**Derek Holton**<dholton@maths.otago.ac.nz> Department of Mathematics and Statistics, University of Otago, Box 56, Dunedin, New Zealand.**Challenges for University Mathematics Education: Reflections on the 1998 ICMI Study Workshop.**In December 1998 ICMI held a study conference in Singapore on the teaching and learning of mathematics at the university level based in issues raised in a Discussion Document that appeared in the*ICMI Bulletin,*43(Dec. 1997)3-13. Some papers from the conference were published in a special issue of the*International Journal for Mathematics Education in Science and Technology,*31:1(2000). The ICMI Study Volume will be published by Kluwer Academic some time in 2001. Main themes range over*Research:*How can research results be disseminated widely and provide the basis for future teaching?*Practice:*What is good practice and how do academics learn of innovations in this area?*Maths and other disciplines:*Concerns over the trend towards mathematics as a service subject and who should teach the subject in specialist areas such as engineering and commerce.*Technology:*What is the best use of technology and what changes to curriculum does technology imply?*Assessment:*What alternatives are there to examinations and what are their merits?*Teacher education:*Should there be special courses for potential primary and secondary teachers and what training should tertiary personnel receive?*Policy:*Who makes the decisions and how can they be influenced?

**Glenda Anthony**<g.j.anthony@massey.ac.nz>. Department of Technology, Science, and Mathematics Education, Massey University, PB 11222, Palmerston North, New Zealand.**Undergraduate Mathematics Teaching and Learning: Research Review for Australasia.**(In collaboration with Ruth Hubbard and Philip Swedosh.) This paper provides a review of research in undergraduate mathematics teaching and learning completed in Australasia during the period 1996-1999. Throughout the studies two factors are prevalent: The continuing dissatisfaction with student achievement in higher mathematics in general, and calculus in particular, and the inequitable participation by females and other socio-economic and cultural groupings combined with the overall drift away from the highest intensive mathematics and physical science courses. Recent studies that take a more systemic approach alert us to the need to be aware of the ways students experience the total learning context, rather than just focusing on the mathematical content and presentation of courses. Specifically, studies address the issues of student participation and perceptions, student skills and understanding, instructional innovations, and assessment.**Leone Burton**<l.burton@bham.ac.uk>. Professor of Mathematics and Science Education, Department of Education, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK.**Forging the Links Between Researching and Teaching Practices.**An interview-based study of 70 practicing research mathematicians was undertaken in 1997. This paper reports on the relationship between what these mathematicians had to say about how they come to know mathematics, and how such practices might inform the teaching and learning of university mathematics. It makes the claim that to research is to position oneself as a learner. It points to epistemological discontinuities between reported practices in university teaching and the research practices of these mathematicians. In particular it draws attention to surprising outcomes with respect to thinking styles and to research collaboration both of which have implications for teaching.**Paul Bungartz**<bungartz@math.uni-bonn.de> and Alexander Wynands <wynands@math.uni-bonn.de>. Professors of Mathematics, Mathematisches Institut der UniversitÉt Bonn, Beringstr. 6, D-53115 Bonn, Germany.**Opinion-Research Concerning Teacher-Training-Programs.**In 1998 we made an inquiry asking young teachers who were just trained in the second phase (Referendare). 176 young teachers from 11 German towns answered. The main questions concerned: (a) The mathematical demands in basic courses and main courses; (b) A personal view of the didactical lectures; (c) The meaning of the importance of practical courses; (d) A judgment of the theoretical lectures in pedagogical sciences; (e) An estimation of their own mathematical literacy; (f) A question concerning the subject of the exam-homework. We tried to find a correlation of self confidence, mathematical literacy and the judgement of mathematical demands at university level.**Anthony (Tony) Gardiner**<A.D.Gardiner@bham.ac.uk>. Reader in Mathematics and Mathematics Education, School of Mathematics, University of Birmingham, Birmingham B15 2TT, UK.**Mathematics Graduates' Perceptions of Proof and their Abilities to Recognise and Construct Simple Proofs.**(In collaboration with Dr Candida Moreira, University of Porto, Portugal.) Students in their final semesters taking courses reflecting on the nature, role, and practice of proof in elementary mathematics were assessed on several levels: (a) giving written answers to questions about the nature and role of proof; (b) reconstructing the proof about the sum of angles in a triangle; (c) working on problems requiring proof; (d) being taught to analyse flawed "proofs" and to appreciate standard proof sequences from elementary mathematics (such as Euclid Book I); (e) being examined at the end to see what had changed. The attitudes expressed in answering the initial questions were surprisingly positive. In contrast, the ability to produce simple proofs of familiar results, to appreciate and respect the logical hierarchy required in any sequence of results, or to criticise flawed "proofs" was disturbingly weak. By the end of the course, performance in the first two categories had improved markedly; the third category remained very weak.**Daniel L. Goroff**<goroff@math.harvard.edu>. Professor of the Practice of Mathematics and Associate Director, Derek Bok Center for Teaching and Learning, Harvard University, One Oxford Street #325, Cambridge, MA 02138, USA.**The Impact of Graduate School Policies and Practices on Mathematics Teaching.**Graduate schools enculturate mathematicians in ways that resonate throughout the educational system. Since the introduction of the Ph.D., there have been repeated calls for the reform of this degree. Earning one, the critics say, should be shorter, less exclusively focussed on research, and better preparation for the full range of professional responsibilities mathematicians may fulfill. It is finally becoming clear to all that Ph.D. programs cannot have as their only goal the cloning of current faculty. As recent changes in policies and practices at U.S. graduate schools begin to affect the teaching of mathematics, it is important to place these developments in their pedagogical, economic, and international contexts.**Joseph Kyle**<j.kyle@bham.ac.uk>. Senior Lecturer, Department of Mathematics and Statistics, The University of Birmingham, Edgbaston, Birmingham B15 2TT, UK.**Supporting Academic Practice for Mathematics, Statistics and Operational Research (MSOR) in the UK.**(In collaboration with Pam Bishop, University of Birmingham.) On 1 January 2000 a discipline-based network of centres was established for higher education in the UK, including an MSOR Centre which will: support and enhance academic practice in teaching MSOR; coordinate networks of MSOR academics; disseminate innovation and good practice in learning, teaching and assessment; create a forum for the exchange of information, ideas, philosophies and research findings; exploit and harness change associated with new technology, integrating this into pedagogic developments. The presentation will give an account of the Centre's programme of work to date, emphasising plans to liaise effectively within the UK and internationally, and to review, advise on and encourage MSOR-based research and development in learning and teaching, including the use of communication and information technology, to meet the needs of the MSOR discipline.**Dushan Pagon**<dushanp@hotmail.com>. Department of Mathematics, Faculty of Education, University of Maribor, Koroska c. 160, SI-2000 Maribor, Slovenia.**New Approaches to Teaching Mathematics at the Universities: Experiences from Slovenia and the Czech Republic.**In the last decade the role of computing aids in mathematics education has significantly increased. The new technology opened new perspectives for teaching and learning mathematics at all levels. From our point of view there are at least the following aspects of this process that should be thoroughly examined: The use of CAS opens a new way to motivate students for doing mathematics, replacing the most unattractive part of their work. The implementation of new technologies calls for changes of curriculum, replacement of some topics that are out of step with new ones. Students obtain an important possibility of making their own investigations in different mathematics topics. Also there is a new possibility to (self) evaluate students mathematical knowledge. So the strategies of teaching should be updated. We demonstrate the significance of the above processes and give some suggestions based on concrete examples arising from our five year experience in the frame of the Tempus Joint European Project.