Friday, January 29, 2016

Extra Reading

There's been a spate of an interesting articles popping up on the web recently. The first one was from David Wees: http://davidwees.com/content/planning-lessons/.  There's a lot of excellent advice here.

 I find myself choosing an appropriate task based on some understanding of anticipated student thinking, then imagining how students might approach the task and what they will think about, then considering how to sequence the different strategies student might use toward a big mathematical idea, and then creating the resources to enable me to use the instructional activity in the classroom. This level of planning is sustainable.
This very much meshes how I've been approaching planning recently. I usually start with an area like probability or a particularly activity like "no rectangles" and work backwards to create a sequence around it.  Then I turn to considerations of how the students will react and what should I modify to make the material better and or what I'm trying to emphasize during the exercise.

What I find in addition to this level of planning is I have to evaluate how things played out afterwards. Math Club lessons rarely (if ever) go perfectly especially the first time you try them. Its valuable to be constructively critical about each session and think about what could be improved. Right now, I find most of my areas of focus are on how I react and what I say during a session. When you're in front of a large group of kids, there are a ton of split second decisions that you're continually making based on behavior, kid's questions the pacing that each group is taking etc.


The second article I like was from Ben Blum-Smith: https://researchinpractice.wordpress.com/2016/01/28/lessons-from-bowen-and-darryl/

The biggest takeaway for me was how exceedingly careful they are with people talking to the whole room. First of all, in classes that are 2 hours a day, full group discussions are always 10 minutes or less. Secondly, when students are talking to the room it is always students that Bowen and Darryl have preselected to present a specific idea they have already thought about. They never ask for hands, and they never cold-call. This means they already know more or less what the students are going to say.
Again this aligns with some of the techniques I've been playing with. Having kids talk in front of the class is really hard for flow. Even if they manage to project loudly and clearly enough for the others to hear, a student explanation is often harder to follow. This doesn't mean its not valuable to do them. Developing group communication is clearly an important skill. But I try to pace these out carefully. I'm also pre-selecting volunteers whenever I have the opportunity to do so based on what I see their work looks like (and also to get everyone up in front) When I do cold call, I'll often specify what kind of answer I'm looking for  "Is there anyone who solved this problem using a regrouping strategy?"  One thing, I'm not doing currently is actively looking to parse mistakes in front of the class. I see teachers doing this in various posts. But for us I feel its so hard for the students to follow along that it can quickly become a one on one session with a room sort of biding its time until you're done. I'm reserving these moments for true one-on-one interactions during the hour.

Finally, I saw this homework sheet for fourth graders (It appears to be from the Continental Math League)





For the most part these problems are solvable by algebraic means. But if you give them out what do you expect pre-algebra students to do with them?  I think the wrong answer here is to have parents setup equation and show how to solve 2(x - 15) = x + 15 for example. I doubt that will stick or provide long term benefit when its so far out of sequence and not embedded within a curriculum. Instead, these are generally looking for bar method or guess and check table like solutions. I tried a few out on my beta tester to confirm that yes these are actually quickly crackable that way.  That said, I question whether it makes sense to do lots of problems like these if you're going to gain the skills to algebraically attack them in a few years anyway. And while developing guess and check skills can be valuable, I find I'm more often fighting over-reliance on it and trying to design questions to encourage other strategies. So for now my instinct is "use with caution."


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