Assignment 3: Math Project (Tessellations, Part 1)

Our group (Erwin, Gigi and Stanley) worked on the Islamic Tiling project. I chose the tiling pattern that consisted of ninja-star-looking units. (This was my first impression of the pattern.) Using a more sophisticated description, the unit cell that I identified had the general shape of an equilateral triangle, with the edges composed of a sine-like curve (1 period). There was an empty space in this unit cell, which contained a Star-of-David-like hexagram. Individually, I was not able to re-create the unit cell--err, pattern. (Forgive me: I keep calling it a unit cell because the chemist in me keeps popping out and remembering first-year chemistry and molecular stacking patterns.) Using straightedge and compass, I created a (more-or-less) similar curvy triangle. The part which gave me the most trouble was creating the empty hexagram with only those two implements. Gigi tried to help me with it and she may have figured it out. (The diagram is on one of the three pages of work.) I did not get through the entire project, but that was the point, wasn't it? To give it a try.

In terms of evaluating the benefits of this project, I think this project caters to the student's artistic flare and mathematical prowess. The first part (drawing the pattern, describing the pattern in words) appeals to those people inclined towards art, not requiring any math skills (except trying to keep things in proportion). The second part (recreating the repeat shape with straightedge and compass, making minor modifications) caters to the mathematician. It requires visual analysis of the shape to look for patterns that can be recreated using the geometry knowledge that students have thus far. Teaching analytical skills will be helpful not just in math but in so many other areas of life. One weakness of the project is that it could be overwhelming for students who cannot see the pattern that can be recreated with the two simple instruments. Tessellations are covered in the Math 8 IRP. Some of these might be difficult. (I will admit: I got a bit frustrated that I could not recreate the hexagram in the middle.) Of course, this problem could be alleviated by choosing simple tiling patterns for the students. I would not modify this too much, but I would pre-select some not-so-challenging tiling patterns or at least have two sets of patterns (medium and hard). One constraint of using this project in my classroom would be time. I might not know how long to prolong this project or how many class sessions to allocate for in-class work. Overall, I could see this being used in my class to get their creative juices flowing.