Re: the calculus wars

nate (schmolze who-is-at students.wisc.edu)
Mon, 24 May 1999 18:08:12 -0500

A somewhat complementary / extension of the "problem based approach" Tim
mentioned. It is part of an American /Russian pratnership in math and
science education.

"Physics as a Way of Thinking" -- An Interview
(Answers to some questions posed by Peter Moxhay of Best Practices in
Education to Irina Lyublinskaya and Mikhail (Misha) Ivanov on their
Conceptual Physics course)

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P.M. The most outstanding feature of what we see Misha and you doing in the
physics classroom (and Valerii Ryzhik in geometry class) is the use of
what, for lack of a better term, we've been calling a "Socratic method"
approach. Is this in use anywhere in the US?

I.L. Our humanities teachers are using the Socratic method most of time.
Problem-based learning is something very close to it too, and is taught in
many places. I haven't seen it in physics though.

P.M. So in some sense you're teaching physics and math more in the style of
the liberal arts. Misha, have you seen this style used in physics anywhere
in the US? How would you propose making this teaching style available for
emulation by interested teachers outside of Russia?

M.I. I have visited American high schools in Chicago, California, New York
City, New Jersey, Boston, and, of course, Arkansas. I've had meetings with
teachers and teacher educators at Caltech, Stanford, Harvard, Berkeley,
Yale, MIT I have not seen anything like what you're calling the "Socratic
method" in physics or math. Besides personal contact, workshops for teacher
training, and so on, I think that we can try to transfer teaching styles
through video and (eventually) by CD-ROM and the Internet.

P.M. Irina, can you distinguish between problem-based learning and what,
for example, we see Misha doing during class (Socratic method)?

I.L. Problem-based learning is more structured than the Socratic method.
Any problem-based learning should start from a Socratic-type discussion to
set the problem to be discussed. In problem-based learning the problem is
given at the outset, usually by a teacher.

P.M. Irina, you've told me that there was a certain time barrier to get
over before students got used to this new classroom style. What was the
time period? A month or two?

I.L. It takes about one-and-a-half to two months if you meet students for
about three-and-a-half hours per week.

P.M. Can you expand a little on this? What were the classes like before at
Arkansas that allowed the students to just listen? What takes place in
class now that forces the students to think?

I.L. Basically, Conceptual Physics was taught the same way as regular
physics -- lectures with demonstrations, very teacher-oriented. Although
the teaching was good, the traditional approach divided everything into a
large number of topics (mechanics, heat, and so on). This didn't give the
students a picture of physics as a general approach to understanding
nature, because it was too fragmented. Also, there was no math. You can't
explain all physics in one semester and without using mathematics.

The new approach has a logical structure which eliminates this
fragmentation. It allows students to reason and deduce results following
from questions posed by the teacher or by each other. It helps students to
talk about what they see in the world around them and can test themselves.
In class, the teacher acts as a facilitator, directing the discussion.
Students choose the phenomena to be discussed; they present their ideas to
each other; they think aloud about how to demonstrate a phenomenon or test
their approach to a question.

For many students, it takes a breaking-in period for them to learn how to
talk in front of each other, how to reason aloud and to justify their
opinion on a physics question -- that's what the initial two months are
spent on. Since most of the problems are open-ended there are no right or
wrong answers. What matters is how deeply you delve into the problem, how
many different sides of the question you take into account. This helps to
encourage all students to engage in productive discussions.

P.M. For what grade level, or levels, is the course intended?

I.L. This course can be offered as early as junior high school. I think
that at present no physics course created in the US is offered as early as
8th grade. Most of textbooks have either too much mathematics for that
grade level, or they have no math at all.

The problems which are developed in this course can be offered at different
levels -- 8th, 9th or 12th grade. The open-endedness of the problems and
the use of multiple outcomes allow for different approaches involving more
math or less math. Of course, 12th-grade students will consider the same
problems in more detail with mathematical calculations, while 8th graders
will learn a more qualitative approach.

An important factor for the use of this course in earlier grades is that
problems are mind-provoking and relevant. They are about what students see
and what they think they know.

P.M. It is interesting that you have recast the approach to lab experiments
for the course, based on suggestions Misha has made from his experience in
his school in St. Petersburg. Why did you see a benefit in doing this?

I.L. Home and class projects are important part of any science course. Many
US schools do not offer physics because of the cost of equipment. This
course incorporates a series of projects which can be done anywhere using
easily-available, inexpensive supplies. The projects are relevant, simple
and are not recipe-type, and they are designed and developed by the
students in the process of doing them.

P.M. What will your new textbook offer that isn't available in existing
textbooks in English? Don't any existing texts give a good picture of the
scientific method, or use conservation of energy as a unifying principle?
Could you just take an existing American textbook and use the Socratic
approach with it?

M.I. I know of a number of American texts where there is not only a good
presentation of what science is, but also the idea of the scientific
method. First of all there is Feynman's "Lectures on Physics" -- after
reading that book that it became impossible for me to go on teaching as I
did before. Also good are Clifford E. Swartz's "Phenomenal Physics" and
Paul G. Hewitt's "Conceptual Physics."

But I have not found any textbook on school physics, in the US or
elsewhere, that uses conservation of energy as the main thread of the
discussion.

I.L. I haven't seen any textbooks which take the scientific method as the
basis for problem solving -- in the sense of using it for any problem,
small or large. This course consistently uses the scientific method as the
model for a way of inquiring, thinking, analyzing, collecting data,
calculating, reasoning, etc.

M.I. It would be possible to try to use American textbooks with the
Socratic method, of course. But I think it would be very difficult for
teachers, especially for teachers who like to teach according a single
textbook. I know of a couple of American textbooks on Conceptual Physics
which are not only interesting for me but which I could use it in my
teaching at the Phys-Tech High School. But these texts have a number of
defects -- they don't have a large number of problems suited to the
Socratic approach; they have no math at all or else the math is too
complicated; or they make an artificial division of physics into mechanics,
heat, etc.

I'd like to mention that in our book, "Physics as a Way of Thinking," the
problems are not only illustrations of the theory -- rather they're the
primary materials for the teaching of thinking.

P.M. Misha, I sent you a newspaper article describing a recent study of
science teaching in several countries -- the conclusion was that science
teaching in the U.S. lacks focus -- that it's "a mile wide and an inch
deep." What do you think of the conclusions of that study, based on your
work in the collaboration with ASMS?

M.I. I absolutely agree with the conclusions of the study -- a mile wide
and an inch deep. This is really one of the main points of my work on
Conceptual Physics -- you've got to go deeper, but not wider. There is a
serious time constraint in giving a one-semester first course on physics,
so don't make it too wide!

It is impossible, in such a course, to develop in students both knowledge
(of all topics in physics) and also understanding. What is really needed is
focus and the focus is thinking. So we need to give up on the idea that the
students will come out of the course knowing everything -- instead, we
should focus on a few selected topics and on teaching the students to think
like physicists. Only after this can we recommend that the students take a
more traditional, "wider" course.

For further information on the Conceptual Physics course, please contact
Dr. Irina Lyublinskaya at the Arkansas School of Mathematics and Sciences.

----- Original Message -----
From: Timothy Koschmann <tkoschmann who-is-at acm.org>
To: <xmca who-is-at weber.ucsd.edu>
Sent: Monday, May 24, 1999 3:52 PM
Subject: Re: the calculus wars

>
> Glenn, the problem-based learning I had in mind was not the same as
> "project work", it's a particular teaching method organized around
problems
> that was developed in professions education (med schools, actually) and
has
> now started to migrate into secondary education. Ironically, it was
first
> introduced at McMaster up in your neigborhood, though it's now used at
> schools all over the world.
>
> As to dealing with the "intricacies of discipline-specific theoretical
> models", if it works as a replacement for the med school curriculum (and
I
> don't think it comes any more intricate than that), I think it would work
> anywhere. You might try contacting some of the folks at the Illinois
Math
> and Science Academy to learn more about how teachers have used PBL in
> secondary schools.
>
> The model you describe of teaching in the abstract and then attempting to
> make concrete is exactly the thing that PBL sets out to turn on its head.
> The idea is that you start from an authentic problem (in all the senses
> developed in the recent discussion) and then assist the learners in
> discovering what they would need to know in order to tackle the problem.
> ---Tim
>
>