Mashing up thoughts over the last 2 days... or maybe 40 yrs?
on how to create optimum learning spaces for math..
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first idea: the abstract
Seth Godin's post today was on the value of abstract in math. I love what he brings attention to..
Abstract numerical thought is an important skill among educated people...
He explains this through TEd talks, were he says that the speakers generally have:
a conceptual tricky idea, one with a lot of moving parts. And there is a lot of shorthand and arm waving ... basically, it's similar to a quadratic equation.
He goes on to say:
If you need the other person to slow down and explain every little bit, you've missed the point. The point is to do abstract conceptual thought. To get in practice taking the accepted status quo and questioning it, at least for a little while, at least this or that part of it.
I think this is a skill, a rare one. The ability to be facile in the manipulation of ideas, both theoretical and established, is a valuable one, and I think the TED videos and art of reading books (at least the first ten minutes of each) are two great ways to getting better at manipulation of ideas. It takes practice, and it's worth it.
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Also, about a week ago a colleague shot this article to me - on best ways to learn math. The article says that..
The real-life examples, it seems, obscure the math that is being learned.
And goes on to show how their research, they admit not conclusive, shows kids being more successful...
Then the students were asked to apply the concept they learned to a different situation. Those who learned by abstract symbols did markedly better.
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second idea: the relevant
The last couple of days, Dan Meyer's always invigorating posts on getting out of the way and getting kids to ask authentic questions fed my wrestling with all this. Some insight into Dan: his
recent talk at CMC North 2009 really pounded in this idea for me: people wanting a true understanding, as opposed to a mental challenge of abstraction, need to come to grips with irresolution. Erica McWilliams calls it - knowing what to do when you don't know what to do - as opposed to freaking out or giving up - or giving the answer - or giving a weak example - when you don't know what to do.So the one piece from Ohio's research I feel the need to address is:
The real-life examples, it seems, obscure the math that is being learned.
Maybe it obscures it because we haven't actually been giving real-life examples.
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third idea: the urgent
I recently collected my thoughts on what is really new in learning.
Then I did the same for why it's radically new..
I've been working on a concept the last year to make a change and just embedded it in a more widespread movement away from 7 hour a day damage.
The big idea... to embrace individualized learning and individualized learning spaces that the web allows.
One size doesn't fit all, it never did really. Public school is creating dispensable, disengaged, disenchanted learners. But now we have the means to change that. We can network our way out of this if we will just quit faking cures.
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the mash-up:
Balance. No more standardization. Everybody doesn't need to be doing the same thing in the same way.
If we can define a class... I think we've cheapened it. If we can assume a method for all learning... same thing. If we keep promoting content over learning... we're missing it. We're imposing a biased way to look at the world.
I'm passionate about authenticity because I've watched too many kids disengage over the games we play in school. I've seen too many teachers exhausted from playing the games.
My thinking right now... unless you have at least one of two skills:
1. the ability to get what is real vs what is fake modeling
2. the ability to be patient with irresolution
you play off Godin's thinking and Ohio's suggested data, and go with the abstract.
I do believe too much damage is being done via weak of problems in an algebra book to real life.
I was pumped to look into via abstract
radiolab's presenting parabolas... I even talked myself out of making a case against the hyperbolic lamp light posing as a parabola. But I became truly saddened to see a telephone wire's dip posing as a parabola. And the bar of soap, and the obviously-not-parabolas. Our modeling really sucks. No wonder kids turn in powerpoints with 4th grade level math posing as pre- calc.
If math were a sham - I'd have no problem with all this. Math is an incredible language for explaining/simplifying the world...we miss it when we use Greek to explain a shoestring.
Impatient with irresolution, we all seem to be floundering for motivators. Daniel Pink's new book - Drive, suggest the greatest motivator to be progress. Not where a kid is, not even what they're studying, but that they are learning.
I'd love it if the new standard assessment was how a person (student or adult) answered this: What did you learn yesterday?
No new answer, no progress, no motivation, no A.
I think a main -if not the main- skill we need to be instilling in our kids - is that of self-regulation/assessment/refinement/automation. Another
slide from Dan's talk speaks to that. If we can get iteration going... so that progress becomes more visible..how cool would that be.
Impatient with irresolution, we all seem to be floundering for motivators. Daniel Pink's new book - Drive, suggest the greatest motivator to be progress. Not where a kid is, not even what they're studying, but that they are learning.
I'd love it if the new standard assessment was how a person (student or adult) answered this: What did you learn yesterday?
No new answer, no progress, no motivation, no A.
I think a main -if not the main- skill we need to be instilling in our kids - is that of self-regulation/assessment/refinement/automation. Anotherslide from Dan's talk speaks to that. If we can get iteration going... so that progress becomes more visible..how cool would that be.
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In our quest to do better.. embrace discomfort ...
in our quest to help kids...let's be less helpful. Give space for student-centric individualization and automation to happen.
hey...
maybe you just need to be less helpful with us as well - and we need to be more self-automated.
more great insight I needed to hear from Dan on organic learning spaces:
I’m all for letting this unfold organically, but class time is too scarce to leave this entire thing to chance. We need some kind of plan for your students — a series of questions, an activity — in case we need to prompt their imaginations.
and from two of his readers:great responses to his post on weak examples...
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