Using GSP to enhance visualization and create connections in
Trigonometry and Algebra III
by
Gail Engel
Concepts
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
circle
Transformations and Matrices
(This is not developed yet)
*
Trig IDentity
on Sine of the sum of angles