Discussion group 12 in ICME11 Rethinking doctoral programs in mathematics education

The discussion group will deal with three overarching themes, one in each of the three sessions. Each session will have a short introduction, where background and frameworks are presented. Participants will then work in small groups and discuss a set of more elaborated issues and questions under each theme. Session 1 will focus on The Goals and Processes of Doctoral Programs in Mathematics Education, Session 2 will focus on Participants of doctoral programs and session 3 on A vision for doctoral programs in mathematics education. Questions will include 1) What are the goals of different programs? 2) Who are the participants and 3) Is there a central core of knowledge that doctorates in mathematics education possess?

Session 1, coordinator Peter Sullivan

The Goals and Processes of Doctoral Programs in Mathematics Education This component of DG 12 will facilitate sharing of approaches to doctoral education in mathematics education across in various countries. It will be analogous to the TIMSS lesson study approach, with the focus being doctoral programs, and the researchers being participants in the DG. This comparison of approaches aims to: - increase understanding of the diversity of goals and processes for doctoral study in mathematics education; - allow reflection on common elements of the doctoral programs, and critical consideration of features that differ; - facilitate identification of the best features of various programs and support participants in reviewing their own approaches; and - provide commonality of understandings that will provide the background for sessions 2 and 3 of this DG. A range of perspectives on the focus questions below will be sought. We welcome participants from all countries. All participants will be invited to prepare, in advance, written responses to the following questions. The following are some focus questions, with some indicative issues that could be addressed): What are the goals for doctoral programs in your University? (e.g., is priority given to candidates learning to research, contributing to new knowledge, being inducted to academician?) Are particular perspectives privileged on the nature of knowledge, argument, theory, and methodology? (e.g., are some methods favoured over others, are there cultural perspectives on what constitutes evidence?) What are the expectations for candidates’ background for entry to doctoral programs? (e.g., what mathematics studies are expected, what practical education experience is required, are there pre-requisites for prior research?) What is the content, and what is the demand for coursework? (e.g., are coursework studies core, and if so what are they, are they elective, if so from what range of courses?) What are the expectations for supervision, of both the supervisor(s) and the candidate? (e.g., how many times would the supervisor(s) read Chapter x, how many minutes would supervisors meet with full time students each month?) What are the requirements for the thesis? (e.g., what is the word length, are there specifications for quality, are there alternatives to a thesis, what is the minimum full time equivalent time for study?) What is the process for examination, and what guidelines are given to examiners? (e.g., is there a viva presentation, can examiners confer, is it possible to “fail”?) To what extent is professional and practical knowledge valued? (e.g., are curriculum or resources development projects considered as an alternative to conventional research?) Are there differences between mathematics education and other education theses, and other doctoral theses? (e.g., are students directed to a particular topic or can they choose, do requirements for entry vary between programs?) What are the expectations for candidatures to participate in the life of the Faculty and University? (e.g., are their expectations for tutoring, attendance at non required seminars, mentoring of other candidates?) It is noted that goals and processes vary between institutions, and we are only asking participants to report for their University, not their country The co-ordinator of the session, Peter Sullivan, will analyse and synthesise some of the responses for the first session, and Barbro Grevholm will synthesis others for the second session.

Session 2, coordinator Barbro Grevholm

Participants of doctoral programs in mathematics education

In this session we will focus the people who participate in the programs, the doctoral students, the supervisors and teachers of doctoral courses. What academic and professional backgrounds should individuals admitted to graduate studies aiming at mathematics education research have? - What is the case today and how could it be changed? - What kinds of problems are linked to recruitment of doctoral students? - What influence do the backgrounds have on the outcome of the education?

The doctoral student’s ability to write is crucial for success. How can this ability be developed systematically during the program?

Doctoral students often come with ideas about what to do research on. The choice of research problem is crucial, its limitations and precision is an important and difficult process. The importance of having a burning interest for what you are investigating is often critical for the doctoral student. What experiences do we have about these issues?

How can we define new areas for research internationally? Is there any common consensus about these new areas? How do we ensure that the research problems doctoral students choose are relevant for mathematics teaching and learning in school or other educational institutions? What research problems are supervisors prepared to work with?

Do we have any experience from systematic exchange programmes for doctoral students? How can such programs be built up?

How are supervisors educated and how can they develop their skills? What education for supervisors do we know about? What are the demands for supervisors in order to be accepted as such?

What do we know about the subtle relation and work between student and supervisor? What degree of freedom do doctorates have in choosing a supervisor for their degree? What variables influence them to choose their supervisor? If there is any barrier of lack of freedom in making the decision to have her/his supervisor, what is it that caused that to happen?

What is the role of supervision and how do we offer competence development for the supervisors? What are the responsibilities of the supervisor?

Session 3, coordinator Robert Reys

A vision for doctoral programs in mathematics education

Background Doctoral programs in mathematics education vary greatly within and across countries. Some doctoral programs require K-12 teaching experience prior to admission. Others require collegiate teaching experience. Still others require no prior teaching experience. Some institutions require full-time residence for multiple years in order to complete a degree, other programs can be done on a part-time basis and a doctorate be completed while working full-time in another position. Programs also vary greatly in the range and depth of mathematics content required, as well as the manner in which research competence is acquired. Some view this diversity in programs as a strength, others as an area of concern. It certainly raises at least one important question: Is there a central core of knowledge/experiences that doctorates in mathematics education possess? An equally important question is: Should there be a common core of knowledge for graduates with doctorates in mathematics education. That is, when someone says they have a doctorate in mathematic education, what is reasonable to assume about the knowledge they possess with respect to mathematics education.

If the answer to this question “Is there a central core of knowledge that doctorates in mathematics education possess?” is Yes, then several natural questions follow, including: What should constitute this common core of knowledge? Who should decide what constitutes this common core? How should it be delivered? How should competence in mathematics education be assessed? Should there be an accreditation of doctoral programs in mathematics education?

One could argue that answers to these questions would provide useful guidance to doctoral granting institution. Others may argue that such information would be too prescriptive, and therefore run the risk of curtailing creativity and uniqueness currently associated with doctoral programs in mathematics education.

One vision for the future A vision for the future is that doctoral programs in mathematics education become more convergent. Does this mean that all doctoral programs in mathematics education would be alike? No, definitely not. Such convergence does not exclude interdisciplinary experiences, but it would insure that doctorates in mathematics education would share a common core of knowledge. Unless a common core of knowledge exists, it is hard to justify mathematics education as a discipline of study.

The Association of Mathematics Teacher Educators developed a document entitled Principles to Guide the Design and Implementation of Doctoral Programs in Mathematics Education that included the identification of core knowledge areas. At the least this effort provides some talking points regarding a ‘common core of knowledge’. If there is agreement that some refinement of this type of effort would be of value internationally, then perhaps some plans could be made to move at ICME-12 in that direction.

The organising team of DG12 is considering the opportunities to produce a pre-ICME11 booklet if we get written contributions to our invitation above that are good enough to be published as a working material. Please follow the development here.

Everybody interested in active participation in the work of DG12 is kindly asked to send in the abstract of her/his possible communication in the amount of one page, containing also the name, affiliation, e-mail address and 3-5 key words. The abstract must give clear understanding about what the author wants to discuss and what are the most important conclusions he has come to. Each member of the organizing team should receive it no later than March 1st, 2008. Until April 1st the authors of accepted contributions will be informed about acceptance and asked to send in the full paper in the amount of 1000-2000 words until May 1st.

News, 20080415 There will be written contributions to the work in DG12 from the following persons: Agnis Andzans Sang Sook Choi-Koh Barbro Grevholm Vena M. Long Robert Mayes Michaela Regecov Robert Reys Filippo Spagnolo Peter Sullivan

These papers will be available on this webpage soon after the 1st of May 2008. Any other interested contributors are asked to contact Barbro Grevholm or Peter Sullivan.

For DG12 a booklet has been produced and printed. This booklet will be available at the sessions of DG12. It is also available for anyone who wants do download it from this web page. See files below. It contains the programme of DG12 and all written contributions to the discussion group. We want to express our sincere thanks to Professor Agnis Andzans and Dr Dace Bonka and the University of Latvia for the work with the production of this booklet.