- Scott Steketee gave a talk on making the connection between functions in geometry (e.g. the well-known transformations of the plane) and (linear) functions in algebra. His basic idea was to use geometric transformations in order to go from transformations of the number line, to function diagrams, to Cartesian graphs. One interesting point he made was that transformational geometry makes it possible to introduce function notation early on without the risk of confusion between f(x) and f·x. (In a strictly algebraic context, I prefer to wait until function notation is needed to talk about composition and inverse functions, so Algebra 2 or Precalculus.)
- Michael Pershan and Max Ray gave a talk on introducing complex numbers that was so compatible to my own pedagogy that I added my recollection of it to the Kinesthetics part of my Web site. Their approach also started with transformations of the number line. I was surprised and pleased when Max came up to me after the talk to say that they were familiar with my approach to complex numbers.
- Brent Ferguson gave a talk on compass and straightedge construction of numbers, given a starting line segment of length 1. Most interesting: new-to-me approaches to dividing a line segment into n equal parts. I was familiar with this traditional method, which I learned in high school:
Brent's students came up with other methods. Here is one particularly elegant one:
[This earlier post on geometric construction includes links to several more.]