MathEd Forum

August 22, 2014
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 Grattan-Guinness, "History or heritage? An important distinction in mathematics and for mathematics education" in American Mathematical Monthly 111 (1) (2004) 1-12

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. 1285-1287

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 books-Calculus 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 twenty-five 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 non-experimental 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 non-experimental 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.

12:00-1:00 p.m.LUNCH BREAK
(Light refreshments provided)

1:00-2:00pm 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. Twenty-six 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