Welcome Mathematics Teachers.
Educators often talk about creating conditions that make the
"light go on" for their students. This hands-on fractal unit is a way
to turn those lights on for all of your students.
Fractals are an example of the extaordinary beauty of mathematics. It is my
hope that this process of introducing the beauty of fractals to your
students will be extremely exciting. I believe that your students will
increase their understanding and love for mathematics as they work on
the fractal lessons and projects that follow.
This fractal geometry unit was designed during my studies in the
Master of Science Teaching program (MST) at the New Mexico Institute of Mining and Technology (NMT) in Socorro, NM. My goal
has been to create for myself and other high school mathematics
teachers a fractal unit that will challenge our students with
some enjoyable and interesting mathematics activities.
At the beginning of this fractal unit, you will introduce your students
to some of the classic fractals by guiding them through the fractal lessons.
It is here where they will learn more about fractal characteristics
such as "self-similarity" and "fractal dimension." Also, as the
students study the perimeter and area of these fractals, they will be
able to apply additional higher-level math concepts such as finding
"the sum of geometric series" and "limits." In addition, you
will model for the students how to design MSW Logo computer programs
and how to use the Xaos program to create these fractals.
Then, the most exciting part of the fractal unit begins. Your students
will apply what they have learned as you set them free to work in small
groups on the hands-on fractal projects.
After finishing their project assignments, each group will give a
presentation to the class describing what they have learned from their fractal project. Also, there is an assessment test at the
The unique part of this fractal unit is the technology
aspect that is included. Computers can help students to understand the
process of geometric iteration and to quickly visualize the astounding
fractal images. I also believe that students will improve their logical
thinking skills by learning some of the basics of computer programming.
Here, they can apply all these skills in a way that's fun.
This fractal unit has been successfully tested out with my own
students. My students really enjoyed this fractal unit and learned
quite a bit. This was a particularly appropriate unit for the end of the school year. At a time when students had tired
of textbook activities, the fractal unit refocused their attention and encouraged them to dive deep into an exciting math
I feel that this lesson could be also be used as an independent study
project for a gifted student or for a student who has to be home-schooled for a while. Such students would still need occasional
guidance from a math teacher, however.
I am grateful to all of my professors and the Master of Science Teaching staff at New Mexico
Tech for their help with my studies, and to my family (Carol,
Carolene, Craig, Ben, Noah, and Alec) for providing me the time to work
on my studies.
Teachers, please contact me if you have any questions, comments, or
suggestions about this fractal unit. I will appreciate your responses.
In addition, feel free to share this webpage with your colleagues.
Thoreau High School
PO Box 96
Thoreau, NM 87323
phone: (505) 721-4500