These activities are taken from the Journal of Education, Volume 178, No.2, 1996 (pp. 15-32)

A ROLE FOR TECHNOLOGY IN MATHEMATICS EDUCATION

By: Albert A. Cuoco and E. Paul Goldenberg

**I have created the examples presented in the
article using The Geometer's Sketchpad. I then converted them to
JavaSketchpad for exploration in an Internet Browser. Let's begin
exploring. First a few rules for using JavaSketchpad:**

**The red points indicate points that can
be manipulated or moved within the sketch. Try dragging these points
around in each sketch to see how it impacts the plotted points **
**Clicking the red 'X' at the bottom
right of the sketch refreshes the sketch (erases traces). This only
works when there are traces on the sketch and will not work when loci
are present or no traces are present **
**The 'M' Button stretches or shrinks
the scale of the grid (This will be important as the point we are
wanting to look at is beyond our range so you will have to shrink the
scale often.) I am working on a fix for this problem**
**I've included boxes that you can click to perform various actions especially in the first sketch **
**Download the entire file located here in GSP 4.0+ format: cuocogoldenberg.gsp**
- View the text document of a possible assignment scenario here: April 14th, 2006
- Finally, view a GSP file that Michael, Jay, Noel, and I came up with as an extension: heron_sine_area.gsp

**1a. Using the following sketch contruct
triangle ABC and random point P on segment AB. Construct a line through
P that is perpendicular to AC through a point D. Construct a line
through P that is perpendicular to BC through a point E. **

**1b. Where should P be located along AB to
minimize DE? Try Sliding P back and Forth. If you at first do not see
the point (AB, DE) in the upper right (1st) quadrant drag point 'M' to
the left to see point (AB, DE) Then try dragging P back and forth
again. **

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*2. Another way to look at this relationship is to
create a locus of those points. This is much more manageable to view
the graph with traces. Again it is best viewed by moving M to the left.
*

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*3. We carry out an additional step. Drawing the
altitude from C to AB we notice that when P passes through the foot of
this altitude the point (AP, DE) is at a minimum. Again it is best
viewed by moving M to the left. *

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