PANEL D ISCUSSIONS

*Panel Discussion*

"*ICMI Study on The Teaching and Learning
of Mathematics *

*at Undergraduate Level"*

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

ABSTRACT

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

*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

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

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

ABSTRACT

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

- 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),
- 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),
- The ICMI Study book on "History in Mathematics Education", edited by J. Fauvel and J. van Maanen.
- 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.