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  • 1. Häggström, Johan
    et al.
    Norén, Evavan Bommel, JorrytKarlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.Sayers, JudyHelenius, OlaLiljekvist, YvonneKarlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    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,
Karlstad, January 26–27, 20162017Conference proceedings (editor) (Refereed)
  • 2.
    Jankvist, Uffe
    et al.
    University of Southern Denmark.
    Ryve, Andreas
    Mälardalen University.
    van Bommel, Jorryt
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Waege, Kjersti
    Norvegian University of Science and Technology.
    Future challenges of mathematics education research in the Nordic region: Young researchers’ perspective2011In: Proceedings of NORMA 11: the sixth Nordic Conference on Mathmatics Education / [ed] Guðný Helga Gunnarsdóttir, Reijkjavik: University of Iceland Press, 2011Conference paper (Refereed)
    Abstract [en]

     In the last decade research in mathematics education has grown and consolidated in the Nordic countries. New and younger researchers are entering the field as a result of the organization of solid doctoral programs and the growth of teaching and research environments in higher education institutions. The social, cultural and economic contexts of our countries have also changed in the last decade. The question of which are the main challenges for research in the years to come is worth exploring for a community starting a new decade of work. The intention of the panel is to generate a discussion in the community by having young researchers present their views on: (1) which topics of research the Nordic region has contributed to the world and that deserve being strengthened in the future; (2) which new topics of research that may become relevant as social changes pose new demands on our knowledge and understanding of the practices of mathematics education in the educational system; and (3) which institutional affordances and constraints young researchers experience for the development of research 

  • 3.
    Liljekvist, Yvonne
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Olin-Scheller, Christina
    Karlstad University, Faculty of Arts and Social Sciences (starting 2013).
    Professional Learning Communities in a Web 2.0 World: Rethinking the Conditions for Professional Development2017In: Teacher Empowerment Toward Professional Development and Practices: Perspectives Across Borders / [ed] Amzat, I. H. & Valdez, N. P., Springer, 2017, 269-280 p.Chapter in book (Refereed)
  • 4.
    Liljekvist, Yvonne
    et al.
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    van Bommel, Jorryt
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Kunskaper för matematikundervisning: ett lärarutbildarperspektiv2013In: KAPET, ISSN 1653-4743, Vol. 9, no 1, 101-106 p.Article in journal (Other academic)
  • 5.
    Liljekvist, Yvonne
    et al.
    Karlstad University, Faculty of Health, Science and Technology (starting 2013).
    van Bommel, Jorryt
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Mathematical knowledge for teaching as a measure of coherence in instruction materials on the Internet2013In: Proceedings of Eighth Congress of European Society for Research in Mathematics Education, CERME 8. Alanya, Turkey: ERME.: Working group 17: From a study of teaching practices to issues in teacher education / [ed] Behiye Ubuz, Cigdem Haser, Maria Alessandra Mariotti, Ankara: Middle East Technical University , 2013Conference paper (Refereed)
  • 6.
    Liljekvist, Yvonne
    et al.
    Karlstad University, Faculty of Technology and Science, Department of Mathematics.
    van Bommel, Jorryt
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Networking theories: The 'kom project' and 'adding it up' through the lens of a learning situation2011In: Proceedings of the Seventh Congress of the European Society for Research in Mathematics Education / [ed] Marta Pytlak, Tim Rowland, Ewa Swoboda, Rzeszów: University of Rzeszów , 2011, 3001-3002 p.Conference paper (Refereed)
  • 7. Moerlands, Frans
    et al.
    van Bommel, Jorryt
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Alla kan räkna med ägg2017In: Nämnaren : tidskrift för matematikundervisning, ISSN 0348-2723, Vol. 1, no 201, 15-21 p.Article in journal (Other (popular science, discussion, etc.))
  • 8.
    Palmér, Hanna
    et al.
    Linnéuniversitetet.
    van Bommel, Jorryt
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Exploring the role of representations when young children solve a combinatorial task2017In: 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,
Karlstad, January 26–27, 2016 / [ed] J. Häggström, E. Norén, J. van Bommel, J. Sayers, O. Helenius, Y. Liljekvist, Linköping: SMDF , 2017Conference paper (Refereed)
  • 9.
    Palmér, Hanna
    et al.
    Linnéuniversitetet, Institutionen för datavetenskap, fysik och matematik, DFM.
    van Bommel, Jorryt
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Problemlösning som utgångspunkt: Matematikundervisning i förskoleklass2016Book (Other (popular science, discussion, etc.))
    Abstract [sv]

    Förutom en introduktion till ett problemlösande arbetssätt presenteras genomförda problemuppgifter med tydliga kopplingar till styrdokumenten. Varje problemuppgift har testats och bearbetats, och i boken finns förslag till fördjupning eller förenkling av problemuppgifterna. Författarna ger även exempel på hur eleverna kan utvärdera både problemuppgifterna och det problemlösande arbetssättet. Boken vänder sig till blivande och verksamma lärare i förskola, förskoleklass och de tidiga skolåren.

  • 10.
    Palmér, Hanna
    et al.
    Linnéuniversitetet.
    van Bommel, Jorryt
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Ebbelind, Andreas
    How about teaching young children mathematics through challenging problem solving?: Symposium2015Conference paper (Refereed)
    Abstract [en]

    A considerable amount of research shows that it is both possible and plausible to teach young children mathematics. However, there is less agreement regarding the content and the framing of such teaching. In this symposium we will present and discuss possibilities with teaching young children mathematics through challenging problem solving. Based on empirical studies of children 3-6 years old we will imply that it is both possible and plausible to teach young children mathematics through challenging problem solving. This since the children in the presented studies both learn a lot of mathematics and enjoy the activities they are involved in.

  • 11.
    van Bommel, Jorryt
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Att få de rätta felsvaren2014In: Matematikundervisning i praktiken / [ed] Karin Wallby, Ulrica Dahlberg, Ola Helenius, Johan Häggström och Anders Wallby, Göteborg: Nationellt centrum för matematikutbildning (NCM), 2014, 261-266 p.Chapter in book (Refereed)
  • 12.
    van Bommel, Jorryt
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Att få de rätta felsvaren2012In: Nämnaren : tidskrift för matematikundervisning, ISSN 0348-2723, Vol. 3, 13-16 p.Article in journal (Other academic)
    Abstract [sv]

    Erfarna lärare har kunskaper om elevers vanliga missuppfattningar i matematik. Genom att på ett klokt sätt ta hänsyn till det då diagnostiska frågor konstrueras, kan elevers svar avslöja en del om hur de tänker. I artikeln finns exempel på sådana svar och missuppfattningar.

  • 13.
    van Bommel, Jorryt
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Didactiek van de rekendidactiek2013In: Rekenen-wiskunde op niveau, Utrecht: Utrecht SciencePark de Uithof , 2013, 15- p.Conference paper (Refereed)
    Abstract [nl]

    Didactiek van de rekendidactiek!

    Waar moet ik aan denken als lerarenopleider bij het geven van rekenen-wiskunde in een cursus didactiek? Welke stappen moeten studenten maken om de didactiek tot zich te kunnen nemen en wat zijn belangrijke factoren om mee te nemen in de voorbereiding van didactiek lessen?

    Antwoorden op deze vragen staan beschreven in mijn proefschrift Improving teaching, improving learning, improving as a teacher – Mathematical knowledge for teaching as an object of learning.  De studie beschreven in het proefschrift werd uitgevoerd door lerarenopleiders rekenen-wiskunde in een cursus didactiek op een Zweedse lerarenopleiding (vergelijkbaar met de Pabo). De lerarenopleiders wilden hun lessen in didactiek verbeteren om zo de wiskundedidactische kennis van studenten te verbeteren. De methode die gebruikt werd was een zogenaamde learning study, een mix van design research en de in Japan gebruikte lesson study. Specifiek voor een learning study is dat een leerteorie, meestal variatietheorie, wordt gebruikt zowel in het plannen als in het analyseren van lessen en testen. Door te focusseren op het leerobject wordt er gezocht naar kritische factoren voor het begrijpen van dat leerobject. Vier zulke aspecten kwamen in de studie naar voren om in acht te nemen bij het onderwijzen van reken- en wiskundedidactiek.

    In de presentatie wordt er kort aandacht besteed aan het design van de studie, waarna het resultaat wordt gepresenteerd, ondersteund met voorbeelden uit de verzamelde data. Om de studie te kunnen plaatsen binnen de context van de Zweedse lerarenopleiding zal een kort overzicht van het Zweedse schoolsysteem en de bijbehorende structuur van de lerarenopleiding worden gegeven. Afsluitend wil ik graag kijken naar in welke mate de resultaten herkenbaar en toepasbaar zijn voor lerarenopleiders in Nederland.

  • 14.
    van Bommel, Jorryt
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Een learning study voor het verbeteren van het onderwijs in rekendidactiek aan een lerarenopleiding2014In: Panama-Post, ISSN 1877-444X, Vol. 33, 27-34 p.Article in journal (Refereed)
    Abstract [en]

     The aim of the study described in this article was to improve the teaching of the didactics of mathematics. A Learning Study was conducted during a course in the didactics of mathematics at a teacher training college, and three lessons were planned and analysed with the help of variation theory. The object of learning consisted of five elements of Mathematical  Knowledge for Teaching (MKT ) and for this object of learning, four critical features were found. To be able to formulate goals for a lesson, to be able to give detailed descriptions, to have adequate mathematical knowledge and to be able to take a role as a mathematics teacher appeared to be necessary for understanding the object of learning, MKT .

  • 15.
    van Bommel, Jorryt
    Karlstad University, Faculty of Health, Science and Technology (starting 2013).
    Giving young children a mathematical challenge.2015In: Innovation, Experimentatin and Adventure in early childhood, 2015, 211-212 p.Conference paper (Refereed)
    Abstract [en]

    This paper shows the implications of children (age 6) working with challenging mathematical problem-solving tasks in statistics.Historically mainly arithmetic has been taught in preschools (Saracho & Spodek, 2008) and Sarama & Clements (2009) state numbers and quantitative thinking as the main area of research for young children.The study presents results of a design-research project with the purpose of innovating and improving classroom practice (Cobb & Gravemeijer, 2008). The design was both process and utility oriented (van den Akker, Gravemeijer, McKenney, Nieveen, 2006) aiming at developing design theories regarding the learning in these designed settings.The task was to determine; What will the outcome be when I draw two beads out of a bag with two red and two yellow beads? First the children were to predict the outcome resulting in a bar-chart. The beads were then drawn thirty times while they, based on own strategies, documented the outcome. Finally the mathematical outcome was discussed and an explanation was found. Furthermore the documentation per se was focused on.The ethical regulations for research in Sweden where followed, where guardians and children approved the participation.The results of the documentation showed the following: The children had used a diversity in their documentation, corresponding to levels of abstraction. Few children managed to document both outcome and number of draws. During the discussion, they explored and tried to understand each other’s documentation. This task and children’s documentations supports the idea that challenging mathematical problem-solving tasks can (ought to) be used in early childhood mathematics education settings.

  • 16.
    van Bommel, Jorryt
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    How to teach Mathematical Knowledge for Teaching2011In: Proceedings of the Seventh Congress of the European Society for Research in Mathematics Education / [ed] Marta Pytlak, Tim Rowland, Ewa Swoboda, Rzeszów: University of Rzeszów , 2011, 3008-3009 p.Conference paper (Other (popular science, discussion, etc.))
    Abstract [en]

    Teachers in mathematics not only need a deep understanding of mathematics but also need knowledge on how to teach the mathematics (Ball & Bass, 2003; Grossman, 1990; Ma & Kessel, 2000). How to teach such Mathematical Knowledge for Teaching (MKT) was the focus for the study described here. Five aspects of MKT were chosen to work with. The goal was to improve student teachers' understanding of the relations between these five aspects, or "interrelating components". The components chosen were: pupils' preconceptions, models for explanation, related (hands on) materials, suitable exercises and curricular knowledge. A Learning Study as a form of design research, was conducted where four critical features concerning MKT were found.

  • 17.
    van Bommel, Jorryt
    Karlstad University, Faculty of Technology and Science, Department of Mathematics.
    Improving Teaching, Improving Learning, Improving as a Teacher: Mathematical Knowledge for Teaching as an Object of Learning2012Doctoral thesis, monograph (Other academic)
    Abstract [en]

    This thesis concerns teaching in mathematics teacher education and is based on the implementation of a learning study at teacher training. The overall purpose was to investigate in what way teacher training could facilitate and improve student teachers’ Mathematical Knowledge for Teaching (MKT). In the learning study design, MKT was conceptualized as an object of learning with a meta-character, which meant that it was applicable to and transferable between different content areas of mathematics. This made it possible to vary the mathematical content between lessons but to keep the object of learning constant. Four critical features of the object of learning were found, giving insight in some of the problems related to teacher education. Student teachers had to be able to formulate proper aims for a lesson and to give detailed descriptions of elements of MKT for coherence in their MKT to occur. A focus on student teachers’ role as mathematics teachers had to be established and finally, sufficient mathematical knowledge was found to be a prerequisite for their MKT to develop. The study shows that enactment of these critical features improved the teaching by the teacher educators, which in its turn improved the student teachers’ learning with regard to MKT. The study also indicates that the prescribed design is worth considering for future collaborative efforts of improving teaching where other objects of learning with a similar meta-character are involved. 

  • 18.
    van Bommel, Jorryt
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Learning study as the object of learning: plenary talk2013In: WALS The World Association of Lesson Studies Internatioonal Conference 2013. Lessons and Learning Studies in teaching Research: Conference Programme & Abstract and Papers / [ed] Holmqvist Olander, M., Kullberg Bergstrand, C., Kullberg, A., Göteborg: University of Gothenburg , 2013Conference paper (Refereed)
    Abstract [en]

    LS in Teacher Education

    In what ways can Lesson study and Learning study be represented in teacher education, to enhance pre-service teachers’ teaching and learning, as both Lesson and Learning study in some respects can be said to be experience based?

    Lesson study is a method used by experienced teachers to develop teaching, to meet curriculum goals, and to help learners develop certain learning prerequisites. Lesson studies are accomplished through research lessons build on teachers’ collaboration and self-critical reflection. In learning studies, researchers and teachers collaborate to find ways to get students to discern so called objects of learning. Learning study, based on variation theory, is inspired by lesson study and design experiments and focuses on the object of learning and how it should be varied. Both lesson and learning studies have shown positive results in practice. They enhance teachers’, researchers’, and students’ knowledge, and develop learning and teaching. However, the models are foremost used in primary and secondary school by experienced teachers, and not that much at university level or practiced by pre service teachers.

    Using lesson and learning study in teacher education might be a fruitful way to test and discuss teaching and learning, which are two important aspects of a teachers’ work

  • 19.
    van Bommel, Jorryt
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Lortie visits Karlstad: A study on reasons to become a teacher2008In: Kapet, ISSN 1653-4743, Vol. 4, no 1Article in journal (Other academic)
    Abstract [en]

    Thirty years after Lortie wrote Schoolteacher, part of his study was revived through a study amongst teacher students at Karlstad University. The study focuses on recruitment and reaffirmation and the aim of the study was to find out why teacher students choose to become a teacher. Just over two hundred students responded to a questionnaire and, in addition, around twenty students were interviewed. In line with Lorties results, it turned out that the main reason to become a teacher anno 2008 was the possibility to work with children and people. Even contribution to change could be considered as a dominant motivation for choosing the profession. The results of the study could have consequences for teacher educators but even for recruitment offices

  • 20.
    van Bommel, Jorryt
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Mathematical Knowledge for Teaching as the Object of Learning in a Learning Study2011In: WALS The World Association of Lesson Studies: International Conference 2011: Professional Community for Enhancing Learning 26-28 November 2011: Programme Book / [ed] Programme sub-committee of WALS 2011, Tokyo: The University of Tokyo , 2011, 198- p.Conference paper (Other (popular science, discussion, etc.))
  • 21.
    van Bommel, Jorryt
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Patterns of variation: some examples2011In: WALS The World Association of Lesson Studies : International Conference 2011: Professional Community for Enhancing Learning 26-28 November 2011 : Programme Book / [ed] Programme sub-committee of WALS 2011, Tokyo: The University of Tokyo , 2011, 208- p.Conference paper (Other (popular science, discussion, etc.))
    Abstract [en]

    Supervision of Learning Studies in mathematics over the past years have let to a number of clear examples on the patterns of variation. In a Learning Study, Variation Theory is used both in preparing and analyzing the lessons and four patterns of variation are central: Fusion, Separation, Contrasting and Generalization. The mathematical concepts addressed in the poster are equal sign, half, unit fractions, and square 

  • 22.
    van Bommel, Jorryt
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    PCK at Teacher Education: A Learning Study2009In: WALS The World Association of Lessons Studies International Conference 2009: Collaborative Knowledge Creation through Lesson and Learning Study. 7-10 December 2009. Conference Programme & Abstracts of Papers / [ed] Leung Yuk Lun Allen, Hong Kong: The Hong Kong Institute of Education , 2009, 34- p.Conference paper (Other (popular science, discussion, etc.))
    Abstract [en]

    At WALS 08 a paper on an alternative design for a learning study was presented (A learning study improving teaching at teacher education in mathematics, van Bommel & Liljekvist) and we would now like to present results of the conducted learning study. The study was carried out with university students and their student teachers at a teacher training course in mathematics and the aim (object of learning) of the learning study was to develop a structure of Pedagogical Content Knowledge (PCK) in mathematics. PCK can be described as subject matter knowledge for teaching and good understanding of PCK implies an awareness of interrelating components of importance for teaching a particular topic in mathematics. The five interrelating components chosen by the university teachers in this study are preconceptions, models for explanation, related (hands on) materials, suitable exercises and curricular knowledge. Pre and post tests consisted of preparing and writing down a lesson plan within a specific mathematical content. Each lesson plan was evaluated on 15 aspects consisting of the five interrelating components mentioned above and the correlations amongst them. Analysis shows in which of the 15 aspects students results progressed during the learning study and in which ones it did not. For instance there was a clear progression in the correlation between the expressed curricular knowledge and the exercises chosen in the lesson plan. The analysis gave us indications of the critical aspects needed for deepening an understanding of the structure of PCK. In our presentation we would like to share some of the results of our analysis and also point out the changes we made regarding the learning study lessons.

  • 23.
    van Bommel, Jorryt
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Preparing Student Teachers with MKT2011In: Proceedings: the mathematical knowledge needed for teaching in elementary schools / [ed] Jarmila Novotná and Hana Moraová, Prague: Charles university , 2011, 336-344 p.Conference paper (Refereed)
    Abstract [en]

    This study aims to contribute to ongoing research concerning how MKT isconstituted at mathematics teacher education. The Learning Study (LS)presented in this paper focused on Mathematical Knowledge for Teaching(MKT) amongst student teachers (ST). The data consists of three videotapedseminars and pre and post tests written by ST. Analysis with Variation theory(VT) resulted in a description of critical features to take into account whenteaching MKT to at teacher education. In this paper the critical feature related to the curriculum is explored

  • 24.
    van Bommel, Jorryt
    Karlstad University, Faculty of Health, Science and Technology (starting 2013).
    Räkna med ägg2016In: Nämnaren : tidskrift för matematikundervisning, ISSN 0348-2723, no 4Article in journal (Other (popular science, discussion, etc.))
    Abstract [sv]

    När elever möter matematikinnehåll genom arbete med konkret och laborativt material är det av vikt att steget från konkret arbete till abstrakt och generell matematik inte tas för snabbt. Eleverna bör ges möjlighet att också möta halvkonkreta och halvabstrakta representationer. Författaren beskriver hur elever kan utveckla sin taluppfattning genom en äggkartongsmodell

  • 25.
    van Bommel, Jorryt
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Teaching MKT2012In: Proceedings of NORMA 11: the sixth Nordic Conference on Mathmatics Education / [ed] Guðný Helga Gunnarsdóttir, Reykjavík: University of Island Press , 2012, 714- p.Conference paper (Other (popular science, discussion, etc.))
    Abstract [en]

    Teaching mathematics requires a deep understanding of mathematics but also knowledge on how to teach the mathematics (Ball & Bass, 2003; Grossman, 1990;Ma & Kessel, 2000). The aim of the study was to find ways of working with mathematical knowledge for teaching (MKT) so that student teachers (ST) would consider aspects of MKT in planning future teaching. A Learning Study was conducted in a mathematics teacher-training course and 47 ST participated. Duringa cycle of 3 seminars, 5 aspects of MKT were addressed and ST were tested before and after each seminar by writing a lesson plan. The 5 aspects of MKT were: pupils preconceptions, models for explanation, related (hands on) materials, suitable exercises and curricular knowledge. The 3 seminars and 3 sets of pre and post tests were analyzed with help of Variation Theory (Marton & Booth, 1997).What was possible to discern at the seminar concerning MKT the enacted OoL, was related to the lived OoL: what ST actually discerned as shown in their tests. Through a focus on the MKT as the Object of Learning (OoL), differences in learning could be identified and conditions necessary for learning to take place were described in terms of critical features (CF). These were subsequently implemented in the study and there was a clear improvement in the way the 5 aspects were addressed by the ST. The four CF found were: 1) Curricular goals must be seen as something to choose from (not as a whole package to work with). 2) Contextual experiences have to be created and reflected upon from a teachers perspective. 3) Components have to be described clearly in order to connect with other components. 4) The underlying mathematics should be understood when discussing an activity from a teachers point of view. During the presentation the CF will be described more completely using examples from the data

  • 26.
    van Bommel, Jorryt
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    The teaching of mathematical knowledge for teaching: A learning study of primary school teacher education2014In: Nordisk matematikkdidaktikk, ISSN 1104-2176, Vol. 19, no 3-4, 185-201 p.Article in journal (Refereed)
    Abstract [en]

    A group of Swedish teacher educators conducted a learning study in order to identifycritical features concerning the teaching and learning of Mathematical knowledge forteaching (MKT). Three seminars and 300 tests were analysed using variation theoryrevealing four critical features to take into account in teaching student teachers inmathematics education: namely their need to i) formulate proper goals for a lesson, ii)outline the lesson plan in detail, iii) shift perspective from the role of being a teacherto being a mathematics teacher, and iv) understand the underlying mathematicsof the lesson topic at hand. Thus, these are the four features of importance to thelearning and teaching of MKT.

  • 27.
    van Bommel, Jorryt
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Variation theory after a learning study2013In: WALS The World Association of Lesson Studies Internatioonal Conference 2013. Lessons and Learning Studies in teaching Research: Conference Programme & Abstract and Papers / [ed] Holmqvist Olander, M., Kullberg Bergstrand, C., Kullberg, A., Göteborg: Uniersity of Gothenborg , 2013Conference paper (Refereed)
    Abstract [en]

    After learning study was introduced in Sweden 2003, several schools have been conducting learning studies. During 2009-2011 a boom was visible due to possibilities for financial support from the government through the mathematics initiative. Learning study became a well-known concept at schools all over Sweden. Some evaluations of the governmental support have pointed out important factors for sustainability of learning study as professional development. The question of sustainability of a learning study has also been addressed at several previous papers at previous WALS conferences.

     

    Some schools have incorporated learning study in their daily practice by which sustainability is achieved; others have tried to maintain the professional development of their teachers in other ways. One such way is to work actively with variation theory outside a learning study setting. In a learning study, variation theory is used both as a tool for analysis and as a tool for planning lessons.  To obtain sustainability of a learning study, variation theory is often put forward as a main key for its sustainability. Teachers state that they use the knowledge obtained through learning study while planning their other lessons. A question can be raised: in what way can variation theory be used to obtain sustainability of professional development obtained through conducting a learning study?

     

    This paper reports on examples of the use of variation theory outside a learning study setting. A group of teachers continued with supervised professional development after having conducted a learning study. Discernment and the patterns of variation theory were frequently used to describe the content of lessons and to adjust tasks used in the lessons towards the intended object of learning. During the presentation, examples will be given of the use of variation theory of the participating teachers.

     

    Through learning study, variation theory as a theory of learning is implemented but as learning study is not possible to conduct for every lesson opportunities for further use of variation theory have to be made explicit. Variation theory as a tool for planning lessons can be developed further and the phase ‘after’ a learning study can be elaborated on. 

  • 28.
    van Bommel, Jorryt
    et al.
    Karlstad University, Faculty of Health, Science and Technology (starting 2013).
    Dahlberg, Ulrica
    Wallby, Anders
    Uppgifter som kan användas med responssystem2016Other (Refereed)
  • 29.
    van Bommel, Jorryt
    et al.
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Liljekvist, Yvonne
    Karlstad University, Faculty of Technology and Science, Department of Mathematics.
    Developing pedagogical content knowledge: A learning study2008In: WALS The World Association of Lesson Studies: International Conference 2008 1-4 December: From Teaching to Learning: Programme Book, Hong Kong: The Hong Kong Institute of Education , 2008, 58- p.Conference paper (Refereed)
    Abstract [en]

    This paper reports a design of a learning study at mathematics teacher education. The object of learning is to develop a structure of pedagogical content knowledge in mathematics. Pedagogical content knowledge can be described as subject matter knowledge for teaching and implies an awareness of interrelating components of importance for teaching a particular topic in mathematics. Interrelating components addressed in this article are preconceptions, connections to governing documents, models for explanation, suitable exercises and hands-on materials. The object of learning is not content or lesson specific, but an overall object, applicable to several lessons/topics in the course. The nature of the object of learning and other characteristics of the study, call for an unusual, but still well developed design of the learning study. The focus this article is on the design of the learning study, which will be presented and discussed. A hypothesis of the study is that students who get exposed to such pedagogical content knowledge at several occasions with different (mathematical) content would be able to transfer this knowledge to a new topic. The study takes place in a mathematics course for prospective primary school teachers in the later part of their studies. Briefly the design is as follows: pretests (3) are conducted after lessons not taught within the learning study cycle. Posttests (3) are conducted after learning study lessons. Two different groups will undergo all tests. The results of the pre and posttests together with video observation, analysis and research are base for the development of the object of learning in the learning study cycle. Because a natural progress in results can be expected, the progress within the pretests can be compared with the progress within the posttests. Of course the results on pre- and posttests will be mutually compared as well.

  • 30.
    van Bommel, Jorryt
    et al.
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Liljekvist, Yvonne
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Facebook and mathematics teachers’ professional development: Informing our community2015In: CERME 9 - Ninth Congress of the European Society for Research in Mathematics Education: Proceedings of the Ninth Congress of the European Society for Research in Mathematics Education / [ed] Konrad Krainer; Naďa Vondrová, Prag: Charles University Prag , 2015, Vol. 1, 2930-2936 p.Conference paper (Refereed)
    Abstract [en]

    Nowadays, communication and cooperation on social network sites, such as Facebook, have become common. These sites are also used within teachers’ professional development in both formal and informal ways: they create and form new opportunities to communicate and cooperate. This paper discusses how mathematics teachers’ informal participation on social network sites can inform the mathematics education research community. 

  • 31.
    van Bommel, Jorryt
    et al.
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Liljekvist, Yvonne
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Improving teaching at teacher education in mathematics: A learning study2008Conference paper (Refereed)
    Abstract [en]

    This paper reports a design of a learning study at mathematics teacher education. Theobject of learning is to develop a structure of pedagogical content knowledge in mathematics.Pedagogical content knowledge can be described as subject matter knowledge for teaching andimplies an awareness of interrelating components of importance for teaching a particular topic inmathematics. Interrelating components addressed in this article are preconceptions, connectionsto governing documents, models for explanation, suitable exercises and hands-on materials. Theobject of learning is not content or lesson specific, but an overall object, applicable to severallessons/topics in the course. The nature of the object of learning and other characteristics of thestudy, call for an unusual, but still well developed design of the learning study. The focus thisarticle is on the design of the learning study, which will be presented and discussed. Ahypothesis of the study is that students who get exposed to such pedagogical content knowledgeat several occasions with different (mathematical) content would be able to transfer thisknowledge to a new topic. The study takes place in a mathematics course for prospective primaryschool teachers in the later part of their studies. Briefly the design is as follows: pretests (3) areconducted after lessons not taught within the learning study cycle. Posttests (3) are conductedafter learning study lessons. Two different groups will undergo all tests. The results of the preand posttests together with video observation, analysis and research are base for the developmentof the object of learning in the learning study cycle. Because a natural progress in results can beexpected, the progress within the pretests can be compared with the progress within the posttests.Of course the results on pre- and posttests will be mutually compared as well

  • 32.
    van Bommel, Jorryt
    et al.
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Liljekvist, Yvonne
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Teachers’ informal professional development on social media and social network sites: when and what do they discuss?2016Conference paper (Refereed)
  • 33.
    van Bommel, Jorryt
    et al.
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Liljekvist, Yvonne
    Karlstad University, Faculty of Technology and Science, Department of Mathematics.
    Testing the same group again and again: An alternative design for a Learning Study2008In: WALS The World Association of Lesson Studies: International Conference 2008 1-4 December: From Teaching to Learning: Programme Book, Hong Kong: The Hong Kong Institute of Education , 2008, 59- p.Conference paper (Refereed)
  • 34.
    van Bommel, Jorryt
    et al.
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Liljekvist, Yvonne
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Olin-Scheller, Christina
    Karlstad University, Faculty of Arts and Social Sciences (starting 2013), Department of Educational Studies.
    Capturing, Managing and Analyzing Teachers' Informal Professional Development on Social Media2018Report (Refereed)
    Abstract [en]

    Teachers’ professional discussions have now expanded onto different platforms on social media. Collecting such digital open accessible data from social media brings new challenges for educational researchers. Teachers’ discussions on Facebook are the focus of this study and the methodological issues coming from capturing, managing and analyzing our data are explored.

    Different social media generate different types of data and the difference between dialogical and monological communication becomes clear. Further, the issue of anonymity requires special attention, as one has to redefine what can be considered public information. As the data is relatively easy to gather, it can result in large quantities and a stratified sample of the data is suggested, both for qualitative and generalizable results.

    This report aims to convey our findings but also raises some unresolved questions, for instance concerning the use of different modalities or future technological development. 

  • 35.
    van Bommel, Jorryt
    et al.
    Karlstad University, Faculty of Health, Science and Technology (starting 2013).
    Liljekvist, Yvonne
    Karlstad University.
    Olin-Scheller, Christina
    Karlstad University, Faculty of Arts and Education, Department of Education.
    Making the invisible visible: on professional development initiated by the teachers themselves2015Conference paper (Refereed)
    Abstract [en]

    New technology provides teachers with a variety of ways for choosing forms and content of professional development. Teachers in Sweden widely use Facebook as a way of professional development. Within Facebook teachers create groups and pose questions and responses in issues regarding teaching they themselves choose. Our research focuses on the subjects mathematics and Swedish and maps what kind of questions and comments teachers post in relation to the different parts of pedagogical content knowledge (PCK), as described by Shulman.

    Our question is if there are specific parts of PCK that appear of more interest in such Facebook groups. The outcome has implications for pre-service and in-service teacher education as the outcome will inform on challenges and difficulties teachers encounter once practicing as a teacher. Such challenges and difficulties have previously been hidden as teachers have not publically discussed these issues

  • 36.
    van Bommel, Jorryt
    et al.
    Karlstad University, Faculty of Health, Science and Technology (starting 2013).
    Liljekvist, Yvonne
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Olin-Scheller, Christina
    Karlstad University, Faculty of Arts and Social Sciences (starting 2013).
    What do teachers reason about and when?2016Conference paper (Other academic)
    Abstract [en]

    Social media makes it possible to now study teachers’ informal professional development, something that previously has not been possible. Our study (DNR 2015-01979) probes teachers’ participation in social media, in specific in Facebook groups constructed by and for teachers themselves. Our data consist of around 600 posts and their comments from 6 different Facebook groups concerning the teaching of the school subject mathematics or Swedish, obtained through a stratified sample over a period of one year (van Bommel & Liljekvist, 2016). These data have been categorized using the Shulmans framework (1987) and further analysed using systemic functional linguistics (Halliday & Matthiessen, 2013). The results show that the linguistic features questions and offers are most frequently used (92%) whereas statements and calls are not existing to the same extend. Pedagogical content knowledge dominates in the questions and offers posted in the Facebook groups (63%). A difference between groups in mathematics and Swedish emerged: 13% vs 5% of the posts were categorized as Content Knowledge. Thus, the study shows that teachers constructing their own professional development focus on pedagogical content knowledge, further, teachers have different needs within different subjects.

     

    Halliday, M.A.K. & Matthiessen, Christian M.I.M. (2013). Halliday’s introduction to functional grammar. 4th ed. London & New York: Routledge.

    Shulman, L. (1987) Knowledge and teaching: Foundations of the new reform. Harvard Educational Review: April 1987, Vol. 57, No. 1, pp. 1-23.

    van Bommel, J., & Liljekvist, Y. (2016, October). Teachers’ informal professional development on social media and social network sites: when and what do they discuss? Paper presented at the ERME, Berlin, Germany.

  • 37.
    van Bommel, Jorryt
    et al.
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Liljekvist, Yvonne
    Karlstad University, Faculty of Technology and Science, Department of Mathematics.
    Ottersten Nylund, Cecilia
    The "KOM project" and "Adding it up" through the lens of a learning situation2010In: Mathematics and mathematics education: cultural and social dimensions : proceedings of MADIF 7: the seventh Mathematics Education Research Seminar, Stockholm, January 26-27, 2010 / [ed] Bergsten, C., Jablonka, E., Wedge, T., Linköping: SMDF , 2010Conference paper (Refereed)
  • 38.
    van Bommel, Jorryt
    et al.
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Palmér, Hanna
    Institutionen för matematikdidaktik vid Linnéuniversitetet.
    From Solving Problems to Problem Solving: Primary School Teachers Developing Their Mathematics Teaching through Collaborative Professional Development2015In: KAPET, ISSN 1653-4743, Vol. 11, no 1, 72-89 p.Article in journal (Other academic)
    Abstract [en]

    In many countries, problem solving in mathematics plays a substantial role in the syllabus, promoting the basic aim that pupils develop a deeper understanding of mathematics. However, in many countries there are few classrooms in which mathematics teaching through problem solving has truly been implemented. This article reports findings from a study of Swedish primary school teachers who, within a collaborative professional-development initiative, worked to improve their mathematics teaching, focusing on problem solving. Several studies have reported on the mathematical knowledge primary school teachers have, do not have, and ought to have. This article, however, does not evaluate the knowledge possessed by the teachers but instead focuses on how the professional collaborative learning initiative influenced the teachers' awareness of problem solving as content. The collaborative professional-development initiative had a cyclic design in which changes in the teachers' awareness became visible in their jointly produced lesson plans and pre-tests. Changes in these documents show how the role of problem solving in the teachers' mathematics classroom shifted in accordance with the historical development of problem solving as content in school: problem solving as a context, as a skill, and as an art.

  • 39.
    van Bommel, Jorryt
    et al.
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Palmér, Hanna
    Linnéuniversitetet.
    How to solve it: Students’ communication when solving problems in groups2015In: Nordic research in mathematics education: Proceedings of NORMA14, Turku, June 3–6, 2014 / [ed] Silfverberg, H.; Kärki, T.; Hannula, M. S., Turku: The Finnish Research Association for Subject Didactics , 2015, 329-338 p.Conference paper (Refereed)
  • 40.
    van Bommel, Jorryt
    et al.
    Karlstad University, Faculty of Health, Science and Technology (starting 2013).
    Palmér, Hanna
    Linnéuniversitetet.
    Matematik i soffan: kombinatorik i förskoleklass2016In: Nämnaren : tidskrift för matematikundervisning, ISSN 0348-2723, Vol. 43, no 3, 15-20 p.Article in journal (Other academic)
  • 41.
    van Bommel, Jorryt
    et al.
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Palmér, Hanna
    Linnéuniversitetet.
    Slow down you move too fast2017Conference paper (Refereed)
    Abstract [en]

    One way to characterize students' representations is to distinguish between concrete, semi-concrete, semi-abstract and abstract representations. In a previous study with 6-year olds we surprisingly found that – while solving a combinatorial task - the children who used semi-concrete representations in their documentations were more systematic in the process of finding solutions with less duplications than the children who used semi-abstract representations. As a continuation, we have provided 6-year olds with a specially designed application focused on combinatorial task. The aim of the application is to provide an opportunity to develop an understanding of combinatorics and its systematisation by letting children work within the semi-concrete level. The first results of the study indicate that the children indeed develop significant skills when working within the semi-concrete level, for instance they seem to have obtained a good understanding of what the concept different combinations entails. 

  • 42.
    van Bommel, Jorryt
    et al.
    Karlstad University, Faculty of Health, Science and Technology (starting 2013).
    Palmér, Hanna
    Linnéuniversitetet.
    Young children exploring probability: with focus on their documentations2016In: Nordisk matematikkdidaktikk, ISSN 1104-2176, Nordic Studies in Mathematics Education, ISSN 1104-2176, Vol. 21, no 4, 95-114 p.Article in journal (Refereed)
  • 43.
    Österholm, Magnus
    et al.
    Umeå universitet.
    Bergqvist, Tomas
    Umeå universitet.
    van Bommel, Jorryt
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Liljekvist, Yvonne
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Utvärdering av matematiklyftets resultat: delrapport 12014Report (Other academic)
    Abstract [sv]

    Denna rapport är en första delrapport inom utvärderingen av Matematiklyftets resultat. I detta skede har utvärderingen pågått i cirka sex månader. Arbetet har under denna period till största delen bestått av planeringsarbete inför kommande insamling och analyser av data. 

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