On the Importance of Doing the Math

MathEventually, and to the regret of many Americans, someone has to do the math. And, it appears, to the regret of many American presidential candidates, a variation of this folk “wisdom” applies to them as well.   With the clock running out on the third Presidential debate, and only enough time left for one more question, the moderator finally asked a question about education in a way that led to a discussion of science education. Better late then never, I guess, because, in the end, Presidents do have to do the math policy – and the science policy, and the engineering policy, and the Education policy that prepares people to be and carry out all of those policies.

I guess that wasn’t surprising. Americans don’t like to do the math – or the science, or the engineering. For some Americans, I suspect, that is because these subjects are difficult.  Years of disciplined study are required to learn how to be a good engineer, and how to do good engineering—and a person can’t learn very much science by reading labels on beer bottles lying under tables, no matter by how many points their team may have beaten the other team.

For other Americans, I suspect, that is because science and math and engineering tend to have right answers and wrong answers – and the decision of the judges (sometimes, experts; often, bosses) is almost always final, no matter how upset a person or a person’s parent “feels” about “that idiot judge’s” decision, or how extensively the judge’s decision will impact the person’s future, or are how well the judge’s decision fits the person’s theology, cosmology, or preference.  Please note: the decision of the judges is more likely to be considered final in decisions regarding answers to questions, less likely with regard to questions themselves.

But, one thing Americans like even less than doing the math is being told that they aren’t doing very well at doing math.  To the moderator’s credit, he mentioned America’s poor performance, noting that even though the United States spends more money than any other country in the world on education, American students fall behind many countries in standardized testing of math and science.

Unfortunately, however, the moderator did not provide specifics, thereby foregoing a possible “teachable moment”; perhaps the moderator was too genteel to confront the candidates with the details.  So, here are some details:

“The scores from the 2006 Program for International Student Assessment showed that U.S. 15-year-olds trailed their peers from many industrialized countries. The average science score of U.S. students lagged behind those in 16 of 30 countries in the Organization for Economic Cooperation and Development, a Paris-based group that represents the world’s richest countries. The U.S. students were further behind in math, trailing counterparts in 23 countries.” [According to an article written by Maria Glod that appeared in The Washington Post on December 5, 2007 under the headline, “U.S. Teens Trail Peers Around World on Math-Science Test”]

As the article continued, “[t]he disappointing performance of U.S. teenagers in math and science on an international exam, in scores released yesterday, has sparked calls for improvement in public schools to help the country keep pace in the global economy.”

Of course, interpreting results expressed in terms of averages can be misleading.  To illustrate: “the average person” is not actually a real person; and so, can never actually accomplish anything, anywhere.  Furthermore, as Hal Salzman and Lindsay Lowell argue in “Making the Grade”, in the May 2008 issue of Nature, “[A]verage test scores tell us nothing about the distribution of students with the very best test scores.”  And it is those “stars”—along with a declining number of “backyard tinkerers” like Steve Jobs and Steve Wosniac—actual people, not mathematical constructs, whose creativity, curiosity, and “vision” DO lead to breakthroughs, subject to cultural disposition and organizational tendencies I have argued elsewhere; see my essay “Comments on Richard Florida’s The Rise of the Creative Class“, in the online magazine, WE,.

This low performance in math and science has been accompanied by an even lower ranking among countries of the world in health care.  According to the World Health Organization, the United States was ranked 37th in a 1997 listing, which was the most recent I could find.

For comparison, France—the country who gave the US “liberty fries”—finished first; Great Britain, 19th; Costa Rica, 36th; Slovenia, 38th; and, to the great embarrassment of nine US Presidents (seven rolling over in their graves, with two more still alive and rolling over), Cuba, 39th.

Somehow, Americans seem able to insulate themselves from pondering implications of ranking so poorly, often by screaming all the louder, “we’re number one!” – as if having a football team about which one could scream such blather were all that was required to make it so. (Such screaming by Britain’s infamous “football hooligans” hasn’t prevented the British Empire from being tossed into history’s dustbin.)  When screaming isn’t enough, a few Americans can tacitly resort to a version of “the tragedy of the commons” and simply go to business school, manage money instead of developing technological breakthroughs, get paid better—and leave the complexities of math and science for someone else to learn.

This approach offers a further advantage of improving a person’s prospects of becoming a boss and so, a judge whose decisions about what is right usually end up being final (see above!).  Unfortunately, as British portfolio managers discovered in the early 20th century discovered the hard way that strategy usually provides only temporary relief—and from the country’s point of view, only for a few portfolio managers.

For some Americans, screaming about football teams still not enough. Some of them find comfort in deities, such as the one that supposedly placed Earth at the center of the universe for the first 1500 years of the common era. That’s a pretty big mistake for a perfect and all-knowing deity to make, I think.  It makes me wonder what other mistakes that deity might have persuaded all those Americans studying their beer bottle labels under tables to believe (like “creative design” is a “theory”, when it barely qualifies as a hunch and as-practiced is merely an assertion) and to not-believe (like evolution is not-correct).  And, flat-Earth cosmology confounds and complicates the already difficult task of teaching science.

My purpose here is not to dump on beer drinkers who’ve had a few too many, particularly since I have done more than my own share of worshipping the porcelain god.  Rather, I want to argue that, in effect, successful reification isn’t necessarily the same as success.  That is, “everyone’s saying it’s so” doesn’t always “make it so”.  Nor does “everyone’s saying it’s so” LOUDER.  Eventually, as I wrote at the beginning of this essay, someone has to do the math.

In an era dominated by international finance and global capitalism, and regulated by nationally-identified and, therefore (according to General Systems Theory), insufficiently complex regulators, what matters—and all that matters—is THAT a country is #1.  I wish I could say, “It ain’t so.”  But I can’t.  No one can.  The only people who can say, “It is so.” are those at the top of the heap, who have worked hard enough, and creatively enough, and collectively enough to occupy (still, though only contingently) with the US the place that the US had grown accustomed to occupying alone (back when this country did the math, and the science, and the engineering—and the exploiting: of Native Peoples, natural resources, and imperialist objectives).

To put this all into perspective, let me end with a personal anecdote.  Back in 1971, I studied engineering at an “Institute of Technology”.  I graduated with a 3.19 grade point average.  For several years, I wondered what that grade point meant.  About 15 years later, I had opportunity to raise this question to a highly accomplished professor of engineering; indeed, he was listed in “Who’s who?” in his field of engineering. He told me that when he had started to teach (at a large Midwestern state university) in 1956, the average grade point average was about 2.5.  (I began to breathe a bit easier.)  He continued, saying that the average grade point average for engineers at his school for the year I graduated was 2.85;  (I began to feel better about myself.)  He finished by telling me that the average grade point average for that then current term was 3.5—quickly adding: “and the students aren’t nearly as good as they used to be,”

There are many possible explanations for the trend he described, and I readily acknowledge that those explanations might have been supplanted since by still other, different explanations.  Furthermore, it’s not clear that the hill the US used to occupy the top of hasn’t itself changed from below.  Climate change may require different kinds of solutions, grounded in different skills and different knowledges.  Staying on top might require relocating to a different hill, even if it couldn’t be clear before beginning to move how far up the new hill the old skills and knowledges might sustain us.

There are only a few things I am sure of.  One is: we can’t stay where we are, whether on a hill or under a table.  Another is: we’ll have to learn our collective way from where we are to where we hope to be.  And: the challenge is so great that we need all of us working hard together, learning how to do so when old ways won’t work, to contribute to the effort.

letcherTo me, that makes education crucial to this country’s future.  What will be required to avoid losing?  If people detect either that they are no longer being challenged by their work, or if they find themselves reading beer bottle labels under tables, then I would suspect that the country is on its way to History’s Great Dustbin.

Robert A. Letcher, PhD
June 10, 2009

Robert A. Letcher, Ph.D describes himself as “an academic with a disability instead of a portfolio, a writer, and a Qigong practitioner who tries to help people learn”.

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Comments

  1. Rose says

    I understand your comparison of high school and college students from the U.S. and Japan. I don’t think you can use that information for 12 year olds and make the same connection. I question whether or not 12 year olds are developmentally ready to internalize the concepts involved in algebra when they haven’t mastered the basic addition, subtraction, and multiplication facts. I deal with students every day at school who primarily struggle with those basics first, then they try to recall the next step.
    My main point is that before we can expect them to ‘learn’ more difficult concepts we HAVE to give ensure they have enough time to have the basic math facts in their instant recall. I agree that the students who have mastered the basics can learn algebra at 12 years old. Unfortunately, many kids aren’t at that point.
    I was fortunate to visit Japan in 2005. When I visited an elementary school, I asked about the math program. I was told that students are not allowed to progress to higher levels until they have reach proficiency in concepts taught.
    I even purchased two math textbooks while there. The sheer difference in the number of pages was staggering – our texts have hundreds of more pages. I asked and was told that their text was mastered over the course of a school year. The book was less than a hundred pages, and the concepts were not multi-layered.
    One last point from my soap box: Although I don’t profess to know the right age level at which to increase the intensity/difficulty of math concepts, I am convinced that we need to slow down at the early to middle elementary levels. Then, by middle school (?) or early high school levels, students would have a more solid foundation on whi

  2. Robert A. Letcher says

    Thanks for venting toward my essay… Let me share one of my experiences that bears upon your quandary over whether algebra should be taught in high school or in 6th grade. I had the great good fortune to study for the doctorate at an Ivy League school. It happened that many Japanese graduate students also came to study in the same program. In conversation with one of them, I learned that Japanese students learned in their tenth grade the same mathematics which US grad students (not math or science majors) struggled to learn as grad students.
    In this light, either students learn as much as the other guys, or the other guys eat our lunch. It’s not a matter of the “right grade level”. of course, there are always unintended consequences. But, there are also BIG differences for competitiveness between working on difficult math problems all evening and playing nintendo all evening.

    Here’s something else i wrote for We! Magazine…

    Hello Charlie Rose staffer
    by Robert A. Letcher, PhD

    First, thanks for your wonderful show, night after night. I tape it and watch it the next day. Second, thanks for your effort to rescue science from the morass the last few years have mired it in. It is last night’s final installment in your science series that moves me to write.

    Your esteemed guests touched on many key challenges, but it seemed to me that they overlooked Pogo’s comment of long ago: “We have met the enemy, and he is us.”–near quote. At every level, from young children to senior faculty, people are influenced by what Christopher Lasch (thirty years or so ago?) called “The Culture of Narcissism”. Everyone wants to do well, receive high grades, trophies, promotions. That’s possible in kiddie-league T-ball, third grade poetry, junior high reading, high-school history, college sociology–and such; all areas where grade inflation is easy, creates happy consumers, leaves more time for professors to pursue institutionally validated research, avoid having to challenge post-modern sensibilities, and wreaks only incidental, essentially untraceable, easily rationalizeable damage to the larger world.

    In the great scheme of things, science is much more than a process. It’s a DISCIPLINE. There are scientifically right outcomes and scientifically wrong outcomes–and it would be very difficult to reward a person for having designed a bridge that fell down, for example. Grade inflation is riskier in science and engineering. The same goes for indulging narcissistic tendencies–riskier in science than in poetry.

    Some months ago, in reaction to yet another news article on people disagreeing over whether the “new math” worked, I wrote the following essay in response to an article in The Columbus (Ohio) Dispatch. Please note that every sentence is a question:

    “What if the explanation for poor math skills (see As Math Scores Lag, a New Push for the Basics, 11/14/2006) were sociological, not merely pedagogical? What if my generation did so well at math more because, as Sputnik babies, we felt our society’s telling us, we need good mathematicians to protect us from Russians and less because of how we were taught? And what if today’s students have internalized the meaninglessness of products that engineers and scientists appropriate mathematics to develop today? What if (as a discouraged graduating female engineer once wondered out loud to me) they have seen the ecological callousness of corporations which those engineers and scientists generally work for and whom they would also work for, if they did well in math? And what if they have rejected the depraved irresponsibility of the institutions that apologize for all that? Why would they ever want to work hard enough to be good mathematicians? In not doing well in math, could they be telling us something more profound than changing pedagogy could ever address? Sustainability, anyone?”

    I fear that even your excellent treatment of science will fail unless its proposals are examined in this wider context. I urge you to try to bring about a discussion of such matters.

  3. Rose says

    Has anyone looked at the math and science curriculums for clues to our dismal ranking? I teach 5th and 6th grade math. In the last 10-20 years the texts have gotten increasingly more advanced. Is that the answer to falling scores? I think not. By force-feeding students to ‘learn’ more difficult skills at a younger age, we are sacrificing the time needed to ensure that students master the basics. For example, in the 6th grade math text from which I currently teach, students are asked to solve algebra problems at a level 30 years ago would have been at high school level. Yes, they can solve the problems, BUT, only after struggling to remember that 17 – 9 = 8, or 7 x 4 = 28. If students were given the time to master the basic facts, they would then be more able to tackle problem solving skills when they are developmentally ready.

    Add to that the pressure teachers have to follow the standards set by each state, which are tested each spring. It basically forces us to push students too quickly through material, hence, little or no mastery is achieved.

    Add to that the shift in parental attitudes. Helicopter parents abound. Heaven forbid if someone lets Johnny figure out that life isn’t always fair. Children are over-scheduled with activities, and they have little to no free time to ‘be kids.’ School often does not come first on the priority list, yet schools are expected to produce successful people into society.

    I’m sure there’s more, but I must get back to my school bag of papers to correct. My 12 hour day isn’t over yet. Thanks for giving me an opportunity to vent.

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