Panel Discussion

"ICMI Study on The Teaching and Learning of Mathematics

at Undergraduate Level"

Coordinator: Derek Holton, University of Otago, Dunedin, New Zealand


A short history of the Study will be given to set the background for a deeper discussion of three of the main areas of the Study.

Educational Research: One of the goals of the Study was to determine what educational research carried out at this level of formal education had to offer; to evaluate the researches potential to help us understand better the observed problems and to offer strategies for tackling these; and to identify the current limitations of research and suggest orientations for its future.

Practice: Recent changes in undergraduate mathematics teaching have been in response to external factors that impinge on the teaching of the discipline, as well as a result of different epistemological views of mathematical learning. Several innovative teaching approaches were highlighted in the Study. These include new approaches to teaching topics of a traditional curriculum, as well as attempts to redefine the nature of undergraduate mathematics teaching and learning.

Technology: Innovations in this area affect both curriculum and pedagogy. Much of the Technology area of the Study centred on the use of technological tools for supporting students learning, particularly via visualisation, computation, and programming both during and after formal lecture time. Consideration was given to technologies potential to foster more active learning, to motivate explanations of surprise feedback, to foster co-operative work and to open a window on students thought processes.


Members of the Panel :

- Michèle Artigue, Université Paris 7, Paris, France

- Derek Holton, University of Otago, Dunedin, New Zealand

- Joel Hillel, Concordia University, Montreal, Canada

- Alan Schoenfeld, University of Berkeley, California, USA


Panel Discussion
“Mathematics Is For All”

Coordinator:  William Yslas Velez, Professor of Mathematics and University  Distinguished Professor,
Department of Mathematics,
University of Arizona, Tucson, Arizona, USA


As mathematicians we believe that mathematics is useful, beautiful, and necessary in order to address the scientific problems that society confronts.  We would all like to have a citizenry that is mathematically literate. Yet, many of us complain about the small number of students who choose to study mathematics in college or to choose mathematics for their major.  Interestingly, there have been considerable efforts at increasing these small numbers and these efforts have been directed at sections of the population that have not historically participated in the mathematical enterprise.  The purpose of this panel is to learn about these efforts and how to integrate these efforts into the culture of a university mathematics department. 
Every country has “minority” populations that do not participate fully in the mathematical enterprise in that country.  Minority populations oftentimes have to overcome more barriers than the majority population, barriers that stand in the way of the full expression of latent mathematical ability.  These barriers take on many forms. Preparatory schools may not fully prepare students for the rigors of a university curriculum.  The lack of financial resources is a common impediment.  Social structures may prohibit the consideration of a mathematical career.  The lack of knowledge about mathematical careers certainly plays a factor.  Perhaps even the organizational structure of the university should factor in.  One of the goals of this panel is to explore these impediments.  
Concern for these under-represented groups sometimes results in special efforts or programs to address this inequity.  These special efforts and programs are designed to encourage minority populations to gain access to mathematical careers.  In many instances, minority mathematicians have led the efforts and have devoted a considerable portion of their careers in an effort to provide better access to the under-served.  The mathematical community can learn a great deal about increasing access to mathematics by looking at minority programs.  Efforts aimed at improving access for minority populations can also increase access for all students, and that is another goal of this panel. 
A common dictum in the United States is that “Mathematics is for all”.  It is the goal of many pre-college programs in the U.S. to have all students complete a solid program of study in mathematics, one that will prepare them to pursue a mathematically based career in college.  When we look at the professorate in mathematics departments at our research universities in the U.S., it is abundantly clear that the professorate is not representative of the U.S. population.  The phrase, “mathematics is for all”, does not appear to apply at the level of university professor of mathematics.  The percentage of women is nowhere near equity.  Historically, there were three main minority groups in the U.S., African-Americans, Mexican-Americans and Native Americans.  These minority populations are almost invisible among the professorate at research universities in the U.S. 
This panel will provide the opportunity to learn about these special efforts to increase the participation of minority populations in mathematics.  Panelists will be invited to provide examples of the work that they have done to increase the accessibility, for minority groups in their countries, of mathematics and mathematics-based careers.  Examples will be chosen that will give full evidence that these efforts have a broader appeal and, when incorporated into the way a mathematics department functions, will serve to increase the interest in mathematics in more students, not just minority students. 

Members of the Panel : 

- Megan Clark, Centre for Mathematics and Science Education School of Mathematical and Computing Sciences Victoria University, Wellington, New Zealand

- Cyril Julie, School of Science and Mathematics Education, University of the Western Cape, South Africa

- William Yslas Velez, Department of Mathematics, University of Arizona, Tucson, Arizona, USA

Panel Discussion

"On the role of the history of mathematics in mathematics education"


Coordinator: Fulvia Furinghetti, Department of Mathematics, University of Genoa, Italy


In recent years, important works on the relationship between history and mathematics education have appeared:

  1. The Proceedings of the "European Summer University on History and Epistemology in Mathematics Education" (Montpellier, France, 1993, Braga, Portugal, 1996, and Leuven/Louvain-la-Neuve, Belgium, 1999),
  2. Two books based on the elaboration of papers which were presented during the satellite meetings of HPM (History and Pedagogy of Mathematics, one of the ICMI affiliated international groups), the first edited by R. Calinger (MAA 1996), and the second edited by V. Katz (MAA 2000),
  3. The ICMI Study book on "History in Mathematics Education", edited by J. Fauvel and J. van Maanen.
  4. Journals for Mathematics Teachers and/or Mathematics Education Researchers have published special issues on the History of Mathematics in Mathematics Teaching (e.g. For the Learning of Mathematics in 1991, Mathematics in school in 1998 and Mathematics teacher in 2000). The re-born newsletter of HPM (International Study Group on the Relations between History and Pedagogy of Mathematics) is becoming (we hope) a forum where piece of information and ideas are shared.


These material and the experiments carried out all over the world make further discussion on the role of the History of Mathematics in Mathematics Teaching both possible and necessary. In recent discussions the expression "integration of History in Mathematics Teaching" appears frequently. Which ideas are behind this expression? The main idea is that of using History as a mediator to pursue the objectives of Mathematics Education. This means that, these objectives, together with the study of the historical evolution of concepts should be analysed. This work has to be carried out by educators and historians in a collaborative way. Among the benefits, which are expected to result from this work, is the new perspective offered by History to consider students' difficulties in learning Mathematics. To make teachers active actors in this process we need to give a convenient place to the History of Mathematics in pre-service and in-service teacher education.


Members of the Panel :

-Fulvia Furinghetti, Professor of Elementary Mathematics from an advanced standpoint, Department of

Mathematics, University of Genoa, Italy.

-Masami Isoda, Associate Professor, Institute of Education, University of  Tsukuba, Japan

-Man-Keung Siu, Professor of Mathematics, Department of Mathematics, University of Hong Kong, Hong Kong SAR, China.

-Constantinos Tzanakis, Associate Professor, Department of Education, University of Crete, Greece.



ICTM2 Home