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### Nordic Graduate School in Mathematics Education

The Nordic Graduate School is situated at Agder University College in Kristiansand, Norway

and financed by NordForsk 2004-2008

The aim of a Nordic Graduate School in mathematics education

- support and develop the education of researchers in mathematics education in the Nordic and Baltic countries,
- create constructive cooperation in order to raise the scientific quality of research in mathematics education,
- give all doctoral students in mathematics education access to the activities of the Graduate School
- create cooperation among a greater group of doctoral students and supervisors in order to share experiences and opportunities to improve the education of researchers.

The utmost aim is to create a network of cooperating partners, who can continue to collaborate after the five years of the Graduate School.

Activities in the Nordic Graduate Schoolin Mathematics Education

- Common courses created with the added competence from all researchers in the Nordic countries and international partners
- Summer schools building on earlier good experience from similar arrangements
- Seminar-series in specific research areas as a complement to local series and workshops on subjects or issues of main importance
- Competence development for supervisors and exchange of experience
- Partnership and collaboration with distinguished international scholars
- Creating a database for ongoing work, theses and greater development work in mathematics education
- Mobility stipends and special financial support for doctoral students

Courses that has been offered from 2004

- Theory of science from a mathematics education perspective
- Metaperspectives on mathematics and the learning of mathematics in a technological environment
- History of mathematics with emphasis on modern mathematics
- Theoretical aspects of mathematics education with emphasis on the French School
- Problemsolving
- Theories of learning and teaching mathematics
- Research design and research methods
- Views of knowing and learning: Constructivism and sociocultural theory
- Gender and mathematics education

Summer school

- 2004 - four students and the director took part in the YERME summer school in Podebrady
- 2005 - 30 students took part in the NoGSME summer school in Jyväskylä
- 2006 – 20 students took part in the NoGSME summer school in Dømmesmoen at the HiA campus
- 2007 – NoGSME offers a summer school in Laugarvatn in Iceland, 40 participants
- 2008 – NoGSME will offer a summer school in Denmark or Sweden

Seminars for supervisors

- Sept 2004 in Vasa, Quality in research
- April 2005 in Korsør, Quality in theses
- Sept 2005 in Trondheim, The supervision relations
- Nov 2005 in Lund, Reviewing of papers
- May 2006 in Vasa, Research education programmes in maths education
- October 2006 in Denmark, Education of new supervisors
- February 2007 in Norway, Reviewing of scientific papers and publication policies
- October 2007 in Sweden

Workshops

- Sept 2005 in Trondheim, workshop on Classroom research
- May 2006 in Kristiansand, workshop on Research on mathematics textbooks
- November 2006 workshop on Theoretical frameworks for research on use of ICT in mathematics education
- April 2007 in Sigtuna, workshop on Research on mathematics and language
- November 2007 workshop on Justification in mathematics and science education research and the role of theory in the justification

The board of the Nordic Graduate School in Mathematics Education

- Barbro Grevholm, director
- Christer Bergsten
- Trygve Breiteig
- Ole Björkqvist
- Gudny Gunnarsdottir
- Madis Lepik
- Mogens Niss

Cooperation with Nomad

- NoGSME has a close cooperation with Nomad, Nordic Studies in Mathematics Education
- Doctoral students and supervisors are invited to publish in Nomad
- In each issue of Nomad a few pages are devoted to the NoGSME programme and activities

International centers of excellence are working partners.

- Institute of Advanced Study, La Trobe university, Gilah Leder
- Concordia University, Anna Sierpinska
- University of Michigan, Hyman Bass & Deborah Ball
- University 7, Paris, Michele Artigue
- University of Klagenfurt, Didaktik der Mathematik, Williblad Dörfler

National Graduate Schools

- A Finnish Graduate School in mathematics and science education since 20 years
- A Swedish Graduate School in mathematics didactics 2000-2006, 21 doctoral students were taken up, 8 has finished so far.
- A Danish Graduate School in mathematics and science education started 2004.

Research in the Nordic countries –some examples

Morten Misfeldt defended his dissertation in January at the Danish University of Education. The title is Mathematical writing and it consists of a monograph. The thesis reports research into the ways various technologies support mathematical writing. One of the main theoretical outcomes is the attempt to view mathematical writing simultaneously as a creative writing process and as a mathematical problem-solving process.

Kristin Bjarnardottir defended her thesis at Roskilde University Center. Her thesis carries the title Mathematical Education in Iceland in a Historical context of socio-economic demands and influences. The data consists of historical documents from the development of school mathematics in Iceland and her dissertation is a monograph. The Icelandic educational system and the socio-economic implications on mathematical education are subjected to a historically based analysis.

At the University of Helsinki, Iiris Attorps defended her dissertation Mathematics teachers’ conceptions about equations, a monograph (a substantial volume with 231 pages). The aim of the study is to describe and clarify the mathematics teachers’ subject matter and pedagogical content conceptions about equations. The research shows that some of the teachers included in the study do not have clear conceptions about what the pupils should learn in algebra at compulsory school. Both expert and novice teachers have various apprehensions of the pupils’ difficulties concerning equations.

Kristina Juter defended her dissertation at Kristianstad University. The title of her work is Limits of functions, UniversityStudents concept development and she has followed university students during their first course of tertiary mathematics and inquired into their development of the limit concept. One of her results is that many students complete basic courses in calculus without ever understanding the notion of limits, or even understanding that they do not understand limits. Kristina Juter interprets her findings to argue that connectedness and continuity are essential features of teaching and learning limits to prevent students from failing.

Lil Engström carried out the defence of the thesis in Stockholm and the work is called Möjligheter till lärande i matematik (Opportunities to learn mathematics, a monograph in Swedish). The study examines how teachers formulate mathematical problems, how they use the experiences students have gained and what use they make of the potential of computer software. One result is that the teachers’ ability to pose thought-provoking open-ended problems is the most important factor as it significantly influences what the students learn. Lil followed three teachers (in Sweden and Switzerland) and a group of student teachers and the software used was Cabri-Geometrie.

Mette Andresen defended her dissertation, Taking advantage of computer use for increased flexibility of mathematical conceptions, at the Danish University of Pedagogy. Mette Andresen's study is part of a larger project in Denmark called World Class Math & Science. In a sub project each student had a laptop, with computer algebra software, at their disposal. Participants gained the experience that computer use in upper secondary school mathematics has a potential. Mette’s questions were: "Is flexibility a supportive construct for articulation of experiences of teaching and learning within a modelling approach? Is it useful for realisation of the learning potential of students' concept formation?"

Gunnar Sjöberg defended his dissertation at Umeå University in the Graduate School of Pedagogical work. The title is If it is not dyscalculia - what is it then? He investigated the concept of dyscalculia in the research literature and found that it is an ill-defined or not defined concept. The pupils he followed from grade five in school to upper secondary school were said to be in mathematics difficulties but many of them later succeded in the subject. One crucial factor seems to be the short time these pupils spend on mathematics learning, often less that half an hour per school week.

Monica Johansson at Luleå University of Technology wrote about Teaching mathematics with textbooks - a classroom and curricular perspective. The focus is the relationship between the textbook and the curriculum. She shows that the textbook influences not only what kind of tasks students are working with during the lessons, but also the examples the teacher presents on the board, what kind of concepts are introduced and how they are introduced. The study shows the relative autonomy of the mathematics teacher in relation to the most common teaching tool in Swedish classrooms - the textbook.

Örjan Hansson is, as is Monica, a member of the Swedish Graduate School in Mathematics Education.. The work carries the title Studying the views of pre-service teachers on the concept of function. Three different groups of pre-service mathematics and science teachers for grade 4-9 were his informants.

- The concept of function is rarely a well integrated concept and the pre-service teachers’ view of the concept is represented by a less developed knowledge structure than one could wish for. Thus there are many implications for the teaching of pre-service teachers.

Andreas Ryve's dissertation took place at Mälardalen University. The title is Approching mathematical discourse. Two analytical frameworks and their relation to problem solving interactions. His main aim is to investigate how conceptual understanding and problem solving can become natural parts of mathematics teaching and thus of students' mathematical knowledge construction. He shows that the classroom discourse can be characterized in terms of subject oriented, didactically oriented and problem solving oriented discourses.

More examples

- Approaching proof in a community of mathematical practice
- Assessing mathematical creativity
- Understanding mathematical texts

Coming up are the following

- Historical theses in mathematics education
- Problem-solving in small groups

Entering a new era for Nordic research in mathematics education

- A critical mass of reserchers and studies
- A community through NoGSME and Nomad
- Doctoral education in ME at more universities
- Nordic conferences and books....

...... how will this influence mathematics in schools?

Contact-information

- For more information contact
- Barbro Grevholm, Barbro.Grevholm@hia.no
- Department of mathematical subjects
- Agder University College
- Serviceboks 422, N-4604 Kristiansand, Norway
- Visit our website: http://www.nogsme.no

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