David Biddle (Cornell): An example of using writing and language to describe the 3-dimensional sphere as the union of two solid tori: experiences from teaching a Freshman Writing Seminar in Mathematics.
Abstract: During the Academic year Fall 2003-Spring 2004 I had the immense pleasure of teaching a Freshman Writing Seminar here at Cornell; in particular I had the chance to teach the course in two consecutive semesters. This experience enabled me to revamp the course for the Spring semester based on my observations and the students' feedback. In the first part of the talk, I will discuss in general the types of writing the students employed to describe not only their mathematical ideas, but also to respond critically to the various contexts in which the ideas were first introduced. Secondly, I will talk specifically about one sequence of assignments that enabled the students to develop the language necessary to complete a descriptive essay assignment: the essay essentially had the students describe visually the 'complement' of a (standard position) solid doughnut sitting inside the 3-dimensional sphere. What amazed me the most was the vastly different ways the students handled the assignment. The students encompassed wholly the spirit of the course, which can be best expressed in the words of mathematician/inventor Charles Hinton:
"Whatever pursuit we are engaged in, we are acting consciously or unconsciously upon some theory, some view of things. And when the limits of daily routine are continually narrowed by the ever-increasing complication of our civilization, it becomes doubly important that not one only but every kind of thought should be shared in."
Daina Taimina (Cornell): Mathematical Way of Thinking - When Is It Creative?
Abstract: In an ordinary mathematics class, the program is fairly clear cut. We have problems to solve, or a method of calculation to explain, or a theorem to prove. The main work to be done will be in writing, usually on the blackboard. If the problems are solved, the theorems proved, or the calculations completed, then teacher and class know that they have completed daily task. Is this teaching how to think mathematically? Getting to know new mathematical facts and there applications - it is creating new knowledge in students heads - but is it creative thinking?
The tools of mathematics are abstraction, symbolic representation, and symbolic manipulation. However, being trained in the use of these tools no more means that one thinks mathematically than knowing how to use shop tools makes one a craftsman. (Schoenfeld)
I will discuss some history of " teaching mathematical thinking" and will talk about my own experience - how handiwork tool helped me to teach geometry more creatively and how the same work now is inspiring artists to learn about mathematics and to use mathematical ideas creatively in their own work.
4:15pm: Mathematical Knowledge for Teaching, Oliver Club (colloquium), Mallott 406.
David Bock (Cornell): The New NYS K-8 Mathematics Curriculum Guidelines (tentative)
Abstract: Report from the Albany NYSED meeting re: the new state math curricula, which was the "rollout" for the new K-8 guidelines.
The originally scheduled seminar has been postponed until April 11 due to a conflicting seminar in STS which is of interest to several members:
"The Sanskrit Knowledge Systems Project and the Very Idea of a History of Science"
Christopher Minkowski (Dept. of Asian Studies, Cornell University)
Mar 14, 2005, 04:30 pm,
374 Rockefeller Hall
Will Harris (Cornell and Georgetown): Computer Software and Constructivism in the Teaching of Abstract Algebra
Abstract: In the summer of 1994, I attended a workshop given by Ed Dubinsky and Uri Leron on the use of the computer programming language ISETL in the teaching of abstract algebra. Workshop participants worked through the presenters' text on the subject and participated in discussions of pedagogy and the theory of learning (constructivism, in particular).
In this presentation, I will give you an introduction to ISETL, illustrate how the software is to be used in the teaching of abstract algebra, and relate my experiences in running the course in this fashion.
Sunethra Weerakoon (Cornell and University of Sri Jayewardenepura, Sri Lanka) : How my teaching evolved over the years and what I want to do next
Abstract: Basically, I will tell how I transformed from the stage of "letting students self-learn the stuff" to what I am today through various stages and discuss ways and means of propagating the same in the Sri Lankan education sector with the intention of seeing a positive transformation.
Sal Restivo (Rensselaer Polytechnic Institute, Nottingham University UK, Harvey Mudd College): Where does Mathematics Come From? Reflections on God, Einstein's Brain, and Social Construction
Neil Davidson (University of Maryland): Twelve Step Recovery Program for Teachers Addicted to Lecturing (Lectureholics)
Abstract: