This is a reflection I wrote about a math lesson on tessellations that I taught to my peers. I was not that familiar with tessellations myself before I taught the lesson. Teaching the lesson to others helped me expand my own thinking. Since I was learning as I taught, this reflection offers evidence of myself as a life long learner.

There are many things that went well with our peer teaching groups on Friday. We decided to teach in centers and I taught tessellation at my center. Mine was the first group you observed.

First of all, I think our whole group did a good job of facilitating movement around the centers. Students were placed in a group quickly and efficiently and times at the center were clearly defined. I also feel I did a good job being prepared and organized. Several emails indicated my overheads were helpful in clarifying the various types of tessellation and some students also said the use of Escher’s pictures in a book helped pique their interest in the topic. I think my use of basic shape patterns helped students get started without squelching their creativity.

I am very pleased with the reflective thinking aspect this lesson seemed to invoke from students. Many of my peers indicated they had either never heard of tessellation or knew very little about them. Several emails mentioned that by approaching the topic through an “art” aspect, even those who considered themselves math-phobic could expect success in the endeavor. I think asking students to create their own tessellation with different shapes also encouraged them to think reflectively to decide if a figure would tessellate or not and why that was so. This was much more reflective than giving them ready made shapes, for example, and asking them to make a tessellation using those shapes.
I also feel very good about the amount of cooperative learning that occurred at the center. Students who were more confident and were willing to take risks aided the progress of those students who weren’t exactly sure how to proceed. It was very gratifying to hear students ask a question of the group as a whole and to allow that sharing of knowledge. Also, it stretched their thinking enough to cause them to ask a question and then say, “Oh, now I see!”

Since you observed my table first, I think you probably saw the least effective lesson of the cycle. During the first group, I attempted to explain too much information myself rather than allow the students to discuss and share among themselves. As I “let go” of later groups, the flow of ideas seemed much more free. Also, a student in my second group provided me with a wonderful example of a tessellation (attached) to show both that group and the two that followed. I had considered making a tessellation before the lesson to use as an example, but decided against the idea because I thought it might narrow the amount of reflection going on. If I taught this lesson again, I would definitely have such an example to show the groups.
One email asked me to think about what plans I had made for a student who became easily frustrated with the project. This was a thought provoking question for me because I really had not prepared for such a situation. (A big oversight in an actual classroom!) After careful consideration, I think there are two things that may help such a student. First, I might allow the students to begin with a simpler tessellation to begin with. This would allow them to experiment and experience a certain amount of success. Secondly, I believe the lesson could be more effectively using partners. Then an easily frustrated student could benefit from the partner’s influence.

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