Our team’s mathematical art project was based on John Critchett’s algorithmic digital artwork. We chose to explore his spirolateral artwork, partly because it appeared to be simple and elegant. Also, what caught our attention was how simple geometric objects were used to generate stunning artwork.
We employed several problem-solving strategies when we were attempting to recreate and extend Dr. Critchett’s artwork. Yes, I think that we methodically followed most of the strategies identified by the so-called “seven stages of problem-solving.” These seven stages are a) identifying the problem, b) understanding the problem, c) finding a strategy, d) sorting out the available information, e) analyzing the problem, f) keeping track of progress, and g) evaluating the findings. It was definitely exciting to recreate the original artwork. At least for me, what was even more interesting than the actual problem-solving processes was the dynamics involved in creative problem-solving activities.
Our team went through several discomforts. These ranged anywhere from trying different techniques of solving the problem to dealing with the frustrations of not a finding a solution to thinking about abandoning the problem on hand to finally overcoming the frustrations. Despite being teaching candidates who would have solved numerous problems over the course of our mathematical lifetime, our mental discomfort was evident when we were struggling. From our past struggles with mathematics, we know and have experienced the joys of overcoming these struggles when we finally solve problems.
I often wonder how easy it would be for novice learners or chronically struggling students to abandon learning mathematics altogether, because they might not have had enough opportunities to add layers of mathematical success. This brings me to a question that has popped up now and then over the years. That is, as teachers, how do we identify and present problem solving activities that are interesting, engaging, and challenging so that it makes sense and meaningful connections to students’ lives outside the classrooms?
I think that the actual mathematics involved in recreating this artwork is trivial. What was interesting to note was how geometric objects in conjunction with simple mathematical rules generate complex geometric patterns. I think that the potential mathematical learning involved in this particular activity would be to pose questions that go well beyond just constructing spirolaterals. Some of these questions can be of the following form:
Why don’t you devise your own rule to generate spirolaterals?
Can you create new and unusual geometric patterns?
Can you design a routine (algorithm) to generate spirolaterals?
How would you prove that your spirolaterals will form closed loops?