I know the last few loyal followers have been holding their breath in anticipation of the results of my first efforts as a teacher. Sorry for the wait.
I was fortunate enough to teach this lesson three different times. As would be expected, each attempt resulted in a unique outcome. For my first effort, I had Sequence 2. This was the group of kids with whom I had spent the least amount of time. Although the three pre-algebra sections are not deliberately grouped by ability, a definite caste system seems to have materialized with Sequence 2 performing near the bottom. Still, I decided to teach my lesson as-is, despite advice to the contrary from my placement teacher. It turned out including the proof was a bad idea, as she had warned. It took way more time than I had estimated and consequently, I was not able to stress key aspects of the lesson. In looking at student work, I found that I had not clearly communicated the fact that c2 refers specifically to the hypotenuse and that it always goes in the same place in the theorem. For example, a2 does not equal b2 plus c2. I also discovered that my instructions on the handout could have been clearer, and that the students would have benefited greatly from working more examples together in class.
Next up was Sequence 5. I had worked with a few of these students before, so I was definitely more comfortable and my sentences flowed with greater clarity. I decided to cut the proof from the lesson and spend more time working through examples. Student work greatly improved as a result, but there was still some confusion over the order of the variables in the theorem, with several students jumbling the equation. Exit Slip feedback suggested that I had not stressed that the relationship only works for right triangles.
For the final group of the day, I had Sequence 4, which was the group that I had observed for EDU320. The lesson went much more smoothly as a result of the relationship I had established with those students. The simple fact that I was able to call them by name made things much easier. Despite my disappointment over skipping the proof earlier, I left it out again so that I could work even more sample problems and stress the importance of keeping terms in the proper order. One interesting thing did happen that I had not expected, though. I had made many efforts to make this a culturally sensitive lesson, and I made mention of great geometers from China, Egypt, Greece, and the Mayan culture. When I was mentioning the Egyptians method of using ropes to measure distance, I inadvertently suggested that this was an antiquated technology. One student in the class who is of South American heritage raised his hand to inform me that it many parts of the world, this is still the preferred method. He was pleased at my mention of the Mayas, and even took an opportunity to teach me some Mayan words, but it was clear that I had erred and should be careful of that in the future. He is typically a problem student, prone to gang related discipline problems, but his interest in his Mayan heritage helped him to focus on this activity. He did not finish the entire worksheet, but what he did do was correct and flawlessly organized.
In general, I thought it was a success. The students said that they enjoyed the hands-on activity with the ropes, though in the future, I would eliminate the 5-12-13 rope, as it was clearly too complicated for them. If I had another day, I would definitely revisit the proof, but only after the students had the main idea down cold. Access to a Powerpoint projector would have been helpful, but I know that I can not depend on technology, so it is probably better that I learn to work without it.