Some spare time, so I thought I’d dump some thoughts out onto the blog…

Something I’ve realized in reflecting on my first few weeks: as much as I would like to, I can’t teach a conceptual lesson with inquiry and a gradual build to the punchline and then give them homework and expect them to apply it right away without me having worked out at least one or two explicit example. My students don’t have the mathematical confidence yet to make those jumps on their own. I’ve become a lot more explicit with the things I expect from my students at the end of the day (which I think has helped) and started to do much more I do/we do/you do. It’s actually made me reflect more on the Bloom’s Levels that I use as a guide for monitoring how much I’m really challenging my students. I’m starting to realize that in my own idealized world of the classroom, I never had a place for the low-level blooms skills – identify, list, categorize, name, etc (especially identify in a geometry class). However, I’m realizing these are the skills that are best for formative assessment and quick corrections – I’ve started using these types of low-level questions and skills on the first few bellwork questions just to see if the students are on-board with the basic concepts we learned yesterday. It also builds that mathematical confidence, which I think is the biggest block many of my students have. I guess I’ve started to think of Blooms as a hierarchy – first I should asses lower-level skills (identifying, listing) and gradually build to assessments with the higher-order skills (comparing, synthesizing, creating) – which I guess makes sense, but I wish someone had told me this before I jumped into planning lessons with all these wonderful higher-order thinking activities without giving them enough time to process and practice using the lower-order skills.

Last little thing I’m thinking of: we’ve been moving through angle relationships and into parallel lines and those relationships (all really as an excuse to continue refining algebra, which all of my students need). I want to do an activity which works as the following: every group starts off with a certain number of poker chips and a certain number of geometric figures (lots of intersecting lines, etc). They are in charge of finding every missing angle in the figures by using properties such as vertical angles, corresponding angles, etc. As they work through the problems, they can pay me one chip and I will tell them the measure of one of the angles they are missing (they pick the angle). At the end of the activity, the number of chips they have left is their score for the day. So, the less times you need to ask for an angle, the higher your score will be. Any problems not completed will result in a penalty. So, if the total points for the day is 10 and each group starts with 14, then one group asks me for 6 angle measures before finishing, then they would get an 8/10 for the day.

The chip = points aspect requires them to decide how many angles they can find without any help, which is really the skill I want them to have anyway: given only a tiny bit of information, tell me everything there is to know about a figure. It also makes them think about when they absolutely have to ask for an angle – and, when they do, which one should they ask for? So, maybe I’ll do this one day too.