Sunday, February 3, 2013

The Hard Parts

I have about 3 hours a day that I spend planning lessons. I'm currently trying to figure out ways of incorporating hard practice into my professional life. Last week, I experimented by allocating half of that time towards careful thinking about what students would struggle with during my lessons. I write these things down in a document that I call the "hard parts" document.

Overall, I was happy with the first week of this experiment. My lesson quality was better than what I had been averaging in the first semester, even though it was a tough week for me (I was sick and didn't sleep much from Monday to Wednesday). Focusing on the hard parts of each lesson felt difficult and required constant mental effort. Forcing myself to write down observations made the whole process visible, and kept me from getting in a rut. 

Here's a selection of my "Hard Parts" document I produced on Tuesday, a day that went very well for my first period students.
Concrete results came out of my time spent thinking about the most difficult aspects of my lessons. It was only on reflection that I realized that my students didn't understand the utility of closed-form equations for patterns, and I successfully created a plan that attacked that issue. It was during my reflection on what's hard about the unit circle definitions of sine and cosine (for my third period students) that I started worrying about the differences between heuristics and procedures. The solution: instead of directly having my students use the special right triangles to find values around the unit circle, I would start by having them estimate the values of a new function, s(theta), around the unit circle, and only make the connection with exact values later.

Unlike Tuesday, Thursday's class was a disaster for first period, even though I also devoted substantial time to my exercise.

The core of the lesson was the "Skype monthly plan" problem:

 Given the above, how much do you pay per month, and how much do you pay per minute? I thought that this problem would be productive, though difficult, for my students. 

Here's the "Hard Parts" document that produced this lesson plan:

So, what went wrong on Thursday? If I did the exercise faithfully, how did my lesson get so muddled?

A careful read of my "Hard Parts" document reveals some issues with my planning:
  • My goal subtly changed over the course of my planning. I had just a fuzzy idea of what I wanted class to be about at the beginning. I originally was going to focus class on a problem involving plumbers. The difficulties that I began thinking of for the "plumber problem" were no longer relevant by the time that I had chosen the "cell phone problem" instead.
  • Because I didn't focus on the "cell phone problem" I completely missed a student issue that I should have anticipated -- they didn't understand how monthly + per-minute fees worked. That could have been easily taken care of by giving them a chance to evaluate how much you would have to pay under various given plans. 
  • The students also didn't get that November and December referred to the same plan. I could have anticipated that -- it's a misconception that I've seen before, and this is a relatively weak group -- but I didn't devote time specifically to the "cell phone problem."
What I'm realizing is that I have to be careful about plans or problems that coalesce toward the end of my allotted focusing time. Because I'm at the end of my time, and because I've already devoted a lot of thought toward the lesson, I'm tempted to skimp on mental effort for the actual problem that I want students to work on. That mistake can be a fatal one for my lessons.

I can help myself more by trying to come up with a rough plan on the weekends for what content I'd like to cover over the week. That's a bit of planning that I had been doing, but let slide. I think that will allow me to start each day with a bit more focus, so that I can spend the planning time anticipating issues with the day's core exercises.

1 comment:

  1. Dear Michael,

    Hi. I just took your on-line survey re:planning via twitter retweeted by Brian E. Bennett and followed my curiosity to here. I enjoyed reading through your post and am impressed by your honesty and dedication to your detailed reflection of teaching and learning within your classroom. The questions you are asking yourself and the tasks you have set yourself seem to provide a challenging yet rewarding pathway to strive for and maintain purposeful teaching and learning. You may enjoy the outcome from asking your students to read your "hard parts" notes and involve their input. You may like to read Kath Murdoch's ideas for Understanding Checkups ( which could be helpful in some of the issues you felt you faced within your lessons. They are quick by effective and may help if you are limited by time/content.

    I also read your Classroom Footage page which you expressed difficulty in opportunities to observe. I agree it is hard. I have found that teaming up with my energetic colleague who is as passionate about teaching/learning as I am and creating a shared blog has been one of the most rewarding pathways toward professional development. She's now on the other side of the word and we're still collaborating! It isn't necessarily traditional course work PD but it is some of the most powerful, exciting and sticky learning I've had so far in 18 years. I think you're on the right path, keep asking the "hard parts" questions of yourself and finding ways to help your students with the "how" (not just the "what") and you are well on your way. Your school is lucky to have you!

    Natasha Hutchins