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MathGroup Archive 2000

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RE: Mathematica for High School Students

  • To: mathgroup at smc.vnet.net
  • Subject: [mg24127] RE: Mathematica for High School Students
  • From: "Ersek, Ted R" <ErsekTR at navair.navy.mil>
  • Date: Wed, 28 Jun 2000 02:11:46 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

I want to clarify some things I said earlier:

The way I see it a high school teacher/college professor/text book author
should set the curriculum of a course such that all students except those
who are simply in the wrong class can keep up.  Of course nearly all seniors
in a typical high school will have far less ability than students in the
freshmen class at MIT, and that should be reflected in the 
curriculum. 

Also I think one shouldn't be REQUIRED to learn about features in
Mathematica that are not
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 (as required learning) of less
than intuitive features in Mathematica. Obviously I am not saying one
shouldn't be permitted to learn more difficult subjects.  I think mostly the
same stuff should be taught that was taught before 1998, but use of
Mathematica should make it easier to learn.  Since a lot of stuff should be
easier thanks to Mathematica, more material can be crammed into the
curriculum.

_____________________

Dave Park wrote:
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?
______________________

Ted Ersek Replies:

Banned features: None

Stuff that should not be required learning: 
  Any use of level specifications
  Making buttons from scratch
  Box expressions for 2D expressions
  Cell expressions 
  Manipulating notebooks 
  Elaborate pattern matching

Features for a Computer Science course on Mathematica should include
functional programming, non-trivial pattern matching, UpValues/DownValues,
The Mathematica evaluation process, ....

I am not qualified to say at what level use of Map, Apply, Thread, ....
should be integrated into the curriculum for average students.  I think it
might be appropriate to gradually introduce these features in the 3rd and
4th year of college. On the other hand it might be good if
science/engineering students were required to take a computer science course
in Mathematica during the first or second year of college. If that were the
case these features should not be considered "difficult" after they have
this course.


One of the notebooks Dave Park provides uses Map and pure functions to
manipulate equations step-by-step. This sort of thing equation manipulation
is much easier to follow once a package by Roman Maeder is loaded.  Hence we
don't need Map and pure functions for this application. Download the package
from:

http://www.mathsource.com/Content/Enhancements/Algebraic/0209-124

After down-loading the package I can do the following:


In[1]:=
<<EqualThread.m


In[2]:=
3x+4y/b==6(x-y);


In[3]:=
%-3x

Out[3]=
(4*y)/b == -3*x + 6*(x - y)


In[4]:=
%*b/4

Out[4]=
y == (b*(-3*x + 6*(x - y)))/4


In[5]:=
Factor[Map[Expand,%]]

Out[5]=
y == (3*b*(x - 2*y))/4


If Expand has the Listable attribute (and it normally doesn't) Map isn't
needed in the last line above. Once the EqualThread package is loaded the
lines above are sufficiently intuitive that I might use something like this
if I were a 9th grade algebra teacher!  Except I might add a line to
(init.m) that gives Expand the Listable attribute, and instruct the students
to copy it to their computers.
 
-----------------------------------
Dave Park asked:
Would you allow the young student to use Solve?

Ted Ersek Replies:
Yes, and encourage them to do so. In other areas I agree with Dave Park on
how students should be permitted to learn topics more advanced than the
standard curriculum.

---
Regards
Ted  :)



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