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doctoral programmes in the Nordic research communities
Barbro Grevholm
University of Agder, Norway
Introduction
In the Nordic countries doctoral research studies within the area of didactics of mathematics have long been carried out in doctoral programmes for general education or pedagogy. As recent as in the 1990ies programmes in didactics of mathematics were created in Sweden and Norway. Finland and Iceland still do not have specific programmes in didactics of mathematics. The first doctoral programme in Norway in didactics of mathematics was founded in 2002 at University of Agder. Earlier (with the name Agder University College) this institution had functioned as a networking point in mathematics education for all of the academic institutions in Norway. As the programme in University of Agder has now been working for a little more than five years an evaluation has taken place this May done by Anna Sierpinska from Concordia University in Montreal. In the process of preparing this evaluation the Mathematics Education Research Group at Agder (MERGA) had an opportunity to rethink the doctoral programme based on the experiences since 2002.
The time for revision has come and after we have received the evaluation report careful considerations will be made and the changes implemented. In this paper I will discuss some of the issues we found important in the development and for possible future changes.
About terminology
In Sweden and the Nordic countries mathematics education is called matematikdidaktik (or similar words in the different languages), didactics of mathematics, thereby following the German and French tradition rather than the AngloSaxon, when it comes to the notion. In Sweden mathematics education is translated to matematikutbildning, which means education in mathematics, including school level and other levels. Thus there is a risk of misinterpretations when using the word mathematics education as a name for the research field. Here I will use both these notions interchangeably.
The structure of a doctoral programme in Norway
In this section I offer a short description of some characteristic features of the doctoral programme in didactics of mathematics in University of Agder. Although Norway is not part of the European Union the country has adopted the so called Bologna system for structuring the academic education. This means that the bachelor degree should take 3 years, the masters degree 2 years and the doctoral education 3 years.
Thus in Norway the doctoral education in general is a three year study with course work and research leading to a written thesis. The course work in general is one semester but in the programme in didactics of mathematics at University of Agder the course work covers one year of fulltime study. The prerequisites for study are a masters degree in mathematics or mathematics education and teaching experiences. The research education leads to a thesis that will be examined by three examiners, and two of them are external. Examiners must be professors or on professors level in the academic system. The examiners read the thesis and produce a written document, where they classify the work as acceptable for defence or not. If the work can be accepted after minor revisions a student can get some months to revise the work and then have it valued again. After the acceptance the doctoral student is allowed to defend the thesis in a public viva (disputation), where also external persons can criticise and discuss the content. The examiners act as opponents during the public defence (disputas). The dissertations are published in a university series. There is no national Graduate School in Mathematics Education in Norway yet, but plans to start one. On the other hand, the Nordic Graduate School in Mathematics Education (see more below) is situated in University of Agder. University of Agder is at the moment the only university that offers doctoral courses in mathematics education at a regular basis in the Nordic countries.
Exemplifying with the programme of University of Agder, it can be noticed that each doctoral student will get at least two supervisors (a main supervisor and a cosupervisor) and an individual study plan is made up each year, followed by a yearly report to the board about the outcome of each study year. Also supervisors reports to the board are handed in and carefully followed up. Two courses are compulsory, Theory of science from a didactics of mathematics perspective (5 study points) and Research methodology in Mathematics Education course (15 study points). If the student does not have a course in History of mathematics in the masters education such a course is compulsory at doctoral level. One or two courses are running each semester and they normally attract doctoral students from the whole of Scandinavia.
It is possible for a student to distribute the stipend time over 4 years if the student takes on a teaching load of 25 % parallel to the doctoral studies. The administrative process for the student starts with applying for a stipend, which is actually a position as a doctoral student at the university. The student becomes employed by the university and gets all rights of an employee. The monthly salary is rather good and the position includes all societal rights if the students gets sick or has to take parental leave. After having received the stipend, the student has to apply to be taken up in the doctoral programme and this includes writing a research proposal (in collaboration with the two supervisors). There is a board for the doctoral programme to advice the faculty board in issues concerning the doctoral programme. This board evaluates to proposal and if it finds it good the student is taken up in the programme.
In the programme six doctoral courses have been developed and they are offered to students on a regular basis according also to the wishes of the students. A majority of the students work at UiA and the rest of them have a stipend at some other university or university college and do their work there. The courses are thus constructed so that they can be taken as distance courses with limited time for presence at UiA. A student working at another university normally has one of the supervisors there and the other at UiA. Students can take courses at other universities after agreement with the supervisors.
The programme has in 2008 24 students taken up and there are about 15 professors working as supervisors.
In addition to what is offered at UiA the students have profited from extra resources offered by the Nordic Graduate School in Mathematics Education, which started in 2004.
Collaboration in Graduate Schools
National graduate schools
Research areas that are small with only one or two students and one or two faculty are vulnerable and it is tempting to create cooperation between institutions. The idea to build National Graduate Schools has developed in Finland, Sweden, and Denmark. Finland was first in 1995, followed by Sweden in 2000 and Denmark in 2005. Finland has repeated the initiative once, in Sweden it is so far a one time activity between 2000 and 2006. In 2008 UiA has together with three partner institutions applied to get a Norwegian Graduate school. Many reasons have been presented for having national graduate schools. There is a wish to increase the number of students finishing in time, a wish to shorten the actual study time (which normally can be longer than the formally expected time), to offer a richer study environment for the students and to offer competence development for the supervisors. In Sweden an evaluation of 16 national graduate schools was published in 2006 (Persson, 2006). The report points out that there have been some problems, such as lack of knowledge about and experiences in didactical research, inadequate planning and organisation of the activities, in some cases insufficient supervisor competence, difficulties to cooperate and antagonism between different fractions in the subject fields, financing problems and so on. The evaluation of the outcomes is more positive. Most doctoral students have finished in reasonable time and supervisors competence has developed well. National and international networks have been established and are strengthening the opportunities for further development and improvement of research in subject didactics. The relations to the core subjects have been highly improved. There seems to be a promising labour market for the new doctors. Persson (2006) points out that when establishing new graduate schools these experiences must be taken into account. There must be adequate supervisors competence from the beginning and resources for competence development of supervisors must be set aside. Not too many institutions should be involved and very good preparations are necessary for a graduate school to function well from the beginning. All participating institutions must agree about the aim and goals of the activities. Common guidelines for students conditions and financing must be agreed upon.
The Nordic Graduate School in Mathematics Education
The Nordic Graduate School in Mathematics Education is based on funding from the Nordic Research Academy (NordForsk). It is a five year activity during 20042009 with the idea that after five years the cooperation built is strong enough to survive by support only from the involved institutions.
I will present the Nordic Graduate School in Mathematics Education, its aims and some of its activities. The Graduate School is a network of about 40 Nordic and Baltic research environments with graduate education in mathematics didactics. Around 120 supervisors and 86 doctoral students are part of the network in 2008. An account will be given of doctoral courses so far, of seminars for supervisors and of workshops and summer schools that have taken place.
The aim of a Nordic Graduate School in Mathematics Education  NoGSME
The aim of the Nordic Graduate School as it was decided by the application to NordForsk in 2003 (The Nordic Research Academy) is to
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 (Grevholm, 2004a).
Activities in the Nordic Graduate School in Mathematics Education
The activities in the Graduate School can be summarised in the following points (Grevholm, 2004b, 2005a):
Common courses are created with the added competence from all researchers in the Nordic countries and international partners (Grevholm, 2004c)
Seminarseries in specific research areas are offered as a complement to local series and workshops on subjects or issues of main importance (Grevholm, 2005b)
Competence development for supervisors and exchange of experience is offered
Partnerships and collaboration with distinguished international scholars are built
Creating a database for ongoing work, theses and greater development work in mathematics education
Mobility stipends and special financial support for doctoral students are given.
Courses that have been offered since 2004
The courses offered are of two kinds. Courses that are given on a regular basis at some of the participating universities are open to all doctoral students in the network. They are advertised each semester. Other courses are initiated by the board of NoGSME. The board collaborates with some interested colleagues in one of the participating universities and the course is constructed and given at that place, with financial support from NoGSME (Grevholm, 2004d, 2005c). The regular courses so far have been given at University of Agder in Norway. The courses that have been initiated by NoGSME have taken place in Copenhagen University (Winslw, 2006), Denmark Pedagogical University, and Norwegian University of Technology, Roskilde University, Ume University and Helsinki University. In the making is one course in Malm. Here are the courses given or ongoing so far:
Theory of science from a mathematics education perspective, UiA
Metaperspectives on mathematics and the learning of mathematics in a technological environment, UiA
History of mathematics with emphasis on modern mathematics, UiA
Theoretical aspects of mathematics education with emphasis on the French School, Copenhagen University
Problem solving in mathematics education, UiA
Theories of learning and teaching mathematics, UiA
Research design and research methods in mathematics education, UiA
Views of knowing and learning: Constructivism and sociocultural theory, Denmark Pedagogical University
Gender and mathematics education, Norwegian University of Technology
Justification of research in mathematics and science education with special emphasis on the role of theory in such justification, Roskilde University Centre
Research on assessment in mathematics education, Ume University
Conceptions in mathematics, Helsinki University
Mathematical literacies, Malm University College
Students get travel support to come to the courses and they can also apply for mobility stipends if they want to spend one or two months at another Nordic university. The mobility stipend covers real costs for travels and accommodation.
Summer schools
Summer schools have been offered each year and much appreciated by the doctoral students. The main part of the programme is taken up by work in groups, where each student can get her research project discussed and commented on. The groups are lead by international experts in the field, which is highly appreciated by the participants. Among these experts we have had excellent and well know researchers who have inspired the students. The friendship and mutual understanding that is built in these summer schools are expected to be the foundation of longstanding cooperation of the students in their coming careers (Grevholm, 2004b, 2006b).
Seminars for supervisors
A crucial component of doctoral education is access to good and experienced supervisors. In order to assist the environments in strengthening the competence of supervisors NoGSME is organising seminars and competence development programmes for supervisors. They have focussed much on quality issues in research education and publications (both papers and theses) (Grevholm, 2006c). NoGSME has built a close cooperation with the journal Nordic Studies in Mathematics Education (Nomad) in order to enrich these programmes. Here are some of the themes of the seminars given so far:
Quality in research in mathematics education, Quality of theses in mathematics education,
Supervision of doctoral students, Reviewing of papers in mathematics education, Research programmes in mathematics education, Critical situations in supervision of doctoral students in mathematics education, Review process of papers for scientific journals, Outcomes of research in mathematics education, and Scientific profile and characteristics of journals in mathematics education.
The seminars most often have between 20 and 30 participants and quite an important network of researchers is growing from the meetings that take place there. International scholars have been invited and generously offered from their expertise. Some of the invited researchers so far have been Frank Lester, Diana Lambdin, Uri Leron, Erkki Pehkonen, Gunnar Gjone, Carl Winslw, Morten Blomhj, Paola Valero, and Gabriele Kaiser.
Workshops
NoGSME organises workshops on central research issues of interest for the participants in the Graduate School (Grevholm, 2007a). The activity involves both doctoral students and supervisors. The first workshop dealt with classroom research in mathematics education. The second workshop focussed on research on mathematics textbooks. The experts here were Birgit Pepin and Linda Haggarty. Here a Nordic network for research on mathematics textbooks was created. A third workshop on research on use of ICT in mathematics education took place with 25 participants and two invited experts, Luc Trouche and John Monaghan. The fifth workshop was on mathematics and language with Heinz Steinbring and Candia Morgan as invited guests. A workshop on Justification of research in mathematics and science education with special emphasis on the role of theory in such justification was lead by Mogens Niss and it was closely linked to the corresponding doctoral course. Patricio Herbst was one of the invited lecturers. In the latest workshop about Use of ICT in mathematics education neither salvation nor catastrophe several Nordic researchers contributed, such as Mette Andresen, Per Eskil Persson and Christer Bergsten.
The board of the Nordic Graduate School in Mathematics EducationThe board consists of the director, one member from each of the five Nordic countries and a representative for the Baltic countries. Board members currently are Barbro Grevholm, director, Christer Bergsten, Sweden, Trygve Breiteig, Norway, Ole Bjrkqvist, Finland, Gudny Gunnarsdottir, Iceland, Madis Lepik, Estonia, and Mogens Niss, Denmark.
The members of the board are not paid for their work, but contribute for idealistic reasons and as part of their positions at the home university. The board meets about three times a year in connection to other NoGSMEactivities. The board is responsible for the initiatives and work and has to report to The Nordic Research Academy once a year. Most of the board members are also active in their national society for research in mathematics education and in national graduate schools.
Cooperation with Nomad
NoGSME has close cooperation with the journal Nomad, Nordic Studies in Mathematics Education. Doctoral students and supervisors are invited to publish in Nomad and in each issue of Nomad a few pages are devoted to the NoGSME programme and activities (Grevholm, 2006a). Here they can publish in their Scandinavian mother tongue or in English.
International centres of excellence are working partners
To get support for the application to NordForsk in order to get financing for NoGSME we turned to a number of important international centres of excellence and asked them to write letters of support for us. Leaders from these centres have then been involved in our plans and activities in different ways. The centres we collaborate with are Institute of Advanced Study, La Trobe University, Gilah Leder, Concordia University, Anna Sierpinska, University of Michigan, Hyman Bass and Deborah Ball, University 7, Paris, Michele Artigue, and University of Klagenfurt, Didaktik der Mathematik, Willibald Drfler.
Another important discussion partner has been Jeremy Kilpatrick, who is well informed about Nordic conditions relating to mathematic education. He has among other things been a guest professor at Gothenburg University and the supervisor of some Swedish doctoral students. All the above mentioned features of the Nordic Graduate School has been used to argue for a Norwegian national Graduate School in ME in the application sent in recently.
Results and outcomes of the Nordic Graduate School
The activities of the Nordic Graduate School are building strength in Nordic research for the future (Grevholm, 2006d). The knowledge and contacts that doctoral students and supervisors are getting from the events together offer insights that can not be achieved from reading books or by other means. In the future these links will be important and valuable for the field of mathematics education. Models of organising research education and supervision can be compared and developed and fruitful ideas from one university can be spread to other places (Grevholm, Persson & Wall, 2005). It is especially important for the Nordic Graduate School to build the contacts with colleagues in the Baltic countries.
Some features in order to strengthen the quality of researcher education
Ninety percent seminars
Mathematics education as a field of research is developing in the Nordic countries but it is still a young area and there is a need to assure the quality of the work and to live up to international expectations and standards. A number of initiatives have been taken in order to raise quality. For example, both in the Swedish Graduate School (Leder, Brandell & Grevholm, 2004) and at UiA in Norway we have introduced what is called ninety percent seminars. This means that when the student and supervisors agree that there is a manuscript of about 90 % of the final thesis a seminar is organised. To this seminar an international scholar, who is expert in the area of study, is invited. He or she reads in advance the 90 % finished manuscript and gives constructive and creative feedback during the seminar, which is organised as a dissertation. The intention of the seminar is to inspire the doctoral student to raise quality in the final phase of writing and to get fresh ideas how to improve the dissertation and to be aware of possible criticism before it is too late. The seminars have proven to be of utmost value to both the doctoral students and the supervisors. International scholars have generously given from their expertise in these discussions.
International studies
Another feature of importance for quality is international collaboration and studies abroad. There is an expectation for the students to spend one semester at another university, thus learning about a different academic institution and meeting other mentors and supervisors. This has functioned in Sweden, where the programme is often taken over five years but has been difficult to realise in Norway within a three year programme. The students feel the time pressure too hard for going away for such a long period of time. As compensation we have invited many international scholars to give seminars at UiA, but this is of course not the same as spending time abroad. We are working on how to improve this feature of the education. Internationalisation is also a concern of the Norwegian and Swedish educational authorities (SOU 2004:27). The issue of internationalisation is one that will be handled after the evaluation of the programme.
Models for supervision
Supervision is a crucial part of the doctoral education. In order to ensure good and continuous quality in supervision we have at UiA decided to have at least two supervisors. Supervisors move, get sick or retire and it is important that the students are not left in an unstable situation. Joint supervision and other forms for organising supervision must be considered. At Lule University of Technology a dynamic model of supervision with many levels have been used and proven successful (Grevholm, Persson & Wall, 2005). The model mirrors an apprenticeship theory for the doctoral education, which seems to be embraced by many of the supervisors. International experiences from work with quality of supervision and design of programmes have been followed closely by the Nordic community (Lester & Lambdin, 2003; Schoenfeldt, 2003).
Public defence of the dissertation
A public defence of the dissertation and invited international opponents is typical of the Nordic doctoral educations. It seems very important to have open discussions, where anyone can question and criticise the dissertations. Also the publication of theses, which makes them accessible in libraries to everyone, is valued in the democratic Nordic societies. The publishing of thesis is the normal situation in Finland and Sweden and often is the case also in Denmark and Norway. Nowadays in addition to the printed books with theses there is often also an electronic version on the internet.
A Nordic Journal for Mathematics Education
The close collaboration with the journal Nordic Studies in Mathematics Education, Nomad, is of great value to supervisors and doctoral students in the Nordic countries. This journal is the natural choice for the fist publications of the students. But many of them prefer other international journals as ESM, JMTE, IJSME or FLM.
Crucial or critical issues for the mathematics education doctoral programme in Norway issues to investigate in the evaluation of the programme
Supervision in a new research field
Trying to build up and expand a new research field is not an easy task. The most problematic issue has been that here have not been many experienced researchers, who can function as supervisors. In Sweden, for example, many mathematicians accepted to be supervisors when the national graduate school started. Some of them realised that they could only be of help for general matters in the education and someone else had to do the actual mathematics education supervision. But others actually thought that they had the expertise (being expert mathematicians but amateurs interested in teaching and learning of mathematics). Thus over the years there has been a number of situations, where the board of the graduate school had to assist in finding new supervisors, often by using an international scholar as additional supervisor. Also it happens that the student and supervisors are not getting along in a good way and a shift of supervisor has to be made. This is difficult when not many choices are available. Thus some supervisors have been used to an extreme extent over some years.
As the access to experienced supervisors was limited there was a need to build competence. This has been tried both in the Swedish Graduate School and in the Nordic Graduate School. The success was limited in the first case because of lacking interest among the group of supervisors. In the Nordic Graduate School it seems to work well. The education of new supervisors is crucial for future survival of the area and we are focussing on getting all the new doctors to participate, thus fostering the future generation of supervisors. The quality of supervision is critical for the outcomes and here international contacts and links are of extreme value.
A first national conference on supervision of doctoral students was held in Sweden in 2003 and some research has been carried out in this area (Strmberg, 1979; Strmberg Slveborn, 1983; Lindn, 1998). The international community in mathematics education has also cared for the issue of supervision (Hart & Hitt, 1999; Leder, 1995; Bishop, 2000).
Intersubject collaboration
Collaboration between researchers in mathematics, mathematics education and general education has been tried in all the Nordic countries with varied success. In the beginning of the Swedish Graduate School there seemed to be a mini Math War going on. Later this faded away, probably because the mathematicians realised that what was going on is not dangerous for them, on the contrary. This development is even visible in the evaluation of the graduate schools in Sweden (Persson, 2006).
Issues of format and language in theses
The format of the thesis monograph or selection of papers with preamble (kappa) has been much discussed in the graduate schools. The tradition from pedagogy is to write a monograph and from mathematics it is a selection of published papers with a preamble. As most of the students have been situated in mathematics departments they have been strongly influenced to write a selection of papers. From the twelve theses in Sweden finished so far there are only a few strict monographs. One wrote the licentiate thesis as a monograph and the second part of the thesis as a selection of papers. Another discussion is how many of the papers must be published in journals before the dissertation. In mathematics there has been a development towards accepting theses where none of the papers are published. So there has also been shifting traditions in mathematics education. One of the Swedish students had 6 published papers in the thesis and others had only two or three non published papers.
Another critical issue is the question of language for the dissertation  mother tongue or English? In Sweden there has been a public debate about scientific papers written by Swedes in bad English. They are claimed to make fools of themselves internationally. It is obvious that almost every nonnative English speaking writer is much better in expressing fine nuances in the mother tongue than in English. But it is also clear that writing in English opens for international readers. And later on researchers must write papers in English anyway. Not using mother tongue leads to a poor scientific language in the local languages and publications that will not be read by teachers in school. There are many pros and cons to consider before the decision on language is taken. In the end it is up to the student and the supervisor and must be taken in each specific case taking care of the circumstances for each student. A student who has writing difficulties anyway will have still worse problems if the writing is in English. In the programme in UiA careful discussions are held between the doctoral student and the supervisors before the decision about choice of language is taken.
Financing during and after the dissertation
The sources for financing doctoral studies differ from one place to another. In Sweden and Norway the student must have guaranteed financing for the studies before he or she can be taken up in a doctoral programme. The state offers a number of doctoral positions and there can be positions inside specific research projects. The student is employed by the university for 34 years and has legal rights as an employee. The salary can be compared with that of a beginning teacher. After the dissertation the position is finished. There is a lack of post doctoral positions in didactics of mathematics and this creates problems for those who want to go on at once after the dissertation and qualify themselves to become a docent. In Sweden and Finland this is an academic title for which one must qualify through research and publications after the doctoral degree (the same as Habilitation in Germany). The normal rule of thumb is to publish as much as a second thesis. An application must be made to the faculty and the scientific work is evaluated by external international experts and a public popular scientific lecture is given and evaluated by a scholar in another research field. Based on these activities the decision is taken about becoming the docent title. In Sweden the main supervisor of a doctoral student must be at least on the level of docent.
In Norway an academic teacher can apply to be promoted to docent, based on the scientific production and experienced. This position could be considered to be at the level of a professor in nonNordic countries.
In the Nordic countries academic studies are free, no costs are paid by students but all is paid by taxmoney. Thus the salary of a doctoral student can be used entirely for the private consumption.
Vulnerability of small research environments
Another critical issue is the fact that many research environments in mathematics education in the Nordic countries are small with only one or two faculty and one or two students. It is difficult to solve the supervisor problem and to create a vivid and inspiring work situation in a community of researchers. One solution for this situation is collaboration between two or more institutions or to be part of a graduate school. The earlier evaluations indicate that graduate schools are efficient in offering what the student needs as a complement to a small environment (Persson, 2006).
Opportunities to finance collaboration in graduate schools or Nordic networks
Collaboration in networks of graduate schools is rewarding and helps to assure quality. But there must be financial resources for such work. In Finland the graduate school succeeded in getting a continuation but in Sweden so far this has been unsuccessful. It is critical to find opportunities to solve this problem. In Norway it remains to be seen if the application is successful. The research environments that have been built up during the time of the graduate schools can very easily be torn down again if there is no continuation of the collaboration.
Gender balance
The Nordic communities in didactics of mathematics seem to be equal proportions of female and male students. But among supervisors there is an overweight of male academic teachers. Continued work needs to be done in order to improve the lack balance among supervisors. The Nordic professors in didactics of mathematics were male dominated until 2003 when suddenly four female professors were appointed. Another additional female professor in 2007 almost creates gender balance in this small Nordic group.
The importance of knowledge of mathematics by doctoral students in the programme
The fact that the program is situated in a mathematics department indicates that mathematics plays an important role. A solid foundation of mathematics must be part of the bachelor and masters education that forego the doctoral education. In the Swedish Graduate School the emphasis on mathematics was still greater as doctoral courses in mathematics were a substantial part of the coursework.
The participants in the Norwegian doctoral programme
Doctoral students
Who are the doctoral students in the Norwegian programme? Most of them are Norwegian students with teacher experiences either from school or university level, then often as teacher educators. Some have rather long teaching experience and thus are not so young any more. Few students come directly from the basic academic education. Many of the students have taken their masters degree at UiA and an interest for research has been created and they later come back to continue the studies at doctoral level. Some students have academic positions as teacher educators and are encouraged by their institution to take a doctoral degree in order to fulfil their career at university. One of the students is a retired school consultant and has much experience from school development and curriculum development in Norway. He is excellent writing about the Norwegian development of school mathematics over 50 years. Most students are in an age where family, housing and children are important questions. Thus they cannot easily move, go abroad or change their conditions. Long courses demanding presence at other places than the home university is problematic. These are all conditions that influence the opportunities in the doctoral programme and they must be taken into account in the planning of activities for doctoral students.
Teachers and supervisors
The supervisors in the doctoral programme have different backgrounds. The average age of the supervisors at UiA is 61 years and many have a long and varied experience as teachers, teacher educators and professors before they entered the programme. Only one supervisor is below 50 years of age, which is problematic for the future of the programme. The research education of the professors also varies from mathematics, to history of mathematics, to mathematics education. All are active researchers in didactics of mathematics or history of mathematics and have been so for a long time. A few of the professors have experience from building up programmes and management of doctoral education. Only a few had experience from supervision of doctoral students before the programme started in 2002 and not all had developed and taught doctoral courses. The professors come from six different countries in four different continents so there is a natural internationalisation in the community of researchers at UiA.
The future of doctoral programmes in mathematics education in the Nordic countries?
Do we have a critical mass of researchers in order to keep the activities alive? How do we ensure quality and endurance of programs? What opportunities are there to improve the programmes and in what ways?
Is there a need for more persons in the labour market with a doctoral degree in mathematics education? Do we need research on doctoral education in mathematics education? Will society continue to ask for research in mathematics education?
There are many questions to inquire into and try to answer about postgraduate education in the Nordic countries (Grevholm, 2007b). The cultural and social conditions are similar in the five countries and problems are often the same. Also solutions seem to be similar and the public debates have parallels.
In Norway the doctoral education was restructured in 2002 and the Ph D was introduced to replace earlier degrees. An intense debate is going on about how much resources should go into research and Norway is lagging behind the other Nordic countries so far. The number of new doctors is increasing though, but many seem to need far longer time than the planned three years. Many universities are worried about the prolonged study time and try to implement incentives to shorten the study time.
The government in Sweden has shown great concern about the research education. It was restructured in 1998 and a first evaluation of the results was published in 2007 (Hgskoleverket, 2007). One outcome is that the students that graduate within a period of five years have increased from 16 to 28 % of the population. The number of degrees has increased with 50 % after the reform and stays at that level. In 1990 0.6 % of the working population (between 25 and 64 years of age) had a doctoral degree and that increased to 1.0 % in 2005. An investigation in 2002 took care of specific questions about the doctoral time and the time after graduation (SOU 2004:27). Doctoral education has expanded with 100 % between 1990 and 2000. In Sweden the number of doctoral students is about 13000 (fulltime equivalents). It would be astonishing if there were no problems in such a strongly expanding activity. A large generation of persons born in the 40ties is in the process of retiring and the new academics with a doctoral degree seem to have a prosperous labour market to enter into. As mathematics knowledge is seen as one of the tools a citizen in a modern society will need, it seems probable that questions about teaching and learning mathematics to still larger groups of the population will be in focus. Most governments realise that we are moving into an international society, where the human capital resources in the form of education and competence are the means to survive and compete internationally through excellence and growth.
Acknowledgement: The work presented here is partly financed from NordForsk (project number 90969 at University of Agder) for which we are grateful.
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Winslw, C. (2006). HYPERLINK "http://isis.ku.dk/kurser/blob.aspx?feltid=52630"Didactics of mathematics the french way. (Edited booklet). Center for Naturfagenes Didaktik, Text no.15. Kpenhavn: Kpenhavns universitet.
Contactinformation
Barbro Grevholm, HYPERLINK "mailto:Barbro.Grevholm@hia.no" \n _blankBarbro.Grevholm@uia.no
Faculty of Engineering and Science
Department of Mathematical Subjects
University of Agder
Serviceboks 422, N4604 Kristiansand, Norway
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