Calculus and Pernicious Myths

Most of the Arts as we have them today are largely an outgrowth of the philosophy of Rousseau  and his Romanticism. That is dangerous. Silly atheist cant to the contrary, Atheistic Romanticism, in the form of Communism and Fascism, has killed more people than any other faith or ideology in the history of the world. With the growth of journalism schools embedded in the Leftist academy, we now see that the modern flavor of Romanticism has crept out of the Arts and English Departments and in to our news outlets. Romanticism creates myths such as Rousseau’s Noble Savage, and keeps on believing in those myths in the face of contrary evidence. A highly dangerous habit in the Press Corps.

My major beef with Romanticism in the MSM is that it can’t count. And that means, in today’s high tech society, that it often turns out to be the enemy of freedom.  (I’ve gone into that in detail before.) In fact, given the low expectations about subject matter knowledge, journalists can’t do much of anything else, either, and that, too works against the very freedom the Press claims to protect.

But this is a post about math, or at least math concepts. It is a crying shame that, back in the 50s when Sputnik spurred the development of the current US high school math and science curriculum, that physics and physics envy ruled the day. Because for most people, high school calculus is a joke, and the time would be much better spent on statistics. If one has read Innumeracy  by John Allen Paulos, one should have been struck by the main mathematical aspect of that book: there were exactly zero references to the Calculus, and most of the examples came from probability and statistics.

The reason that Paulos concentrated on probability and statistics is that those are the non-intuitive concepts that drive policy and decision making even on the personal level, and they are the most subject to distortion by the media. Every time an assertion is made that can be described by statistics (and this is especially true of anecdotal examples that the MSM brings out without referencing statistics), the first questions an educated human ought to ask is: what is the mean, and how broad is the distribution?

The MSM has a habit of cherry-picking stories off of either tail of a distribution. The lack of logical training of most reporters comes through in this kind of argument. This allows them to buy into myths that may or may not have been true once upon a time, but are no longer supported by facts. Ginny just reminded me that one of those myths is that there is a large segment of the poor who would do better in life if only they had better access to education.

If you were to look at the mean of the distribution of intelligence versus socio-economic status in, say 1920, there would be an awful lot of smart kids left out in the cold, even though their parents were hard working and imparted the meta-skills necessary for success.

My paternal grandfather became an engineer is this time period. My maternal great-uncle was probably a genius, but didn’t. Both of them had the kind of meta-skills that keep one out of the poorhouse (statistically) in today’s world – they worked hard and  they got married and stayed married. But my great-uncle was the son of a farmer and had an eighth grade education, and he had to teach himself mechanics. Self-taught or not, he was the only person in Leesburg that Arthur Godfrey would let touch his expensive and rare clocks, and my great-uncle repaired them every time they stopped working. What would he have done if he’d had access to an education? Well, I doubt that I’d be the first person in that family to hold patents, that’s for sure. But just one generation later, and of his brother’s four kids (my great-uncle died childless), two had aptitude and went on to college, and two didn’t and didn’t. The reality behind the myth was changing.

That’s not to say that every Boomer who wanted and deserved to go to college did, but with each passing generation, that myth of the buried genius is getting harder and harder to support with facts. Poor attitude and work habits bring down more poor kids than lack of access to education. As we cull more and more of the capable from the ranks of the poor, this under-resourced population is getting smaller. As Ginny noted on this blog:

Ours is not the world of Dickens; it is a world when the greatest injustices are done by people to themselves: staying in school, staying married, staying employed – these are choices. The fate that buffets us may be a culture that undervalues learning and undervalues renunciation of the sensual present for the well-prepared future, but it is diverse and the choices ours. Our schools may be lousy, but we have the internet and libraries. Waiting to marry and staying married is likely to be better for us, better for our children – to pretend that this gap is not one of choice is to infantilize us.

Are there still kids who can’t get access to an education due to poverty? You betcha. Our immigration patterns are going to ensure that at steady-state there is going to be a small, unfortunate pool of deserving kids who don’t get access. Can the media dredge them up? Sure. But the question is, how many of those kids are out there, is the population of them growing or shrinking, and what is the marginal cost of finding and educating them? Most important of all – what is the most cost-effective means to reach them without creating useless bureaucracies and more opportunities for rent-seekers? Most of our Press corps can’t even understand the statistical techniques used to get answers to those first three questions, or indeed to ask them in the first place, in most cases.

When we don’t ask the right questions, we leave things as they are, we construct ineffective solutions, or we solve the wrong problems. We allow poor schools to keep on destroying the futures of good kids, and we pour money into the Department of Education for useless initiatives.

But if we ourselves have not been educated in math and statistics, we fall prey to the idiocies fed us every day in the media. So I’ve come to the conclusion that one of the most beneficial changes we could make to the high school curriculum in this country is scrap calculus as the major college-bound math subject and require probability and statistics instead.*


* If you think you want to become a scientist or an engineer (or, God help you, a mathematician), by all means take calc – as an elective.

15 thoughts on “Calculus and Pernicious Myths”

  1. John,
    Thanks for the quote; you and those who think like you on this blog – and real life – has had an influence on my family which is generally not very good at math or science. My oldest daughter had to take (and it was painful) a stat class to write her master’s thesis. The second graduated last year, but is planning to take a statistics course this summer to get her out of the job she now has that doesn’t use her double major in religion and Czech. Armed with that math course, she can qualify for more research-oriented jobs. And the third is in her last year of high school and has already decided to take statistics rather than the pre-cal students usually choose. Of course, they all took routes in college that required practically no math beyond the high school level; my father was an engineer but those genes seem to have disappeared in me as well as my children.

  2. As a retired career engineer/tech manager, I look back and agree heartily that statistics would be more useful to more more people. As I participated in “career days’ at high schools it was clear that many students were intrigued by my little tech “magic shows” that illustrated some tech career path (chemistry, electronics, etc.) but they were far past taking a math suite that would open up science/engineering as a career. The only occupations “familiar” to them were those seen on TV (policeman/detective, sports, acting, medicine, law, and on and on). To seriously pursue medicine or science/engineering requires very early (elementary) and persistent interest in math that simply isn’t “featured” in “pop” education.

    If nothing else, a basic grounding in statistics might enable a political consumer to see through the snake oil that passes as “economic development” and “jobs policy” in politics. We might even avoid a young mother or dad standing up to endorse an asshat real estate scam as creating opportunity for their children.

  3. Mark – the Boomers were the first generation to get really wide educational access across their entire cohort. My mother is technically a Boomer – re. the previous paragraph.

    Here’s my view of the time dynamic of educational access in the US:

    WWI generation: education mostly for elites

    WWII generation: GI Bill and broader access

    Boomers: excellent access

    Gen X: even better access, but debt up to our eyeballs

    Gen Y: more people from that cohort go to college than are actually capable of doing college level work, at least from my experience TAing them.

  4. I’m often told kids can’t afford college today. My universal answer is that they can easily afford it if they join the military. The almost universal response is, “Well, they shouldn’t have to do that.”

    I find that a bit curious. We can easily make a case that the kid who goes to college on the GI Bill (or whatever they call it today) is paying for his own education. That would seem to be a good habit to acquire. I suspect the reality is that not everyone can’t find someone else to pay for their education, and they abhor the notion of paying for it themseves..

  5. While I would agree with John in general terms, culture or your definition of “college” and “college exprience” is a factor.

    My parents came of age during the dustbowl; my grandmother wanted her daughters to go to high school & my mother literally worked her way through high school (because she had to earn her room and board to stay in town – they lived too far in the country for easy access). Both she and her sister got college degrees in the thirties, but lived in co-ops. The story was always different for land grant colleges versus private ones, midwestern farm families versus children from the industrialized north. 50-60% of our freshmen graduate from a 4-year school in 7 years after their first class with us; our tuition is around $1100 for in-state students. (The ones that don’t do well are the ones that end up at the schools LBJ or Dan Rather entered.) Sure, this isn’t the $600 it was not too long ago, but not that much, certainly not for our students whose favorite mode of transportation is a souped-up, full-size (or bigger than full-size) truck.

    What I sometimes find irritating are that the same people who think the government should pay the complete bill for education are quite often the same people who believe there should be no tests of competence for graduating from high school and no test criteria for people entering college. We can educate only the 25% (or whatever) that really give a damn and pay their way – which means the government should also make sure they major in ways that in some way help the general good – or we can leave it open and let people find their way. I dont mind my money paying the tuition for the guys that worked hard at the prison, but there is absolutely no reason my taxes should pay the tuition of the guys that signed up for the class just so they could sit in the back of an airconditioned room in the middle of a hot Texas summer.

  6. I recall an article in “American Heritage” magazine a few years ago which asserted that the educational system in the 20th century US was getting a bad rap because it was attempting to educate an enormous cross section of the population, as opposed to the select members of the upper classes for whom education, in any formal sense, was reserved in earlier times. And, given the demands of this expanded mission, the contention was made that the schools were not doing too badly, although there were clearly some difficult problems that needed to be addressed.

    My reaction to this article at the time was mixed, and it has remained so as I have thought about this situation over the years, and monitored my own children’s progress through the school years.

    While I do agree that the mission of the school system has expanded greatly over the last century, I cannot agree that it has done a very good job, either of educating the youth of our society, or of using wisely the enormous amounts of money and resources provided for that enterprise.

    Certainly, the egalitarianism of Rousseau and his intellectual heirs, beginning with the disastrous excesses of the French Revolution, and moving through the the various permutations of anti-individualist philosophy that so damaged the western cultural construct over the years, has entrenched itself in educational theory with a vengeance, resulting in the ludicrous spectacle of highly gifted students, who wish desparately to learn, and who have the ability to reach high levels of achievement in complex subjects, begging for the opportunities and resources to pursue advanced course work, and being denied, while enormous amounts are spent trying to educate youngsters who don’t even want to be in school in the first place, and disrupt the classes for students who do.

    Secondly, the arrogant attitude of those in charge of educational theories and philosophies towards any attempt by non-educators to have a voice in the subjects taught and methods employed, unless those non-educators are members of some PC-approved pressure group, has resulted in a system which so de-motivates the interest, and undermines the educational enthusiasm, of young children, that after a few years many students adopt a zombie-like approach to the school day, turning off their natural curiosity and willingness to explore new things, and replacing it with a fixation on sports and cultural hipness, especially when that hipness emphasizes a contempt for education as a basic value.

    We are witnessing the slow, terrible collapse of a great idea—that every child should receive all the education he or she can attain. This tragedy is the direct result of the influence of collectivist theories in academia, which work against any appreciation for the individual differences among children, instead clumping everyone together in broad categories based on age, and, unfortunately, race and sex, (one of the truly repugnant effects of the race/gender model dominant in post-modern educational theory).

    In a world which relies economically, militarily, and culturally on ever increasing technical and scientific knowledge, the average American student has been ill served by an educational structure which places more emphasis on the orderly movement of numbers of students through the system than any committment that those students are truly equipped with the intellectual tools needed to flourish in the 21st century.

    An artificial construct of overly-extended childhood, replete with confused theories and disjointed subjects, has, not unsurprisingly, resulted in a continuing “crisis” of uneducated and disinterested students, drop-outs, and falling competency, as measured by any comprehensive method. This problem will not be addressed in any significant form, other than the constant chant that “schools need more money”, until the coercive nature of the system is re-examined, and parents are allowed, and, indeed, required, to assume more direct responsibility for the education of their children based on that child’s individual aptitudes and requirements.

    The continued rule of the enormous, bureaucratic monstrosity we have now, with its cookie-cutter approach to all situations, and dumbed-down course materials geared to the lowest common denominator, will inevitably result in the worsening of the position of the US in the world’s economy, and the scientific/technical development which drives it.

    There are only so many marketing and public relations jobs available for those who are hip but can’t read or write. Somebody still has to develop the products and services they package and sell, and this will not be another American if current trends continue much longer into the future. You cannot staff the modern equivalent of Edison’s laboratory with illiterates and innumerates.

  7. Behind every social problem there is inevitably the government creating the problem in the first place.We would be better off with a voucher system.I don’t know that much more would be taught,but at least it could cost half of what it does now.

  8. A few thoughts…

    1)Math–calculus, statistics, whatever–will not be successfully taught in the average public school as long as “education” degrees are required for teachers. The kind of mind that is good at things like math does not take kindly to the squishiness and preachiness of the typical ed school curriculum.

    2)Most people learn things better when they can see how they’re used. I suspect the average K-12 textbook, as well as the average K-12 teacher, is weak on meaningful applications.

    3)Veryretired–“There are only so many marketing and public relations jobs available for those who are hip but can’t read or write”…most marketing jobs require excellent writing, reading, and public speaking skills, and many also require significant quantitative skills. This is also true of the higher-paid sales jobs. In addition, sales jobs require considerable emotional resiliance, which I suspect is often undermined by “self-esteem building” programs.

  9. “Most people learn things better when they can see how they’re used. I suspect the average K-12 textbook, as well as the average K-12 teacher, is weak on meaningful applications.”

    My 12 year old thinks math is hard and boring — but he’d put up with it if it did not seem useless. I tell him it is not useless, but the way it is taught does not convey it.

  10. VeryRetired – there are two camps in marketing – the touchy-feely artsy-fartsy advertising types, and the quantitative psychiatrists who try (and sometimes succeed) to model human economic behavior. I’m in the latter camp. And there are a lot more jobs on my side of the divide – the world only needs so many advertising agencies.

    Lex- I’ve come to the conclusion that it’s going to be my job to teach the relevance of pretty much all of science and math to my kids through extra-curricular activities.

  11. I seem to have upset some readers with my reference to marketing and PR. I used that area of business as an example of a purely adjunct line of work, much like cheerleaders are to a sports team. And, as with cheerleaders jumping around on the sidelines but no team out on the field, my clumsily attempted point was that there was no need for fluff if there was no product or service to begin with.

    I’m sure there will always be a great need for well educated and highly skilled market researchers and PR people to tell us why we need three more types of shampoo based on avacado peels and the essence of koala bear urine. I apologize for any offense.

  12. Very Retired – no offense taken – no one in marketing goes in to it thinking that it’s a well-loved profession – it’s like being a lawyer. But also, most people confuse advertising, sales and PR with marketing – they are not the same thing, and require different skill sets. The jobs where you can BS your way through life are few and far between, and mostly in advertising and some PR (although you have to be pretty savvy in many PR jobs to keep your butt out of jail).

    Quantitative skills are just as important in most business jobs as they are in science – it’s jsut that the error bars around the figures are much higher in business than in science.

  13. The essence of quantitative marketing in the product development stage (where I work) is to keep the firm from investing in something no one will buy – hence it lies at the core of our current tech-based capitalist system.

    An example where resources are wasted (at least in my case) is cell phones. I don’t use 9/10ths of the features. Perhaps Motorola’s marketing department figured that the production costs of making several runs outweighed the waste of putting features on a phone that most people never use, but I suspect that the real answer is that their product development people are full of techies who love gadgets, and not full of people who ask “what is the value of this crap”?

    In order to avoid that kind of wasted over-featuring (not to mention making products that no one will buy), my company does a lot of research. Here are some links to the basic pricing models and consumer behavior measurement instruments that involve more statistics than the average math majors knows.

    The basic quesiton I ask is “why would anyone buy the crap that my R&D department comes up with”? That’s a fundamental economic question, it’s not trying to get someone to buy shampoo with sheep’s placenta in it.

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