ࡱ> VXU[M[ Abjbj 1ΐΐ8%L L 84,#0(?",>j~ @/B/B/B/B/B/B/$K24f/(,f/{/`z"z"z":@/z"@/z"z"-| /oD4.,//H#0F.5!r5$ /5 / z"f/f/z"#05L Y: Some Thoughts on Survey Team 1 topic: Recruitment, entrance and retention of students to university mathematics studies in different countries by Derek Holton, Fiona Hagan, Eric Muller, Juha Oikkonen, Oscar Adolfo Sanchez Valenzuela, and Ren Zizhao Abstract The aims of this communication are to: Generate discussion among mathematics faculty on what is happening with student enrolments in undergraduate mathematics courses; Find more data on enrolments at various levels; and Receive information on innovations implemented by Departments of Mathematics to make mathematics more appealing; and hear what people have to say on the subject. In section 1 of what follows, we outline the working programme of the Survey Team. In section 2 we present data from several countries some of which show evidence of a reduction in graduating student numbers. In the remaining sections we ask for your assistance and comments on: Why student numbers might be falling; What can and is being done to combat any decline; Are we producing enough mathematics graduates for societys needs; and What is your department doing with respect to recruitment, entrance and retention of mathematics students? What we, the Survey Team, are trying to do is to tell you our thinking so far and to ask for your help and suggestions in whatever way you can. If you have something to communicate then please email Derek Holton, New Zealand, ( HYPERLINK "mailto:dholton@maths.otago.ac.nz" dholton@maths.otago.ac.nz) for comments in English; Oscar Adolfo Sanchez Valenzuela, Mexico, (adolfo@cimat.mx) for comments in Spanish; Eric Muller, Canada, ( HYPERLINK "mailto:emuller@brocku.ca" emuller@brocku.ca) for comments in French; Ren Zizhao, Peoples Republic of China, (renzz@mail.neea.edu.cn) for comments in Chinese; and Juha Oikkonen, Finland, (Juha.Oikkonen@helsinki.fi) for comments in Finnish. The Survey Team We suspect that the reason that the IPC established the Survey Team on this topic was that in an increasing number of countries, students appear to be moving away from enrolling in undergraduate mathematics courses. The Team is to survey and review all factors that may be responsible for this situation and to report on innovative ways that Department of Mathematics have responded to reverse declining trends in student enrolments in their courses. We began work at the start of last year and so far we have organised two questionnaires. One was disseminated through the Delta conferences mailing list. Another has been distributed to Departments of Mathematics in Canada and Mexico. We have collected data on student enrolments at both secondary and tertiary level from other sources, have reviewed the literature, and had many discussions with interested academics. We begin by outlining some of the things that we have found so far, mainly data, and seek your help for other things that we havent found. Youll realise that we are a small group with little funding and that we have other jobs to do, so we wont be able to cover every area of the subject in the time allocated. Some Figures Here we present some of the data we have collected. The USA: Below we give data for bachelors, masters and doctoral mathematics degrees in the USA since 1966. The first graph gives absolute numbers and the second provides mathematics degrees as a percentage of degrees in all fields of the corresponding three types.  EMBED Excel.Chart.8 \s Figure 1. Absolute numbers of US bachelors, masters and PhD graduates  EMBED Excel.Chart.8 \s Figure 2. USA percentage of maths graduates to graduates in all fields. Except for short periods in the 1980 and the 2000s, the graphs show a decline in Mathematics graduates in all three levels and as a percentage of graduates in all disciplines. Of course these data dont tell the whole story, as most mathematics departments in the USA have large enrolments in their first and second years because students enrolled in other majors often have to take some mathematics courses. France: Here we have data both on the baccalaureate and on university level enrolments. Unfortunately these data are for all science enrolments as we were unable to obtain data for mathematics on its own.  Figure 3. French students gaining the science baccalaureate from 1962 to 2004.  Figure 4. French enrolments in the first two years of science at university. As one expects, the trends in the number of students completing the science baccalaureat is reflected in the trends of the number of students in the first two years of science at university. 2.3 New Zealand: In this section we provide data on student enrolments in mathematics in the last year of secondary school. Because of the difficulty of obtaining national figures we only give the university figures for the University of Otago since 1990. 19851990199520002005Pure Mathematics6245Applied Mathematics4942Maths + Calc7949867085037048Maths + Stats11223118971212512120 Figure 5. New Zealand numbers of school students taking the given courses in the given years 199019952000200520062007Mathematics231208240239200Statistics196253243203169451427461483442369 Figure 6. University of Otago total enrolments by Effective Full Time Students from 1990 to 2005. Whereas the number of students in Maths + Stats show a steady increase the number of students in Maths + Calc have fluctuated with a significant decrease in numbers between 2000 and 2005. The latter trends are reflected in the total enrolments at the University of Otago. 2.4 Singapore: We are grateful to the National University of Singapore for the data on students graduating with mathematics majors as well as masters and doctoral degrees. We have graphed these in Figures 7 and 8.  EMBED Excel.Chart.8 \s Figure 7. Singapore numbers of graduating majors in mathematics from 1987/88 to 2006/07.  Figure 8. Singapore postgraduate student numbers 1987/88 to 2006/07. The data shows an increase in the number of mathematics undergraduate degrees until the mid 1990s and shows a general decrease in these numbers from then on. 2.5 Peoples Republic of China: In this section we provide projected four-year data for the number of mathematics students in the final year of schooling and for the number of students entering a university mathematics course (actual). 20067,270,00020078,040,00020088,370,00020098,720,000 Table 1. Mathematics student numbers in the final year of schooling. YearCandidates Recruited students 2004 6,909,600 4,473,4002005 8,768,000 4,750,0002006 9,249,700 5,630,0002007 10,100,000 5,670,000 Table 2. Students entering a mathematics course at university The number of students completing mathematics majors at university in 2007 is about 65,000. This number would be higher but there is a quota system. So it is clear that undergraduate mathematics numbers are increasing in China. What is the situation in your country? 3. What is the problem? What are the stated and perceived reasons for any decline in mathematics student enrolments in your country? Is it that mathematics is boring and hard and there are no jobs at the end of it, or that government policies are responsible, or that internal politics of mathematics departments prevent adequate responses, or are there any other reasons? Please send us your views or references to pertinent publications. What Can be Done? There are a number of things being done by departments in various parts of the world. We mention four of them that have been communicated to us, they are maths centres, technology, improved teaching and outreach programmes. We hope to expand on these topics and to add more to the list. You could help us by telling us about innovative approaches taken by mathematics departments and institutions that have been tried and that have succeeded in maintaining enrolments or by reversing declining enrolments. 5. What Next for the Survey Team? We plan to look at various questions that we havent been able to answer so far. The most crucial of these are the following. 5.1 Are we producing sufficient numbers of mathematics graduates? This is too big a topic for the Survey but we would like to make some comments on it. The point is that if the number of mathematics graduates is declining it is possible that we are not producing sufficient mathematical resources for the community in which we live. That would be a real problem. To put that in context, do we know how many mathematics graduates of any kind we need for the future of our various countries or indeed the world? Are we producing sufficient mathematics majors to produce an ample supply of secondary teachers? Are we producing sufficient doctoral students for research requirements and for teaching future mathematics undergraduates? Do you know of any studies on the subject that have been done in your country or anywhere else in the world? If so, we would very much like to know of it. 5.2 What is happening in your university mathematics department with respect to Recruitment, Entrance, and Retention? As a department do you actively recruit students? What do you do and how successful are your efforts? (Note that we distinguish between recruitment - attracting new students to a specific department- and outreach - putting mathematics in the forefront of human activity.) Do you have entrance restrictions or do you take anyone who wants to do mathematics? Are your entrance requirements set nationally? What is your retention rate like? Do you lose many students who enrol in a maths major programme? Do you gain maths majors as the students progress through the years of their degree? What do you do that can be shown to have improved your student numbers? 5.3 Is your department doing well at the moment? If it is, then we would like to know if that is the trend in your country. If it isnt, what are you doing that is making the difference? On the other hand if your department is not doing well, why is that and how do you think you might be able to turn things around? Wed like to hear from you on that too. 5.4 What have we overlooked? It is almost certainly the case that there is some important angle of this topic that we have overlooked. Please let us know what it is and how we might find information to address it. References Below we provide some of the sources that are the basis of our collected wisdom so far. Ben-El-Mechaiekh, H., Buteau, C., and Ralph, W. (2007). MICA: A Novel Direction in Undergraduate Mathematics Teaching, Canadian Mathematics Society Notes 29, 6. Bishop, A.J, Clements, M.A., Keitel, C., Kilpatrick, J. & Leung, F.K.S (2003) (Eds.) Second International Handbook of Mathematics Education. Dordrecht: Kluwer Academic Publishers. Cabri-gomtre.  HYPERLINK "http://www.cabri.net/cabri2/accueil-e.php" http://www.cabri.net/cabri2/accueil-e.php Convert, B. & Gugenheim, F., 2005. Scientific vocations in crisis in France: explanatory social developments and mechanisms, European Journal of Education, 40, 4, 417-431. Conway, J. (1997), A Wealth of Potential but an Uncertain Future: Todays Mathematics Departments, Notices of the AMS, 44, 4, pp 439-443 Duverney, D. (2005).  HYPERLINK "http://smf.emath.fr/VicSociete/Rencontres/France-Finlande-2005/DuverneyGB.pdf" http://smf.emath.fr/VicSociete/Rencontres/France-Finlande-2005/DuverneyGB.pdf Ewing (1999). Towards Excellence. American Mathematics Society.  HYPERLINK "http://www.ams.org/towardsexcellence/" http://www.ams.org/towardsexcellence/ Hillel, J. (2001). Computer Algebra Systems in the Teaching of Linear Algebra: Some Examples. In D.A. Holton (Ed.) The Teaching and Learning of Mathematics at University Level: An ICMI Study, pp. 371-3804. Dordrecht: Kluwer Academic Publishers. Hodgson, B.R. & Muller, E.R., (1992). The impact of symbolic mathematical systems on mathematics education. In B. Cornu and A. Ralston (Eds.) The Influence of Computers and Informatics on Mathematics and its Teaching, pp. 93-107. UNESCO Document Series 44. Paris: UNESCO. ICMI 16 (2007).  HYPERLINK "http://www.amt.canberra.edu.au/icmis16.html" http://www.amt.canberra.edu.au/icmis16.html Kent, P. and Nosss, R. (2001). Finding a Role for Technology in Service Mathematics for Engineers and Scientists. In D.A. Holton (Ed.) The Teaching and Learning of Mathematics at University Level: An ICMI Study, pp. 395-404. Dordrecht: Kluwer Academic Publishers. Muller, E.R. (1991). Maple laboratory in a service calculus course. In L.C. Leinbach, J.R. Hundhausen, A.M. Ostebee, L.J. Senechal & D.B. Small (Eds.) The Laboratory Approach to Teaching Calculus, pp. 111-118. Mathematical Association of America Notes 20. Washington, DC: Mathematical Association of America. Muller, E. (2001). Reflections on the Sustained Use of Technology in Undergraduate Mathematics Education. In D.A. Holton (Ed.) The Teaching and Learning of Mathematics at University Level: An ICMI Study, pp. 381-394. Dordrecht: Kluwer Academic Publishers. NSF (2007). Science and Engineering Degrees: 1966-2004.  HYPERLINK "http://www.nsf.gov/statistics/nsf07307/pdf/nsf07307.pdf" http://www.nsf.gov/statistics/nsf07307/pdf/nsf07307.pdf. Oikkonen, J, (to appear). ICMI Bulletin. Phipps, P. Maxwell, J.W. & Rose, C.A. (2007a). 2006 Annual Survey of the Mathematical Sciences (First Report). Notices of the American Mathematical Society, 54, 2, 230-245. Phipps, P. Maxwell, J.W. & Rose, C.A. (2007b). 2006 Annual Survey of the Mathematical Sciences. Notices of the American Mathematical Society, 54, 7, 876-889. Phipps, P. Maxwell, J.W. & Rose, C.A. (2007c). 2006 Annual Survey of the Mathematical Sciences. Notices of the American Mathematical Society, 54, 10, 1333-1334. Ralph W, (2000). Journey Through Calculus. CD-ROM. California, USA: Brooks/Cole. Shannon, F. J. (2004). Classics counts over calculus: A case study. In I. Putt & R. Faragher & M. McLean (Eds.), MERGA 27 Conference: Mathematics Education for the Third Millenium Towards 2010. Townsville: James Cook University. Acknowledgements We would like to thank the large number of people that have had significant input into this work to date. In particular we would like to thank all of those people who responded to our questionnaires as well as Pierre Arnoux, Michle Artigue, Chong Chi Tat, Daniel Duverney, Maurya Green, Garry Harris, Lim-Teo Suat Khoh, Lynn Steen, and Sitoe Yew Kok.     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