18 July 2008

Math Wars? Stop the Hate!

This news article makes it sound as though parents of public school students should be secretive about teaching their own children how to do mathematics in the traditional way. It had a silly parents-being-persecuted sort of tone, and yet after reading this several times I've yet to see where the problem might be. In fact, I saw no hint of criticism from the public school whatsoever:

http://ap.google.com/article/ALeqM5jIknLQBhUVOj_QjvWRCm2sxwA4JQD91UHBDG0 Got the link from a post on Joanne Jacobs' blog, which you can view by clicking my post title. I think. Not being mathematically inclined, I'm still not sure how to link posts without the long nonsense. I'd like to say, at "this" blog, and if you click "this," you go right there. I haven't figured out how to do that, so if you're a smartie, would you leave me a comment and clue me in?

So... I'm no math expert, but I imagine the silly methodologies some public schools use to teach mathematics leave much to be desired. I don't understand how with "state standards" and NCLB laws that substandard (by any standard) math programs would be in place for long. But whatever. You know what? I really don't care how you teach your child math, or what they're doing in the public school to teach math so long as they aren't counting condoms in kindergarten. (Yes, I was being ridiculous on purpose, so no flaming in the comment section, please!)

Does the child know how to do the math? Does the child have a good grasp on how math works and how to apply the principles? I'm concerned about those two things. As an aside, I have one "gifted" child go through the public school's math silliness of adding left to right and whatnot. Strange, strange methods are used in these classes. It would be NICE if the schools at least endeavoured to have short classes for the parents so that they can help with homework when the kid doesn't understand why Mom is doing it "wrong." When Patrick would bring home multidigit addition and subtraction problems, I'd sit there perplexed. Thankfully, he could do all the math himself and didn't need help often. And G is in special ed and almost never receives homework.

To hear some tell it though, we need to pick up our Math Swords so that we can slay the Math Dragon in our Math Wars. Good grief. How about you teach the child the way you think he'll learn, and then if it doesn't work, try something else? I do have a problem, though, with skipping over learning some rote facts and methods altogether, though. From the article:

"... Long division wasn't on the agenda. As many parents across the country know, this and some other familiar formulas have been supplanted, in an increasing number of schools, by concept-based curricula aiming to teach the ideas behind mathematics rather than rote procedures."

"They call it the Math Wars: The debate, at times acrimonious, over which way is best to teach kids math. In its most black-and-white form, it pits schools hoping to prepare kids for a new world against reluctant parents, who feel the traditional way is best and their kids are being shortchanged."

In our district, some of the sillier aspects of the Everyday Mathematics program are alleviated because children are required to drill their times tables and learn division. I've said this before, but some of the worksheets are very interesting and force children to think of mathematics in everyday situations.

3 comments:

  1. When you compose a post,there will be a chain looking icon. Click on that and put the website address in it. Once you get it put onto your post that your making there will be this <> at the end. That is where you would type "this" or what ever you want to type. I hope that helps a little.

    Aunt B. AKA Brandy

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  2. There are only a few basic "Math Concepts" in simple arithamatic and elementry algebra. If a person understands them, they know all the concepts of basic math. The rest of "Elementry Math" is learning to do arithamatic according to these basic concepts. Really, it is that simple folks. Below is a two page basic "Math Concepts" book. Enjoy:
    "A Two Page Algebra Book"
    By
    Carl M. Bennett, BEE; MS(3)

    Mathematics is a language for expressing precise, logical ideas. The basic language of mathematics is common Algebra.

    Algebra is based on the definitions of two rules of how to “operate on” or combine two real numbers to form another real number, and five other definitions of the characteristics of these operations needed to make Algebra logically consistent and practical as a language of logical thought.

    The first rule is called addition or the “+” operation on two real numbers.

    For two real numbers a, and b, a + b is defined as the real number c which is equal to the combined value or “sum” of the numbers a, and b.
    For example 3 + 5 is defined as 8 or 3 + 5 = 8.

    The second rule is called multiplication or the “x” operation on two real numbers.

    For two real numbers a, and b, a x b is defined as the real number c which is equal to the combined value or “sum” of the number b added to itself a times.
    For example 3 x 5 is defined as (5 + 5 + 5) = 15.

    To be logically consistent and practical, both of the above operations, addition (+) and multiplication (x) must have the four basic characteristics defined below.

    1 - Both addition (+) and multiplication (x) must be “associative” in character.

    This means that the order in which we associate and add the numbers a + b + c, gives the same real number. That is to say, if we first associate and add (a + b) and then add c, or we first associate and add (b + c) and then add a, we get the same real number.
    For example, (3 + 5) + 7 = 15 gives the same result as 3 + (5 + 7) = 15.

    This also means that the order in which we associate and multiply the numbers a x b x c, gives the same real number. That is to say, if we first associate and multiply (a x b) and then multiply by c, or we first associate and multiply (b x c) and then multiply by a, we get the same real number.
    For example, (3 x 5) x 7 = 105 gives the same result as 3 x (5 x 7) = 105.

    2 - Both addition (+) and multiplication (x) must be “commutative” in character.

    This means that the order in which we add the numbers a, and b, gives the same real number. That is to say, if we add a + b, or we add b + a, we get the same real number.
    For example, 3 + 5 = 8 gives the same result as 5 + 3 = 8.

    This also means that the order in which we multiply the numbers a, and b, gives the same real number. That is to say, if we multiply a x b or multiply b x a, we get the same real number.
    For example, 3 x 5 = 15 gives the same result as 5 x 3 = 15.

    3 - Both addition (+) and multiplication (x) must have the “identity” characteristic.

    This means that for addition (+), there must be a real number, I, when added to any real number a, always gives, a + I = I + a = a. For addition (+), this "identity" is I = 0.
    For example 5 + 0 = 5.

    This also means that for multiplication (x), there must be a real number, I, when multiplied by any real number a, always gives a x I = I x a = a. For multiplication (x) this "identity" is I = 1.
    For example 5 x 1 = 1 x 5 = 5.

    4 - Both addition (+) and multiplication (x) must have an “inverse” characteristic

    This means that for addition (+), a real number b is the addition (+) “inverse” of any real number a, if and only if a + b = 0. The addition (+) “inverse” for any real number a, is the “negative of its real value”, defined as "minus a" or -a, since a + (-a) is always equal to the addition (+) "identity", I=0, that is to say a + (-a) = 0, for all real numbers a, of both positive or negative value.
    For example (-5) + (-(-5)) = (-5) + 5 = 0.

    For simplicity we often write –5 + 5 = 0 = 5 – 5, but 5 – 5 is mathematically, actually 5 + (-5). The “minus (-) notation” only tells us that -a, is the negative in value of a. Thus minus (-) is not actually a valid algebraic operation on two real numbers like addition (+) is, since the minus (-) operation is neither “associative” nor “commutative” as defined above.
    For example, 7 - 6 = 1 is not the same as 6 - 7 = (-1).

    This also means that for multiplication (x) a real number b is the multiplication (x) “inverse” of a real number a, if and only if a x b = 1. The multiplication (x) “inverse” for any real number a, is the reciprocal of its real value, defined as the real number (1/a), since a x (1/a) is always equal to the multiplication (x) "identity", I=1, for all real numbers except zero = 0.

    Zero has NO multiplication (x) “inverse”, since (zero) x (any real number) = zero, thus not the multiplication (x) "identity", I=1, as required for zero to have a multiplication (x) “inverse”.

    This is why "division by zero", for example, a x (1/0) or a /0, is NOT allowed in common Algebra.

    For simplicity we often write, for example, 25 / 5 = 5, however; 25 / 5 is mathematically, actually 25 x (1/5) = 5. The "divide (/) notation" only tell us that a number is the “inverse” of a real number. Thus divide (/) is not actually a valid algebraic operation on two real numbers like multiplication (x) is, since the divide (/) operation is neither “associative” nor “commutative” as defined above.

    For example, 8 / 2 = 4 is not the same as 2 / 8 = 0.25 or the rational, real number, one quarter, (1/4).

    To be logically consistent and practical, both of the above operations, addition (+) and multiplication (x) must have the one additional basic joint characteristic as defined below.

    5 - Multiplication (x) must be “distributive” over addition (+), that is,

    a x ( b + c ) = (a x b) + ( a x c ) and ( a + b ) x c = (a x c ) + ( b x c ) for all real numbers.

    The above "rules and characteristics" define common Algebra. Every logically and mathematically correct manipulation of any algebraic equation involves these "rules and characteristics" or a composite of them.

    © Carl M. Bennett, 18 August 2006. May be reproduced only for educational and research purposes.

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  3. Or you can highlight the word that you want the link to be and then go to the hyperlink icon and put in the web address. After you hit OK then it should automatically put it in and when you publish the post it should put it in a different color.
    Mine doesn't always change the color.

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Non-troll comments always welcome! :)