THE
FIELDS INSTITUTE FOR RESEARCH IN MATHEMATICAL SCIENCES

FIELDS
MATHED FORUM MEETING AGENDA
Theme:
History of Mathematics and Statistics
and Their Place in Curriculum
March
31, 2012, 10AM  2PM
Fields Institute, 222 College Street, Toronto



MORNING PROGRAM
10:00 a.m.  12:00 noon
10:00  10:15 a.m. Reports: OAME, OMCA, OCMA, CMESG, CMS, and
other.
10:15  10:50 a.m. Craig Fraser (University of Toronto)
Original Sources in the Mathematics Classroom
The historian and philosopher Thomas Kuhn pointed out that it is
very unusual in any branch of science to study original scientific
sources. The learning of the subject is done completely in terms
of textbooks. To the extent that older contributions are relevant
they are absorbed into the textbook literature and are taken as
known in current research. A case might be made that the example
of mathematics is different. Several commentators have argued that
the learning of mathematics is enriched by reading original sources
from the history of mathematics. My presentation will examine this
thesis and look at some of the issues that arise in the use of primary
source material in the teaching of mathematics.
Works to be discussed:
William Dunham, Journey Through Genius The Great Theorems of Mathematics
(Penguin, 1991)
Harold M. Edwards "Read the masters!", in Mathematics
Tomorrow, Ed. L. A. Steen (1981)
Ivor GrattanGuinness, "History or heritage? An important distinction
in mathematics and for mathematics education" in American Mathematical
Monthly 111 (1) (2004) 112
Thomas S. Kuhn, "The essential tension Tradition and innovation
in scientific research," in The Essential Tension: Selected
Studies of Scientific Tradition and Change (University of Chicago,
1977)
Ranjan Roy, "Learning by reading original mathematics,"
Notices of the American Mathematical Society (October 2011), pp.
12851287
Biography: Craig Fraser is Acting Director of the Institute
for the History and Philosophy of Science and Technology at Victoria
College, University of Toronto, and is Chairman of the International
Commission for the History of Mathematics. His primary area of research
is the history of analysis and mechanics in the eighteenth and nineteenth
centuries. He has documented a major foundational shift in the writings
on calculus of Euler and Lagrange as the calculus was separated
from geometry and made part of pure analysis. He has done research
on the evolution of the calculus of variations since 1800, focusing
on the work of such mathematicians as Hamilton, Jacobi, Mayer, and
Hilbert. He is also interested in celestial dynamics since Laplace,
and relativistic cosmology in the 1920s and 1930s. Fraser is the
author of a number of articles: on Euler and Lagrange, on the history
of mathematics in the eighteenth and nineteenth centuries, and of
two booksCalculus and Analytical Mechanics in the Age of Enlightenment
(1997) and The Cosmos a Historical Perspective (2006). Fraser has
taught the history of mathematics at both the graduate and undergraduate
levels for over twentyfive years.
10:50  11:25 a.m.
Georges Monette (York University)
Why You Need to Ask How in Order to Know What
Understanding statistical ideas helps us make sense of the torrent
of information we face in our daily lives. One of the most important
statistical principles is not mathematical in character. It is the
principle that to understand data you need to know how it was obtained.
Data, on its own, says very little. We need to develop the habit
of digging below the surface to find out how a sample was obtained
in a survey; how treatments were assigned in an experiment. The
widely known adage 'correlation is not causation' expresses the
danger of causal conclusions based on nonexperimental data. However,
a rigid insistence on randomized experiments for causal inference
might be as problematic as the uncritical misinterpretation of correlations.
The importance of a balanced view is well illustrated by the history
of R. A. Fisher's contributions to statistics. Fisher is one of
the leading statisticians and scientists of the 20th century who
developed the theory and practice of randomized experiments in the
1920s and 30s. His contributions have had an enormous impact on
research in almost every field. However, in the 1950s and early
60s, his insistence on randomized experiments for causal inference
led him to mount an energetic defense of tobacco in the face of
mounting nonexperimental evidence of its harmful effects. The story
of Fisher's apparent failure to find the right balance serves as
a poignant illustration of important issues in causal inference.
Biography: Georges Monette is an Associate Professor in
the Department of Mathematics and Statistics at York University.
He obtained his Ph.D. at the University of Toronto in statistical
inference. He has had a long association with York's Statistical
Consulting Service and has worked on applications of statistics
in a wide range of disciplines. Consulting is a form of teaching
in which complex concepts need to be conveyed to collaborators and
clients who often have little statistical and mathematical background.
In addition to teaching academic courses, he teaches workshops on
statistical visualization and longitudinal data analysis.
11:25  12:00 noon
James Stewart (Professor Emeritus, McMaster University)
Why, and how, should we incorporate history into the mathematics
classroom?
I will try to answer the questions in the title of this talk in
the spirit of the late Kenneth May.
Biography: Degrees from Stanford University and University
of Toronto. Taught at McMaster University and University of Toronto.
Author of many high school and university mathematics textbooks,
translated into a dozen languages.
12:001:00 p.m.LUNCH BREAK
(Light refreshments provided)
1:002:00pm AFTERNOON PROGRAM
Angelica Mendaglio (McMaster University)
Humanizing Mathematics
The human stories behind mathematics are too often omitted from
the classroom. There is no better way to make a student feel that
they are having a subject be imposed upon them than by presenting
it as a sequence of facts listed by textbooks. Mathematical problems
have captivated the minds of some of history's most creative, brilliant
and interesting characters  what better way to motivate a student
to engage with a mathematical object than by introducing them to
these minds and these problems? I will be discussing some of the
human stories behind mathematics and the reasons why students want
to know them.
Biography: Angelica Mendaglio is currently a Master's student
at McMaster University. She became enthralled by pure mathematics
and, in particular, abstract algebra during her time as an undergraduate
student at Trent University, and has since become interested in
mathematics education as a means through which to bring this joy
and beauty in mathematics to the public eye.
Gordon Doctorow(Nova Southeastern University)
My History of History in Math Classes
I've never taught a math and history class, but I have, over my
years as an educator, introduced historical material in my computer
science and math classes, both at the high school and university
levels. I will discuss my experiences.
Biography: Five years as a computer programmer and technical
writer. Twentysix years as a math/computer science teacher at high
school level. Two years as a computer science lecturer at York University.
Currently, adjunct faculty at Nova Southeastern University, teaching
an online Master's course in math education and supervising Ed.D.
students.
Miroslav Lovric (McMaster University)
Newton's Opticks and Universal Arithmetick
I will discuss the math content of the two Newton's books owned
by McMaster University (Opticks and Universal Artihmetick). What
are they about? What are Newton's thoughts on teaching math? Based
on Newton's Opticks, a few instructors created a learning object
 to help students to discover and explore the complex mind of
Isaac Newton. I will discuss a rationale for its construction, as
well as a critique of its use in mathematics and beyond.
Biography: Miroslav Lovric is a professor in the Department
of Mathematics and Statistics at McMaster University. His areas
of research interest include differential geometry, modeling in
medicine and biology, mathematics education and connections between
art, mathematics and architecture. Besides publishing in his research
areas, Miroslav published textbooks on vector calculus and mathematics
for life sciences, and is presently working on a book about mosaics
and symmetry.
2:00 p.m. Adjournment