Tuesday, April 19, 2005

Math is one of the success skills.

There are only a few skills that appear necessary for success. They appear to be: reading, writing, mathematics, fitness, problem solving, interpersonal, and face & name memory.

I am going to focus on mathematics.

Mathematics is a very badly taught skill in schools, that was really brought home to me when I was reading "The Design of Everyday Things" where Norman talks about Learned Helplessness. Students actually end up knowing less math coming out of school then when they went in. They learn to become dependent on the teacher for explanations. This is very bad in my eyes.

I have tutored many people in math and other subjects plenty of times, starting in high school. If you count other students cheating off my tests, it goes all the way back to the 1970's when I was in elementary school:)

Math is simply a language. And there is an important thing you have to learn first. Numbers are stand-ins for actual quantities. 1 is the same as *, ** is the same as 2, and so on.

Numbers are just an abstraction to make writing numbers a lot faster and easier. We could make our numbers be anything at all. Many early number systems, such as Greek and Hebrew just used letters to represent numbers, but unlike how we use letters to represent unknown quantities in algebra, they were constants. It would be similar to us saying a=1, b=2, c=3, and so on.

Just by counting things I've been able to teach my 2 year-old daughter to count.

Addition is straightforward enough. a group of ** and a group of **** put together are ******. but that would be a real pain to do the national budget with. so we use numbers instead of tally marks. The Roman numerals are little more then tally marks and doing calculations in that system is very hard.

So ** added to *** are *****, or 2 and 3 are 5, or 2+3=5. It is easy to see that the last is very easy to write. If you are starting to teach a young child to do math then start with physical quantities: blocks, pennies, pens or other small easy to move things. I would save candy for subtraction.

Subtraction is much the same. Though you have to make sure that at first you only subtract smaller quantities from larger quantities. Once they are familiar with that concept you'll see something interesting happen. They'll ask you, "What happens if we subtract a larger number from a smaller number?" Then you know they are ready for introducing negative numbers. You don't need to introduce number lines or anything like that. Number lines are important later, but so much later so learning them now doesn't really help. Negative numbers are just that negative. They'll deal with them just fine.

Math is a language. 1+1=2 because we defined it that way. Children learn to speak because we use words around them, they imitate us and we correct them. We don't even have to think about doing it. Math is a little more difficult for us to teach because we tend not to use it explicitly. We have to change, but it is worth it to help our children be successful.

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