Math-Facts or Math-Principles?
Another term Manisha and I dislike - next to "word-problems" - is "math-facts". We prefer to think in terms of mathematical principles. What is the difference? Isn't it all the same once you have to add two numbers? Yes and no. Yes, they may appear to be the same when you are adding 2 and 2, but no, it is a matter of perspective.
The word math-fact implies that (2 + 2 = 4) is a discrete chunk of information that is unrelated to, say, (2 + 3 = 5). It is saying that this stands alone and cannot be derived from a more general principle. An example of a fact is the date of US Independence. It cannot be derived from other information. It is something you have to memorize - or better yet, look it up on the internet. That's what it is for.
Math on the other hand has principles. Addition is a principle. Once you know the principle, all "addition facts" get subsumed under it. Once you know (2 + 2 = 4), you can derive (2 + 3 = 5). Knowing what addition is all about enables you to add in real life when you have to add numbers you have never added before.
Both Manisha and I have a common secret - we never learned multiplication tables! On the other hand we became very good at figuring out the problem in our heads because we knew the basic principles involved. (We excelled in math and ended up going to an elite engineering college.) We are happy to see Supriya go in that direction as well. She knows the principles of addition, subtraction, multiplication and some rudiments of fractions. That's what we want to build on.
posted by MP at 5:33 PM
3 Comments:
Even though mathematical facts can be derived from principles (and the process should be understood prior to an attempt at fact memorization), simple and/or common addition, subtraction, multiplication, and division equations are memorized by most people for speed of use. While I am able to sound out most of the words I read and use, for speed in reading and writing, I have committed the sounds of individual letters, letter combinations, and in fact, many of the words to memory. This enables me to accomplish more in less time.
They are called "facts" because they are not in dispute. 2 plus 2 does, in fact, equal 4.
By the way, although commonly understood as July 4, 1776, the date of US Independence is questionable in my mind as the resolution which came to be known as the Declaration of Independence was adopted by the congress on July 2, 1776. It was the formal parchment copy of which that was adopted on July 4, 1776 and not signed by all until August 2, 1776 (the final hold-out being New York I think).
Of course, none of this will stop me from celebrating on the Fourth of July, or from misspelling, or miscalculating in the future. My only hope is that when I screw up, I do it so fast that I have enough time to go back and do it again - the right way.
Lynne
1:50 PM
Here's Manisha's take on your comment (& I agree with her):
"Interesting! I see it differently. For one thing I've neither memorized any math facts nor any words. I happen to remember some of them (both math facts and words) because I have come across them often enough. And I firmly believe that that is how it should be.
>They are called "facts" because they are not >in dispute. 2 plus 2 does, in fact, equal 4.
Very true, but my gripe is about connotation. The connotation remains that facts are to be looked up (or memorized) as opposed to figured out. "I don't know" is never a valid answer for arithmetic questions, whereas it is a valid answer for a great many facts."
11:33 PM
(Excuse this very late comment, I only just found your blog in the past few days!)
I had bought a couple of math workbooks for my daughter (5 1/2), just whatever they had at Target or the grocery store, and at first I saw nothing wrong with their math problems.
Then I purchased the Miquon math workbooks, and they had pages which actually taught tricks and techniques, not just "math facts." For instance, they might have a page with 2+2, 2+3, 2+4, 2+5 etc. so that the student would realize the pattern. If they didn't remember 2+5 they could simply recall 2+4 and add one more. Similarly, they had pages with 2+5 and 5+2, 3+4 and 4+3, etc. The earlier workbooks had no logic to the questions whatsoever, they were entirely at random and only meant to "drill" students on their memorization, not to teach them the rules of arithmetic.
It is amazing how much "educational" material is not actually very well thought out!
11:39 PM
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