Science and Math Curriculum: A historical Perspective

(The following analysis is based on the California state standards for education, but I doubt the results would be significantly different in other states.)

This is based on a fun question that I posed to some friends (the question is fun — the answers are scary).

When teaching history, the state standards mandate that students analyze fairly recent events (say, US v. Nixon, 1974). I agree that these things are important. Now, if we turn out attention to the hard sciences, how up to date are the state standards in these?

In Biology, a rough survey (I’m neither an expert in biology nor in state standards, take this with a grain of salt) takes us all the way forward to the exciting 1930s showing cell biology and enzymes. The division between prokaryotes and archaea (first proposed in 1970, accepted in 1990s) is still missing. This would be the equivalent of not covering any of the recent events (Gulf War, 9/11) in a history class.

Chemistry: We stop short of “quantum chemistry”, 1926, but we do cover stuff from 1912 — that’s the equivalent of covering World War I, but only giving hints that it was followed by another war.

Physics: we get all the way into the exciting 19th century  with the recent discovery (~1865) of Maxwell’s equations on electromagnetism. A hint of Michelson-Morley (~1890) is added, so I guess at least we have the 19th century licked. This would be the equivalent of covering the civil war, but only giving hints that the reconstruction happened (World War I? World War II? That’s waaay too cutting edge).

Math: At least, by introducing some calculus, we get all the way to the cutting-edge of the 17th century. Newton and Leibnitz would both be happy to know that their discovery of calculus (whoever was first) is taught to the students as a cutting edge mathematical subject. Sadly, the 19th century never happened in high school math, as modern set theory is not even hinted at. Lagrange, Euler and the 18th century are also missing. This is like not teaching the American Revolutionary War. Hey, at least the American continent was discovered…

I find it amusing that this corresponds to the xkcd strip describing purity of subjects. I find it horrifying that we are turning out high-school graduates who are not aware of “cutting edge” (meaning, hundreds of years old and stale) research in the hard sciences.

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5 Responses to Science and Math Curriculum: A historical Perspective

  1. neb_namwen says:

    I feel like this analysis involves a fundamental category mistake about the structure of human knowledge and the nature of education.

    Sometimes we see in science fiction the image of a “more advanced” society whose advancement is demonstrated by the acceleration of its educational system — for instance, teaching calculus in elementary school because they have, as a society, advanced past the point where calculus is difficult. But students don’t learn as a society.

    Picture human knowledge as a building that is constantly being remodeled. Over the years, society reshapes the building to improve its function, adding new floors and towers, sometimes rebuilding a wing that has fallen into disrepair, but only occasionally making major structural changes to the lower floors.

    Meanwhile, everyone enters the building on the ground floor. Some will work their way up to the upper floors and join in the risky construction work up there, others will find work on one of the middle floors. But, the building as a whole is not sinking into the ground, which means that, while the “advanced physics” tower has been remodeled several times in the last few centuries, it is not any closer to ground level than it ever was.

    History and literature are anomalies in this picture because they continue to produce new content on a human time scale even in the absence of new theoretical frameworks. In the last ten years, ten more years of history have happened which can be understood at a high school level as well as at the highest levels of scholarly research. In contrast, I’m not aware of any recent results in mathematics which can be readily explained in less than an hour to someone who is just squeaking by with a B- in algebra. It should also be pointed out that, standards notwithstanding, the fact that there keeps being more history has the predictable result that most schools don’t, in fact, cover it both comprehensively and with any depth. Certainly, adding 100 years of history to the curriculum in the last century has not involved incorporating 100 years of progress is historiographic methods into the high school curriculum.

    Look back over your examples of new knowledge and old knowledge and think carefully about where in the edifice of human knowledge they lie, and how they are holding up. I think most of the new knowledge that’s generally accepted in the academy but that we don’t teach in high school is stuff that you need to have finished high school (or gotten an equivalent education in the subject elsewhere) in order to deal with in a rigorous way. Frankly, nobody who isn’t a research mathematician really needs to worry about modern set theory — but if I ran the world math department, I’d teach more statistics and less calculus, and certainly do away with that ridiculous epsilon-delta stuff that, historically, was primarily of interest to the mathematical research community at the point when it wasn’t yet clear that calculus was consistent with the rest of algebra.

    There’s probably a better overall strategy for incorporating new knowledge into our school-age curricula, but I don’t think the situations in the humanities and the sciences are nearly as different as you make them out to be.

    • moshez says:

      I used history as an example, not because I think history is a well taught subject in schools (it’s not), but because it’s obvious to explain to people how big the gaps are by the analogy.

      However, I completely disagree about the possibility of explaining “modern” math to someone who is “squeaking with a B- in Algebra”. I think that explaining the Hilbert hotel stuff and some basic calculus of infinities *is* something you can do in an hour to the average high school student. I know this for a fact, because it used to be the way I picked up girls in high school (yes, I actually got phone numbers that way).

      Students don’t learn as a society, true, but society can get significantly better at teaching. You seem to suggest dropping epsilon-delta stuff in high-school, but I don’t think it’s even introduced in high-school…I agree that informal calculus is all that’s needed, and that statistics is also sorely missing. I think explaining about basic set theory is a good segue into explaining about computability (the halting problem proof is better understood if the concept of diagonalization is understood), and I think explaining to people why programs have bugs is actually important. I think we *can* bring people up to date on the forefront of mathematical research by showing some of the topics but without delving into the hard problems — there’s no reason not to introduce model theory, set theory, computational statistics, etc — just don’t make them solve the hard problems as exercise.

      Likewise, I think it’s critical that people will understand the basics of quantum mechanics and black body radiation, because I am sick to death of explaining to people how radiation works, how cancer is (sometimes) caused by it and why microwave radiation cannot bump electrons.

      Biochemistry is something we’re all naturally exposed to with pharmaceuticals underpinning (for better and for worse) modern society. Maybe we’d get less belief in homeopathy if people understood how chemistry really works.

      Biology is a curious example. If you go to any of the creationist sites, the lie that stands out most phenomenally is not what you expect — it’s that evolution is being taught in school at all. We do a poor job of educating people in how biology works, to the point where I had to explain to a friend (who has graduated a traditional public high-school, a respectable college and is now in training for being a medical technician) why description of evolution as “giraffes have long necks because they try to reach the top of trees” is wrong.

      People come out of high-school with misconceptions and gaps that, to someone into the hard sciences such as myself, would be a lot like someone never hearing that WWII was this big war between Germany and a bunch of other countries. I use the analogy of history to explain how big the gaps seem.

      You seem to agree that we’re using a suboptimal educational strategy, though, and just objecting to my metaphor, not that it’s impossible to get people significantly higher in the building of human knowledge.

      • neb_namwen says:

        You seem to agree that we’re using a suboptimal educational strategy, though, and just objecting to my metaphor, not that it’s impossible to get people significantly higher in the building of human knowledge.

        That’s pretty much it. I think the use of history to show the scope of the gaps is misleading both because the gaps you mention should be measured in different units and because the way history is taught has gaps just as big as those in the sciences if you turn it sideways.

        I guess what I object to is the implied claim that, since we can incorporate new material into history curricula, we should be able to do “the same thing” in science curricula, not because I don’t think anything needs to be done, but because I don’t think it’s the “same thing”. (I would also dispute that we’re reliably capable of stretching our history curricula without incurring other costs.)

        I’m professionally interested in math and science education, but I’ve been talking way past my actual knowledge, so I’m going to slow down a bit…

        One factor I think is making your analogy ring false to me is the way that time affects the salience of history in the popular consciousness. The facts of history are most salient when most recent, then most of them fade into obscurity and a few big ones remain salient. The interpretation of history follows a bit behind this curve. Science and mathematics for the most part don’t work this way — the most popularly salient science is what has stood the test of time, while the most popularly salient history is today’s front page headline. For this reason, I’m not sure an analogy between a curriculum which omits recent history and a curriculum which omits recent science is apt. That our history curricula tend to be narrowly focused on “our” history (whoever “we” is in context) and organized around received and/or politicized notions of what that history is supposed to mean, seems to me to be the better analogy.

  2. JB says:

    At least you are lucky not to have suffered the Set Theory fashion (Bourbaki …) that we had to endure in Europe … I´d rather have good foundations than last minute gossip from clueless pedagoges.

  3. Hila Zadka says:

    Well, I sometimes read your blog, but this time my disagreement with you is big enough for me to respond 🙂

    I tend to agree with neb_namwen regarding the better strategies to teach history. And as I’m not an expert in the field (and moreover – know nothing about the American education system) – I feel I cannot say much more about it.

    But regarding teaching biology and other sciences:
    1. The chemistry taught in high school (at least Israeli ones) is more than enough for one to understand that homeopathy has absolutely nothing to do with science, facts, empirical data etc. People believe in many things that have nothing to do with any of the above (here is one random example – god). So what? they enjoy its placebo effect – good for them! (no cynicism in my last sentence).
    2. Recent (recent being, let’s say, last 2-3 decades) discoveries in biology (not talking right now on other sciences, but I have the feeling it is true at least for several of them) are not understandble to a complete layman (someone who didn’t learn the basics of the field – e.g. mendelian and molecular genetics, cell biology bla bla bla). True, I am able to explain my research question to a layman, and it might even seem to him quite interesting. But this is misleading – I will not be able to explain the complexities, the models I’m using, the really interesting stuff – without this layman having a basic understanding in neurobiology, neuropsycholgy, and even some mathematics. From my point of view, this is the kind of understanding that should be achieved during undergraduate studies. It happens that the relevant discoveries where made more than a century ago! Obviously, high school studies should give the student the even more basic knowledge – discovered more than 2 centuries ago (you mentioned earlier Darwin and Lamark…).
    3. I know you’re extremely good at finding the examples who will “contradict” my previous argument. Of course, I bet you can find a few examples of recent discoveries in biology that are completely understandable to a layman (i.e. high school student). But I still think that while most recent discoveries can be written as a pretty title in “Scientific American”, a high school student cannot really understand their full meaning.
    4. Every once in a while (usually quite a long “while”), the science discovers something that “rocks our (scientific) world”. This kind of discoveries, which make the stuff taught to high school students wrong or extremely inaccurate, should obviously be taught. But, again, these events are (sadly? happily?) quite rare.
    5. I agree that the teaching strategy of sciences in high school (at least what I know from Israel) is far from optimal, but on a whole different level.
    6. I apologize for my English being like 10 levels below yours. You are more than welcome to blame it on the Israeli education system, again (although I must say, given my life circumstances, I’m not sure it’s the system’s fault ;-).

    Shana Tova!

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