The Brotherhood of Pythagoras

Simple questions: How many people do you know who don’t know that ¾=.75=75%? Or that all of them are fractions and represent a portion of a solid, whole entity of many parts?

I wonder about this when I hear it argued that, for example, because there are more illegitimate children born to white women than to black women, that the phenomenon is a worse problem among whites. Do some commentators not understand that 29% of 106 million is going to amount to a larger whole number than 70% of 17 million?*

Over at Avery’s and Cobb’s, the discussion for a bit has been about Math and the general consensus of its “difficulty.” (Tangent: I’ve often said that learning math is easier than learning foreign languages, in that the rules don’t change and that there are a finite--usually--number of answers to a given equation--or translation, to continue the metaphor.)

Cobb says of his sojourn in a “bonehead” university math class:

I learned everything I was supposed to learn since arithmetic in two semesters.

(No worries, bro. I had to take a “bonehead” science course. I took the path of least resistance: biology. Got an ‘A,’ but in the regularly bio class I received a ‘B’; and the professor was being generous.)

And Avery, who has taught math to elementary school students, says this:

Here's my take on the reasons behind our [American] lag: we accept mathematical illiteracy. It's not uncommon to hear people say, "I just don't do math" or "I never was any good at that." And I'm not talking about kids here, I'm talking about adults; not them jokers standin' on the corner, either. I'm talmbout college-edumacated; experts in their fields...will tell you that they aren't good at math and don't fool with it on those grounds. And most of us, even if we don't like it, we'll at least accept it. Now if somebody tried to say that about reading, they'd get blasted out of the water. Mathematics is just as fundamental as reading.

In my formative years, I was raised my great-aunt—the one I talk about all the time--and great-uncle (RIP). Neither had much education beyond high school. However, they did something very simple with regard to my math education, which has had a rippling effect on how I’ve viewed math since.

When I was four, they start me off with addition and subtraction charts; the next chart was a multiplication chart; the next one, division. Now I’m not going to sit here and say that I figured out immediately that 12+12+12+12+12+12+12+12+12+12+12+12 amounted to the same as 12x12. The theory, however, was that, through repetition of the chart content, I’d be able to parrot that 12x12 equals 144 at the drop of a hat and figure out what it meant later. What my aunt and uncle did is called Building a Foundation.

Oh, I looked like the kindergarten genius alright, but I’m not so sure. All over the landscape, I see little kids of all races commit to memory all manner of foul language and “charming” rap lyrics. From that, it could be concluded that the GIGO axiom is alive and well and living in many American homes, and, unfortunately, in all too many black and latino homes. And, conversely, there could be all manner of “little geniuses” out there waiting for someone to impart the most basic of math literacy to them.

Sure, it’s easy for someone with no offspring to tell others how to raise their children, but, dang, it ain’t that hard to read “Little Red Riding Hood” to your kids--or whatever the latest tomes are for the pre-school set. And, it certainly isn’t difficult to tell them that 1+1=2 or that 81/9=9 and everything in between. All of the implications of those equations will usually follow.

Maybe I was just blessed. However, that doesn’t mean that other children can’t get a little (or a lot) of that particular blessing as well. Caring and time are all it takes.

More from La Shawn.

BTW, here’s a site that I’ve been looking for an excuse to publicize: Who Are The Greatest Black Mathemeticians?

*Estimates of the female population percentage of black and white Americans, assuming that it is 50% for each.

UPDATE: Not sure how to calculate (or, rather, don't feel like calculating) the number of black and white women existing in the US against the number of illegitimately births in 2000--404,000 and 904,000, respectively. But there are the numbers; from the Census.

Comments

[AH·C]

Reminds me of the set of 45s records that had the all of the +,-,/&* tables of 1 - 12 put to music. Tho it's been over 3 decades, a lot of them come right to mind as if it was yesterday. Talk about being embedded deep in my mind

I'd love to find something similar for my kids, they'll thank me when answers just pop in their mind automatically. Heck, Hooked on Phonics works for me as well. :)

[caltechgirl]

Yes! You're totally right. Math and science illiteracy (innumeracy) are too widely accepted in this country. People have the perception that they'll never need math or science in their lives, so it doesn't matter. If they need either, they think there will be a computer there to do it for them. Yet math and science education not only teaches math and science, it teaches problem solving skills and rational thinking that ARE necessary for the rest of your life.

Ironically, with manufacturing etc. jobs leaving this country at such a high rate, the vast majority of newly available jobs will require some math or science experience. The job force won't have those skills if they continue to be innumerate.

[baldilocks]

Thank God for growing up in the pre-calculator Age!

[Randy K]

When I was in Junior High I had a Math Teacher who as punishment would assign the multiplication tables when you miss behaved or didn’t do your homework. You started at 1x1 and continued until 12x12… for the first week. Every week after that it increased by one factor, i.e week 2 13x13, so by Christmas it was around 26x26, and then would go down by one after Christmas break. Since I had a tendency not to remember to do my homework I did this… a few times… ok… 20 or so time… a year… for 3 years… needless to say, when I went to High School I was in the Honors Math program. To this day I have few problems with multiplication and division. Smart Teacher I’d say…

[AH·C]

Sometimes I get really frustrated with the younger gen in my office when they botch up things like a simple email message or costing out a proposal. Arrgh, this is what the public school is unleashing upon us, people condemned to a lifetime of unrealized potential as better paying jobs are siphoned off elsewhere.

Fortunately, some take full advantage of the mentoring, others I'm afraid will end up in some deadend job once they get laid off. Flipping burgers or building mobile homes in a factory comes to mind -- mundane & repetitive.

Heck, I even have a guy that can't even drill into sheetrock to hang a demarc board w/o breaking a bit and brags about taking home-ec because that's where the girls were at. No matter how many times I go over with him on how to fill out his timesheet & expense reports, he still doesn't get it. And he's aiming for Senior Field Technician? Sigh.

[LarryConley]

I've noticed something similar with reading literacy. Its not that these people CAN'T read (This being on a bus the person was obviously reading a book.. or just turning pages which I consider unlikely). But when they get up to get off the bus.. they somehow miss the sign RIGHT IN FRONT OF THEM that says wave hand under the green light (motion sensor obviously) to open door. This is written in Inch high lettering with an arrow pointing up at the light. It is isn't that they CANNOT Read.. or do Math...I think it just never occurs to many people to apply those skills to what is going on around them.

Then there are people who need a calculator to figure out how much they owe for a $9.99 meal + tax and tip (8% tax 15% tip for delivery added together since where I work we don't tip on the tax portion of takeout)...
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Answer is actually $12.50 since we don't use anything less then quarters when ordering out :)

[Solomon]

Are we really going to get serious about educating our young? I'm not talking about programs or grand speeches on the subject. I'm talking about a fundamental change in how we do things here in America.

We talk all that stuff about "rap lyrics" being remembered over classwork but please, many parents just glad the kiddos are out the damn house (also rap lyrics are being spouted out across all races and ethnicities here). I'm 33 years old. Still young enough to "be down" and old enough to "know better". And I REFUSE to just talk about the good ol' days. I want to fix the mess.

First of all, many of you idealogues need to back the f*** up from education. ALL OF YOU. Left, right, sideways, slantways, whatever. A consensus need to be developed on what we need to teach. No ifs, ands, or buts. We adults need to be ADULT ENOUGH to agree on this consensus. The reason why the kids are getting the "ass end" cause many of we adults lead with our asses and not with our brains.

[Silicon Valley Jim]

I’ve often said that learning math is easier than learning foreign languages

Turns out that it depends how old you are. Very young children (less than about three) learn foreign languages as if they weren't foreign; an American boy being raised in an English-speaking household with, say, a Korean-speaking grandmother will use the same part of his brain to understand Korean as to understand English, and the same part of his brain to speak Korean as to speak English (the location in the brain that understands is different from the location that produces speech). Neuroscientists have verified this. It also accords with my experience, in which I sometimes switch from my good English to my poor Spanish or Korean, etc., with a child of this sort, who appears not even to realize that there are two languages involved. Our brains use different locations to understand and produce speech of languages learned after age three. So, prior to age three or so, learning a foreign language is easier (it won't even be perceived as foreign). Afterwards, it's harder than learning mathematics.

It's astonishing to me that many of those educated in the humanities seem to be proud of their ignorance of mathematics, and also that many less-educated folks talk as if knowledge of mathematics implies less knowledge of other things, as if this were a zero-sum game.

Not that the quality of the English spoken in America is anything of which to be proud, either.

[baldilocks]

Solomon: (also rap lyrics are being spouted out across all races and ethnicities here)

I *did* say that.

[baldilocks]

Jim: I learned my foreign languages fairly easily while in my twenties, but I learned math earlier (obviously). The learning methods are the key (in both subjects areas).

[baldilocks]

Solomon: My aunt and uncle found a practical method that worked. Sorry you don't want to read about it.

Since you are the one with children--I have none--I will bow to your greater experience in child-rearing.

However, I will back up off of nothing that I have an opinion about. Not for you or anyone else.

Just so we're clear.

[Ed]

Sasha Castel's blog has a humorous comment about election challanges to the tune that if lawyers could do math, they would have gone to med school instead of law school.

[Solomon]

Got a little ahead of myself on the rap music thing, Juliette Sorry 'bout that.

Solomon: My aunt and uncle found a practical method that worked. Sorry you don't want to read about it.

My comments were in general, Juliette. Yes, your aunt and uncle obviously did a fine job with you. But we, as a society, don't approach education like your aunt and uncle do. We get caught up in idealogy and theology. We end up agreeing to disagree in educational issues so things just sit and fester. I'm tired of that. And I WILL NOT sit here and blame the youth for all the failings like a rising number of adults do. Youth learn from we adults and we frequently fall short. Especially in education. Less government involvement, more government involvement. Vouchers. Charter schools. BLAH! How about we deal with the meat of the issue: we just not educating our children right.

However, I will back up off of nothing that I have an opinion about. Not for you or anyone else.

You better not. I don't read this blog for soft azz opinions and water-down rhetoric. You start doing that and we gotta go a few rounds in the ring. ;)

And I'm dead serious about the idealogues. We will get nowhere in educating our children properly if idealogy going to play a big part (especially in public education). I don't have the time nor patience to argue the fundamentals of any and every theology as it applies to our young folks education.

[Jason Bontrager]

AH-C said "I'd love to find something similar for my kids" regarding musical math tutorials. Such things apparently do still exist. A quick Google search found this: http://www.songsforteaching.com/mathsongs.htm (Sorry I don't know how to make links active in these comments). I don't know if it's quite what you want, but I'm sure there are other examples out there.

[liz]

As the proud parent of 3, count 'em, 3 kids--

1. Juliette is talking about the rote mastery of math facts, or arithmetic. Addition, subtraction, multiplication tables (you can add division tables if you like)

2. Arithmetic raps:

http://www.walmart.com/catalog/search-ng.gsp?search_constraint=COMBINED_AUTHOR%3A3920&search_query=Rock+N+Learn

2. Rote mastery has been out of fashion for two or more decades. It is an ideological flag to fall in behind, that "rote drill is boring" and "will turn kids off". As a result, we have kids who have to count on their fingers to add 8+7 and aren't really sure if it is the same as 9+6. The mastery of math facts makes the grasp of all higher mathemathics so much easier.

I mentioned over chez Cobb mental maturation and the rapid acquisition of math. The short version is that little kids (under about 10) can and should memorize math facts, but there are neurological reasons that understanding the division process, for example, waits until the kid is over 8 or 9.

3. There is the whole teaching of reading. If you don't have kids and aren't interested in education (in the general sense) you have missed the "whole language" debacle.

this is a good introduction

http://my.execpc.com/~presswis/phonics.html

There is a reason that the greater percentage of convicts are illiterate--lousy teaching, not lousy learning. Reading without a great deal of automaticity (which very very few children can get from whole language instruction) remains laborious and exhausting.

4. I believe that lower SES kids have been systematically short-changed, not in a conspiratorial way, but because of the confluence of factors having to do with underfunded schools, less experienced teachers being shunted into lower performing schools, and the demands placed upon schools in lower SES areas.

5. Yes, you ought to read to your kids but you should also know to look for the signs of a specific language disability so your kid, no matter how many books you read, will not learn to read without specific direct instruction.

http://www.interdys.org/servlet/compose?section_id=5&page_id=95

[B. Durbin]

You can still get the Schoolhouse Rock animations— in fact, you can get the whole run plus extras in one DVD package.

I seem to recall some studies that show how our brain changes during various stages of childhood; the upshot is that learning by rote is the preferred method for small children because that's the way our brains are set up at that time. You gradually switch over to other forms of learning so that the rote stuff is done by the time they hit puberty. That's why you do fill in the blanks in third grade but essays in high school.

It bothers me that my college required English 101 (how to write) for all incoming froshlings regardless of ability (I took the one tiny loophole out, and it WASN'T my 5 on the English Language AP.) They automatically assumed that incoming students were incapable of constructing paragraphs and papers (the description alone was enough to make me blanch.) My high school, private college prep, had a class on writing term papers that you took either freshman or sophomore year, and every paper you wrote after that class had to display a level of competence commesurate with the information imparted by that teacher, and he was a stickler.

Children rise or sink to expectations. I will have high ones for my children, rather than just assuming that "they can't possibly do that."

(One more thing: on the subject of math, I highly recommend that everyone try to get to basic calculus, because far from being as scary as advertised, it's the math that makes the other maths make SENSE!)

[Cassandra]

Mathematics education is SO important, yet we don't stress it enough. Math teaches one to THINK: to reason one's way through a difficult problem, organizing the information at hand and then selecting the rules that can be used to solve the problem.

It teaches a methodical way of problem-solving that is extremely useful when intuition fails: something that I as an intuitive thinker with an extremely good memory was slow to see the value in.

But to be a truly formidable thinker, you have to be able to reason your way to the right answer if memory or intuition won't take you there.

And I couldn't agree more with B. Durbin: Basic Calc is actually EASY! It's the ALGEBRA that trips up most beginning calc students.

I hated math in high school, yet as a returning adult I tutored college algebra, probability and stats, and calc. You can learn this stuff as an adult - I did it in my 30s. In fact, the discipline you gain as an adult makes it far easier, I think, to master the subject matter.