October 2nd, 2005
'Aesthetic computing' turns algebra into art
Do you remember your math classes when you were a kid? Were you fascinated by equations or did you feel bored enough to look at the birds through the school’s windows? If your answer is the second one, there is hope — at least for your kids. A professor at the University of Florida has worked for ten years on the concept of aesthetic computing. This new approach can be used to teach algebra by encouraging students to express equations as pictures or stories. "The basic idea of aesthetic computing is to make abstract ideas or algebraic formulas ‘real’ through drawings, sculptures or computer graphics." So far, only a dozen teachers have followed a workshop about the concept and might use it for their future classes. But if enough math teachers read this column, this might change…
Before tackling this important educational question, here is the entertaining introduction of the University of Florida news release mentioned above.
High school algebra teacher Bunny McHenry has her share of students who would rather be doing something else. There’s the girl who loves to draw. There’s the drummer who can’t sit still long enough to choke down the basics.
It’s those students McHenry hopes will get help from an experimental new approach to teach algebra. Known as aesthetic computing, the approach encourages students to express equations as pictures or stories. It was pioneered not by teachers or education experts, but rather by a computer science professor with a background in simulating complex systems and a fondness for obtuse terms like "multimodeling."
This professor, Paul Fishwick, has invented the notion of aesthetic computing several years ago, and you should read this overview. Here are some excerpts.
The first step is to recognize that there already are aesthetics in mathematics and computing. Mathematicians talk of beautiful proofs, physicists talk of symmetry in their group structures, and computer scientists talk of well crafted programs and algorithms.
The only problems with today’s computer science aesthetics is that they are limiting given the aesthetic landscape found in art, with its plethora of styles, periods, and genres.
[Personal note: as a software developer for a number of years, I often thought that I was an 'artist,' but it's nice to read that a University recognizes it.]
Fishwick says for instance that computer scientists are using a wide variety of modeling types for portraying information and algorithms, such as finite state machines (FSM).
Let’s look for example at a FSM with three possible states S1, S2 and S3. Below is an illustration showing different ways to represent this machine: (a) a 2D diagram; (b) spheres; (c) a fluid flow metaphor; and (d) an agent metaphor (Credit: Paul Fishwick).
This image comes from a presentation given by Fishwick at the International Conference on Visual Languages, held in September 2003, Miami, Florida. The title of the talk was "Exploring Multiple Visualization Perspectives with Aesthetic Computing" and here is a link to this paper (PDF format, 6 pages, 485 KB).
Below is an excerpt about the concept of aesthetic computing.
Within this area, there is an attempt to balance qualitative with quantitative representational aspects of visual computing, recognizing that aesthetics creates a dimension that is consistent with supporting numerous visual perspectives. I introduce one aspect of aesthetic computing, with specific examples from our research and teaching to illustrate the potential and possibilities associated with alternate representations. We show that by linking with aesthetics, we surface some important philosophical and cultural questions regarding notation, which turn out to be at least as important as the algorithmic and procedural means of achieving customized model component representations.
I obviously don’t know if this computer science professor will revolutionize math teaching, but here is own optimistic conclusion.
How will mathematics and computing change as a result of efforts in aesthetic computing? The first change is in the improved psychological metrics such as memory, comprehension, and motivation, assuming that tests for these confirm our expectations. This, in turn, leads to more people understanding and working with formal structures, thus democratizing the field.
If you’re a math teacher, please let me know waht you think about this approach.
Sources: University of Florida News, September 28, 2005; and various web sites
You’ll find related stories by following the links below.
