A math session in the park the other day got me thinking. Do we need our students to be on the same page? Here are some thoughts.
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Teacher authority is almost always at the center of the classroom, whether it’s by setting the course of study or controlling each day’s activity. As Peter Gray said in his recent post, “both sides [traditionalists and progressives] believe that good learning is a function of good teaching; they just disagree on what constitutes good teaching.”
Out of this, grows the necessity to be on the same page. Maybe you’re not reading along, or perhaps your mind is simply somewhere else, but in either case, we have a problem. The student’s not picking up what the teacher’s laying down.
By designing and legislating a standardized school system, we have made the statement plain; everyone should be learning the same stuff, pretty much. Looking over how much stuff that is to cover, and given the high stakes we place on testing this knowledge, it’s no secret the standards take up nearly all our time. So if a student isn’t on the same page, we really do have a problem. “You need to get this, and now is when we’re doing it.”
I think we can do better.
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The other day I met up with some people at Prospect Park to do some math. For a while it was Nick Fiori (our department chair), a fifth grader, Paul Lockhart, and me. We were trying to figure out the minimum number of calls needed to share everyone’s gossip in a network of ___ people, a fairly tricky problem and certainly non-standard. Paul has a PhD in Math, Nick has one in Math Ed, I’m halfway through a masters in each, and the fifth grader is a fifth grader. Is it even possible that we were on the same page?
Certainly we were all thinking about the same problem, but in dramatically different ways. I have neither access to the sort of combinatorial graph theory that Paul knows, nor the fresh thinking of that fifth grader. I have only learned from my experiences. Amazingly, we all contributed to the problem, and surely continued our process of mathematical development.
By our individual trajectories, we have developed what I call “personal insights” – the connections we’re able to make between our current problem and our own previous work. Insights can be shared or common, but in my experience they form most easily when the work you do is personally appealing and meaningful. That often means being on different pages, even different books, to extend the metaphor.
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Not only is it OK, but I think it’s essential to building rich cooperative scenarios. Our society, our minds, and our problems all require different approaches, novel thoughts, and varying levels of expertise to function. It’s nonsense to think you can master, know, or solve everything. Even our most comprehensive curriculum brings us nowhere close.
By filling our classes to the brim with common, standard material, we lose a critical amount of uniqueness that drives personal and societal development. We also sacrifice the time we could spend following our interests towards personal insights and expertise.
Differentiation in the classroom shouldn’t be a response to differing ability. It should respond to differing interest.