My liberal arts math class will be the subject of some blogging this semester, as it already has. But another course I am doing has me pretty excited too. It’s an independent study I am coordinating with one of our majors on Computer Explorations in Geometry. Basically, my student is going to be selecting 10-12 different Geometers Sketchpad projects from a booklet and then doing them, explaining the math behind his constructions along the way.
I am a big, big fan of Geometers Sketchpad. I think that pound for pound, it’s the best mathematical software out there for educational purposes — a perfect combination of low price (just $40 for the student version) and high functionality. It provides a simple pallette of tools, and it’s kind of amazing what you can do with them within the software. For example, in the test bank book, I used Sketchpad to create interactive bell curves for graphics related to questions about normal distributions (e.g.: “Which of the following normal distributions has the largest mean?” followed by three graphs of bell curves). It’s got great uses in Calculus too, which I have not really exploited yet. And it runs great under Linux using Wine.
I teach a junior/senior level geometry course for math and math education majors here, and the last time I taught it, I had the students do two of the Sketchpad projects in the booklet my student will be using. At the time it was just basically a token gesture for including technology in the course; but those students really poured themselves into those projects and had to learn a lot of old-fashioned geometry in order to make the constructions. At the end of the course, I wondered what it would be like to have the entire course just consist of a whole bunch of Sketchpad projects, presented and explained by students at every class meeting, with no lecturing. This study is a sort of “proof of concept” for that idea, and we’ll see how it flies.
I’ve been thinking a lot lately that you don’t really understand a mathematical idea until you implement it with a model, especially a computer model (e.g. Sketchpad, spreadsheets, C++ or Python code, etc.). This kind of philosophy seems to be creeping further and further into my pedagogy…
Filed under: Math, Teaching, Technology
I made an attempt to familiarize myself with Sketchpad about 2 years back doing a similar directed study where I took a student interested in secondary education in mathematics and directed them to explore various technologies for implementation in the classroom. We divided a semester into three parts using Maple, Sketchpad, and general Internet resources. I just couldn’t get into Sketchpad for some reason and still lean must more towards Maple or Matlab for implementation of mathematical concepts. I guess I ought to give it another try.
The thing I like about Sketchpad is that it’s very minimalist. Basically all you get to work with is a ruler and compass, and a few tools for transformation and coordinate geometry, and the rest is built out of that basic set of tools. That makes it impractical for many uses but it also allows me a lot of control over what I am doing with it. And of course there’s certain things Sketchpad just doesn’t do, like linear algebra.
[...] 11:00–12:00: Independent study [...]
[...] Topics in Geometry is also running in the fall, and I am going out on a limb in the class this time by (1) not using a textbook at all, and (2) instead, using Geometers Sketchpad for everything. The independent study I supervised this semester, first blogged about here, was a terrific success; I intended it to be a proof-of-concept for the idea that you can run a really good, mathematically rigorous geometry course that consists entirely of technology-centered student activities. [...]
[...] Scott Steketee is a developer of Geometers Sketchpad, a dynamic geometry software package which I’ve blogged about before. He and his son are doing a cross-country bike ride to promote Sketchpad and its statistics-oriented cousin Fathom, and they’re going to blog the trip. From the web site, here’s a nice explanation of the connection between cycling and Sketchpad: I’ve been bicycling since I learned to balance a bike. Not only great for recreation and competition, cycling is the world’s most efficient form of transportation. Bicycling is based on a simple and elegant technology that’s the most effective and environmentally sound method of travel for short trips. [...]