**ABOUT THIS SITE**

I recently heard a catch-all phrase from a College Board Summer Institute instructor regarding the teaching of Advanced Placement Calculus he said, "students should learn to 'Verbally NAG' mathematics". The 'verbally' means that students should learn to communicate in written and spoken form about the problem, they should be able to explain verbally what the problem is asking for, what methods may be used; and what the solution/s reveals.

The NAG portion of the statement is an
acronym for **Numerically**, **Algebraically** and **Graphically**.
**Numerically** indicates that students should understand what
the numerically values of a problem mean, what changes as the
numbers vary; what occurs as values approach positive or negative
infinity, zero, etc. **Algebraically** indicates that students
should understand how to use algebra to manipulate a problem in
order that a complex problem may be broken down into a simpler
problem. And lastly, **Graphically** indicates that student
should understand what visual representations or models could
be established.

The concept to "Verbally NAG"
holds true for all mathematics, as we work toward ensuring advanced
mathematical understanding for **ALL STUDENTS**, and can be
facilitated through the effective use of technology. The use of
technologies in the mathematics classroom enables the student
and teacher to experiment, discover, conjecture, and build intuitive
mathematical understanding. Technologies can create deeper more
varied; and yes, at times, uncertain environments in the mathematics
classroom (however, these uncertain days are well worth the aggravation--the
result is deeper understanding from students and teachers). This
web page will present some applications of technologies and illustrate
how these technologies are able to transform a standard routine
procedural problem of mathematics into an exciting revealing discovery
for students; and teachers alike.

For examples of some very dynamic uses
of the technologies see the web pages of two of my most esteemed
and learned colleagues: **Ms.
Amy Hackenberg** and **Mr.
Brian Lawler**. The technologies used include the internet,
word processing, spreadsheets, **TI
graphing calculators**, **Geometer's
Sketchpad**, and **Graphing
Calculator/NuCal**.