My class ends. I erase the board, tuck the unused worksheets on top of the folders and head out into the hallway when I see Benjamin. He has not been to class once, so there is no way I can’t go call him out on it. “You know, the reason I’m trying new material is because you signed up for the class.” Benjamin was in my class last cycle, and when he signed up I told him I initial told him he couldn’t take it because I had already taken this course. Then I caved. Both because he’s awesome to have in class, and because I like coming up with new stuff. “Why not just repeat the class from 2 cycles ago…” Benjamin replied “it’d be easier for the both of us.” What Ben is saying there is that today’s class was a struggle. You know it’s bad when even the kid who hasn’t even been there for two weeks can see how bad it is.
Instead the class sucked
So I had an idea for a lesson. This lesson would fit right in with the unit where we finish talking about average median mode and start talking about standard deviation. In the past I have kids just do a huge mega table to understand the calculation side of it. What I don’t do is get the students to understand why such a calculation is important in the first place. So today I decided to make the new lesson. I thought that this lesson could involve the data that the kids generated in Friday’s circle, some practice with calculating the average, and the idea of “reliability.”
What I had them do was look at some bar graphs of the data from the last class. They could look at the bar graph and think about why the graphs show different ‘spreads.’ These bar graphs could then be used to calculate the average by looking at the values. They can then take that average and look at it in the context of the rest of the values on the graph and be able to make a statement about which graphs show the most clustering around the mean. I figured students would come up with their own ideas of which ones are clustering around, and then say stuff like “Graph A has the smallest range, so the numbers might be close to the mean” or “Graph D has most of the responses as one value, so that one is really close to the mean.” This would all lead to a magical debate, after which the class would realize that we need an approach to look at these data sets in order to figure this out. Then I would say “Well that’s why we have the standard deviation!!!” The kids would cheer, and high five each other, then I would get into the powerpoint.
So what went wrong?
Is it a bad task?
Maybe, I think the ideas could have been easily discerned from more cherry picked data. Just because I wanted to use data that the class generated doesn’t mean that the data will lead the kids to make the mathematical conjectures that fit my lesson objectives. The idea of using a bar graph to discern the average was a totally new concept. I thought it would be review but it ended up bogging down the conversation with questions of which average was right. Also, the question on the task wasn’t really relevant. I asked kids to say which numbers seemed the most “reliable,” e.g. If we were to draw a value from the set, can we say that the value should be close to the mean with some reliability? That was too abstract. I am using real data, I should lean on the context more. Maybe something like “If the mean was chosen to represent how everyone in this set thought, and everyone took these numbers really seriously, which set would have the most angry people in it?”
Does the class have the right culture? I don’t know, we do the circles, we have been doing partner work, we have also been doing boring worksheets and attendance has been sporadic. If I want to take kids on some kind of conceptual journey, I am going to need to structure the class so that this kind of journey is normal. Today whenever there was a space for conversation it was met with crickets and disdain. A little like the kids are saying “Dude, can you stop talking and just tell us the answer already!” This was especially the case with kids who weren’t there for most of the cycle.
Am I even teaching the right thing? Mean absolute deviation makes a lot more sense. Having kids do all this standard deviation business for a standalone 8 week statistics module may harm them if they only see it as a series of calculations.
What do I do now?
After talking with the push-in teacher for the class, it is clear I need to get more concrete. I’ll probably roll out the powerpoint, or skip standard deviation altogether and opt for the MAD. Lastly, I might curl up into a ball with a pint of cupcake frosting and hope that tomorrow I’ll wake up with the fortitude to teach my way out of this situation. (I’ll also probably think of some awesome come back for Benjamin too, and imagine my self saying whatever it is and picture him having a response like “Wow Carl, that one sentence has left me both smarter, and humbled. I want to be a better man.”)