To



or not to

:

THAT

is the

(ion)


A mathematical exploration WebQuest designed for students in middle or high school


by


Sharon Swihart


Olivet Nazarene University



Introduction Task Process Resources Evaluation Conclusion Teachers

INTRODUCTION

You have entered a world of strange and unusual shapes with a name that somehow seems fitting: FRACTALS. The name itself seems to conjure up images of small broken pieces and that is what these fascinating figures seem to look like. What IS a fractal? Is it more than an interesting shape? Who uses them and for what reason? In this WebQuest you will find answers to these questions and begin your understanding of fractals.

top
top of page


TASK

Through this WebQuest you will become more familiar with fractals by exploring a variety of resources. First you will develop a working definition of what a fractal is as a group. Then you will move into your roles of Mathematician, Historian, Application Expert and Artist to learn more. Finally, you will come together as a group to share what you have learned. You will hand in a written report containing at least four pages (one from each member of your team) and any activities required by your role. Finally, you will present what you have learned to the class using a PowerPoint Presentation.

top
top of page


PROCESS

  1. As a group visit two or three of the first Web sites listed. Discuss and decide together on a working definition for a fractal.
  2. Now decide which role each member of the group will fill.
  3. Explore the supplied Web resources to answer the questions and do the activities suggested in your individual roles.
  4. After you have done the activities and collected your information in written form, meet together to share what you have done and learned.
  5. Combine your written reports into one folder, along with any other activities your role required, to be submitted to the teacher when the project is complete.
  6. Prepare a PowerPoint presentation to present to the class that combines what each member discovered, beginning with your fractal definition. Plan to have the class also do one of the activities done by the group.

Mathematician:
 Your job will be to explore fractals mathematically. Your results, first in written form, should include answers to the following:

  1. To what branch of mathematics do fractals belong?
  2. What mathematics and tools are needed to produce fractals?
  3. Give an example of a formula that produces a fractal and show the fractal it produces.
  4. What is fractal dimension? What formula is used to determine this? Give an example.

Application Expert:
 Your job will be to determine how fractals are used. In your written report you should include the answers to the following:

  1. How are fractals used in mathematics??
  2. In what other fields are fractals being used and to do what? Give at least two examples.
  3. What is an iteration and how does it apply to fractals?
  4. Go to either A Fractals Lesson or The Fractory and do one of the activities found there to generate your own fractal. Include it as part of your report.

Historian:
 Your job will be to investigate both the history of fractals and some of the current work being done in fractals. Your report will need to include the answers to the following:

  1. How long have fractals been around?
  2. Who is the "father of fractals" and when did he begin his work? Give an example of his work. (Is he still around?)
  3. Who are two other mathematicians who have worked with or are currently researching fractals? Briefly describe what they are doing.

Artist:
 Your job will be to investigate fractals as art. You will need to include the following in your report:

  1. Are fractals mathematics or are they art?
  2. What medium is used to produce fractals?
  3. Who are some fractal artists? (Name at least three.) Are they artists or mathematicians?
  4. Visit a fractal art gallery and bookmark at least two fractal drawings you like. Include a description of them or put their URL's in your written report and make a link to them in your PowerPoint presentation.



top
top of page


RESOURCES

  1. Exploring Fractals
  2. Fractal World
  3. Fantastic Fractals
  4. A Fractals Lesson
  5. Fractal Microscope
  6. Chaffey's Fractal Links on the Web
  7. Fractals, Chaos
  8. The Fractory
  9. Let's Iterate
  10. Gallery of Fractal Art
  11. Fractal Art Gallery
  12. Sprott's Fractal Gallery
  13. Fractals Theme Page
  14. Math Forum
  15. The Spanky Fractal Base
  16. Math Archives: Topics in Mathematics: Fractals



top
top of page


EVALUATION

You will be graded on the answers to the questions from your different roles, your combined written report, and on your PowerPoint presentation to the class. You will be graded individually on the questions, and as a group for the report and the PowerPoint, according to the included Grading Rubric.

top
top of page


CONCLUSION


This WebQuest is designed to introduce you, the middle school or high school student, to a field of mathematics that may be totally unfamiliar to you. It is my hope that you will have as much fun exploring these fascinating figures, their history and their source as I did. I hope also that it may inspire you to continue to learn and explore, not only fractals, but also the many other interesting math fields that exist.


Introduction Task Process Resources Evaluation Conclusion Teachers


The background fractals were generated at the The Fractory.
Thanks, guys!