The International Commission on Mathematical Instruction
Bulletin No. 47 
December 1999

A Progress Report on ICMI Study 11:
The Teaching and Learning of Mathematics at University Level

Derek Holton


The ICMI Study was planned during 1997 and its Discussion Document appeared that year in the December issue of this Bulletin.  In December 1998, the Study conference took place in Singapore.  We expect a special issue of the International Journal of Mathematical Education in Science and Technology to appear early in  2000, with selected papers from the conference.  The Study Volume is planned for publication sometime in  2001.

Study Rationale
Over the last  10  years or so, there have been major changes in tertiary education.  Many of these changes have impacted on universities in general but they have certainly had a profound impact on mathematics.  Among the changes are

  1. the increase in the number of students attending tertiary institutions;
  2. the increasing difference between secondary and tertiary mathematics education with regards to purposes, goals, teaching approaches and methods;
  3. the rapid development of technology;
  4. the requirement for universities to be publicly accountable.

Alongside these are also the changes in pedagogy and curriculum that have taken place at the pre-university level.

As a result of the above, ICMI felt that now was an opportune time to bring mathematicians and mathematics educators together to share experiences and ideas.  By pooling resources and discussing issues it was hoped that the best of research and practice could be disseminated to a wide audience.

Study Conference
The Study Conference was hosted by the National Institute of Education, Singapore, from December 8th to 12th, 1998.  The organisers did a tremendous job in looking after both the scientific and general needs of the participants.  As with most ICMI conferences there were plenary sessions, panel discussions, working groups and invited papers.  The emphasis at the conference was on pooling ideas and hence the working groups were an integral part of the meeting.  To give some flavour of the matters dealt with, we list below the plenary sessions, the panel topics and the working group issues.

Plenary Sessions
Why must the professor be a stimulating teacher?  Towards a new paradigm of teaching mathematics at university level: Claudi Alsina,
What can we learn from didactic research carried out at university level?:  Michèle Artigue,
Research on university-level mathematics education: (Some of) what is needed and why:  Hyman Bass
Teaching and learning mathematics at the university level:  a personal perspective:  Bernard Hodgson
Redefining university mathematics:  the stealth campaign:  Lynn Arthur Steen.

Panel Discussion
The Secondary/Tertiary Transition:  Frank Barrington, Myriam Dechamps, Francine Gransard,
Mass Education:  Garth Gaudry, Gilah Leder,
Technology:  Ed Dubinsky, Celia Hoyles, Richard Noss.

Working Groups
Secondary/Tertiary Interface:  Leigh Wood,
Mathematics and Other Subjects:  Jean-Pierre Bourguignon,
Technology:  Rosalind Phong,
Preparation of University Teachers:  Harvey Keys,
Assessing Undergraduate Mathematics Students:  Ken Houston,
Trends in Curriculum:  Joel Hillel,
Practice of University Teaching:  John Mason,
Mass Education:  Nestor Aguilera and Hans Wallin,
Preparation of Primary and Secondary Mathematics Teachers:  Honor Williams,
Policy Issues:  Hyman Bass,
The Future of Research in Tertiary Mathematics Education:  Annie Selden and John Selden.
(The names given here are the Chairs of the various working groups.)

Study Publications
As we said earlier, two publications will result from this Study.  The study Volume is currently in progress and more will be said about this in a later issue of the Bulletin.

The more unusual, for ICMI Studies anyway, of the two publications is the special issue of  iJMEST, the International Journal of Mathematical Education in Science and Technology.  At the conference, participants were invited to extend the papers that they had given there and submit them for the special issue.  After the refereeing process had been completed, fifteen papers were accepted to appear in the selected papers edition.  These papers are:
Factors influencing first-year students? success in mathematics, Glenda Anthony,
MATLAB in first year engineering mathematics, Len Colgan,
On a research programme concerning the teaching and learning of linear algebra in the first year of French Science University, Jean-Luc Dorier, Aline Robet, Jacqueline Robinet and Marc Rogalski,
Perception of the tertiary learning environment:  is mathematics worth the effort:  Helen Forgasz and Gilah Leder,
The history of mathematics as a coupling link between secondary and university teaching, Fulvia Furinghetti,
The student experience of mathematical proof at university level, Keith Jones,
The visibility of models:  using technology as a bridge between mathematics and engineering, Philip Kent and Richard Noss,
Redesigning the calculus sequence at a research university: issues, implementation and objectives, Harvey B Keynes and Andrea M. Olson,
Mathematical reasoning and familiar procedures,  Johan Lithner,
Asking mathematical questions mathematically, John Mason,
A reform in undergraduate mathematics curriculum:  more emphasis on social and pedagogical skills, Marrti C. Personen and Taina Malvela,
Assessment of learning in university mathematics, Geoff Smith and Leigh Wood,
Policy issues in the teaching and learning of the mathematical sciences at university level, Jan Thomas,
A metacognitive intervention in mathematics at university level, Rosetta Zan,
Classroom Notes:  A capstone course for pre-science secondary mathematics teachers, Mary Margaret Shoaf.

These papers cover a wide area of topics relating to the teaching and learning of mathematics at university level.  Anyone wishing to order a copy of this special issue of iJMEST may contact the editor Martin Harrison (
Any other enquiries regarding this Study can be made to the Chair of the Study at the address below.
Derek Holton, Chair
Department of Mathematics and Statistics
University of Otago, Box 56
Dunedin, New Zealand