hundreds or thousands or millions?

As I've said innumerable times, I'm no good at math. Things went so badly for me in high school math that I only passed it in the 11th grade because my teacher (an eccentric genius, if ever there was one) allowed students to supplement their exams with offbeat historical tidbits for "extra credit" -- and he was nice enough to announce what these questions might be the night before the exam, which gave me time to study history instead of math in the hope that I might be able to pass. Fortunately, in the 12th grade I was able to avoid math entirely, and I have ever since.

I say this not because of any false pride in my mathematical shortcomings, but because I don't want to come across as some sort of elitist condescending prick who ridicules people who lack basic math skills. However, I can do basic arithmetic, and I know certain things almost intuitively. Like, I know there's a huge difference between 118 and 10,000. I also know there's a difference between "dozens" and "hundreds" and "thousands" and "millions." Some of the accounts I have read make it clear that there are people who either don't know the difference or don't care. (Am I an asshole for caring?)

To not know because of ignorance is at least somewhat excusable. For example, I've forgotten my algebra and my calculus, and I was never any good at either -- especially the latter. This caused me problems with the SATs and other standardized tests.

I suppose you could argue that it should have. But these days, math is getting harder and harder to fail, so maybe I should start over.

In Philadelphia, a principal's practice of changing failing math grades given by a teacher has attracted local attention:

Beginning this school year, principals will have to justify grade changes and report them to their regional superintendent, said Paul Vallas, the district's chief executive officer.

"It should discourage people from changing grades for no legitimate reason," he said.

Vallas announced the change after The Inquirer raised questions concerning retired Edison High School math teacher Alan Soslow, who complained that the Edison principal overrode nearly 60 of the failing grades he gave students during his last four years of teaching, ending in 2003.

"This has to stop," Soslow, who taught math for 35 years, said of the grade-changing. "It's very degrading. It's fraud."

Principal Jose Lebron believed that the low grades were the teacher's fault:
Lebron, in letters to Soslow notifying him of the grade changes, also cited the "exorbitant amount of failures" and wrote "obviously, there is something definitely wrong in terms of your instructional approaches and techniques, grading procedures and overall programmatic objectives." He said he received numerous complaints from parents about Soslow's teaching style.

However, Soslow got only positive marks on his written teacher evaluations - which he has kept - and he maintained that he only sought to uphold high standards in his classroom.

...

Soslow, who spent his entire career at Edison, had proof to back up his marks. He kept his grade books and other detailed records, showing a reporter that he failed students who continually scored low on tests, had excessive absences, or refused to do the work.

There were classes in which he failed half or more of his students - which is above the districtwide average.

About 20 percent of district high school students failed core subjects last year; the highest failure rate, nearly 25 percent, occurred in math.

District officials asserted that any teacher who fails half a class should analyze his or her practices and find ways to help more students succeed. Principals also should be questioning and supporting teachers with high failure rates, said Gregory Thornton, the district's chief academic officer.

While a high failure rate in math can be blamed on a teacher, depending on the school, it's also quite possible that it might be the fault of the students who fail. Unlike other subjects, math (whether you like it or not) is pretty objective. If there are 100 questions on a math test, and you get less than 60 of them right, you fail. Unless the test is graded on a curve. (Or unless you have a sympathetic teacher who allows "bonus" questions involving obscure historical trivia....) But even then, someone has to fail.

Should failure not be allowed?

According to Joanne Jacobs, a problem in Philadelphia is that teachers themselves fail:

Philadelphia's middle school teachers are having trouble showing they're qualified [Sorry that Inquirer link doesn't work.] to teach their subjects. Many are former elementary teachers who aren't subject-matter specialists. Half of the "district's 690 middle school teachers who took exams in math, English, social studies and science in September and November failed," reports the Inquirer. Nearly two-thirds of middle school math teachers failed the exam.

The district will offer test prep classes to teachers who have to retake the exams, and will try to hire people who know math to teach math.

But isn't that a little unfair?

I mean, if the goal is to prevent success, first we must prevent failure.

And it really shouldn't matter whether the "correct answer" is that there are, say, hundreds, or thousands, or millions, of dead bodies in a given factual scenario. In life, there are no "correct answers." Math should be intuitive and relevant:

The NCTM [National Council of Teachers of Mathematics] is also excited about "constructivist" teaching methods. Purists will argue about the meaning of this term, but this philosophy is associated with the following beliefs:

1. Belief that children must be allowed to follow their own interests to personally discover the math knowledge that they find interesting and relevant to their own lives.
* Rejection of the concept of a common core of basic math knowledge that all children should learn.
* Rejection of the traditional process of math education whereby teachers ask questions and present problems which have been carefully chosen to lead students to discover teacher-targeted math knowledge.
2. Belief that knowledge should be naturally acquired as a byproduct of social interaction in real-world settings.
* Devaluation of classroom learning and learning from books.
* Emphasis on knowledge that is needed for everyday living.

This information comes from William G. Quirk, Ph.D., who explains further why the NTCM doesn't want traditional math to matter:
If you buy "traditional K-12 math is obsolete", the NCTM has you set up to accept their strategy for replacing traditional K-12 math content:

* Make math appreciation the primary goal, not building a remembered knowledge base of specific math facts linked to specific math skills.
* Emphasize what can be done with calculators and computers
o Discard topics that don't easily fit.
* Emphasize social goals and psychological considerations.
* Substitute general content-independent "skills" for genuine math knowledge.
* Still call it math and still use traditional math names, but with entirely different meanings for "arithmetic", "algebra", and "geometry"

If he's right, then appreciating how many dead bodies there might be is a highly personal process. To one person, there might be hundreds. To others, there might be thousands, and depending on social skills and psychological considerations, still others might see the answer as millions.

Aren't higher numbers more relevant to what's going on in the world? If the goal of math is to make things relevant, then the numbers have to be higher, because otherwise, people might not care as much.

What this means is that the hangup that bloggers like me have with finding accurate numbers reveals an educational deficiency which is being remedied.

I should be glad. Because it means my being bad at math really wasn't any shortcoming on my part. And my hangup about it only reflects the wrong social attitudes of the times in which I grew up.

This is all changing.

We should be glad.

AFTERTHOUGHT: Might it be time to stop using judgmental language in describing the different answers people get to complex human math problems? Words like "exaggerated" strike me as judgmental if not reactionary.... Should they even be part of our, um, vocabulary?

MORE: Is feeling good is more important than numbers? Charles Krauthammer came up with a quote from Mayor Nagin about priorities:

Mayor Ray Nagin has announced that, as bodies are still being found and as a public health catastrophe descends upon the city, he is sending 60 percent of his cops on city funds for a little R&R, mostly to Vegas hotels. Asked if it was appropriate to party in these circumstances, he responded: "New Orleans is a party town. Get over it."
Cool.

(See ya later, alligator!)

posted by Eric on 09.09.05 at 08:03 AM







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Comments

I inherited a natural math aptitude. However, I always disliked the repetitious homework and I intuitively questioned why very many people had to know how it worked in order to use it. Split the class in two and let the math nerds learn how it works and have everyone else learn how to get the right answer. These are two different things, in this day and age of computers.
Caught where there is not computer handy and you need a math answer? Get someone on your cell who has access to a computer. Next question.

notherbob2   ·  September 9, 2005 1:10 PM

Why, under these new progressive standards, even I could be hired as a math teacher! Will wonders never cease?

"....progressive, permissive, regressive education," as H. L. "Bill" Richardson called it. I'm against it. I'm Conservative.

As that great architect Ralph Adams Cram put it so well: "Inequality is the first law written in the Book of Man"

And irony after that. Wicked Wanda, the most brilliant physicist on this planet, favors permissiveness because it leads to anarchy and chaos. Holy Dawn got "D's" in math and science because, she worked hard, she was too dumb in those realms (though she excels in athletics and in music, just as her holy Negro wife Norma excels in painting and sculpture), yet she favors discipline because it leads to Divine order and holiness.

My twin brother Dave is one of those men of ability, the men of the mind, whom Ayn Rand championed, yet he has never read a word of Rand. Here I am, one she would dismiss as an irrationalist mystic, and yet I read her all the time.

Dave was a genius in math and science. He was doing trigonometry back in 5th grade. I got "D's" and "F's" in math because I was both dumb and lazy. In 1st grade, I turned in an empty math workbook -- and explained that I wrote it in invisible ink! In 6th grade, our teachers divided us up into the smart group (Dave and his friends), the average group (most of the other kids), and the dumb and lazy group at a table in the back (me and a few other naughty kids, we had a lot of fun). Hierarchy! That is the Divine order.

I took a lot of remedial courses in arithmetic, and sort of self-taught myself basic math on my own, enough to count my money. While taking a refresher course in mythology at Olohne College in Fremont, CA, from Mr. J. Scruggs (the best teacher I ever had in any subject), I found myself doing the exact reverse of what I had always done throughout grade school -- I did a math problem on my own just for the fun of it, i.e., calculating how many warriors there are in Valhalla by multiplying the number that will pour out from each door when Heimdall blows his trumpet at the Ragnarok. Somewhere I have that paper but I'm too lazy to dig it up right now.

At least I know that 2+2=4, no matter what Big Brother says, and that 6,000,000=6,000,000, no matter what Holocaust deniers say. Unfortunately, I can't say the same for the kids coming out of today's schools, who will be ripe for any propaganda from professional liars. I'm against that.

"At least I know that 2+2=4, no matter what Big Brother says, and that 6,000,000=6,000,000, no matter what Holocaust deniers say. Unfortunately, I can't say the same for the kids coming out of today's schools, who will be ripe for any propaganda from professional liars. I'm against that."

"Figures don't lie -- but liars sure do figure."


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