Title: Math and Art: The Good, the Bad, and the Pretty
Abstract: Dust off those old similar triangles, and get ready to put them to new use in looking at art. We're going to explore the mathematics behind perspective paintings---a mathematics that starts off with simple rules, and yet leads into really lovely, really tricky mathematical puzzles. Why do artists use vanishing points? What's the difference between 1-point and 3-point perspective? What's the difference between a perspective artist and a camera? We'll look at all of these questions, and more. We'll solve artistic puzzles with mathematical theorems, using hands-on examples.
Title: How to Grade 300 Math Essays (and survive to tell the tale).
Abstract: Because of the emphasis placed on collaborative learning and on laboratory exploration, mathematics instructors are increasingly assigning student writing in our classes. Those of us who assign written work have noted that mathematical essays provide students with a forum for clarifying their thoughts, for expressing their creativity, for emphasizing concepts rather than merely reciting rules, and for allowing their instructor a heightened awareness of students' perceptions of the material.
Written assignments, however, can create hurdles for both instructors and their students. Two of the most formidable obstacles we instructors face are these: Firstly, if we must teach writing, we wish to do so without detracting from the mathematical content of the course. Secondly, we have to grade the writing once it appears (in large quantities) on our desks. In particular, we are all searching for a method which will allow us to grade a large quantity of essays in a way that is (a) meaningful, (b) equitable to all students, (c) helpful to the students' writing, and (d) time-efficient. The aim of this talk is to explain how to do just that.
Annalisa Crannell is Chair of Mathematics at Franklin & Marshall College.
She received her professional degrees in three year increments: from
Springbrook High School in 1983, then Bryn Mawr College, then an MA and
finally a PhD from Brown University in 1992. Because she spent much of her
youth wandering the halls of NASA where her mother worked, she decided
early on that her intended career would be a "xeroxer". That ambition is
only slowly being realized.
Crannell's primary research is in topological dynamical systems (also known as "Chaos Theory"), but she also is active in developing curricular materials for a course on Mathematics and Art. She has worked extensivley with students and other teachers on writing in mathematics, and with recent doctorates on employment in mathematics. She especially enjoys talking to non-mathematicians who haven't (yet) learned where the most beautiful aspects of the subject lie.