Should we be on the same page?

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.

* * *

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.

* * *

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.

* * *

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.

8 responses to “Should we be on the same page?

  1. I’m remembering how you solved that problem about getting every subset of n people into a room by having one person leave or enter at every stage–how you related it traversing the vertices of an n-cube. Was that at math in the park a year ago? Anyway, I think that’s a great example of a “personal insight”–it’s like somewhere deep in your head you had made a connection about n-cubes that got jogged by the problem. No amount of standard approaches that someone taught you was going to get you to a solution the way that the n-cube experience that you made for yourself did.

    • Great example! Yeah, that was the same event, one year ago. I find that this is exactly how breakthroughs happen in cooperative settings. Not because everyone has all the skills they need to solve a quadratic or any other standard skill, but because someone has a unique perspective that sheds light on the problem for the other people. It’s through that process of teaching each other our insights that powerful learning can happen.

  2. Paul,
    First the collaboration between you, a fifth grader and Lockhart sounds like one of the most awesome math salons I’ve ever heard of. I love how you describe the the various strengths each person, especially the fifth grader brings to this group.

    Second, I like this idea. More and more I think private schools are getting on a standardization kick, maybe because it’s sweeping the edureform movement in the public school world.

    Still, I would much rather see us standardize on assuring that teachers are addressing students’ individual interests and empowering them to explore those interests. I could really care less whether every physics teacher teaches magnetism or kinematics, and I think we forget how little of this students retain from traditional instruction in the first place (and often, the standardization police are big proponents of traditional education).

    But I’m not sure how you get this message across to the “everyone needs to be on the same page” camp.

    • I think you’re right about private schools. Even at a funky place like Saint Ann’s I think the high water mark is often Ivy League acceptance, and that means a “rigorous academic program” in a fairly traditional sense.

      Obviously every aspect of physics is hugely important in the world, and yet we don’t all need to know it all. I have extreme confidence that every student can attach themselves to and pursue some aspect of physical science. Why can’t we let them do that?

      Look, It’s not about what we think is so important our kids need to learn it. It’s all about what’s important to them!
      (the students – those young people the schools are built for.)

      Thanks for the great comment.

  3. This coming year, for AP Calculus, we’re all going to be on the same page, because I don’t believe I have the management ability to have students working on different things and still be confident they get the full tour by May.

    In Pre-calc, on the other, hand, I’m not beholden to a schedule, just a fairly rich menu of topics the course is ostensibly about. We’ll probably be discussing the same definitions and ideas at the same time, with students choosing among a handful of related problems (or ideally coming up with their own, but we’ll see whether I can foster that successfully or not). Several friends and relations have just donated a bunch of mathy games and puzzles (Soma blocks and such) that students can pick up as diversions if they feel their at a dead end on whatever they’re working on. It’s not the full differentiation-by-interest that you’re pointing at, but I like where you’re pointing and hoping this is a step in that direction….

    • Calculus 1 is one of those places where there is a pretty solid (and reasonably awesome) traditional course. I don’t blame you. I did this for many years and probably would still, for the most part. That said, you should talk to @j_lanier. He is teaching Calc 1 this year, and I am sure he has some great ideas about doing this there.

      I should add that I don’t actually advocate for all-differentiated all the time. There is huge value in communal course work. I used to think of this as the bus we were all on. I was driving, and they could be in the back having conversations about all kinds of interesting things, but other times I want them to look out the left window and see this amazing thing. Then I want us all to talk about it together. This is not a great analogy, but believe me I think there is huge value in a “course” if students want to follow a leader.

      I do think, however, interest-differentiation should be a vital and central part of every course that students take on personal interests, develop their ability in those areas and produce things they are proud of. I plan to do this about 1.5/4 days a week in fifth grade. The rest of the time I will sort of be leading, but very responsive to the students’ ideas, questions, and jumping off points.

      I will always be helping students to ask and answer their own questions. That seems to be the most important thing for self-directed mathematics.

      Thanks for the thoughtful comments.

  4. Pingback: “We shouldn’t be teaching that!” | Lost In Recursion

  5. Pingback: Everyone Brings Something Unique to the Table « AP Silverman

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