Using GSP to enhance visualization and create connections in
Trigonometry and Algebra III

Gail Engel


I have been in Litmus since 1991 and have spent a lot of time using TI-81's and the computer with maple, statview, GreatWorks, and x-funtion. I have not used GSP very much except for a demonstration tool and then it was very limited use. Since I have been enrolled in 708 and 705 I feel like I have been introduced to more ways to use GSP and also I have been shown more connections between Geometry and Trigonometry. Since these connections are in the spirit of the NCTM Curriculum Standards , it is very important to me to help the students find these. I have tried to make connections between Geometry and Right Triangles (ie. Pythagorean theorem, 30-60- 90 rule and 45-45 -90 rule ) In fact I teach my Trig course with right triangle Trig first because I think it connects to what students already know from Geometry. Yet until this summer I have realized that there was a lot more( I am a slow learner).

In the 1990 Yearbook there is an article called "Enhancing mathematics teaching through Technology" by Franklin Demanna and Bert Waits. This article is about the attention of connecting algebra to geometric representations. Even though most of the technology they talk about is the graphing calculator, their ideas can be extended to use of GSP .

Also this article states that"The power of visualization helps students question, conjecture, and discover mathematical concepts" I have tried to do this with the calculator,but have not used GSP that much. I feel hat there are certain concepts in Trigonometry that could be better understood if seen through construction. These "pictures" would help students recall concepts and if they do not recall the formula they can at least derive it if necessary.

Visualization to me is to be able to recall mentally a "picture" of the concept. Since mathematics is abstract, some people have difficulty visualizing so they need to be able to see a "picture" that will help them visualize what is really happening. It may be that technology allows for the greater group of students to understand mathematical concepts that before were lost to them except to memorization.

It is for these reasons that I decided to do my paper on using GSP in Trigonometry and Algebra III.

Most of the students that I have in Trigonometry this year have had little exposure to GSP therefore I am going to spend the first week of school going over elementary drawings and constructions on GSP. Am going to use the Blackline master book that comes with the Key Press Text and also some material that I used last year to introduce GSP to my Applied Math I class. Then I am going to do the following plus any other ideas I come across in class as either demonstrations or class activities.

Here is a list of things I am going to do as of today. The ones that I have sketches, scripts , and Lesson plans will be included on attachments.( the ones with stars have lesson plans)

Law of Sines Proof

of it and Show what the proportion is
equal to the diameter of the circumscribed circle.

Unit circle

to measure degrees( I cannot make it measure
over 180 degrees nor can I get it to measure negative)

Law of cosines

( not included in lesson plans because I am
still confused about the proof)

Unit Circle with all trig functions

related to the

Transformations and Matrices

(This is not developed yet)

Trig IDentity

on Sine of the sum of angles

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