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Discussion: Roundtable
Topic: what computers can do


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Subject:   what computers can do
Author: Cathi Sanders
Date: May 13 2003
On May 09, 2003, Dave wrote:

Assertion for discussion: When referring to a piece of the math curriculum, if a
computer can do it, it is lower-order.

My response:

I?ve been thinking about this one for quite a few days. Maybe I am
misinterpreting Dave?s statement, but here are my thoughts on the subject, and
computers in general:

There are two types of things that computers can do, in my opinion:

1) DO STUFF FOR YOU:

This includes the following: web pages or programs that tell you things; those
websites that have all sorts of useful or not useful information; Software
and/or Web pages that allow you to practice ? including those "drill and kill"
programs and games that may or may not involve brainwork (I haven?t played it
myself but have been told that "The Oregon Trail" was somewhat intellectual).


2) ALLOW YOU TO DO STUFF FOR YOURSELF:

Java applets or Software that you can manipulate yourself to explore a
conjecture either proposed by the author or a conjecture of your own: "Where is
the center of a triangle?" and "If any triangle has a specific point that is the
center, then does any quadrilateral have one also?"

The first category is great; it certainly improves our efficiency, the
appearance of the final result, and many other benefits. I love computers, and
would love them even if all I had was a word processing program, a spreadsheet
program, a drawing program, and the web.

The second category is what can, literally, change the way we teach. For many
years I taught a discovery-based, writing-intensive geometry course using
Sketchpad. My students discovered the properties of quadrilaterals, the centers
of triangles, and the relationships between geometric figures in open-ended
explorations. They proved the theorems they "discovered", and they wrote 2- and
3-page papers about what they had discovered and about the process of
discovery. They wrote journals about what they learned, and how they felt about
what they learned. They described their struggles and their"aha" moments. These
were exciting years. And this is why I teach mathematics.



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