I found that my lesson was a lot shorter than I had intended. Overall, the core of it took about twenty to twenty-five minutes. This may have been partially due to the artificially small class size, but in an actual class, I would have certainly found myself running short. I'm not certain on how I would extend on the fly like that. If my pre-assessments, ongoing assessments, and post-assessments indicated a strong grasp, I could expand into the reals and complex number systems and possibly into the application of complex numbers as fractals. Another option would be to demonstrate some simple closure properties of the sets of numbers (e.g. adding two integers will always yield an integer answer). Alternatively, more exploration of the applications of these numbers in measurements and starting the next part of the unit plan could be more appropriate.
During the Graffiti activity, several of the adults expressed a reluctance to get up as they were, "pretty comfortable right here," but it seemed that once they did, they actually enjoyed being up and moving around. The son definitely enjoyed it and was very active in assigning the adults colors and putting papers and the whiteboard up. They also seemed to appreciate having the opportunity to discuss with their peers what the possible answers would be and the general sense of both collaboration and independence during the activity. While they were working on their own, they had the opportunity to bounce ideas and suggestions, as well as offer help to others. I happened to observe a small bit of peer teaching occur as well during the activity.
One student was still struggling with the idea of rationals and irrationals. His peer pointed out checking to see if it could be turned into something with, "just plain old numbers," instead of, "a bunch of stuff after a decimal point." Her suggestion seemed to help him grasp the idea better.
Doing an on-going assessment of observation and assistance in such an artificially small class size was easy, but also difficult to make it seem like I wasn't hovering over them and not letting them work independently. I feel like this dichotomy would balance out as the class size increased, but after a certain point, would become unbalanced in the opposite direction; monitoring becomes more difficult as the sense of independence becomes easier. This could easily tend towards directionless and chaos.
 |
| Sample of adult student's work |
The use of the video seemed to be an excellent reinforcer and I ended up using that as the post-assessment instead. There was a brief struggle to get the Khan Academy YouTube video to run on the RaspberryPi that was hooked up to my T.V.; instead, we opted to run it through the YouTube app on the Xbox360. Making sure that the technology works correctly is something that should be handled before a lesson begins.
Using the rubric, I found that the students all succeeded. Only one of them got an answer wrong and it turned out to be a result of having been taught that pi = 22/7. Pi is irrational, therefore 22/7 must also be irrational. The student themselves caught the error when the answers were given and understood on their own where the misconception was.
Overall, I think the lesson was successful with this test class and provided me with some good starting points for making improvements and enhancements. In retrospect, I think I would more have liked to test a different day in the unit plan, however, I lacked sufficient materials to do so outside of a regular classroom. I think that would have let me test for potential struggle and chaos points during some of the more hands-on activities and shown where the plan was deficient.
Excellent teaching (even though a select group) and also excellent reflection...that is real teaching, Deja, just like real numbers :)
ReplyDeleteMark