Discrete math demonstration ideas...
RICHARD BOTTING
rbotting at csusb.edu
Tue Jan 31 16:42:40 EST 2006
I often use my key ring as an example of tree structured
data: There is a ring of car keys that has two rings
on it: one for each car, for example. To demonstrate the need
to store a pointer to the root of a tree I pretend to hook
the keys back on the belt and in fact drop them. They
land with a satisfying crash...
(except for the one time when they got hooked on a trouser pocket
as they fell)
You could illustrate graph theory by referring back to
Dudeney's "Button and String method" of solving puzzles
and mazes. Introduce a puzzle -- eg boat+goat+cabbage+....
And then producing a collection of balls
connected by string so that they fit the puzzle
Hold up the start position and the finish and pull
tight.... and there is your solution: the shortest
path through the maze.
Note: I read this analogy in a book of recreational
math to motivate graph theory 30 or 40 years ago.
Hope this helps...
RJBotting
909-537-5327
Comp Sci, CSUSB.
----- Original Message -----
From: math-thinking-l-request at geneseo.edu
Date: Tuesday, January 31, 2006 0:02 am
Subject: Math-thinking-l Digest, Vol 5, Issue 14
To: math-thinking-l at geneseo.edu
[...]
> Message: 1
> Date: Mon, 30 Jan 2006 19:46:46 -0500
> From: Aaron Bloomfield <asb at cs.virginia.edu>
> Subject: Discrete math demonstration ideas...
> To: math-thinking-l at geneseo.edu
> Message-ID: <43DEB376.1010109 at cs.virginia.edu>
> Content-Type: text/plain; charset=ISO-8859-1; format=flowed
>
> Hi, all,
>
> I'm trying to form a collection of demonstrations for discrete
> math
> topics, and thought I'd solicit suggestions from this list.
>
> I'm looking for ways to demonstrate concepts to students in a
> discrete math course (and CS1 / CS2 courses as well) using
> physical
> objects. For example, using a phone book to illustrate a binary
> search
> (I rip it up in the process), or using a conch shell for
> illustrating
> the growth of the Fibonacci sequence. I envision these as
> different
> from KLAs (http://sequoia.cs.berkeley.edu/kla/index.php), which
> generally require class participation. And I see them as
> different than
> the nifty examples as well (as those tend to be interesting
> problems
> that require solving). My thought is to use all three of these
> (nifty
> examples, KLAs, and the demonstrations) together to help form a
> more
> compelling lecture. Essentially, I'm looking for ways to
> demonstrate a
> concept to a class using physical, real-world objects, but without
> having to directly involve them in the demo. And something that,
> with a
> bit of showmanship, can really "wake up" the class -- such as
> blowing a
> conch shell or dramatically tearing a phone book to shreds.
>
> Any thoughts or suggestions? Do such lists exist anywhere? I
> couldn't seem to find any. Of course, I'll make the ensuing list
> publicly available.
>
> Thanks!
>
> -Aaron
>
> --
> Aaron Bloomfield, Assistant Professor
> Department of Computer Science, University of Virginia
> asb (at) cs (dot) virginia (dot) edu
> http://www.cs.virginia.edu/~asb
>
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