Math and Home School and Saxon and Blah, Blah, Blah

So, in some ways I am learning math all over again. In some ways, I am just having my memory refreshed. But this time around  instead of just memorizing math principles. I am learning why. I am learning why because I actually really want to know, but also because Johnny demands that I tell him why no matter what. So here is an example of the why in math that I never bothered to think about in high school.

Negative Numbers: Did you ever wonder why when you subtract a negative number from a number the two negatives make a positive? I never did before. But I knew Johnny would need to know, so I had to think this one through and ask my mathematician husband. It is actually so the rules are consistant. Think of it this way:

 For all real numbers, a - a = 0

So (-a) - (-a) = 0, 

when you subtract  a number from itself then you get zero whether it is positive or negative. This rule has to remain constant so

a - (-b) = a + b, 

because

(-a) - (-a) = (-a) + (a), 

which equals 0.

Tada. It feels nice to be able to prove why a math concept is true instead of just know the rule.

On another math topic: there is a way of teaching math called Saxon Math that has taken over how math is being taught-- and that is BAD. Here is why.

A man named Saxon did not understand math very well. But he did not know that he did not understand math. He made this theory that a student should not have to know how to do a math problem unless it is taught to them. So what has happened? Children are taught every way to add, every way to subtract, every way to multiply and divide.  If you do not believe me check out your child's math book (it doesn't have to be called Saxon anymore. Saxon has taken over). We bought a fifth grade math book for Johnny. All it had was a year's worth of different ways to multiply-- boring, yes. Now, you may think your kids are learning things earlier than you did because it includes scientific notation and exponents. I don't think I hit that until 7th or 8th grade. But that is it-- just every way to multiply. You may be thinking, "this woman is nuts. Why is this bad?" I am going to tell you why I am not nuts and why this is bad. Before Saxon, kids were not told every way there is to do a single problem. Mostly, we were given just one way. Then on tests, we would have problems pop up here and there that we would have to think out and find a different way to solve them. On standardized tests, we would be given a lot of those , "You have never seen this problem before" problems. That was a-okay for most kids, because we had already had to use the "think this problem out" skill. We knew what to do. American test scores were pretty good. In fact, American's were generally considered around the world to be "very inventive" We thought up the machines, the Japanese made them better. Not bad, I think. That is all gone with Saxon. Saxon does not believe a student should have to think a problem out. Saxon believed a student should not have to do a problem unless the student was shown how to do that particular problem. Math changed from a subject that greatly improved one's critical thinking skills to just a bunch of memorizing. In fact, an absurd amount of memorizing. So we tossed aside the saxon theory based math book, and swapped to the traditional way. Here is what I am finding with my own kids:

1. Johnny had an algebra problem where in order to find the answer, he had to divide 81 by 3 (81/3). 2.Johnny said, "the answer is 81/3". 

3. I said write it down and divide it out.

4. Johnny hates any division that he doesn't already have memorized, and Johnny HATES writing it out.

5. So Johnny said to himself. 3 X 10 = 30. There are 2 (30's) in 80. So that is 20. Then there is 21 left, and 3/21 = 7.

6. Johnny yelled out, "The answer is 27. Do you want to know how I did it?"

If Johnny had already been shown this way of diving (removing the tens and then dividing the left over) he would have missed the opportunity to think it out. Johnny has learned important critical thinking skills. Johnny is being trained to solve problems, not just to compute a memorized problem.

Guess what? Japan used to do math more like Saxon. Japan now does math more like the old fashioned American-way (before 1995-ish). And guess what? Americans are continually falling behind the international level. So Saxon math is BAD!