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Re: Research-based Standards: Learning from Physics Teachers
Posted:
Jul 27, 2010 1:21 AM
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On Mon, Jul 26, 2010 at 8:06 PM, Robert Hansen <bob@rsccore.com> wrote:
>
> Does it really appear to you that I haven't both studied and contemplated?
> When you get to the classical training then wake me. You seem to think that
> the path to knowledge is just a good feeling in your head. As I have pointed
> out before, philosophy alone will get you about as far as the 16th century.
> The science of science has advanced considerably since then. And show me one
> post of mine that even suggests that I mean to recite facts.
Your view that science and philosophy went their separate ways in the
1600s does not seem at all well founded to me.
When scientists get philosophical, they get above or outside their
practice and reflect on it. This is as important today as it ever
was. At the AAPT conference, the word "epistemology" was being
bandied about quite a bit. These teachers were there to reflect on
their practice i.e. to get philosophical about it.
A lot of the great physics teachers were also philosophers, not just a
long time ago, but recently. Albert Einstein and Linus Pauling come
to mind. Both were active in human affairs. Linus Pauling got a
Nobel for peace, not just for chemistry. The current exhibit on
Einstein at our local science museum makes it clear that he was deeply
philosophical (partly why his FBI file was so thick -- some of it on
display).
How shall we nurture a philosophical thinking in students? How shall
we talk about ethics? Some professions have an ethical code, and
students may be attracted to a profession precisely because of these
kinds of commitments.
Mathematics is highly philosophical, right down through Bertrand
Russell, Ludwig Wittgenstein to many leading lights today. Douglas
Hofstadter for example.
Introductory courses are often a discipline's best recruiting
opportunity. Computer science is going to have better luck getting
commitments if it deigns to provide a lot of overview, doesn't make
the mistake of enforcing a heads down, ask no questions approach. One
needs to get the 10000 foot picture, before descending into the
details. That's what appreciative courses need to be doing, in
combination with going more deeply into a few selected topics (maybe
just learning a programming language, in the case of CS0, no previous
experience presumed).
> Regarding introductory courses, in physics they have a very poor track
> record right now of bringing it home. I haven't just yet put my finger on
> why that is except that it seems that many schools and teachers don't seem
> to understand that the course they are teaching is introductory (at best).
Would you like to give some more background on where you're coming
from here? You joined math-teach relatively recently. All I've been
able to surmise is that you were good at mathematics as a kid and now
work in the software business in some way. Do you have a web site
that's more biographical than the curriculum survey forum you recently
linked to? Are you in Pensacola?
> And I suppose we can expect no less since the vast majority of those
> teaching it have very little ability in it. But that doesn't mean I am
That's quite a sweeping condemnation.
> against introductory courses. I have never put down the idea of having
> pre-algebra, unless you have pre-algebra and you act as if it is algebra and
> that is as far as you go.
> When one course is an introduction to another you don't go and cover all the
> topics in the other in a superficial and shallow manner. An introduction is
> not a preview. Pre-algebra does not preview algebra, it prepares for it.
You need to make a distinction between mandatory seat time, where you
won't get your high school diploma if you don't jump through this or
that hoop, and college departments needing to woo undergraduates.
In the latter case, it's often a good idea to do lots of previewing,
and to get to those "sexy" topics that everyone wants to learn about,
such as black holes and quantum non-locality in the case of physics,
or some cutting edge theorems in mathematics (e.g. four color,
Fermat's last, density of tetrahedral packings, non-periodic lattices,
fractals & chaos, Egyptian math, Neolithic math... lots of stuff to
get into, even as some nuts and bolts come up (programming a
Mandelbrot set perhaps, Chinese Remainder Theorem problems...).
When you've got them in a mandatory manner, you can afford to say
"this isn't about overview, this is about trusting authority to tell
you what you need to learn to go the next step, on the assumption that
you wouldn't be in this class if the next step didn't interest you" --
which is precisely why so many drop out. They don't share this
assumption.
It's really quite disrespectful of another's intellect to just assume
they want to follow blindly, without getting much hint as to where
it's all going. Even young kids don't always appreciate the "just do
as I say (or else!)" approach.
Of course in a corporate setting you can just say "learn this or we'll
outsource your job to someone more qualified". They always say
schooling is about learning to take orders and follow them dutifully.
The "factory model" of schooling. Perhaps you hail from that era?
Who are your heroes I wonder? We know who Haim despises (e.g. Marx,
Paolo Freire), less whom he admires (if anyone). Wayne admires
Escalante and John Saxon (me too). Got any leading lights you care to
name? Martin Gardner? Admiral Grace Hopper?
> Thus, the un-physics physics classes we are talking about are NOT
> introductions to physics. An introduction to physics would be foundational
> for the treatment ahead. I would start with some concepts from mechanics,
> work on vectors and some notation and then help the students understand the
> art of derivation, a form of (applied) math that they haven't yet practiced.
Dr. Bob Fuller, whom I've worked with, used to teach cadets at West
Point. He and his colleague were very clear that vectors needed to be
learned if real physics were to be mastered and they developed a unit
that would teach about vectors and vector calculus. This was
considered trailblazing and I'm pretty sure it was discontinued for
these undergrads.
You can talk about vectors and still give overview though, e.g. talk
about how Hamilton - Tait were really into Quaternions with vectors
coming into their own later, more as a result of Gibbs-Heaviside.
There's interesting reading on the history (are trade books allowed,
or only textbooks?).
Even while learning about dot and cross product, you can do some stuff
with Quaternions as well, especially on computer (e.g. this Java
applet I wrote: http://www.4dsolutions.net/ocn/oopalgebra.html --
looks distorted until you Necker-flip it in your mind's eye)
Newton didn't have vectors at his disposal, and of course had to
invent the calculus (fluxions). In a math class, it's fun to go over
Bishop Berkeley's strenuous objections to the primitive "calculus
proofs" of those days. He called Newton the devil (very polemical).
It took over a hundred years of subsequent formalisms (Weierstrass,
Cauchy etc.) to give calculus more of what seemed to be a secure
footing. Understanding these threads requires some philosophy of
mathematics, an awareness of history.
Mixing lore with technical skills is a fine art and central to
pedagogical / andragogical effectiveness. What's the right mix? All
tech and no lore is usually the *wrong* mix. Gotta have lore to
provide context.
The math teaching community made a big mistake when it decided to
purge most of the lore, e.g. historical and ethnic threads from early
math teaching. Many testified against doing this (e.g. Milo Gardner,
the Egyptian math expert), but they went ahead to took out the time
line. Most early math teaching is nowadays ahistorical, to the
detriment of the public.
( We're talking with Milo over on the Math 2.0 list. He's mentioned in
the footnotes of this page:
http://en.wikipedia.org/wiki/Rhind_Mathematical_Papyrus_2/n_table )
> And there would be much contemplation involved. That would be an
> introduction. We don't have that now. The life science physics is meant to
> steer the kid around physics, not into it.
Dr. Urone's physics text takes the life sciences approach. Here's a peak:
http://www.amazon.com/College-Physics-Paul-Peter-Urone/dp/0534376886
He's listed on that web page I gave, re Understanding Human Motion,
right after me.
Kirby
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