(Question) Teaching Fractals to High School Students

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Offline paswanson46

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« on: July 24, 2018, 10:24:54 PM »
I am interested in collaborating with a member of this forum on teaching fractals to high school students.  I certainly would be interested in talking to someone who has has had experience in doing this.

Linkback: https://fractalforums.org/collaborations-and-jobs/6/teaching-fractals-to-high-school-students/1638/

Offline 3DickUlus

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« Reply #1 on: July 25, 2018, 01:51:51 AM »
Hi,

There are a number of threads here at fractalforums.org and at fractalforums.com that could be used as the basis for an introduction to fractals and ongoing discussions leading to the more complex intricacies of the math being used to generate fractal images.

This is also a good one to start with https://en.wikipedia.org/wiki/Mandelbrot_set that could, in itself, be transcribed into a short course suitable for students with curiosity about fractals.

Maybe you could outline how you want this to progress, introduction, history and background, basic formulae, recent advances, application of the math etc... teaching fractals to high school students would also, imho, include how to code a formula into something a computer can use to generate an image as in : going from complex plane coordinate input to pixels on the screen. The wiki link above includes "everything you need to know" in order to get started with fractals, but it's just a start, the topic is immense and evolving.

edit1: a more elaborate tutorial https://fractalforums.org/mandelbulb-maniacs/46/mandelbulb-fractals-in-blender/1636/
edit2: in depth study? https://fractalforums.org/image-threads/25/other-polynomial-and-rational-maps/1169/msg8327#msg8327
« Last Edit: July 26, 2018, 04:11:23 AM by 3DickUlus, Reason: typo »
Fragmentarium is not a toy, it is a very versatile tool that can be used to make toys ;)

https://en.wikibooks.org/wiki/Fractals/fragmentarium


Offline Fraktalist

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« Reply #3 on: July 25, 2018, 10:01:41 PM »
There's this awesome site that has free online courses that might inspire you and maybe you can contact some of the people there, pretty sure they'll help out:
https://www.complexityexplorer.org/
I took a few courses there and it really helped my understanding of fractals a lot!

Offline gerrit

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« Reply #4 on: July 25, 2018, 11:04:13 PM »
Fractals for the Classroom: Part One Introduction to Fractals and Chaos Hardcover – Oct 22 1991
by Heinz-Otto Peitgen (Author), Hartmut Jürgens (Author), Dietmar Saupe (Author), E. Maletsky (Assistant), T. Perciante (Assistant), L. Yunker (Assistant), C. Hösselbarth (Illustrator).

There are 3 parts, I have I and II which seems about high school level.

Offline claude

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« Reply #5 on: July 26, 2018, 03:02:40 AM »
There are 3 parts, I have I and II which seems about high school level.

AFAICT there are only 2 volumes of the book.  There are also (at least, though I could only find) 2 more volumes of related "Fractals for the Classroom: Strategic Activities" with exercises and worksheets:
Quote
This book is complemented by strategic classroom activities, which come in several volumes co-authored by Evan M. Maletsky, Terence H. Perciante, and Lee E. Yunker. These activity books directly involve the students in constructing, counting, computing, visualizing and measuring using carefully designed work sheets. These additional volumes focus on the large number of mathematical interrelationships which exist between fractals and the contemporary mathematics curricula found in our schools, colleges and universities.


Offline claude

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« Reply #7 on: July 26, 2018, 03:33:55 AM »
good find!  the springer link claims 4 volumes of activities were planned, but the back cover of the amazon link claims it is the third and final volume.

Expensive, but maybe local library has it.
https://www.amazon.ca/Fractals-Classroom-Strategic-Activities-Three/dp/0387984208 is a shorter link and mostly(?) equivalent.

Offline lkmitch

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« Reply #8 on: July 26, 2018, 04:43:05 PM »
As others have pointed out, there are lots of materials available to help with your course. To my mind, the trick is determining *why* you want to teach fractals to high school students, or what aspects you want to teach. And that ties into how much time is available--is this a one-hour intro, a short course, or a full-term class? I've given several intros and a few short courses to high school students (and younger). The artistic aspects can be a good hook, but then, you need to allow them to play, which requires a platform that is accessible, easily learned, and relatively safe. If your desire is to teach something about shapes and modeling, (e.g., fractals model natural and "regular" shapes model artificial stuff), that can be tough to do well in an intro. And the math (why a fractal as opposed to simply z^2+c) is largely beyond the reach of most high school students.

Good luck!

Offline 3DickUlus

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« Reply #9 on: July 27, 2018, 02:26:03 AM »
@paswanson46 what is your background and qualifications in math? degrees? courses?

help us help  you  :yes:


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