That Wide-Eyed Look

Six ways to inspire awe in children with math and nature.

Math can seem magical through the eyes of a child. Click through the slideshow to uncover the Fibonacci sequence as it appears in nature.

By Mikey Jane Moran

March 18, 2015


Peek into the inner core of a fern to spot the tiny curls of fiddle heads, or baby fern fronds. Show your children the gently uncurling spiral and ask them what it reminds them of. A shell? A millipede? It’s not important to know the exact proportions of the fern, just take a moment to enjoy the wonder of a “perfect” spiral.

Photo by iStock/only_fabrizio


Pick up a pinecone and tell your children to trace the spirals with a marking pen. Count the spirals together: It will always be a Fibonacci number. If pine cones are in short supply in your neck of the woods, acorn caps contain the same pattern.

Photo by iStock/Mimadeo


A day at the beach can be about more than just sunshine and sandcastles. Nearly all shells, most notably the nautilus shell shown here, curl in a Fibonacci spiral. Even more mind-boggling, many waves fold in the exact same shape. Ask children to look closely at shells, draw their shapes in the sand and see if they can spot other places the pattern washes up.

Photo by iStock/Fyletto


Flowers are Fibonacci on display. Inside sunflowers, seeds spiral in Fibonacci numbers. Trace and count the number of spirals and children will always be astonished to find a Fibonacci number every time. For younger children, simply count petals. Most flowers (with the exception of some species like lilies) will have a Fibonacci number of petals. Daisies are a great example and are abundant and fun to pluck. 

Photo by iStock/Natchaphol chaiyawet


Arid climates bring out Fibonacci blooms in abundance. Succulents and cacti are one of the best places to see complex and astounding spirals. Plant a Fib garden with aloe, astroloba and haworthia plants and count the spirals, or simply go dizzy tracing the intricate patterns.

Photo by iStock/hilaryfaith


Have a Fibonacci feast! Serve up the twirls of Romanesque cauliflower raw with ranch dressing or roast to bring out the sweetness in the spirals. Cut into cabbage to reveal the lacey Fibonacci swirls inside. Brussel sprouts are arranged along the stalk according to the golden ratio and the twists are easy for children to see. Show your kids the spinning pattern on a pineapple or artichoke—like pinecones, the nubs and leaves spiral in Fibonacci numbers. For little ones who can’t count as high as 21 or 34, cut an apple in half down the middle to reveal the five-pointed star-shaped configuration of seeds. Playing with your food a little never hurt. Added perk: Fib foods just so happen to be incredibly healthy!

Photo by iStock/7000

Hidden inside an apple there is a secret. Pinecones are magic, and there is something to learn from an artichoke.

Most adults are familiar with the Fibonacci sequence—a series of accumulating numbers where the next number is found by adding the previous two together beginning with zero and one. The chain of numbers produced (0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144…) describe natural phenomenon from leaf growth to the curl of a shell. Even the human body displays Fibonacci proportions.

If you want to get into the nitty-gritty, grab some graph paper and draw out the Fibonacci spiral. This video is a good five-minute refresher.

Each box’s height and width is a Fibonacci number, and when a curving line is drawn through each box, the expanding spiral is easily seen. The curl increases at a rate of 1.168, also known as phi or the golden ratio. It comes down to math, but to children, nature is miraculous if you look close enough.

But how do you get children to look at all when cartoons are more captivating than flowers and pinecones? David Sobel of Antioch University would say the answer is simple: Play. Sobel is a professor and scholar of play. For more than 40 years he has developed place-based environmental education programs that focus on fun—creating houses for “forest fairies” out of leaves and twigs, building forts and making maps. Play influences sustainable behavior later in life, so children should be free to roam, dig, hide, run and construct outdoors. With a little facilitation, these activities can get kids to bond with brooks and birds more than any traditional lesson.

Tell your children to hunt for the curling Fibonacci shape outdoors and they will start to see the patterns everywhere, in the cowlick on their brother’s head and in spider webs—places where there aren’t really Fibonacci patterns. But the beauty is that they are noticing. Instead of staring at a video game screen on long road trips, they are looking at clouds. Walks may take longer as they stop to look at every little thing, but how can anyone complain?

It’s not about being right; it’s about making observations and encouraging children to forge their own connections with nature. Sobel understands the math, but admitted he never quite grasped the whole Fibonacci thing. “Whenever I look at a sunflower, I always have trouble seeing it,” Sobel says. Even if the mathematics are too advanced, it is never too early to start pointing out patterns. Kids need direction to focus their attention—after that, the discoveries they make are entirely their own experience.

“We have to get toward experiential learning,” Sobel says. He recalls romping and tromping outside, playing a tracking game with his friends as a young child. This game sticks out in his memory as when he first made a connection with nature. “Transcendent experiences in nature drive you to the inclination to protect nature,” Sobel said. Exposing the implicate patterns in nature is just one way of bringing society back down to Earth—one scavenger hunt at a time.


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