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February 17, 2006

Innumeracy Watch

Soon after getting my PhD, I went out to buy my first car. The manufacturer was offering very advantageous 1.9% financing, a deal to which I naturally agreed. When I went in to sign the papers, the salesman looked in his little book, and announced, “Your monthly payment will be …,” stating a figure noticeably higher than I had figured. I reached into my breastpocket and pulled out a piece of paper. “According to my calculations, that should be … Why the higher figure, Chet?” (Slimeball car salesmen always seem to have names like “Chet.”) “Oh, that’s the … <mumble, mumble> … insurance.” “I don’t need insurance. I’ll pay the …” There was some hemming and hawing, but the loan papers were redrawn, and I eventually signed.

Which brings us to the sad case of Richard Cohen [via P.Z. Myers], who insists that being ignorant of basic algebra, far from being a handicap, is positively a good thing,

I confess to be one of those people who hate math. I can do my basic arithmetic all right (although not percentages) but I flunked algebra (once), barely passed it the second time…

Here’s the thing, Gabriela: You will never need to know algebra. I have never once used it and never once even rued that I could not use it. You will never need to know – never mind want to know – how many boys it will take to mow a lawn if one of them quits halfway and two more show up later – or something like that. Most of math can now be done by a computer or a calculator. On the other hand, no computer can write a column or even a thank-you note – or reason even a little bit. If, say, the school asked you for another year of English or, God forbid, history, so that you actually had to know something about your world, I would be on its side. But algebra? Please.

Here’s the thing, Mr. Cohen. I don’t care whether you enjoy going through life being cheated by every slimeball named “Chet” who has the good fortune to cross your path. If you’re unable to figure out that the monthly payment, mm, on a loan with Principal, PP, consisting of nn monthly payments at an annual interest rate, pp, is given by the formula1

(1)
m=P(1+p1200) n k=0 n1(1+p1200) k m = P \frac{\left(1+\frac{p}{1200}\right)^n}{\displaystyle{\sum_{k=0}^{n-1}} \left(1+\frac{p}{1200}\right)^k}

well, that’s too bad for you. And I’m sure the Chet’s of this world will be only too glad to “help” you figure out whether it’s time to refinance your mortgage or how best to save for retirement. It’s only money after all…

No, it’s when Mr. Cohen turns to commenting on matters of public policy that his innumeracy becomes a threat to the public discourse. And, most of all, it’s when he offers girls like “Gabriella” the ‘wisdom’ that Math is hard and she needn’t worry her pretty little head about it, that I really get steamed.

I have a 10 year old daughter and I’ll be damned if she succumbs to the societal cues, coming from all side, to the effect that girls are just not cut out to understand math. Wallow in your own innumeracy, if you wish, Mr. Cohen. But keep your mitts off my daughter, thank you very much.

Update:

Here’s the news article that inspired Mr. Cohen’s column. Apparently, a lot of schools are not equipped to teach algebra to their students and the students are not prepared to learn it. Ergo, it must not really be important…

Update (2/18/2006):

A reader (I have the best readers) wrote in to point out that I should have done a bit more … algebra. Using the identity k=0 n1x k=x n1x1 \sum_{k=0}^{n-1} x^k = \frac{x^n-1}{x-1} one can rewrite (1) in the more calculator-friendly form:
(2)
m=Pp1200(1+p1200) n(1+p1200) n1 m = P \frac{\frac{p}{1200} \left(1+\frac{p}{1200}\right)^n}{\left(1+\frac{p}{1200}\right)^n -1}

which, now that I think about it, was probably the form that I actually used.

You Passed 8th Grade Math
Congratulations, you passed!
Congratulations, you got 10/10 correct!

Update (2/25/2006):

You can try your own hand at some of the horrible stuff that Richard Cohen thinks “Gabriela” shouldn’t worry her pretty little head about. I’m not actually that fond of the test. Too many nearly identical questions involving a linear equation in one variable. And at least one of the questions (#6) is of the rote-memorization (“The Gobi desert is in Asia; the Sahara is in Africa.”) variety that Cohen is so fond of.

1 Yes, I think I used a computer to evaluate this expression. Computers are great for tasks like that. They are, like any mechanical aid, an extension of, not a replacement for our ability to think quantitatively.

Posted by distler at February 17, 2006 5:06 PM

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24 Comments & 2 Trackbacks

Re: Innumeracy Watch

Things like this would be hilariously amusing if it weren’t for the scary fact that give the past record of your leaders, something like this could lead to the removal of algebra from the school syllabus.

Maybe it’s time for another plunge into the dark ages with ID replacing Biology and Typing instead of Algebra. Seems like some dystpian, futuristic SciFi story happening in reality, ne?

Posted by: Yagnavalkya on February 18, 2006 12:52 AM | Permalink | Reply to this

Background

To give some background for my international readers, Richard Cohen is a nationally-syndicated columnist for the Washington Post. He is, nominally, a liberal. But, these days, that label is applied to anyone not slavishly supportive of the policies of the Bush Administration.

The LA Times news article, which prompted his column, was about the toughening of High School graduation standards in California, and the complaint that many kids are not meeting the newly tougher standards and, therefore, not graduating.

This is a problem. You have poorly-funded and poorly-run public schools, in many parts of the country. But, rather than try to fix what’s broken (which would require money), the trend has been to simply impose higher testing standards (exemplified by the No Child Left Behind Act) and ‘punish’ schools and students which fail to measure up.

Most everyone (except for Mr. Cohen) agrees that the standards are good. Liberals (evidently, not Mr. Cohen) agree that it’ll actually cost money to equip schools and teachers to enable students to meet those standards.

But, yes, there is a certain congruence between Mr. Cohen’s column and the wider assault on Science and Reason I’ve been writing about recently (see, e.g., I,II,III).

Posted by: Jacques Distler on February 18, 2006 12:39 PM | Permalink | PGP Sig | Reply to this
Read the post Saturday Morning Quick Shots: Great Minds Edition
Weblog: Decision '08
Excerpt: Some followup items, from the ‘great minds think alike’ department: Our good friend and great physicist Jacques Distler has further thoughts on the inexplicable Richard Cohen polemic against algebra… Academic Elephant ponders the c...
Tracked: February 18, 2006 10:06 AM
Read the post What Is the Value of Algebra?
Weblog: Chris Breisch
Excerpt:
Tracked: February 18, 2006 1:03 PM

Re: Innumeracy Watch

For some reason, I am getting your blog as text/html in Firefox 1.5. This started today I think.

Posted by: Zack on February 19, 2006 2:16 PM | Permalink | PGP Sig | Reply to this

Rewrite rules

Should be fixed now. You may have to clear your cache to see the changes, though.

Posted by: Jacques Distler on February 19, 2006 3:19 PM | Permalink | PGP Sig | Reply to this

Re: Innumeracy Watch

“anyone not slavishly supportive of the policies of the Bush Administration”

Jacques, if you liberals ever plan on winning a national election again, you must first get over this traumatized self-pityful attitude. What the heck happened to Democrats? They weren’t always the whiny tree-hugging hippies I see these days. I think the Democrats need to make peace with people like Zell Miller and many more of his kind are needed. Then, maybe, the Democrats could be taken seriously once again.

Posted by: Michael on February 20, 2006 12:49 PM | Permalink | Reply to this

Zell

I think the Democrats need to make peace with people like Zell Miller and many more of his kind are needed.

Needed for what?

Cheap thrills at the Republican National Convention?

Posted by: Jacques Distler on February 20, 2006 12:59 PM | Permalink | PGP Sig | Reply to this

Re: Zell

Miller is a life-long democrat and continues to be one. For decades there was no conflict between him and his party. The problems started when liberals in our country began redefining themselves through hatred or dislike of others, rather than real issues. Miller is one of the few who didn’t go along with the trend. I believe he is therefore a natural authoritative figure the democratic party ought to turn to once they realize their demise with Ted Kennedy and Howard Dean.

Personally I am glad that the Democrats aren’t winning, but I am slightly concerned they are making it too easy. You can’t win just by hating Bush and being “foragainst” every other issue. It doesn’t help either that Dean loses his temper every other week on national TV and screams “YEEHAW” like an orgasmic puppy. We do need a healthy two-party competition and this just isn’t it.

Posted by: Michael on February 20, 2006 7:14 PM | Permalink | Reply to this

Re: Zell

The problems started when liberals in our country began redefining themselves through hatred or dislike of others, rather than real issues. Miller is one of the few who didn’t go along with the trend.

Did you watch the Republican National Convention?

Posted by: Aaron Bergman on February 20, 2006 7:18 PM | Permalink | Reply to this

Re: Zell

Yes, I did. Why are you asking?

Posted by: Michael on February 20, 2006 8:21 PM | Permalink | Reply to this

Re: Zell

No reason. Just curious.

Posted by: Aaron Bergman on February 20, 2006 8:28 PM | Permalink | Reply to this

Once a Hippy…

Miller is a life-long democrat and continues to be one.

The Zell Miller who introduced Bill Clinton at the Democratic National Convention in 1992 is not the same man who addressed the Republican National Convention in 2004.

I suggest you watch a video of his spittle-flecked rant at the RNC before you talk about liberals “redefining themselves through hatred or dislike of others, rather than real issues.”

For decades there was no conflict between him and his party.

Miller’s swing to the extreme right started in 1994, after he nearly lost his bid for re-election as Georgia’s Governor.

I’m probably treating your comments with greater seriousness than they deserve, but …

What the heck happened to Democrats? They weren’t always the whiny tree-hugging hippies I see these days.

Poppycock. For as long as you can remember, they have been labeled as “whiny tree-hugging hippies” by your Republican colleagues, who will continue to label them as such, pretty much whatever the Democrats do.

But, since you seem to disagree, maybe we can narrow down what the heck went wrong, and when. Which was the last Democratic President you consider not to have been a “whiny tree-hugging hippy”?

  • Clinton?
  • Carter?
  • Johnson?
  • Kennedy?
  • Truman?
  • FDR?

Extra credit if you can pin down the exact date when the Republicans became the party of bible-thumping kleptocrats.

Posted by: Jacques Distler on February 20, 2006 8:30 PM | Permalink | PGP Sig | Reply to this

Re: Once a Hippy…

“The Zell Miller […] in 1992 is not the same man [… as] in 2004.”

You see, we disagree here a bit. I think the man has been very consistent. At some point he just had enough of it, and that’s why I suggest to take him seriously.

“I suggest you watch a video of his spittle-flecked rant”

I saw it live and many times afterwards. Remember? It was me who mentioned him first.

“I’m probably treating your comments with greater seriousness than they deserve”

Well, I appreciate your serious answer. Why wouldn’t you take me seriously? Because I have a different political conviction than you do?

“For as long as you can remember, they have been labeled as “whiny tree-hugging hippies””

Maybe so, but that doesn’t mean that *I* have done that.

“Clinton? Carter? Johnson? Kennedy? Truman? FDR?”

I didn’t vote for Clinton and I don’t share the common enthusiams for him, but I respect his performance (as president, not his other occupation). Carter was and is a disaster. Did you hear about how he turned the funeral of Martin L. King’s wife in to a partisan event? He broke a longstanding rule respected previously by both parties that a former president doesn’t publicly besmear a sitting one. The ones before him all deserve some respect. JFK showed that he was tough as nails in the Cuba crisis (though he also takes some blame for letting it happen in the first place) – tough with the Russians and tough with some of his own hot-headed military commanders. Can you imagine Kerry and Edwards handling something like the Cuba crisis? The idea is really scary: world peace at the mercy of a sissy boy and a born-again dessou model.

“Extra credit if you can pin down the exact date when the Republicans became the party of bible-thumping kleptocrats.”

Thanks, Professor, anything for an A. The correct answer is: It all began when Bush illegally won in 2000.

More seriously, I don’t believe in God. I voted for Bush because he is a “straight shooter” (Miller @ the RNC) who isn’t afraid of saying who he is and what he stands for. And I agree with most of his policies.

Posted by: Michael on February 20, 2006 9:41 PM | Permalink | Reply to this

Re: Once a Hippy…

“The Zell Miller […] in 1992 is not the same man [… as] in 2004.”

You see, we disagree here a bit. I think the man has been very consistent.

Then I think you need to go back and read his 1992 DNC Keynote Address (I don’t think there’s a video available).

Can you imagine Kerry and Edwards handling something like the Cuba crisis? The idea is really scary: world peace at the mercy of a sissy boy and a born-again dessou model.

I count my lucky stars the Cold War ended before the current crew started screwing around with matters of National Security. If Bush/Cheney had been in charge during the Cuban Missile Crisis, we would all have been incinerated in a full-blown nuclear exchange with the Soviets.

Luckily, the world we live in today is much safer than the one I was born into. The damage GWB can do to our National Security is much more limited.

Thanks, Professor, anything for an A. The correct answer is: It all began when Bush illegally won in 2000.

Ah. I see you’re young…

Nope. You can’t understand anything about the current state of the Republican Party without going back to Nixon and the “Southern Strategy.” Most of the Party’s subsequent history: Ronald Reagan, Newt Gingrich and the 1994 midterm elections, and — yes — the lamentable George W. Bush, make little sense otherwise.

And I agree with most of his policies.

Policies? Or tactics? There’s a difference. This Administration doesn’t have “policies” in a sense even vaguely recognizable to any previous Administration.

Ask Bruce Bartlett (of the Reagan Administration) or John diIulio or Paul O’Neil or Christine Todd-Whitman or …

Posted by: Jacques Distler on February 20, 2006 10:51 PM | Permalink | PGP Sig | Reply to this

Re: Zell

You’ve got to be kidding. Let me tell you: speaking as a gay man I have put up with more than my share of hatred from the right. Some of it now codified into law. If you think your side of the fence is some paragon of inclusiveness and respect, you are sorely, sorely mistaken.

Posted by: Bryan Van de Ven on February 21, 2006 11:17 PM | Permalink | Reply to this

Re: Zell

Sorry to hear that you have to put up with a lot of hatred because of your sexual orientation, Bryan. I hope you are being for real when you talk about hatred, and not just alluding to the fact that a majority of Americans is opposed to the concept of gay marriage. I’m saying this because it appears to be the only major issue concering homosexuality discussed publicly by the Bush administration.

Posted by: Michael on February 22, 2006 10:59 PM | Permalink | Reply to this

Re: Zell


I’m saying this because it [marriage] appears to be the only major issue concering homosexuality discussed publicly by the Bush administration.

http://www.americanchronicle.com/articles/viewArticle.asp?articleID=5627

for example. Though I suppose it’s nice to see the US and Iran finally seeing eye to eye about something.

Posted by: Matthew on February 23, 2006 6:27 AM | Permalink | Reply to this

Re: Zell

(Googling My Son in the July 2008) Michael and others: I am Bryan Van de Ven’s proud father. His family is supportive of his choices and orientation in life. We respect his sincerity, genuine intellect to speak on a variety of aspects he faces in his life because of his love, tolerance, self - discipline, pride, and appreciation for life which has been molded in him in our family. Our family complexity is multi - racial and talented as well. We are supportive of our son who exudes tolerance through his intellect and growing wisdom on many aspects and on platforms of thought, music, mathematics, physics, and philosophy. We wonder why the energy of a bigoted, clustered “rightists” and “leftists” are not marshaled more on the ignorance of their fears and on the perversions of unlawful acts of their “own” rather than on those of others who have a right to be different. I have a “pride, respect, and love” for my son that matches not many others under today’s trying times and circumstances. I have a married daughter who admires, loves, and appreciates her brother for all the right reasons no matter what. My wife and I feel the same even though we do not know really the how or why he is the way he is. We understand that we are all just “are” ……. here to live, love one another in return, and be the best we are no matter what creed or philosophy we follow grow up in. To get to know him and not judge him I feel is the real virtue and purpose of man / women - kind as a member of humanity and our societies. I do pity and feel ashamed of the exocentric, self - serving political, morale, and religious views of the zealots in today’s society who are not unlike those in the past who have scrambled what it “is” “ to be” “ right and wrong” for ill gotten gain and/ or out of ignorance. It has lead us as created human beings to viral hatreds to the extent that human rights, freedoms, and reason for treating people with respect, decency, and kindness are thrown out the door with the dish water “ in the name of” things insane. Why not live and let live, by getting a life which contributes to betterment of the created human condition whether it prepares one for the future and/or the thereafter as one believes?

Posted by: David Van de Ven on July 24, 2008 7:14 AM | Permalink | Reply to this

Re: Innumeracy Watch

I have a 10 year old daughter and I’ll be damned if she succumbs to the societal cues, coming from all side, to the effect that girls are just not cut out to understand math. Wallow in your own innumeracy, if you wish, Mr. Cohen. But keep your mitts off my daughter, thank you very much.”

Yay! Thanks for posting this, Jacques. I’m just starting out in informatics, and the “don’t worry your pretty head about it” attitude crops up a lot, even among my lecturers, whose job it is to worry my pretty head about it. Best wishes to L with her math. Give her my regards.

–Irrational. (aka Quibbler)

Posted by: IrrationalPoint on February 20, 2006 3:41 PM | Permalink | Reply to this

Re: Innumeracy Watch

Oh, I dunno, Jacques. If people understood algebra, or at least the concept of exponential growth, then we wouldn’t have tens of millions of people sitting around making the minimum payment on their credit card debt. And then all of our fine financial institutions would be cut off from one of the most lucrative legal businesses in existence. Won’t somebody think of the bankers?

On a more serious note, I am all in favor of teaching kids algebra, but it’ll all fly out of their heads unless they take calculus. You don’t really learn algebra until you flex your algebraic muscles in calculus. You don’t really learn calculus until you flex your calculus muscles in college-level classes. And so on.

Posted by: Evan on February 21, 2006 11:39 AM | Permalink | Reply to this

An Old Joke

You’re a Mathematician? Wow! Math was always my worst subject. I mean I did OK in elementary school and in high school and in college. But K-theory completely blew me away!

Posted by: Jacques Distler on February 21, 2006 1:51 PM | Permalink | PGP Sig | Reply to this

Re: Innumeracy Watch

#2 on that test isn’t great, either. Some authors use “whole number” to mean integers rather than “natural numbers”. And “natural numbers” itself sometimes includes zero, sometimes not.

Posted by: Aaron Bergman on February 25, 2006 11:37 PM | Permalink | Reply to this

Statistics

The thing that bugged me about #6 is that, unlike “mean”, “median” and “standard deviation” which crop up all the time, “mode” is almost never used. Asking about it is like Mr. Cohen’s “Where is the Sahara desert?” question: nearly perfectly useless.

On the other hand, testing whether people know the difference between “mean” and “median”, and when one or the other is the relevant statistic to look at, is testing the sort of knowledge incumbent on an educated citizenry.

Posted by: Jacques Distler on February 26, 2006 12:11 AM | Permalink | PGP Sig | Reply to this

Re: Innumeracy Watch

Natural numbers are the positive integers. Whole numbers are the non-negative integers. Speaking from the viewpoint of a fairly well-educated high-schooler, the real problem with math is when idiots like Cohen are in the teacher’s position. His attitude towards teaching the class would be, to quote John Nash in A Beautiful Mind: “This class will probably be a waste of your time and, what is infinitely worse, mine.” Of course, the circumstances are completely opposite: one a mathematical genius, the other a mathematical non-entity.

Too many teachers in middle and high schools these days do not have the requisite training: 27% of high school math teachers don’t have a mathematics major or minor, and 70% of middle school math students have out-of-field teachers. These are people who believe the dangerous falsehoods spread by the innumerate: “It’s all about having the mathematical mind,” for starters. To quote John Allen Paulos in Innumeracy: “People believe that there are mathematical minds and nonmathematical minds, and the former always come up with a solution instantaneously while the latter are helpless and hopeless.” Man, do I want to give “people” (aka Cohen) a good smack upside the head. Can’t blame them, though: they’re so desperate to find out why they have trouble with math and not implicate themselves in the process that they look past the real culprit, which is giving up when the going gets tough.

How did the comments wind up at Red vs. Blue from a Cohen-bashing? Honestly, everything turns into a political argument these days.

Posted by: Drinkwater on March 16, 2006 7:40 PM | Permalink | Reply to this

Re: Innumeracy Watch

Bonjour Mr Distler,

In the “Some Related Entries” list you should add
“Statistical Innumeracy” (September 29, 2003), your post about cancer test results, sensitivity and false positive rate…

Posted by: Raymond Lutz on February 14, 2010 1:18 PM | Permalink | Reply to this

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