Canada's Homeschool

Human intelligence is based, to a large extent, on our ability to make abstractions. Language is an abstraction. Math is an abstraction. Science is an abstraction. Philosophy is an abstraction. Obviously, the ability to make and understand abstractions is important.

But if you want to understand orange juice, you better understand the orange first. If you want to teach a baby the concept of motherhood, you probably don’t want to start with discussion on reproduction. You want to start with something the baby understands and is interested in: Mama. Then build on that.

All of us learned at a pretty early age that hot things can cause pain to us. But we probably learned that abstraction from a concrete, real example. I’m sure my wife and I explained the abstract concept to our son lots of times: “Don’t touch hot things!” But he learned it one evening while he was helping his mother cook dinner.

This reality is based in motivation. My son at the age of 5 wasn’t greatly motivated by a desire to benefit from his parent’s years of experience. However, he was motivated by his desire to not feel pain.

The Pythagorean Theorem is an amazing, powerful tool. But if you want to teach the Pythagorean Theorem to a young person, which approach do you thing will be more successful (image me illustrating these concepts on the blackboard as I talk):

1. Here is a triangle. What is the length of the hypotenuse? You can determine the length of the hypotenuse with this formula: the square of the hypotenuse is equal to the sum of the squares of the other two sides. Here, let’s try it.
2. On a baseball diamond, it’s 90’ from home plate to first base. It’s also 90’ from first base to second base, How far is it directly from second base to home plate? A Greek mathematician, Pythagoras, showed us how to figure this out 2500 years ago: the square of the distance from home plate to 2^nd base is equal to the sum of the square of the distance from home to first plus the square of the distance from first to second. Here, let’s try it.

Certainly, as we get older, our ability to quickly associate the abstraction to a concrete example that relates to our lives improves. As a Homeschool Educator, It is your responsibility to gauge where your student stands on that continuum, and adjust the way you introduce new concepts accordingly. It’s an art. But the glassy eyes probably mean something. And the level of enthusiasm also tells you a lot.

How do you come up with good concrete examples of an abstraction? Think about what excites the student. Here are my typical starting points: sports; money; dating; games; family; electronics; their future.  

See the entire series of Tips at the http://stan0403.edublogs.org/, or at www.MasterMath.info.