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.

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