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Mathematica for High School Students

Hi Ted,

Well, I can see that my high school notebooks didn't come off too favorably
with you; but I would like to continue the discussion because it interests
me; because we do have a difference of opinion here; and because I do value
your opinion. I hope you don't mind if I post this to MathGroup because I
tried to get a discussion going on the topic about a month ago. Maybe I can
stimulate more discussion from the larger group.

(There were two notebooks: one on solving simple equations step by step
using pure functions and Map, and one centered around Gauss' feat of adding
the numbers 1 to 100.)
Ted: The way Gauss added the numbers from 1 to 100 is very easy to explain
without using Mathematica.

Perhaps, but most mathematical ideas can be explained without the aid of
Mathematica. The vast majority of mathematical books don't even mention
Mathematica. The purpose of the notebooks was to teach something about
Mathematica using an idea that might appeal to students. So, it doesn't seem
to be a reasonable argument to say that we can teach Mathematica without
using it.

Ted: The way I see one shouldn't learn about Mathematica features that are
fully intuitive until their 3rd year of college (except in a Computer
Science class about Mathematica). Even in the 3rd and 4th years of college I
would only encourage gradual introduction of less than intuitive features in

And what features of Mathematica are not "fully intuitive" so that the
student "shouldn't learn" them? Would you hazard to put forward a list of
Mathematica statements to which young students would be restricted? Or a
list that would be banned from their use?

Are the functional programming statements ones that you would call not
"fully intuitive"? Is it easier to understand the For statement, than to
understand the Map statement? I can't remember exactly, but it seems that it
was in junior high school that I learned that an equation remains true if we
do equal operations on each side of the equation (other than dividing by
zero). So if you are going to ban pure functions and Map, how would you
implement that simple concept with Mathematica, which presumably the student
already knows?

Would you allow the young student to use Solve?

I believe that there is much work to do in learning how to apply tools such
as Mathematica to secondary education. It is not something that I am
directly involved in, and have no expertise in; but I am still interested.

I would like to put forward several arguments for allowing and encouraging
the full use of Mathematica for the INTERESTED student.

First, there is the great advantage to the student of just gathering sheer
mathematical experience. For most students this is not easy to get. Don't
get in his way, but help him. It is much easier to see a new idea, when one
has the mathematical experience that the idea fits on to.

There are mathematical ideas that are far easier to teach and learn with
Mathematica than out of a text book, such as some of the functional
programming ideas. You can actually see them in action. It is not that the
ideas are difficult or abstruse; they just don't fit into the rigid
curriculum. There is no reason why a bright student shouldn't be exposed to
these ideas.

I don't think that any young student interested in Mathematica should be
shackled in his use of it, or even worse, admonished for using it. I have a
sister fifteen years younger than me. One day when I was home from college,
and reading a book, she said: "I wish I had a book to read." "You don't have
any books?" "They gave us one book, but I've read it." "Why don't you take
out some books from the library." "O No! We're not allowed to do that."
Later I related this experience to a primary school teacher, expressing my
disapproval of such restrictions. Did I ever get a piece of her mind! There
was a very "scientific" method of teaching students how to read. If they
jumped ahead and read something out of order, the whole plan was ruined!

How do we know that the young student isn't another Gauss? We shouldn't
erect any road blocks. We should help as far as we can and see how far he
goes. Richard Feynman's high school teacher put him on to doing variational
calculations. Would you say that he shouldn't have been permitted such
things until his third or fourth year in college? Don't worry, there is
little chance that a student will charge ahead of his or her capabilities; a
far greater danger is that he will fall short of his capability.

David Park
djmp at

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