>I am a secondary math teacher in rural Georgia. I teach all math levels
>and a variety of math subjects. I'm looking for specific
>technology-based lesson plans for the mathematics classroom. I use, but
>only limitedly, graphing calculators, computers, and CBLs. The sharing
>of personal lesson plans and experiences would be greatly appreciated.
>I would love to get a discussion going on this topic as I don't get many
>chances to interact with other teachers!
>
>My school doesn't particularly have a philosophy for integrating
>technology - what's used and if it's used is left up to individual
>teachers, but I feel we need to develop a more concrete program.
Greetings Sheila --
I have several ideas to share regarding your question.
=46irstly, I encourage teachers to check out Povray, a ray tracing =
program.
Using it requires knowledge of XYZ coordinates. This gives necessary=20
reinforcement to key topics, but also gives leeway for creativity, as
ray tracing involves color, shading, the development of scenes, more
like a Renaissance era painter or wood engraver would be into (Durer,=20
Escher).
Students can even make T-shirts from the scenes they make on screen
(requires color ink jet printer and transfer sheets -- Art Explosion's=20
T-Shirt Factory aids this process with Windows software).
Povray is free and multi-platform: http://www.povray.org/
Secondly, you can start phasing in some simple computer programming=20
with the idea of a series and/or sum. Do-loops and sigma notation go=20
together. Any programming language which allows indexed arrays (pretty=20
much all of them) is going to help students understand what sigma=20
notation is all about -- a bridge to the calculus, wherein the sigma=20
becomes the Riemann sum at the limit. Of course spreadsheets work=20
here too (Excel has the sigma icon in its toolbar as I recall).
With Povray, students can learn to stack spheres:
*=20
* *
* * *
Which is also the series 1, 2, 3... and then compute the sum:
Program:
function triangular
parameters N
sum =3D 0
for i =3D 1 to N
sum =3D sum + N
endfor
? sum
endfunc
user: triangular(3)
computer: 6
user: triangular(4)
computer: 10
Here's a picture, with the spheres done in Povray:
http://www.inetarena.com/~pdx4d/ocn/graphics/trinumbs.gif
I've developed all this in more detail elsewhere on the internet.
If you want to read more, there's a website hosted by the Math=20
=46orum and National Council of Teachers of Mathematics (NCTM)=20
where I provide more material. See thread starting 18 May,=20
entitled "Scoping out content (connected math topics)" at:
http://forum.swarthmore.edu/nctm.standards.2000/nctm.standards.2000.A.tac=
o
My general philosophy is that computers should be used to take=20
the drudgery out of repeated application of the same algorithms.
Students should learn the algorithms, including with paper and=20
pencil, but then be given assignments which create visually=20
rewarding results that would be too tedious to do by hand. =20
I also think computers free us to get into spatial geometry earlier.
Unlike graphing calculators, computers are easily empowered to give
us 3D views. Polyhedra need to make a come back, along with their=20
real world applications (crystallography, architecture). Programs=20
like Povray let students focus on the XYZ apparatus and not worry
about messy perspective issues -- something Povray takes care of.
Once you're operating in space, and not just on a flat plane, you
have more freedoms as a teacher to explore concepts such as rotational=20
symmetry and space-filling, as well as sphere packing. I highly=20
recommend this "Beyond Flatland" approach as a hallmark of 21st=20
century high tech mathematics curricula.
Kirby
Curriculum writer
Oregon Curriculum Network
http://www.inetarena.com/~pdx4d/ocn/
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