Talking Math

I recently bumped into the oh-so-cool blog "Talking Math with Your Children."

~ Fun stories that let you watch children learn when you don't have little ones to provide such amusement in your own home.

~ Ideas to encourage math-thinking in kids.

~ The importance of using numbers casually in everyday conversation, and how this habit will affect children's math-thinking.



I could waste a lot of time perusing this blog just for funsies!

For now, two quick comments:
First, the author put together an awesome book of shapes where you're supposed to figure out how "one of these things is not like the others; one of these things is not quite the same."  It will work for 3-yr-olds or 50-yr-olds. 

Second, a quote from the blogger:

Many things that you hope to remember, you can remember by encountering them frequently. Tabitha has never sat down with flash cards to memorize her single-digit addition facts. Yet she is in second grade and is starting to feel confident with them.

This is where I get skittish about "classical ed" for math [accepted by some as "Just memorize the factoids already and don't expect the kids to understand what's going on].  Granted, I realize that some kids do fine with "just memorize it and practice enough that you can rattle off the drill, and then later you'll learn to understand."  But some kids don't handle that well!  How this Tabitha learned is the same way most of my children learned their math facts: if you figure it out repeatedly, soon you've accomplished two things.  One: you've learned it, that is, memorized it.  Two: you understand the concept already ... even to the point that, if you should "forget it" some day, you'll easily be able to figure it out quickly.

Now, go play some math!

Math: Right-Brainers or Left-Brainers

For those of you who have a hard time keeping it straight, left-brained is the orderly, rule-oriented side of the brain, and right-brained is the creative, free-thinking side of the brain.

Conservative people tend to value the school-way to do math. "Do this step. Memorize these facts. Drill these facts like crazy. Follow this step next. No, you can't do it that way! Do it this way instead." When you're dealing with a classroom full of children whose needs must all be met as best as possible, when you have children who annually change from one teacher to the next, it helps to have standardization in the math program.

Some teachers and curriculum-planners have tried to bring reform to that staid, old-fashioned, rule-oriented way to do math. People may have conniption fits over the changes. "It won't work. That's not the way to teach." Both sides have their points. The old way of teaching math leaves most kids without understanding of what's truly going on with their computations. On the other hand, with the newer ways of teaching math, there are problems. There's too much instability as kids change teachers annually. Kids mature at different rates, and teachers become impatient for "results" (that is, good scores on the standardized tests) instead of developing math-brains and math-smarts. Occasionally, teachers will even go so far in wanting kids to "understand the process" that they give equal credence to right and wrong answers. If a teacher doesn't understand math, she's going to have a booger of a time helping kids to understand math. And so, sometimes the best a school can aim for is to give up on math, but to make sure the kids can manipulate their numbers and do their arithmetic.

And, YES, there is a difference between arithmetic and mathematics.

Arithmetic is a tool. Being adept at arithmetic involves not only some understanding of what's going on with the numbers and why they work the way they do, but it also involves memorizing addition tables and multiplication tables and some formulas. Becoming good at arithmetic involves enough practice and drill that processing those numbers becomes simple.

But math? Ahhhh. Math is beautiful. Math is like art. Math is creative. Mathematics explains and explores and delves and marvels.

Amazingly enough, arithmetic is NOT necessary to understanding mathematics. Kids can begin to understand decimals and negative numbers before they've done the grunt-work of learning their addition and multiplication facts. Kids may begin to toy with number theory before they can earn A's and B's on their third-grade math worksheets. Kids know something about fractions before they've learned to count to twenty. Kids can wonder at the concept of infinity before they've learned that 6x5=30.

Good math teachers want their kids to learn (eventually) to do their arithmetic painlessly. Arithmetic is a vital tool for mathematicians. But as Penrose and Marilyn Burns and Sir Cumference will show, mathematics is a treasure over which little hearts can delight ... even prior to having mastered simple arithmetic!

Teaching math is like teaching reading. You can teach a kid his phonics and he may be able to decode words, but the higher priority is to teach him to cherish books and reading. Phonics is merely a tool. Same for math. Teach the left-brained arithmetic (hopefully on a timetable that fits the individual child), but don't let arithmetic sap the child of his wonderment over mathematics.

Astounding Math Skills

Why does no one care that I know that the sine of 60 degrees is half the square root of 3? You'd think it was irrelevant knowledge or somethin'. And when my kid in the living rooms asks me (near the computer) to look up a number on the trig calculator and holler out a sine for him, he is not satisfied with half the square root of 2, or half the square root of 3 -- he wants a decimal. What's up with that?

Pout. You'd think people would appreciate my math skills....

Today's Laugh

I haven't made time to hunt up jokes this week since my last batch of pre-dated blog jokes ran out. A bunch of you probably saw this one already on the newest episode of my favorite geek show, Big Bang Theory, but I'm posting it anyway since I busted gut over it!


Why did the chicken cross the Mobius strip?
To get to the same side.

Observations

There must be something on the Y-chromosone that drives a person to vacuum the vehicle before taking it on a trip. Those without Y-chromosones tend to think that the 1-hour trip to the friend's house isn't much different than a 15-minute trip to the grocery store. And a 5-hour trip to Grandma's isn't much different from a 1-hour trip to the friend's house. At least, not when it comes to vacuuming a van. (But, hey, if he wants to vacuum periodically, I'm thrilled! That's one less thing that I've left undone for far too long!)

The President wants to require the small-print on our credit-card bills to be in larger print. If he does, if he does require this, won't the companies need more paper for the larger print? Doesn't the use of more paper mean that more trees will suffer a needless death? Isn't it ungreen to require more paper being sent to us in our monthly bills?

When we checked into the hotel last night, I noticed a line on the charge-slip that said a complimentary copy of "USA Today" would be delivered to our room each morning. If we chose to refuse this service, our bill would be credited by 75 cents per day. I asked the clerk to clarify. "So we'll save 75 cents a day if we don't get charged for the paper that I wouldn't read anyway?" He assured me, "No, ma'am. The paper is free. You don't get charged anything for the paper." I pointed out that he would charge me 75 cents less per day for the room if I chose not to get the paper. "That's right, ma'am." I decided it wasn't worth figuring out. Just knock off the 75 cents per day and keep the paper you weren't charging me for.

Guess what? A paper showed up outside our door this morning anyway. I'm not eeeeven going to try to figure this out!

Today's Laugh

Two mathematicians, Joe and Richard, were having dinner in a restaurant in Portland, Oregon, and arguing about the average mathematical knowledge of the American public. Richard claimed that this average was woefully inadequate, while Joe maintained that it was surprisingly high.

"I'll tell you what," said Richard, "when I get back from the bathroom we'll ask our waitress a simple calculus question. If she gets it right, I'll pick up dinner. If not, you do. Okay?"

They agreed, but once he'd left, Joe called the waitress over. "When my friend comes back," he told her, "he's going to ask you a question. You should respond 'one-third x cubed' no matter what the question is. Got that? There's five bucks in it for you." She happily agreed to the gag.

Richard returned from the men's room and called the waitress over. "The food was wonderful," he started. "Incidentally, do you know what the integral of x-squared is?"

The waitress looked startled, then pensive, almost pained. She looked around the room, at her feet, and made gurgling noises. (Joe was starting to sweat.) Finally she said, "Ummm, one-third x cubed?"

Joe beamed in relief as an astonished Richard paid the check and an irritated waitress muttered under her breath, " ... plus a constant."

Today's Laugh

The square root of -1 asked pi, "Why can't you be more rational?"

Pi retorted, "Oh, get real!"



(Stolen from a t-shirt slogan that I saw on a banner-ad on the Drudge Report recently.)

Subtraction Made Easier

I hate checking the kids' subtraction when they have problems like
5006
-347.

I can do it. I am a mathematician, after all. But right now, my brain is stressed enough keeping up with the laundry and bread-baking, so checking three people's math daily without answer keys is just more effort than I wish to expend.

But you know what I discovered today? (Oh, this is SO cool!)

I'll use the above problem for an example.
Rather than having the 6 run next-door to the 0 to borrow (or "regroup" as we're supposed to say in these modern days), and then have the 0 run next-door to the 0 to borrow, and then have the 0 run next-door to borrow from the 5, and then to trickle the regrouping all the way back,...

have the 6 run-next door to the 500. Borrow 1 from the 500, and it becomes 499. And then you're all set to subtract the rest of the problem!

How easy is that?

A Capella Math

My kids linked to some of these things recently. I don't know how to post a You-Tube picture, but I can post a link to the Klein Four's song Finite Simple Group (of Order Two). These guys are mathematicians from Northwestern University, and they sing a capella. They're good singers. And they're hilarious. And they're mathematicians! "Finite Simple Group" is a song about love, but it's drenched and steeped and riddled (pun intended) with mathematical terms.


Under "quick links" on the Klein Four website, you might want to click on "Bottle Choir." They came up with a 27-note set of bottles to blow into (beer bottles, wine bottles, etc). They play Lo, How a Rose E'er Blooming in parts sort of like a handbell choir would operate, only they're blowing into partially filled bottles instead of ringing handbells. We sat here in awe last night as Gary played the song, and even applauded the guys when it was done.

Math

A friend mentioned Homeschool Math Blog which I checked out. It looks like it's got some good advice, some helpful teaching hints, and a lot of nice links. I'm going to set Maggie to some of the games whose links were posted on March 11.

And you might want to check out a few math funnies from students' tests.