Usually I am totally frustrated by the speed of mathematical education given to my daughter. I really feel that much more time and work must be done to get childern through the historical basics so that they can deal with the modern mathematical requirements of the world we function in. I have always used when people take calculus as the gauge of speed of math education. For example my father took Calculus as a junior in college while I, a generation later, took Calculus as a sophomore in high school. So I reached that milestone five years earlier than the generation before me. There was a cost for that speed up. My father has a much better feel for numbers than I do and can estimate results with far greater accuracy. However, it was an important price to pay if I was going to pocess the math skills I needed to pursue my career of choice in 1992.

Now another generation has past, and I feel our children need to be exposed to higher level math at an even earlier age than I was. It is critical if this generation is going to be able to comprehend the analytical models being used to attack problems today. There will be a feel cost for this just as there was for me versus my father, but how many people can really visualize an obect in N-demensional space anyway?

In the final weeks of fourth grade for my daughter I can not express to you the joy I felt when she came home with a probability problem and a matrix. Now my daughter may not fully understand that this was the math work she was given, but I did. The probability problem was a two dice problem with a comparison of getting a specific roll like 12 (1/36 same as all the others) versus getting a specific total like 7 (1/6). Then they listed all the possibilities and assured that they total to 1 or 100%. The second problem was an expected value matrix. This is the old problem of a guy is a room with three doors. Two of the room lead him down a hall for some amount of time before returning him to the room and the third door leads to freedom. They had to figure out the expected time it would take to get out of the room. This is cool stuff, and they were able to do both problems. I can only hope this kind of higher math instruction continues next year in fifth grade.

From your writing I've come to know some delighted knowledge about the fourth grade. That is really valuable to me. Thanks and hope in future you'll give us more concept like this.

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