (Coben & Weeks, 2014). To restrict the teaching to an elementary use of mathematics will not cover all the knowledge that is actually relevant to practice. In routine use, mathe- matical reasoning can be almost invisible and many artefacts in the nursing profession often depends on this invisibility. But at times nurses will need to understand under- lying mathematical models to sort out what is happening or what has gone wrong (Pozzi, Noss & Hoyles, 1998).The results of the current study show that the teaching of first-year students did not support conceptual understanding of mathematics including discussions about mathe- matical reasoning or relevant mathematical concepts. Instead, the students were ad- vised to forget their previous mathematical skills – in particular if they felt insecure about mathematics – and apply “safe” methods with a strong focus on instrumental use. For example, in drug dose calculations a triangular arrangement of dosage (d), concentration (c) and volume (v) was used in relation to the “formula” d=cv, instead of reasoning about how to solve an equation. Discussions about the use of  mathematicsand underlying models were absent in the teaching.

  • 9.
    Hansson, Örjan
    et al.
    Kristianstad University, Faculty of Education, Research environment Learning in Science and Mathematics (LISMA). Kristianstad University, School of Education and Environment, Avdelningen för Naturvetenskap.
    Juter, Kristina
    Kristianstad University, Faculty of Education, Research environment Learning in Science and Mathematics (LISMA). Kristianstad University, Faculty of Education, Avdelningen för matematik- och naturvetenskapernas didaktik.
    Drug calculations in nursing education: is mathematics a problem?2018In: Proceedings of the 42nd conference of the international group for the Psychology of mathematics education / [ed] E. Bergqvist, M. Österholm, C. Granberg & L. Sumpter, 2018, Vol. 5, p. 244-Conference paper (Other academic)
  • 10.
    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)
  • 11.
    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.

  • 12.
    Redfors, Andreas
    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, Research environment Learning in Science and Mathematics (LISMA). Kristianstad University, School of Education and Environment, Avdelningen för Naturvetenskap.
    Juter, Kristina
    Kristianstad University, Faculty of Education, Research environment Learning in Science and Mathematics (LISMA). Kristianstad University, Faculty of Education, Avdelningen för matematik- och naturvetenskapernas didaktik.
    The role of mathematics for physics teaching and learning in upper-secondary school2018Conference paper (Refereed)
    Abstract [en]

    The aim of this three-year study is to further contribute to the understanding of how relations between Reality – Theoretical models – Mathematics are communicated in different kinds of instructional situations (lectures, problem solving and labwork) in Swedish uppersecondary physics. A developed analytical framework from the pilot (Hansson, Hansson, Juter & Redfors 2015) is used to focus the analysis of the classroom communication on relations made (by teachers and students) between Reality – Theoretical models – Mathematics. Results from classroom studies during spring 2018 will be reported and discussed at the conference.

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