Wednesday, May 11, 2005

3 Keys To Teaching Math

When you boil it down there are really only three keys to teaching math or anything really.
1. Concept: The idea behind what is being taught. For example: Numbers are a shortcut we use instead of quantities.
2. Problem: A common problem that requires understanding of this concept. For example: How do we keep trade of all the toys we have? A great way to use this is to add in history, when Isaac Newton was working out gravity he invented Calculus to explain what he was trying to say more easily then anything that was available at the time.
3. Practice: Using several related problems to see how the concept is applied. Algebra becomes a lot easier once I realized that a curve is nothing more then all possible solutions to a particular equation. I have to graph dozens of equations before that piece of inspiration came to me.

In most schools lectures generally start with the concept followed by lots of practice but ignore how the problem relates to real life. So students start asking, "what is this good for?" and too often the answer from the teacher is, "I don't know. " with a subtext of "I'm not going to find out what it's good for, I just got to get through this material for the test, if you pass the test I don't care any more." Which is why students start asking, "Will this be on the test?"

Some schools use just practice, hoping your children with somehow figure out the concept on their own, this is called discovery learning. Admittedly this happens all the time in real life but the people who do this are generally and rightly called geniuses. Discovering something for the first time is hard, really hard, amazingly hard, That is why the Nobel Prize is such a big deal, but once it is solved it can be really easy to do once you know all the things that went into the problem in the first place.

The combined lifetime efforts of Kepler, Copernicus, Galileo, Newton, Einstein and a hundred other has brought us to our current understanding of the universe, which is taught to kids in a few hours of Astronomy class. Trying to have all children do that from scratch is a silly waste of time.

How to use them

How you use these depends on how your children learn. Some children prefer to be given a problem to solve, other like the concept first and a few like to work things out for themselves from practicing. It will also depend on which subject that you are teaching as well. Obviously it is best to use all of them together.

"What would you do if..." is a great way to start. People like to solve problem, especially those that interest them, that is understandable since if a problem is related to something they have interest in they will retain thirty times the material then just a lecture, then you can bring in the concept to help them solve the problem and then the can practice solving other related problems.

Another great way is the historical approach. For example, If you were studying Ancient Greece or introducing circles or finding out more about the Earth you could use this story: Eratosthenes of Cyrene figured that the Earth was round, but how big was it? Well, he had a friend in a distant city with a well that was directly under the sun one particular day a year. He found out how far the cities were apart and measured the shadow in a local well on the same day. He was able to calculate the Earth's circumference to be about 25,000 miles, modern measurements put the Earth's circumference at 24,902 miles. He was off by only 98 miles or about 2%.

This is a great introduction for circles, pi, angles, measuring, averages and history.

Then do some practice to make sure that the concept sticks and to show how it applies to different but related problems.

This should make you a much better teacher.

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