Original article can be found at the Inly News & Events archives page.

Science, Math, and Art Converge in California

November 21, 2008

This fall two creative Inly School teachers—Pam Golden, elementary and middle school art instructor, and Susan Fitzgerald, lead teacher in children’s house one—presented a workshop entitled “Seeing Fractals in Nature” at the American Montessori Society (AMS) fall conference in Garden Grove, California.

“In this experimental session, mathematics, science and art come together through examinations of patterns of fractal growth in trees and flowers,” read the workshop description. “Learn how to arrange bead materials to build fractal branching trees and paint fractal tree mandalas for peaceful meditation in the classroom.”

Here, There and Everywhere
The term fractal refers to a complex geometrical shape that occurs in nature. Studying the design of a single fern can reveal much about the complexity of the entire natural world. Fractal patterns are found in everything from flowers to snow flakes, and once you start looking, you’ll see them everywhere you go.

The topic of fractals is suddenly a hot one in science news. A recent PBS documentary Hunting the Hidden Dimension examined how “mysteriously beautiful fractals are shaking up the world of mathematics and deepening our understanding of nature.” It also showed how mathematical models based on fractals are even being used to detect forms of cancer.

This all sounds like serious stuff for Inly’s 3 to 6 year olds, but both teachers believe children’s house is the right age to introduce such fundamental concepts, and they’ve developed an inventive series of lessons on fractals using 3-D Montessori math materials. Though not part of the standard children’s house curriculum, the lessons are used as a fun extension to enhance core lessons and to show curious students how science, math and art come together in the real world.

On the Road
In October, Pam and Susan had a chance to show other teachers just how this works at the AMS 2009 Fall Conference: “Montessori Education: Inquiry, Involvement, Insight.” The response was tremendous. Having prepared materials for 20 participants, they were surprised to have more than 50 sign up.

It was a good problem to have, and being resourceful Montessorians, they managed to make it work. It worked so well, in fact, that it was hard to get people to leave. “People stayed and stayed and didn’t want to stop making their fractals,” reported Pam.

The inventive use of Montessori math beads to teach the concept of fractals was first developed by Brien Nelson, former teacher and technology director at Inly. Pam and Susan were thrilled to share this brilliant idea with the rest of the Montessori world and said that Brien’s spirit was right there with them the entire time, “without a doubt.”

Montessori teachers from around the country who attended the workshop reported they were excited to bring this lesson back to their classrooms as a cross-curricular extension.

Back in the Inly Classroom
“Math is beautiful!”  A handful of children’s house one students are sitting at individual work rugs on the floor, intently fashion fractals with Montessori beads as their teacher Susan Fitzgerald makes this joyful proclamation. Then they study the fractals they have designed with and smile with pride.

“I love this work so much, I could do it all day,” says Joseph. “This is the best work I’ve ever done,” says Ethan. “Is this multiplication?” asks Marley, who comes over to observe and then creates a design of her own. “This is so cool!”

Susan demonstrates “fractal work” for a new group of children eager to give it a try. First she sets out an illustration of a tree with many branches. Then she sets out a wooden tray containing Decanomial Box with increments of one to ten beads. Beginning with the largest beads and moving to the smallest, the students replicate the design of the tree branches.

Though the students are young (ages 3—6), Susan believes they really “get it” and that the work deepens their understanding of more complex scientific and mathematical concepts to come.

“It is really amazing to see the difference in how the children draw trees now, since they’ve had the lesson on fractals,” says Susan. “To see their pictures of trees before and after, it’s really remarkable. Now they really understand the concept of branching, and they’re drawing in 3-D.”

“If Dr. Montessori were alive today, she’d want to see fractals introduced in children’s house,” Susan believes. “Most children aren’t introduced to this concept until fifth grade, at least, but here we can see that children this young can really understand it on a fundamental level.”

Back in the Art Room
Pam Golden explains that she got the idea from Brien Nelson, former Inly elementary teacher-turned-technology director who died in 2007 from brain cancer. She tells the story of how she and her son Robbie went to Brien to ask a simple question…

“It was about 10 years ago,” she recalls. “Robbie was 8 and he was in EL-1B (now known as LE2). My father had just started getting really into fractals and was finding all sorts of photos on the computer. As an artist I just thought they were gorgeous but didn’t understand them. So Robbie and I brought a photo of a fractal to Brien and asked him, ‘How are these things made??’” A biology major in college with a vast knowledge of the workings of the natural world, Brien was the go-to man for all things scientific at the school.

“So Brien, being Brien, pulled out a big piece of paper and started drawing. Then he said, ‘Hey, we could use the bead chain materials!’ And this is how the whole thing started.”

Brien took the bead chains off the shelf in his classroom, and they all started working with the materials to flesh out their ideas. They began with beads of ten, and moved down to beads of nine, and so on, making branches at each increment.

“This has always stayed with me, and Brien and I always talked about how we wanted to present this at a conference.”

“I just love how math is taught at this school,” says Pam. “I always struggled with math myself, and yet this I really get. You learn differently when you can touch it with your hands, when you can make the connections from 2-D to 3-D.  The more you can connect the visual and kinesthetic with the basic academic concept, the better.”

“One of the most exciting parts for me about fractals is that now I see them everywhere I go, and now I know there’s a reason for them. The more we can connect what we learn in the classroom with what we see in the outside world, the deeper the understanding.”

To learn more about fractals

Visit the following websites:

Fractal Foundation
Using the beauty of fractals to inspire interest in math, science, and art.

NOVA: Hunting the Hidden Dimension
Explore how mysteriously beautiful are shaking up the world of mathematics and deepening our understanding of nature.  Learn about the Mandelbrot set, the most famous fractal of them all. Design a fractal of your own using the online generator.

Unit on Fractals for Elementary and Middle School Students
From Rice University

To learn more about Inly’s science and math curriculum at the children’s house, elementary and middle school levels, click here.