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Re: [Phys-L] other problems with what is (or isn't) on the test



The main topic for today is creativity, originality, and imagination.
This is only one item on a long list of things that are missing from
the typical test, and from the typical syllabus. This is closely related
to the idea of open-ended questions and to the larger idea of critical
thinking, in ways that will be discussed shortly.

Whenever (today or otherwise) I talk about "the building block approach"
please imagine a child building something out of Legos ... something
complicated and imaginative. The question of what to build and how to
build it is open-ended. There is an astronomical number of right answers.

In contrast, please do not imagine a menial laborer building a
block wall. In this situation, if you ask where the next block
comes from, there is usually only one right answer. Similarly,
if you ask where the next block needs to go, there is usually only
one or two right answers. You could ask a multiple-choice question.

With the Legos, reducing it to a step-by-step, multiple-choice,
checklist-oriented activity would spectacularly bad. It would
remove the spontaneity, creativity, and open-endedness.

Here's another analogy: At many universities, the music department
offers a "music appreciation for dummies" course. The students listen
to music and talk about it. There is little if any open-endedness.
This stands in contrast to the course in composition & orchestration
that is taken by music majors, by real musicians, where originality
and artistry are required. There is a great deal of structure, but
also a great deal of open-endedness.

I mention this because all too often, the introductory physics course
degenerates into "physics appreciation for dummies". The students
are on the outside looking in. The students look at physics and talk
about physics, but they don't actually /do/ any physics. In particular,
a) They do not engage in any creative or open-ended activities, and
b) they cannot imagine that there ever could be any creativity or
imagination (let alone artistry) in physics.

I insist that it doesn't have to be this way. Physics, even at the
introductory level, does not have to be a mindless, joyless, multiple-
guess activity.


On 06/16/2012 08:53 PM, Hugh Haskell wrote in part:

I tried to make some inroads in their thinking processes,

Good.

but as pretty much a voice in the wilderness

Not so good.

it was a nearly hopeless task, and one that I probably wasn't
well-qualified to undertake anyway.

I hope you take it as a compliment when I say:
I don't believe that.

Life is not a multiple-guess test. Teaching is certainly not a multiple-
guess job. I mean, seriously, when was the last time a student came up to
you and said "I'm confused, and here are the four possible ways in which
I could be confused. Pick one."

Anybody who has more than a day of experience in the teaching profession
(or any other profession) knows what it's like to deal with open-ended
questions. Everybody on this list knows in their bones how to do it.

There may be some questions about how best to /teach/ this idea, but
that is to be expected.
-- There is no checklist for teaching open-ended thinking.
-- There is no rote method for teaching critical thinking.
-- There is no paint-by-numbers method for teaching artistry.

On the other hand, there are some tried-and-true ideas that we can keep
in our bag of tricks, and there are some known pitfalls to be avoided.
Here are some suggestions from the keen-grasp-of-the-obvious department:

One pitfall is the all-or-nothing fallacy that showed up in the recent
message from Isaac Bickerstaff. Never allow yourself to be put in a
position where the only options are
a) throwing kids into the deep end ("sink or swim") or
b) completely abandoning the idea of teaching them to actually swim.
There are lots of more nuanced approaches, whereby they /gradually/ learn
how to swim.

As a specific constructive suggestion in this department, consider the
music-minus-one approach:
http://en.wikipedia.org/wiki/Music_Minus_One

That is, rather than asking kids to solve a complex real-world problem
ab_initio, you hand them an almost-complete solution and let them provide
the missing piece(s). I do this routinely with flying students, when they
are learning to land the airplane:
A) while I do N-1 of the tasks, the student takes care of the one
remaining task, e.g.
-- the student just takes care of the throttle (and the perceptions
that feed into knowing what to do with the throttle)
-- the student just takes care of the pitch/AoA/trim/airspeed system
(and the relevant perceptions)
-- et cetera
B) same as (A), but with less kibitzing from me
C) the student does _two_ of the N things
D) et cetera, gradually increasing the level of responsibility and complexity.

Here's another pitfall: The unduly direct approach. Imagine plopping a
kid in front of a grand piano and asking them to play the /Hammerklavier/
sonata. That ain't gonna work. If you just give up, that would be the
all-or-nothing fallacy mentioned above, so let's not do that. Instead,
imagine asking the kid to play just the first note. That's doable, right?
Then play just the first two notes. That's doable, right? Then imagine
working your way through the whole piece. If at first you don't succeed,
try harder. TRY HARDER!

That is not going to work. Instead you need to back up many many steps, and
approach the problem indirectly, using ultra-simple level-1 pieces and lots
of scales and études. This is /indirect/ because later, after the student
has mastered the masterpieces, it is OK to forget the level-1 pieces. They
are are not wrong and do *not* need to be unlearned; they just get left
behind or integrated and absorbed ... just as a chick leaves behind its shell
and absorbs its yolk-sac.

Another term for this is scaffolding: To assemble a huge statue, you need
scaffolding ... but afterwards you remove the scaffolding. It's not needed
anymore, and it just gets in the way. You can call this unlearning if you
want, but it's the ultra-simple non-problematic kind of unlearning, because
it's obvious which part is statue and which part is scaffolding. It's obvious
what you need to remove. There is nothing confusing or deceptive.

Remark: Only on the rarest of occasions does it help to tell the kid to
"TRY HARDER". Usually the problem is that the kid doesn't have the requisite
foundation. You have to go back and build the foundation.

Remark: The scales-and-études approach is indirect in another way: There is
some sort of Cartesian direct product: N different scales and études prepare
you to play M different repertory pieces. There is not a one-to-one relationship.

That leads us to two more fallacies, which are mirror images of each other. As
usual, both extremes are wrong.
*) At one extreme is the repertory-only approach, aka learning-by-doing, aka
the problem-solving-only approach. Imagine trying to learn a new subject,
reading nothing but the Schaum's outline. This is nuts. You need more
explanation than that. You need more theory than that.
*) At the opposite extreme is the principles-and-concepts-only approach.
This corresponds to giving the kid an enormous set of Legos, enough in
principle to build almost anything ... but not allowing him to ever
actually build anything. This is also nuts. If the principles and
concepts are not used for interesting and important applications, there
will be zero motivation and zero retention.

As a more positive way of saying the same thing, you need teach both principles
and applications, so that applications illustrate and motivate the theory, and
the theory enables and explains the applications. At this point I do the
itsy-bitsy-spider thing with my hands.

That leads us back to the topic of open-endedness. There are plenty of
things in the world that are not open-ended. If you are the home plate
umpire, for every pitch you need to call "ball" or "strike". It's multiple
choice. You can't split the difference.

On the other hand, there are also lots of open-ended things in the world.
Most of real life consists of dealing with open-ended questions. Some
examples that can be used in the classroom include:
-- building something original and artistic out of Legos.
-- Paper tower contest.
-- Egg-drop contest.
-- Building a trebuchet out of popsicle sticks and glue.
-- The notorious "Mississippi Flow" exercise.
-- Bongard problems.

We need to emphasize open-ended problems in order to restore balance,
because in recent years closed-ended checklist-oriented multiple-guess
problems have been grotesquely overemphasized.

Bongard problems have the advantage that they don't require much if any domain-
specific knowledge, so you can use them on Day One of the course. Also, there
are many dozens of them (unlike the Mississippi Flow problem, which is a one-off).
The disadvantage is that Bongard problems are artificial puzzles. The downside
to puzzles and games is that even if you win the game, it's still just a game.
The idea here is to use Bongard problems as scaffolding, to allow students to
feel what it's like to deal with open-ended problems. In the long run they
won't need the scaffolding, because there are plenty of real-world problems
begging to be solved.

Suggestion: Whenever selecting or creating quiz questions, include a goodly
proportion of open-ended questions. Whenever I see a multiple-guess question,
I wince, and then ask myself whether it could be converted into an open-ended
question.

If you say multiple-choice questions save a lot of time, because they are
easier to grade, then I respond as follows: If we are going to talk about
savings, we need to talk about the costs, too. The cost of overemphasizing
short-answer multiple-guess tests is that they defeat the purpose of the
entire educational system. The cost exceeds your entire salary plus overhead
and more than that besides. Ask the kids whether they would rather learn
a small number of truly useful things, or be "exposed to" a huge number of
useless things that they won't remember anyway.

Combining several of the items mentioned above, and mentioned in other msgs
recently, we come back to the idea that 99.999% of reasoning is subconscious.
Consider the Mississippi Flow problem. Most people have a very hard time
with this problem. Solving it involves racking the brain and sifting the
memory, searching for information that is somehow related to the problem.
If on Day One of the course you ask students to do this, they can't do it,
and telling them to TRY HARDER won't help ... and the direct approach won't
work either. This problem doesn't rise to the /Hammerklavier/ level of
complexity, but the same idea applies: Rather than attacking it directly,
you need to go back and spend a long time working on scales and études so
as to build up the skills necessary to attack the problem.

More specifically: You can't fetch stuff out of your memory in a good way
if you didn't put it into your memory in a good way. This helps explain
why the current overemphasis on fully-scripted problem-solving and multiple-
guess quizzes is so poisonous. If there is a script for solving every
problem that is going to be on the state test, then students naturally get
the idea that rote learning is sufficient. The hallmark of rote learning
is that each idea can be recalled in exactly one way. Technically that
counts as a memory, but it is not a very /useful/ memory. The smart approach
is to mull over each new idea, checking it against previously-known ideas,
looking for connections ... and, conversely, checking for inconsistencies.
If you do this, each idea can be recalled in 100 different ways, which
makes it 100 times more /useful/ than a rote memory.

The point is, you need to make it a habit to give every new idea this
treatment. Don't wait until you have cavities to start brushing your
teeth. Don't wait until you are facing an open-ended question to suddenly
wish you had a more agile, effective mind. Wishing won't help. This is
one of the many things I like about the Harry Potter stories: the kids
didn't get to be powerful wizards overnight. They didn't do it by praying
or wishing. They worked hard for years to develop their skills, including
reasoning and teamwork as well as the more domain-specific skills.

There is a bit of a chicken-and-egg problem here, because until the students
learn how to build up richly-connected memories, they won't be very good at
solving open-ended problems ... and conversely, until they have some success
at recalling off-the-wall and out-of-the box ideas, they won't appreciate the
value of richly-connected memories, and won't be motivated to do the work --
the years of work -- necessary to build such memories.

Here is a bit of an exercise: The association game. Call on students, in
order, so that everybody has to participate. The assignment is to come up
with some word or idea that is associated with the Mississippi.
*) big muddy
*) riverboats
*) riverboat gamblers
*) Lewis and Clark
*) Huckleberry Finn
*) delta
*) flood
*) oxbows and meanders
*) Louisiana purchase
*) war of 1812

Kids who are called on later have the advantage of more time to think,
but the disadvantage that the low-hanging fruit has already been picked.

Then we can go back and take those items two at a time, looking for
other connections. In particular, what do riverboats and Huckleberry
Finn have in common? What does that mean? Could that possibly help
solve the Mississippi Flow problem?

Don't tell me students can't play this game. They play six degrees of
Kevin Bacon for fun. The downside to 6°KB is that even if you win, it's
still just a trivia game. What we're doing here is just as much fun,
but it's better because it's not just a game. We are building up the
skills needed to solve important real-world problems.

More generally, you can play six degrees of physics. The law of universal
gravitation is related to Coulomb's law which is related to conservation
of flux lines which is related to conservation of other things (such as
the butter gun discussed in Feynman) which is related to continuity of
world lines in spacetime which is ............

and over the years we did come up with some ideas to improve the
thinking processes, but as one can imagine, the push-back from
students was fierce,

Students (and parents etc.) get irate if they think you are cheating,
if they think you are not playing by the rules.

Therefore it is super-important to make the point to all concerned
that you're not cheating and you're not even changing the rules ...
you're changing the game. Tell them:
"You don't show up to play football wearing your baseball uniform
and carrying your bat and mitt. It's a different game, with
different rules, different skills, and different equipment."

"So it is with this class. You've spent 12 years learning how to
play trivial pursuits, and there's nothing wrong with that, but
in this class we are playing a whole nother game, It has different
rules, and requires different equipment and different skills. For
starters, rather than touching on a large number of trivial problems,
we are going to solve a small number of important problems. There
will be lots of open-ended questions, and relatively few multiple-
guess questions. There will be few if any questions that can be
answered in 45 seconds. Creativity and originality will be encouraged."

"We will not do hard problems. We will however do problems that
/would have been hard/ if you hadn't learned the right techniques."

You'll have to give that speech multiple times before anybody believes
you ... and then you have to deliver. They've heard (most of) that
speech before, from people who didn't mean it and/or didn't even
understand what they were saying.