On last month's post about the public innumeracy of a Florida school board member, Tom Singer posts an update, which includes a link to a follow-up at the Washington Post blog that started the whole thing. In the course of rounding up reactions to the original, the author, Valerie Strauss, writes:
In fact, there were a lot of readers who responded to the posts saying exactly what Roach suggested: He's been out of school too long. Others questioned why a successful businessman couldn't pass 10th-grade math. (I looked at FCAT 10th-grade questions and couldn't do them myself, but math has always been a crucible for me.)
I've been thinking about the general question of societal attitudes toward math and science again, for unrelated reasons, and this continues to be a *headdesk* moment for me. If you want to know why we're stuck with an utter clown show of economic policy, a good place to start would be the fact that a person who is paid to write about education issues by one of the nation's pre-eminent newspapers can breezily shrug off her inability to do tenth-grade math problems.
As I said before, in a sane world, a public intellectual (even a low-level one like a newspaper writer) would be as ashamed to admit to innumeracy as to illiteracy. In this world, well, we can't seriously expect an education writer to know math, can we? I mean, math is, like, hard, y'know?
Well, her alternative was admitting she hadn't researched her story and that the Florida school board member she tried to make into a hero for fighting "the establishment" was an imbecile.
"math has always been a crucible for me" sounds pretty shame-faced. Not totally, but it's a fairly dramatic gesture at how difficult it was for the writer to do math.
For me, poetry is a crucible. So is dance, for the most part. I can see faintly what it is that gets some people excited and believing that such things are more meaningful measures of a civilization than is technological prowess, but even adequately to engage with either I suspect I would have to spend an hour every day, even though it seems pointless to me, for a decade. And I would have to choose one, I don't think I could engage with both.
So I don't start, I'm happy enough with math/physics, and I can justify my complacency by pointing to how useful the products of math/physics are. Just don't say that math and physics are beautiful as a justification, because there the ground is the same as it is for poetry or for dance; there are quite a lot of things that other people say are beautiful that I don't get. Usefulness is the gold standard for math and science, what they have that the other claimants to the throne do not.
And then, it might be better not to be complacent about the environmental consequences of the technology that math and physics enables, which for some people sets a heavy weight against numeracy. And then again, to wage war against people who are willing to use numbers as a weapon --Wall Street, if you will-- one probably has to be numerate.
The other thing I've never really "got", not for want of trying for hours each day for the last two decades, is writing, and here you see my shame.
What's interesting to me is the distinction between how she describes her relationship with math ("math has always been a crucible for me") compared to how she describes her relationship with standardized testing ("isn't my thing").
I think there's an important difference there. One is admitting a weakness, and characterizing it as a struggle. One is admitting a weakness, and characterizing it as a matter of taste.
Now, I suspect someone who ends up as a writer and uses phrases like "X has always been a crucible for me" is not unintelligent. I'd peg her as someone who never 'lived up to her potential' in math (compared to other subjects), perhaps built up a serious mental block about it, and managed to find a perfectly reasonable way to avoid doing computations for her entire adult life.
I see shame in that, but the shame is upon the education system that conveyed to her that the notion "math is just difficult for some people" is reasonable, not in personal failures on her part.
She's also raised a pretty interesting critique of standardized tests which I think you've completely ignored in your quest to miss no opportunity to get righteously indignant about this topic.
Underwear models and movie stars can make us feel body dysmorphic to the point where we watch our diets and exercise more. Who can shame people into feeling bad about their innumeracy so that they address the issue instead of just shooting the messenger?* What kind of math would a typical individual be motivated to learn or learn to do better? Where would they go that's not too expensive and can cater to their particular style and pace of learning? And (very important) how would they flaunt their newfound skills? People always like prizes. I'm suddenly having visions of bars holding competitive algebra contests. White board sales through the roof!
*NO, not Danica McKellar!
I'm not terribly impressed with her critique of standardized testing, which is very much of a piece with a lot of other education commentary that I find silly and unhelpful. I'll have more to say about this later, probably Monday.
Would you look at that? I'm important!
Peter, I would argue that most people internalize the fundamentals of poetry and dance (and the related art of music, and storytelling in general), at least subconsciously. You might not dance well, and you might not read Emily Dickinson, but you can probably at least tap your foot in time to a song, and you understand and identify with some of the archetypes common to literature. That's part of our shared culture, part of how we communicate. It's actually a very good analogy, because math is another important part of how we communicate. Not understanding compound interest when setting up a retirement plan, or basic statistics when talking about the latest political poll, puts you at a communication disadvantage, the same as you'd be if you didn't understand what Ebeneezer Scrooge represents in a conversation about your miser neighbor, or what the Imperial March from Star Wars implies when the Daily Show plays it over a clip of Dick Cheney.
Underwear models and movie stars can make us feel body dysmorphic to the point where we watch our diets and exercise more. Who can shame people into feeling bad about their innumeracy so that they address the issue instead of just shooting the messenger?*
Well, how about underwear models and movie stars? Remember this bit from a few years back where Australian actresses are plagiarizing my quantum mechanics lecture to sell printers?
When Scott expressed amazement that an ad agency would have the imagination to conceive of plagiarizing his work, never mind actually going through with the dastardly deed, some commenter shot back with "What, you mean you don't recognize those two from your class?" :-)
I'm sure you've seen this Slate article. I'm baffled by the main idea of it, but it too boils down to 'math is too complicated' even calling it a "secret language". This infuriates me to no end.
The standardized test excuse kills me too, along with the common "I don't test well" excuse from students. For most students (some do have learning disabilities that affect performance) it's as simple as not truly understanding the material. I'm looking forward to your thoughts on that.
"...rounding up reactions..."
I see what you did there.
I'll truncate this comment here.
Innumeracy is certainly a problem, but it's also hopelessly naive (and typical of people in narrowly technical fields, sadly) to think that greater numeracy would somehow result in a smarter economic policy...or any other political policy, for that matter. The Humean insight really captures almost all of the action of political economy: reason is a slave of the passions.
I realize this isn't a popular opinion, but as scientists and engineers, I also think our perspective on innumeracy is skewed. Yes, not knowing these things puts people at a disadvantage, but realistically, most people don't need to know them and get a long just fine. My mother is an accountant, someone who works an awful lot with numbers. Most of what she does is simple arithmetic with a few formulas here and there. In other words, she's doing things that one learns in high school algebra (but which requires a college degree for context), and she's in a profession which most people consider math intensive.
I think it's hard for us to see this because we use math and logical reasoning so much in our jobs. We also enjoy just plain thinking about it. It's hard to move to an objective place to see that, realistically, there is really only a small fraction of that knowledge that the average person needs to get along in life. And I'm not sure that's what is being measured on these standardized tests.
Innumeracy scares me when it comes to politicians and people running the country. Unfortunately, nerds are usually not the most popular politicians, so the politicians prefer to hire to nerds to cook the books in favor of their preferred policies. If you can reverse that trend, then I think you may see policy that makes more sense.
Cherish, there's no reason that people in non-technical fields need to learn calculus (although it is certainly as beautiful as poetry, in its way), but basic familiarity with arithmetic and algebra is important for budgeting a household and retirement planning, or buying a house or a car. That's a basic level of numeracy that people need just to get by in day to day life, but people who consider themselves bad at math are often content to live without those skills.
But beyond that, our public school system is set up to deliver a broad education. Your accountant mother probably doesn't need to know the names of the planets at her job, and her boss probably isn't going to base her salary on whether she read the Red Badge of Courage or played trumpet in band. But we set our kids up with that broad base to make them well-rounded individuals and teach them how to think, while exposing them to a number of different fields to prepare them to make a decision on what they want to do with their lives without being handicapped by a lack of basic skills. I think that's a pretty good thing. It's absurd to me to single out math and say, most people aren't going to solve quadratic equations in their job, so we're not going to require you to do it in school.
Well, I think that trotting out that sexist barbie adage is a sign of bad writing. Has she earned her position as a writer, or is she just good at toeing the misogynist party line?
Tom, I think the problem is that most people can do what is necessary for those things, or at the very least can employ a computer to help them. Most of the people who claim to be bad at math can do those things...and often they are claiming to be bad at math because they are comparing themselves to those who tend to use a lot more than the basic necessary math.
Our education system, as it now stands, is NOT set up to deliver a well-rounded education. Because of the requirements of NCLB and the focus on encouraging kids to go into STEM fields, the educational system has removed as much as it can get away with to focus on math and language. Even science is getting cut, as well as other things which I consider pretty important, like art and music. The push, in my mind, is detrimental to all kids as they DON'T get to explore and realize why they may need things like math and language. Removing those things removes context.
And I still think the problem is that those of us who are 'math literate' are expecting people to be further up than they need to be.
I don't think we're really talking about calculus here. If you look back to the test that started this all, it's basically algebra, arithmetic, and geometry.
Heck, one of the questions on the 2006 version asks: if you have 7.2 million acres of forests that are all either natural or planted and 4.4 acres are planted how many acres are natural?
Most of them are a bit harder than that, but they don't involve calculus.
MRW - 4.4 *million*.
Cherish, I disagree that the education system is not set up to deliver a well-rounded education. It may be becoming less so, but as far as I'm aware, kids are still being taught history, my old high school still has a band, and foreign language courses are being taught in more middle and elementary schools. It could be better, but it's still pretty good.
I also disagree that people who describe themselves as "bad at math" can do things like figure out how interest works, or at least, I disagree that they actually do those things. As MRW points out, Valerie Strauss says she couldn't do the FCAT 10th-grade questions. That means she's claiming not to be able to do basic arithmetic and algebra.
I'd love to live in a world where people were expected to be fluent in calculus, but I recognize that I don't. My bare minimum expectations are for adults of any age to be competent with arithmetic and algebra. And I would like them to learn geometry in school, even if they will forget it later in life, because that will help prevent damning a kid to a life limited by a lack of basic education fundamentals. To me, that strikes a reasonable balance.
Where is your balance?
It isn't a "10th grade math" test. It was a test on middle school math that is given in the 10th grade to be sure that HS graduates going on to college can do middle school math.
Although I share your horror at her attitude, we should be more horrified that an "education" reporter doesn't even know what constitutes the basic math curriculum in the public schools. Similarly, we should be horrified that a school board member doesn't know that 62% is a passing (graduate high school) grade on the reading part of that test.
The FCAT (the math section of which is being dropped in favor of end of course tests for the required courses of Algebra 1 and Geometry) is supposed to test achievement relative to the state standards for the particular grade level. All questions are supposedly on grade level ( http://www.fldoe.org/faq/default.asp?Dept=202&ID=668#Q668 ) Probably most of us reading a physics blog learned the math skills before 10th grade (although there is a certain amount of year-to-year overlap), and it's fair to question whether the standards are appropriate, but it is accurate to call it a "10th grade math test".
To be clear, from my email discussions with Roach (the school board member), it sounds like he did not take the FCAT (although Strauss, the blogger, is clearly referring to the FCAT when she says she is unable to do that math). Roach claims his math questions were "all from algebra, geometry, with a little calculus sprinked in." (I'd love to see the actual test he took, and if that's the case, I find it very dishonest to describe a test with calculus as a "10th grade test".)
Also, Roach does, in fact, know that a 62% is a passing grade on a typical test. From the original blog, "On the reading test, I got 62%. In our system, thatâs a 'D', and would get me a mandatory assignment to a double block of reading instruction." (Although note that grade scales are not necessarily consistent, and I believe that 65% is the cutoff for a D in many cases.) What he doesn't talk about is that the FCAT doesn't assign equal weight to all questions, and the percentage of correct questions isn't a good indicator of how well he did. But I assume that 62% would be at the low end of the 2nd achievement level, and an achievement level of 3 is required to graduate. ( http://www.fldoe.org/faq/default.asp?Dept=202&ID=675#Q675 )