M.C. Escher (Dutch) is that kind of artist to me. His father wanted him to be an architect, but he chose to be a graphic artist. He was mathematically brilliant, as is demonstrated in tons of his drawings, prints, and woodcuts. He was fascinated with the Regular Division of the Plane. http://www.mcescher.com/ He was also an illustrator and painter, who created masterfully realistic works as well.
I could have approached the creation of the tessellations in many ways: Tracing Paper Translation- Slide; Tracing Paper Translation- Rotation, but I decided to try the Cut Paper Method (I discovered that an actual teenager came up with it). It's very similar to the Slice Method, but it's a bit simpler, and the resulting shapes are random, which allows the artist more creative freedom in the final results. I tried a few methods, made a couple exemplars, and decided for my students I would also add various instructional devices as well: video, visual diagrams, as well as direct instruction.
The Math Connection
There were two other lesson plans where I’d included geometry where students were required to draw a rhombus, a trapezoid, or an ellipse as a method of seeing the illusion of depth. This lesson was a good segue after having that experience. I asked the students to sketch regular shapes in their sketchbook - just taking it back to the basics - that there are three regular shapes that make up regular tessellations: the equilateral triangle, the square, and the regular hexagon. For a visual example, I showed them how a regular hexagon is used in the pattern of a honeycomb, the nesting structure of the honeybee. However, the artworks -- ah hum…. Tessellations I wanted the students to create were no average semi-regular tessellation! Ours were verrrry irregular with all kinds of convex and concave angles. What I would describe as more organic than geometric, but the math can be found in them.
They got this!
I am very contemplative about my teaching. The average size of my classes was 36, at the highest I had 38 mostly freshman/generalist students. I haven't been able to have a studio-type environment, where I could assign a cerebral challenge and send students off to think creatively to solve the problem, then bring to me sketches that they proudly created and are anxious to share. I'ma be real!
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A student finds a rabbit in her tile.
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My undergrad degree is a B.F.A. and my first professional experience was as a graphic designer. I often forget how much my education at the Philadelphia College of Art informs my teaching methods and production strategies. After each student created their tile (the kinda easy part), I encouraged them to look carefully at the contour and to imagine what image or images could be congruent with it. Before they could create their large painting with no gaps or overlaps, I had them create thumbnails sketches. Instead of free-drawing their design from tile to tile, I encouraged tracing their image over and over, so that they were interlocked and covered the plane. That was important because, as I explained ". . . most of your tessellations are irregular polygons, not parallelograms, nor equilaterals. . ."
Understanding Color Theory - another important component of the project.
While some students were working on their designs, others would mix colors to paint a color wheel. In addition, they were supposed to choose a complementary color pair, then paint tints and shades in a seven-step scale. This introduced them to low key and high key colors, as well as truly developing a sensitivity to color mixing -- discovering on their own -- "is this really orange? How much red do I need to make this orange and not red-orange?"
I would teach this again, and again. I think my students were challenged and quite proud of the results. Students who finished early were encouraged to repeat their design onto ceiling tiles. That presented an interesting challenge because all ceiling tiles are squares. Nevertheless, for my population of students, this worked as a late second-semester project. I'm not sure I would have presented this fist quarter. However, perhaps I am wrong? Perhaps this could have been the BANG! that set things off and kept them engaged from the start? I'll never know. For now, enjoy their creations.
