Seeing Math Through Fractals

Why take class time to investigate fractals? Granted, they are geometric figures and worthy of study for that reason alone. Moreover, their use in art and other areas connects mathematics to the world outside the textbook, as recommended by the NCTM Connections Standard. But a study of fractals also opens discussion of algorithm, dimension, and iteration, concepts that would be above the middle school level if it weren’t for the possibility of illustrating them visually in fractals.

Cynthia Lanius’ Fractal Unit
A former mathematics teacher created this unit for middle school students. The lessons begin with a discussion of why we study fractals and then provide step-by-step explanations of how to make fractals, first by hand, and then using Java applets. But the unit goes further; it actually explains the properties of fractals in terms that make sense to students and teachers alike. Excellent material!

Fractals Unleashed
One of the most comprehensive educational sites on fractals! It includes an illustrated and animated tutorial on the mathematics underlying fractals, examples of applications of fractals, from nature to the Star Trek movies, plus a gallery of images.

Fractal Modeling Tools
These online tools allow users to create images of the Mandelbrot and Julia sets, the Sierpinski gasket, and the Koch snowflake. Go directly to the Fractal Microscope and experiment! Students from middle school through college will be awed by the beauty of the images. As they use the microscope to enlarge any part of a fractal, they can see firsthand the self-similarity of the fractal.

We Want Your Feedback
We want and need your ideas, suggestions, and observations. What would you like to know more about? What questions have your students asked? We invite you to share with us and other readers by posting your comments. Please check back often for our newest posts or download the RSS feed for this blog. Let us know what you think and tell us how we can serve you better. We appreciate your feedback on all of our Middle School Portal 2 publications. You can also email us at msp@msteacher.org. Post updated 4/07/2012.

The Wide, Wide World of Geometry

As the social studies, art, and music classes in the middle school widen students’ horizons, some of your students may become fascinated with the art, costumes, and customs of other peoples in this and other times. The NCTM Principles and Standards calls for middle school students to be able to “recognize and apply geometric ideas and relationships in areas outside the mathematics classroom, such as art, science, and everyday life.”

Here are some resources that can help you connect your teaching to geometry past and present.

Culturally Situated Design Tools: Teaching Math through Culture

This applet software is designed to show students how African, African American, Native American, and Latino cultural designs, as well as modern-day graffiti, are based on mathematical principles. Students can use mathematics to re-create existing patterns and structures, or to make their own designs. Standards-based lesson plans, evaluations, and other teaching materials are provided.

Native American Geometry
This web site focuses on Native Americans’ use of the physical, proportional geometry that originates from the simple circle. Aimed at fourth- to ninth-grade teachers, the site is divided into four sections: foundations, anthropology, designs, and education. You will find some 25 relevant web site links and 50 published references.

Ethnomathematics Snapshots
This web site has 12 short descriptions of the influence of mathematics on culturally relevant activities and products from around the world. These include lunar calendars, African counting words, Mozambican methods of laying rectangles, global three-in-a-row games, Native American petroglyphs, Amish quilts, Inca and Maori strip decorations, Inuit drawings, and Angolan sand drawings. Geometrical themes include iteration, recursion, tiling, symmetry, repetition, reflection, and rotation.

We Want Your Feedback
We want and need your ideas, suggestions, and observations. What would you like to know more about? What questions have your students asked? We invite you to share with us and other readers by posting your comments. Please check back often for our newest posts or download the RSS feed for this blog. Let us know what you think and tell us how we can serve you better. We appreciate your feedback on all of our Middle School Portal 2 publications. You can also email us at msp@msteacher.org. Post updated 4/07/2012.