The last two days in class have been amazing! I have been hitting my students with BIG expectations for the new semester and they are knocking it out of the park.
Yesterday, I was planning a review day to make sure everyone was ready to move on to rational exponents today, but I knew the small groups I had planned based on their exit task from Friday were not going to be enough for an engaging class. As I sat thinking about how I really should have spent more time coming up with ways to engage my students, I thought, “I’ll have them do presentations on what they review in their groups.” I’ve wanted to get these students presenting something since the beginning of they year, but we had yet to do it. So I typed up a quick scoring guide and decided I would have them grade themselves and average their score with mine (document to follow).
This semester I have TWO interventionists with me all day, every day (more on that later), so we each took a group and were able to give focused, one-on-one help to every student, which in itself had me feeling good. Then, the presentations started and the feeling in the classroom was so awesome. Not only did most of the students do a great job given that it was everyone’s first presentations, but it was so easy to tell who knew what they were doing and who needed more help, I felt like I was cheating.
Today, we started rational exponents. (I know. I could just end there. Amazing, right?) I, trying to avoid a lecture (theme), decided, thanks to a post by Ian Byrd, to take the inductive approach. So, I put up 10 or so solved examples of simple rational exponent problems (numerator of 1) that they would know the inverse facts for (e.g., 4^(1/2)= 2, 64^(1/3) = 4). They started by thinking individually about what the fractional exponent was doing and worked their way through dyads and table discussions interspersed with a few whole class clue-sharing sessions as students discovered different things. We took the whole class period, and it was awesome. I was careful to only reveal what was necessary at the time and when they got stuck, we went right back to individual thinking time to let the students come up with new ideas, and climbed up the discussion ladder again. By the end of the block, the tension in the room was becoming so palpable as they started getting closer to realizing that x^(1/2) = sqrt (x) that I think I almost leapt into the air when they got it. My 3rd block class did especially well, so I e-mailed the rest of the 9th grade teachers to tell them to congratulate the students on their status as amazing mathematicians when they see them tomorrow. I was so proud of their inductive reasoning and perseverance I literally came home and told my wife, “I think I’m becoming a good teacher!”