Teaching (a pedagogical framework)

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\pard\pardeftab720\sa240\ql\qnatural \f0\fs24 \cf0 Years of research into teaching
and learning have uncovered some basic fundamental principles of how all people learn. This will
just be a quick overview of how I’ve tried to bridge that research with my practice and
what I’m calling a pedagogical framework.\ But first an excursion into the world of photography.
The photographic technique of framing involves finding something that draws the eye, that
sits around an object to draw the viewers’ attention to that thing. Here’s an example.\
The lady is the object of this picture the eye is naturally drawn to see her there in
the centre as she’s framed by the windows of the subway car.\
This is a strong example of framing as we see this man walking through the arches and
those arches form a frame. The eye is inexplicably drawn towards the centre of the picture where
we see the man.\ In this case, a more subtle frame. And yet
nonetheless it’s clear that the horse is the object of the picture because the tree \’97
which we don’t really look at, it kind of sits in the foreground, the eye is really
drawn towards the horse \’97 provides a frame to see the horse.\
What does this have to do with teaching and learning? Just bear with me.\
First the three pedagogical principles, drawn mainly from this book: How People Learn. It
was written in … I believe it was 1999 and then it was updated again in 2000. Studying
years and years of research they pulled out three fundamental principles of how people
learn. As an outgrowth of that book another one was written called How Students Learn,
specifically in the areas of History, Mathematics, and Science. These books have been absolutely
seminal in forming my thinking and providing the pedagogical framework around which I structure
all the teaching that I’ve done.\ Typically when kids come to school they think
of the world as flat. They have no reason to think of it as round and they come to school
and we tell them the world is round. What studies have shown is that once kids leave
school and they’re asked to explain what they’ve learned: “Well the world is round.” And their
conception of the world is that it’s a giant pancake. That’s an interesting preconception
that kids bring with them when they come to the classroom and teachers need to know that.
Because the first principle out of the book is that “students errors and misconceptions
based on previous learning” are the first thing that teachers have to try to connect
with when they’re trying to teach new content.\ In this example, one drawn from mathematics,
kids are often taught that multiplying is repeated addition. Multiplying is not repeated
addition (although that’s a good place to start) and they think that the answer to any
question, when they multiply, has to be bigger than any of the numbers they started off with.
Given a problem like this, fractions, well kids find that really hard, they just mul…
they see the two the three and they know they have to have an answer that’s bigger than
either of them. If we know that that’s the preconception that kids bring to the classroom
then that can inform our teaching in constructive ways.\
The second principle out of the book is that understanding requires not only factual knowledge,
knowledge of basic facts, but an understanding of the basic ideas or big ideas of the discipline,
whatever the discipline is that happens to be that you’re teaching. Because knowledge
isn’t actually built in hierarchies knowledge is actually built in networks. For example,
take something simple like three quarters. It seems like a pretty simple idea. But the
number three quarters can be represented in a variety of ways. All of these are equivalent
ways to write three quarters. It might have meant money, seventy five percent, it could
be the ratio of three to four, point seven five or another way to write the fraction
three quarters. Now even this extends beyond that because, “three quarters”, well I could
have been saying the money, three coins, three twenty five cent coins, which is seventy five
cents. You see all these ideas are connected one to the other.\
I might have been talking about a piece of cake; that I have three quarters of a cake.
And it’s implicit in that idea that each of those quarters is the same size. That each
piece of cake has to be equivalent in size. But that’s not always true with all ratios.\
For example the ration of three red Smarties to four blue Smarties. I’ve got seven Smarties
in total. And those Smarties don’t all have to be the same size for my ratio of three
red to four blue to be true.\ These implicit assumptions make learning this
material difficult for kids, and we as teachers make assumptions because we understand from
the context that these things are clear. It could be seventy five percent off everything.
That these … All of these ideas actually live a network all one related to the other.
The underlying assumptions that we make as experienced learners is that we take, from
the surrounding context, what the meaning of each of these numbers is. And yet each
one is related to the other.\ That network has to be made explicit. That
network of concepts has to made explicit to students. No matter what fundamental idea
you’re trying to get across to the students. In this case, the idea, the big idea, is really
one of proportion.\ The third principle out of the book is that
“learning is facilitated through the use of meta-cognitive strategies”. The degree to
which we can get kids to think about what they’re learning as they’re learning it will
deepen that learning. And they found that this made only moderate increases for high
performing students, but for low performing students the use of meta-cognitive strategies
made for dramatic increases in their performance.\ Error analysis is a great example of this
kind of thing; you’ve probably caught that one really quick. But as you look at this
picture and try to find the error look how you’re thinking about it. Look how you’re
paying attention to certain details; finding what’s the same, what looks exactly identical?
Where is the difference? Where is the thing that stands out one different from the other?
And if you pause to reflect even as you’re thinking about this now you’ll notice that
you’ve deepened your own thought as you look for the error in just something simple, like
a picture of three Mounties.\ So that’s the framework. That’s the framing.
That’s the … Those are the ideas that sit around any pedagogical approach that you want
to take in class. Any time you want to structure or design a learning experience for students
these three principles:\ Connect with kids preconceptions.\
Learning should be networked. Ideas are networked. You need to understand basic facts but also
the big ideas around which knowledge is structured.\ And engaging kids in meta-cognition as they’re
learning.\ This provides the framework for how we teach.\
There’s one last thing not to exclude in any of this and that’s “community”. It’s alluded
to in that book but not listed as one of the fundamental principles; but “community” is
a pretty big deal. Because the degree to which we can get kids working with each other and
collaborating and helping each other in their learning, which is what genuine learning looks
like, is the degree to which they can deepen and accelerate their own learning.\
This provides a wonderful example of exactly what I’m talking about: Why do geese fly in
this “V” shape? It seems quite distinctive to see the Canadian geese flying in that pattern.
It happens in the Fall, around October, and then again in the month of March as when … as
the geese leave in October and return in March. Why the “V” pattern? Because the flapping
of the wings of the lead goose actually provides a little lift for the geese just behind them.
And that’s true for each goose behind every other goose. And so they’re able to fly greater
distances. Of course this puts undue pressure on the lead goose. So throughout the flight
the geese are constantly shifting positions and rotating their spot in the “V” shape flight
pattern. So that different geese take the lead at different times. And by working together
the geese are able to fly for much greater distances than any of them would be able to
fly on their own. And together they accomplish great things which is the very distant migration
patterns of the Canada geese. Of course over short distances, if everybody goes their own
way, well, yeah, you could have some success, and when they all land that’s what it looks
like. And they all kind of come down and each one chooses their own pattern and the “V”
is broken up. And occasionally, you know, you need to do that, but by and large, for
the most part, it’s through that collaboration that great things become possible. And that’s
part of that framework that I talked about.\ It’s just like we learned in kindergarten:
When you go out into the world, hold hands and stick together.\

11 thoughts on “Teaching (a pedagogical framework)”

  1. Tafevc, I agree. This is great material, but I had a very difficult time concentrating on what was being said because of 'all that jazz'

  2. background music is annoying and his voice is so soft unfortunately it gets on the way of valuable information 🙁

  3. A very interesting video….but what was the teacher thinking when he selected that incredibly distracting background music! Did he realize that he would likely lose a ton of viewers at the first loud saxophone rif?

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