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“AHA!” Moments

“AHA!” Moments

Published: 06/15/2008 by Susan Jarema

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»» Mathematics

We’ve all heard the story about the apple falling on Newton’s head and sparking an idea, and the one about Archimedes leaping naked from the bath shrieking “Eureka!” These tales describe exciting discoveries, or “Aha!” moments—the instant when a long-sought answer suddenly jumps to mind. One of the most wonderful parts of being actively involved in your child’s educational journey is being able to share in the excitement of these moments.

“Aha!” moments usually grow out of hours of thought. They come from incremental learning—but at some point the knowledge suddenly sinks in and takes hold.  Mathematics, which involves varying concepts and is learned in layers, offers many such moments.

Often the “Aha!” moment occurs on its own after your child hears a concept explained in various ways and sees examples demonstrated. Even a lesson in adding fractions can encourage an “Aha!” moment by showing your child several examples and having him repeat the exercise with similar numbers. Slowly bring in more diverse examples. At some point the idea just clicks and your child will understand the rule, which he can then apply to other mathematical problems. You’ll know your child understands the point well when he can take the concept and make up his own problems.

You can also help to create an “Aha!” moment by directing questions or creating an activity that will help your child discover a concept on her own.

One such activity is discovering pi (). Remember
C/d=. Bring a measuring tape next time you are out on your bikes. Measure the circumference and diameter of the different-sized wheels. Plot on a piece of paper the ratio of the circumference and the diameter that you measured (C/d). Continue to add in the ratios calculated for of other circular objects (the larger the circles the better). Soon your child will start seeing a relationship between circumference and diameter (this number is close to ), just as the Babylonians, Egyptians, and Greeks—notably Pythagoras and even Archimedes—did thousands of years ago. Your own young mathematician will have made this discovery as well!

Another great activity for younger children is to discover prime numbers on their own by coloring in different multiples of 2 to 12 on a 100s chart. After your child has coloured in all the multiples (with the exception of 2), discuss the numbers that have not yet been coloured in. Look up the Sieve of Eratosthenes and let your child know that she made the same discovery as the famous Greek mathematician Eratosthenes.

You can also duplicate the events of historical stories. One such example is of 10-year-old German mathematician Carl Friedrich Gauss, who in 1787 startled his teacher by finding the sum of all the whole numbers from 1 to 100 in his head (he multiplied 101 x 50).

I also love seeing children and even adults discover the relationship between the Fibonacci sequence and Phi (the golden ratio 1.61803399…). First, have your youngster discover how the sequence works (each number is the sum of the two proceeding numbers). Afterward, ask him to chart out the ratio of each number in the sequence and the proceeding number (younger children can use a calculator). Your child will soon start seeing that the ratios calculated are approaching Phi.

By asking open-ended questions, directing the lesson and creating discovery activities, you can set your child on the path to making endless exciting findings on her own. Take some time to look for the “Aha!” moments. This is what life learning is all about.

Math Resources

“Aha!” Favors the Prepared Mind
Scientists Explain “Aha!” Moments: Brain Activity Differs When Creative Insight Takes Hold
Encouraging Thinking Skills in Young Children