What we don’t know that sometimes won’t hurt us

Kevin Drum channels Brad DeLong to recall a Calvin and Hobbes sequence in which Calvin’s dad reassures him that it’s colder in the winter because the earth is farther from the sun then than in the summer. Kevin asks for a survey to find out how many people believe that.  As it happens, a small survey was performed a decade or so ago and it turns out that 21 out of 23 graduating Harvard seniors, alumni and faculty do. Ask your friends, it is to weep.  It’s the lede for an unforgettable investigation of why our science teaching doesn’t work, available here (just click on the VoD button in the lower right).

Our science teaching doesn’t work because we teach science as a sort of catechetical stream of truths that students memorize to repeat on exams, but trowel lightly over stuff they already know that is wrong. You can read all about it on the research page at the PhET project.  Because a lot of it makes no difference in daily life (most people can live just fine thinking the earth is flat), this crust of learning flakes off quickly.  Not understanding the seasons is one of the very striking examples of this, and another is the explanation, recited by people who have seen a paper airplane in action (flat wings) and an airplane flying upside down (at least in movies), that an airplane flies because its wings are rounded on top and flat on the bottom (plus some stuff with Bernoulli’s equation).  (Amazingly, even PhET has, among its wonderful teaching simulations,  the wrong model of aerodynamic lift!)

Unfortunately, a real model of lift involves some very hairy differential equations.  If you calculate the pressure difference between the top and bottom of a conventional wing from Bernoulli’s equation, and the implied velocity difference, you do not get the lift on a unit length of wing; you get a meaningless number. The simple model allows something that looks a lot like science (it has an actual quadratic equation!), but this teaching convenience requires students to build a wall between what they know to be true from real observation and what’s expected on the exam.

Very few people have occasion to intervene in aeronautic design or planetary motion, but there’s a lot more science, like heat transfer in and out of your house, that can hurt you if you don’t really get it, and still more, like climate science, that will hurt all of us if we go on voting in profound ignorance.  Teaching science like religion is a practice embedded both in the curriculum and the pedagogy, not to mention how easy it is to test without, like, having to find out whether any actual learning has occurred.

 

Comments

  1. Gary K says

    Just to chime in with a pet peeve: educated individuals who believe that moving a basin of water a couple of yards, from one side of the equator to the other, will affect which direction the water will spiral as it drains. They know there’s this thing called the Coriolis effect, and never mind that it’s ridiculously negligible at the scale of a basin of water draining in a few seconds, as opposed to a hurricane slowly turning over a period of weeks.

  2. Dan Staley says

    but there’s a lot more science, like heat transfer in and out of your house, that can hurt you if you don’t really get it, and still more, like climate science, that will hurt all of us if we go on voting in profound ignorance.

    Indeed – I can assure you the MIL has a shocking lack of knowledge of basic physics (heat up, cold down) to the point that she pays maybe $25-35/month extra in building conditioning costs because of her mismanagement of the curtains, doors, etc. And don’t get me started on directing the dryer vent exhaust. But it is to the benefit of the utilities, so they won’t mind her continuing this way. And we can’t get her to change ingrained habits…

  3. FuzzyFace says

    Yes! Some great points, Michael, when it comes to HOW we teach science. How often do we require students actually to reproduce experiments and explain why they go wrong? To understand where models of the world work and where they do not? I gag when people claim that “the scientific method” means peer-review or consensus.

    • David Nasatir says

      If I recall correctly, and at my age that is an accomplishment, I spent a great deal of time attempting to reproduce some classic experiments (Michelson-Morley for one) during my undergraduate years. Since I was, and remain, a lousy technician I typically failed to obtain the expected results. The post lab discussions were extremely productive for me. Maybe even for my lab partners some of whom have remained friends for over sixty years.

  4. MobiusKlein says

    Did that quiz at home, and the 10 year olds got it wrong.

    The better answer to teach is “because we get more shade!” More shade, colder temperature.
    You can show them more shade – it’s darker, right?

    Then show a sphere and a light, and how it’s true.

  5. Benny Lava says

    I think part of the problem is not that we teach science to be dogmatic. Rather, that we teach things that are wrong. We teach children that water freezes at 32 F and boils at 212 F, or freezes at 0 C and boils at 100 C. But this isn’t true. This is only at standard pressure. Change the pressure and the boiling and freezing points change. Or change it from pure water to salt water. We only introduce the triple point and all the details later. There are all these little white lies being thrown at students so often that I can’t help but think that this makes them more likely to believe in garbage. They don’t know what to believe because they can’t trust their teachers and parents because they lie or don’t know what they are talking about. I tend to reflect on that this time of year when we feed young people full of lies about Santa Claus.

  6. navarro says

    @benny–i’m a 6th grade science teacher and i’ve always verbally qualified the information about melting and boiling points with the phrase “at standard pressure” ever since i started teaching science. in that time i’ve had a grand total of 2 students ask me what that means and when i’ve explained what it means and how it effected boiling points when i lived at 7200 feet elevation in colorado i’ve seen a lot of eyes glaze over. which leads me to ask why it should be considered lying to express the basic concept to students who haven’t got any need for the advanced concepts and gradually introduce them to the advanced concepts as they evince readiness for them? to put it another way, if a 10 year old can grasp infinity in terms of the notion that there is no largest number, am i lying to her if i don’t discuss the difference between countable infinities like the whole numbers and noncountable infinities like the reals?

    • Benny Lava says

      I’ll bet you weren’t the first teacher to teach boiling points. I remember learning that in the 3rd grade.

      Why do you qualify with “at standard pressure”?

  7. Michael O'Hare says

    I didn’t mean at all to suggest that one can’t understand lift without the Navier-Stokes equations. Actually, understanding lift (as distinct from calculating it for a specific airfoil) is not all that difficult. Anything that’s more or less flat that has an angle of attack will lift: a pinwheel blade, a paper airplane, and even (as they discovered in one of the multiple aerodynamic disasters at the new John Hancock building in Boston) a building in a quartering wind. If it deflects fluid down (or perpendicular to the flow), it acquires corresponding momentum in the opposite direction. It’s the same principle by which a jet engine or a propeller make the plane go forward: they throw mass in the opposite direction.

    • Bob Jacobsen says

      Re: Lift and “It’s the same principle by which a jet engine or a propeller make the plane go forward: they throw mass in the opposite direction”

      Yes and no. More specifically, it depends on what you mean by “makes”. To generate a force on air, either for lift, thrust or drag, requires accelerating the air. That’s Newton’s 2nd & 3rd law in action. It’s basically always true (with small caveats in special cases).

      Where it gets complicated is “What makes the air accelerate?” Simple models here are often wrong.

      For example, a modern commercial jet engine gets only some of its thrust from the air it “throws” out the back. A large fraction (in some regimes, more than half) comes from the shape of the inlet. Air gets sucked sideways towards the engine, then turns the corner around the inlet into & through the engine core itself. In the low&slow regime, that turning is the more significant acceleration of the air, and generates much of the thrust.

      And there’s the question of “what” makes it happen. Like a 5-year-old who keeps asking “Why?”, there are levels to that. _What_ makes the air turn the corner into the inlet? Well, it sort-of has to if it’s going to get into the engine. But microscopically, how does a particular little bit of air know to do that? From the pressure gradients that it experiences. What sets those up? Well, that’s the air-flow itself, and the material shapes they encounter. The whole thing is a little self-referential and circular.

  8. says

    Where did the statistic “21 out of 23″ come from? There’s nothing at the Private Universe link that quotes that, nor does the short film clip include that statistic. I find it hard to believe that 21 out of 23 Harvard students, let alone faculty, believe that, at least these days (the film clip I saw was filmed in 1980).

  9. Michael O'Hare says

    Short film clip? The video is about 22 minutes. At about 2:45, the narrator says that 21 out of 23 “students, alums and faculty” gave the wrong explanation.

  10. FuzzyFace says

    Given the number of college graduates who take no hard science courses at all, I don’t find the 21/23 stat to be unreasonable. But I am shocked about the guy who was interviewed and claimed specifically to have studied astronomy and yet gave the same answer.

  11. Ebenezer Scrooge says

    I can’t really see the problem with poor science education for non-STEM people. After all, how much physics do you need to know to make a sensible policy decision on, say, the Superconducting Supercollider?

    - It’s really expensive.
    - The physics is very neat, but has no foreseeable applications. Sometimes, unforeseeable applications happen; sometimes they don’t.
    - Physics is the most fundamental and elegant of the sciences.
    - We now know enough about the economics of technological spinoff to predict that it will be there, but be relatively modest. (Technological spinoff would be in, say, vacuum or magnet or pattern-recognition technology, not in the fundamental physics.)
    - Other sciences are also pretty neat, much cheaper, and promise foreseeable applications (e.g., neurobiology.)
    - There is little appropriable benefit to the United States from doing it here.

    Apart from putting a few cost numbers on, what more did a person need to make a rational decision not to go ahead with it? I’ll accept Michael’s point on home heating, but that’s about it. Non-techies really don’t need much. They need to know when they must consult a techie, but we usually don’t argue that non-lawyers must have legal training to know when to call a lawyer.

    The problem with STEM education is that it is a.) difficult and b.) non-remunerative, compared to the alternatives.

  12. Foster Boondoggle says

    Feynman has an incredibly depressing anecdote about reviewing science and math texts for California in his autobiography. You can read the sad story here: http://www.textbookleague.org/103feyn.htm

    While there are good reasons for setting statewide standards for K-12 science/math education, the result is a camel-is-a-horse-designed-by-a-committee evil. My son’s HS grade chemistry textbook was a horror show of random facts and formulas that required deeper math to explain or understand than they were evidently allowed to assume. So they just presented these definitions and formulas as stuff to be memorized. And don’t get me started on actual math teaching, where the students are required to memorize “mathematical” terms that have no relationship to any term used by a practicing mathematician or scientist.

  13. Foster Boondoggle says

    Of course the root problem with K-12 STEM education is what Scrooge says. The only really talented people who go into it are independently wealthy and/or interested in self-sacrifice. We neither pay enough nor respect the teaching profession enough to attract more than a tiny number of talented people of ordinary means.

    But I disagree with Scrooge on the consequences. After a brief pause in the 1960s and ’70s, the US is back to importing a substantial fraction of its scientific and engineering expertise. STEM is the basis for much future human progress. With our decentralized decision-making and gazillion legislative veto points, having a citizenry that’s both unable to understand scientific facts and also unable to recognize its ignorance is a prescription for repeated mistakes, such as the failure of cap-and-trade for carbon.

  14. says

    Sorry, the clip I saw (someone posted it at Drum’s site) was short. Still, I find it hard to believe. I’m not sure how large the sample was, and based on graduates I know, I doubt it’s true today.

  15. hilzoy says

    Hmm. Having spent a chunk of sixth grade making paper airplanes, I always assumed that airplanes fly because if a tilted plane moves forward through the air so that its higher edge is leading and its lower one trailing, air below it will be forced down while above it there will be a vacuum pulling it up. Later in life I also came to assume that this was wrong, because it didn’t explain why airplane wings were so curvy and airfoil-shaped. I could see that being in part to reduce drag, but I somehow suspected that there was more to that airfoil shape than that. Even after reading the long thingo that Kevin Drum linked to, I still don’t fully get it. (I.e., why the top of the wing should be more crucial than the bottom.)

    • CharlesWT says

      …, but cambered airfoils can generate lift at zero angle of attack. This “turning” of the air in the vicinity of the airfoil creates curved streamlines which results in lower pressure on one side and higher pressure on the other. This pressure difference is accompanied by a velocity difference, via Bernoulli’s principle, so the resulting flowfield about the airfoil has a higher average velocity on the upper surface than on the lower surface. The lift force can be related directly to the average top/bottom velocity difference without computing the pressure by using the concept of circulation and the Kutta-Joukowski theorem.
      Airfoil

    • Bob Jacobsen says

      “I always assumed that airplanes fly because if a tilted plane moves forward through the air so that its higher edge is leading and its lower one trailing, air below it will be forced down while above it there will be a vacuum pulling it up.”

      Interestingly, that doesn’t have to happen. In a non-viscous medium, it _can’t_ happen. Non-viscous mediums have “reversible” flow: Take a movie, run it backward, and what you see is also physically plausible. That means a left-up-right-down sheet moving left (high leading edge) and moving right (low leading edge) have to have the same flows, so there can be no net lift by symmetry. Experiments in liquid helium confirm this.

      It’s the dissipation that viscosity permits that breaks that symmetry and make flight possible. That in turn wasn’t understood until the 60′s. Once it was, suddenly shapes other than traditional wings (like the strakes and winglets that became common on the 70′s and 80′s) were important. Now much of flight aerodynamics is understood in terms of “induced vorticity”.

      “Later in life I also came to assume that this was wrong, because it didn’t explain why airplane wings were so curvy and airfoil-shaped. I could see that being in part to reduce drag, but I somehow suspected that there was more to that airfoil shape than that.”

      The traditional NCAA shapes (the shape people learn to draw in grade school) are very efficient at inducing the pressure differences that keep the air moving in the most efficient directions. They were created using wind-tunnel modeling and early computing, both of which could only handle 2D situations. Starting in the 80′s with the rise of large computers and vorticity-based algorithms, more complicated shapes where possible. Now, with better manufacturing, the entire flow over the aircraft can be considered. That’s what gives rise to the odd-looking shape of the Airbus 380 nose, for example.

  16. Anderson says

    I have decided, without troubling myself with any research, that exaggerated diagrams of the Earth’s orbit are what make people think that the planet’s distance from the sun causes seasons.

    Kids learn that the orbit is an ellipse, and it’s typically illustrated with an orbit much more eccentric than the real one, because the real one looks pretty much like a circle.

    The text in the book may or may not explain the true fact, but most students remember the picture not the text (another research-free conclusion).

  17. Anomalous says

    If a majority of college graduates are really unaware that it is summer in the north when it is winter in the south… Jeez this just can’t be true.

    I know our born agin brothers and sisters don’t care about all that scientific type stuff but how can anybody get through 16 years of full time classroom study without triping over idea that the tilt of the planet in relation to the earth revolving around the sun causes the change of seasons? I bet even GW Bush knows this. I won’t bet $10,000 but maybe a cold beer.

    Hey MobiusKlein- Einstein would have loved that “more shade” explaination. Simple and accurate.

  18. dave says

    was just reading calvin and hobbes to the kids tonight and discovered that actually calvin’s dad got it right! he was miquoted. he explains that its getting colder because of the tilt of the earth!

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