17 Oct 2012

If Bryan Caplan Had His Way, We Would Never Have Heard of David Henderson

Bryan Caplan, David R. Henderson 58 Comments

Bryan Caplan argues that because most people don’t remember or use algebra as adults, it fails a cost-benefit test and shouldn’t be taught. Bryan acknowledges that people who go on to take calculus retain their knowledge of algebra even into adulthood, but doesn’t draw the obvious inference–that people with mathematical aptitude first take algebra, and then gladly go into the harder stuff.

What amazes me is that Bryan doesn’t even give a nod to what (in my mind) is the most obvious reason to continue to teaching algebra to everybody: We are casting a wide net to ensure that we steer the right people into areas where their minds will do the most good. People like David R. Henderson. Had he not been exposed to algebra and its delights, DRH might be a retired hockey player right now, promoting his autobiographical The Joy of Checking.

58 Responses to “If Bryan Caplan Had His Way, We Would Never Have Heard of David Henderson”

  1. Major_Freedom says:

    Caplan’s theory is even more intellectually permissive.

    Since most adults don’t remember or use 90% of the words in the dictionary, present-day dictionaries fail the cost-benefit test, and so we should eliminate those words from all high school dictionaries.

    Or, closer to home, since most adults don’t remember or use economic theory in their daily lives, economic theory fails the cost-benefit test, and shouldn’t be taught.

    I wonder if Caplan will take this logic to its conclusion and argue his way out of a career.

    • Bob Murphy says:

      I wonder if Caplan will take this logic to its conclusion and argue his way out of a career.

      All he does is provide a signal to employers, anyway. No loss.

      • Major_Freedom says:

        That’s why most employers tend to hire new graduates who have degrees in totally unrelated fields, right?

  2. Chris H says:

    Broad-based educations are doubtless a good idea, but there are a lot of ways to have broad-based educations can be done, some of which may involve not bothering with algebra. By arguing for algebra education I think you might be falling into a bit of a trap here Dr. Murphy. The question should not be what should be taught to everyone for clearly not everyone should be taught the same thing.

    In this regard, I think Caplan’s argument is less we shouldn’t have algebra in public schools, but simply added evidence that we should not make kids go to formal education. This matches with his previous arguments about how modern schooling is more important in signaling to employers than in actual teaching (see: http://econlog.econlib.org/archives/2011/11/the_magic_of_ed.html I will note that here Bryan’s talking about higher education, but this algebra arguments seems to offer the possibility to extend the point to public secondary education). In this regard are there a group of individuals who benefit from algebra education? Of course, just as there are groups who benefit from reading the works of Charles Dickens. What this does suggest is however that central authorities are really bad at choosing what each student should learn.

    Ultimately I’d say don’t view this as an argument against algebra per se as an argument against public schools, something that makes sense given the PS about a debate over government support of public higher education.

  3. Ivan Ivanov says:

    Dr. Murphy… I find your lack of faith in freedom disturbing… 😛

    I’d agree a good education system would expose people to as many fields, ideas, and concepts as possible, but it wouldn’t constantly bludgeon people on the head with them, like it’s done today.
    Also some argue that the way math is taught today does more to drive people away from it, then anything else:
    http://www.maa.org/devlin/devlin_03_08.html

    That said, the kind of arguments Bryan Caplan constructs from statistics often strike me as… insane, and there definitely is a lack of nods to obvious counter arguments, etc.

    • Bob Murphy says:

      Dr. Murphy… I find your lack of faith in freedom disturbing…

      And I find your freer-than-thou moralizing annoying. (I realize you were cracking a joke.)

      But seriously, do you guys think I was doing anything besides saying what curriculum I think is appropriate, either in a voluntary private school, or for my own kid if I homeschool him? Do you really think I was advocating sticking a gun in parents’ faces and saying, “Your kid is going to see some binomials today, or you’re eating lead!!” ?

      This was a quick post I fired off right before going to bed. Were it not for the capacity of a Henderson Canadian joke, I wouldn’t even have made it.

      Suppose Bryan wrote, “I think people should be able to drive on whatever side of the road they want. Surveys show that people in England are just as happy driving on the left, as Americans are on the right.” Then I do a one-sentence blog post, “This is stupid.” I imagine within 24 hours all the Ron Paul activists would spread the word about what a sell-out I was, for endorsing government roads.

      I am not even kidding, I feel more stifled by libertarians than evangelical Christians, and I’m members of both movements.

      (Again, I know you were mostly cracking a joke Ivan. I’m not biting your head off, I’m just using this as a “teaching moment”–since I like to cram those down everyone’s throat.)

      • Ken B says:

        Learn or eat lead!

      • Ivan Ivanov says:

        Woah… I actually heard a few complaints about the liberty movement that went in similar vein, but I wasn’t aware it could be THAT frustrating.

        So just to clarify: yes as you noticed I was just cracking a joke, I didn’t mean to moralize, and I would never dream of accusing you of advocating threats of violence against anyone for any reason.

        Like you, I was just making a comment about what I think would be an appropriate curriculum in a voluntary setting.
        My attitude is a bit more permissive, and so I couldn’t resist calling on the general ideal of freedom.

      • John S says:

        “I feel more stifled by libertarians than evangelical Christians, and I’m members of both movements.”

        I apologize for the self-righteous tone of my posts. But I’m very keen on the issue of children’s rights. They don’t have the full rights of adults, but certainly, in some way, public school students’ rights are being trampled on daily. This is an injustice.

        I certainly get what you’re saying about parents having the right to choose the best education for their children. I do NOT advocate imposing the Sudbury Model on all families. However, I do think it’s a beautiful example of freedom in action and deserves more support from the libertarian movement.

  4. Mike says:

    I teach 7th grade math. We are not just casting a wide net. Educators believe that all students need to know algebra. This is the conventional wisdom, but it is a reasonable point to debate. Caplan likes to make unconventional arguments, but we should not fall into the trap of arguing that he is clearly wrong because everyone knows we need to teach algebra. You ought to make it clear how much algebra you think we should make mandatory before you criticize his point.

    • Bob Murphy says:

      You ought to make it clear how much algebra you think we should make mandatory before you criticize his point.

      Mike doesn’t believe in freedom!! He’s treading on my blogging rights!!

  5. John S says:

    The Sudbury School model is the only type of schooling that doesn’t violate the non-aggression principle. We shouldn’t interfere with children’s right to control their own learning. Children are naturally curious, we just need to get out of their way.

    http://www.psychologytoday.com/articles/200604/education-class-dismissed

    • Bob Murphy says:

      The Sudbury School model is the only type of schooling that doesn’t violate the non-aggression principle.

      And Mozart was a Red.

      • Ken B says:

        His really name was Teddy Wilson. The Mozart thing was a nickname.

      • Matt Tanous says:

        Direction is aggression! Education violates the NAP! So does employment! People have the right to control their own working!

        LOL

        • Gene Callahan says:

          That’s a rather tanous conclusion you’ve reached there!

        • John S says:

          “People have the right to control their own working!”

          Sure they do. If you don’t like your job, you can quit. Working is a voluntary exchange of labor for payment.

          Children very rarely have the opportunity to “quit” their school. If a child would rather study science instead of Shakespeare, what right does a teacher have to force him to spend his time on Macbeth?

          How can you (and Bob) be opposed to free, democratic schooling? Shouldn’t the principle of freedom be extended,, as much as possible, to children (or teenagers at the least)?

  6. John S says:

    “Had he not been exposed to algebra and its delights, DRH might be a retired hockey player right now”

    C’mon Bob, you’re better than this type of paternalism. If someone is naturally inclined toward math and given the freedom to learn whatever they want, don’t you think the odds are quite likely they will gravitate toward it at some point?

    Ivan Illich needs more love among libertarians. This book is a classic.

    http://en.wikipedia.org/wiki/Deschooling_Society

    • Bob Murphy says:

      C’mon Bob, you’re better than this type of paternalism.

      Should I be paternalistic toward my own son?

      • Gene Callahan says:

        Fascist!

        • Ken B says:

          Actually Bob asks a good question though. And one for which Libertarians never seem to have a good answer: how to deal with kids. Or the senile. Or the deranged. Or the suicidal.

          • John S says:

            Ken B,

            The school reformer John Holt wrote an excellent book on the rights of children, “Escape from Childhood.” http://arvindguptatoys.com/arvindgupta/escapefromchildhood.pdf

            Seriously, I can’t believe I’m getting so much pushback on the presumably uncontroversial statement that freedom is good for children and teenagers.

            • Ken B says:

              I think to be fair Bob et al are pushing back on how *much* freedom.

              • John S says:

                For 99%+ of children today, I think they deserve more freedom in what they learn. Isn’t this a reasonable opinion?

      • John S says:

        You should allow him to pursue his curiosity as much as possible. You can expose him to certain areas of study, but trying to force him to learn will, at best, lead to temporary retention. At worst, it will lead him to actively hate the subject being forced upon him.

        Decades of evidence exists from the Sudbury School and similar democratic schools that freedom works in education just as well as it does in other areas of life.

  7. joeftansey says:

    “Bryan Caplan argues that because most people don’t remember or use algebra as adults, it fails a cost-benefit test and shouldn’t be taught.”

    I don’t see anywhere in the post where he says it’s a flat out bad idea to teach students algebra. Just that teaching everyone algebra doesn’t seem to translate into long term gains for most people. This is still compatible with the net-theory of education.

    The bulk of Caplan’s post is not even about taking algebra, but whether we should force students to take more math (up to calculus), since those students have better algebra retention rates.

    • Bob Murphy says:

      joeftansey wrote:

      The bulk of Caplan’s post is not even about taking algebra, but whether we should force students to take more math (up to calculus)…

      It’s funny then that Bryan titled his post, “Does High-School Algebra Pass the Cost-Benefit Test?”

      (You misunderstood what he was saying about the calculus stuff at the end.)

      • joeftansey says:

        “It’s funny then that Bryan titled his post, “Does High-School Algebra Pass the Cost-Benefit Test?””

        He never concluded. He never compared (much less quantified) the costs and benefits.

        “You misunderstood what he was saying about the calculus stuff at the end.)”

        I don’t think I did. Caplan: “Non-economists will probably interpret this as an argument for making everyone take calculus. But what about the cost? Does it really make sense to torture everyone with four years of advanced mathematics to ensure that they don’t forget their first year?”

    • Ken B says:

      I don’t see anywhere in the post where he says it’s a flat out bad idea to teach students algebra.

      Look closer.

      “The vast majority of subjects rarely use algebra no matter how proficient they are. … If the students who already take calculus don’t use it in real life, why on earth should we push weaker students to match their achievement?”

      That’s a pretty clear declaration that we shouldn’t.

      • joeftansey says:

        “That’s a pretty clear declaration that we shouldn’t.”

        1) No, it isn’t. It is asking a question. It just means he thinks there’s a steep burden that proponents of more math education have to meet.

        Does anyone really think that Caplan is unfamiliar with the net-theory of education?

        2) Caplan is talking about whether we should have weaker students pursue *calculus*. Bob is arguing that Caplan thinks students shouldn’t take *algebra*. The quote is NT.

        • Ken B says:

          So you and I should just agree with Bob that Jesus is LORD and start praying?

          Sometimes questions are answers too.

          • joeftansey says:

            “So you and I should just agree with Bob that Jesus is LORD and start praying?”

            I don’t get it. Bob is pretty explicit about his religion.

            “Sometimes questions are answers too.”

            Since I’m not going to convince you be re-iterating that it is a rhetorical question, I’ll try a different route.

            Do you really think Caplan meant to argue that algebra is a waste of time? That it’s overall *bad* for us to even teach it (period!) as Bob is suggesting?

            Caplan did not even try to quantify the “torture” students must endure, nor quantify the benefits of learning the skill. He did zero actual cost-benefit analysis. Indeed, as a firm proponent of the signaling model of education, Caplan is extremely likely to see the purpose of teaching students useless information they will never use on the job.

            • Bob Murphy says:

              Joeftansey, below is the email exchange I just had with Bryan:

              =====
              Your interpretation is correct, Bob. Feel free to quote me!

              Robert Murphy wrote:
              I was critical of your algebra post on my blog. In the comments, one guy
              is saying that your whole post was dedicating to the issue of whether
              schools should make everyone learn calculus. I said that no, you were
              questioning whether every student should be forced to learn algebra. Can
              you please give a one-sentence statement that I can quote?
              ==========

              But Joe, since you didn’t think Bryan titled his own blog post correctly, I suppose this won’t persuade you either.

              • joeftansey says:

                “I said that no, you were
                questioning whether every student should be forced to learn algebra”

                I know he’s questioning it. But you’re saying he *argues* that it shouldn’t be taught *period*.

                You wrote:

                “Bryan Caplan argues that because most people don’t remember or use algebra as adults, it fails a cost-benefit test and shouldn’t be taught. ”

                You watered down your thesis enough in your email to blur this distinction. You should have asked Bryan, point blank if the thesis of his post is “Algebra should not be taught because it fails a CB analysis”.

                You also misrepresented my position to Caplan. I never said his post was dedicated to the issue of calculus. I said “the bulk of” it is about forcing kids to take calculus. You’ll see that he only dedicates one paragraph to discussing the algebra-only group, whereas he dedicates 2-5 paragraphs (depending on how charitable you’re feeling) to the relationships between calculus, algebra retention, and payoff.

                This may not have been the main thrust of his post, but it certainly is “bulky”.

              • Bob Murphy says:

                Joe, have you ever been wrong in your life?

              • joeftansey says:

                No. But it’s all selection bias.

            • Ken B says:

              It depends on what the meaning of it is.

              In other words when Bryan said “If the students who already take calculus don’t use it in real life” it refers to the algebra. Read the whole par and that is clear enough.

              • joeftansey says:

                It refers to algebra. Above he wrote:

                “Before you answer, consider one more finding from the paper. Bahrick and Hall constructed a measure of how much subjects “rehearsed” – i.e., used – algebra in their daily lives:”

                But he also writes:

                “Does it really make sense to torture everyone with four years of advanced mathematics to ensure that they don’t forget their first year?”

                “If the students who already take calculus don’t use it in real life, why on earth should we push weaker students to match their achievement?”

                So he asks 3 questions. One in the title about whether algebra fails the CBA, and 2 in the body about whether we should force the masses to take calculus.

              • Bob Murphy says:

                So he asks 3 questions. One in the title about whether algebra fails the CBA, and 2 in the body about whether we should force the masses to take calculus.

                I was actually joking Joe when I said that you wouldn’t even believe Caplan himself, telling you what his post was about. It will be hard for you to become wiser, if you absolutely refuse to admit when you are wrong about something.

                (To give you a hint: Caplan was saying that the results of that survey showed how few people retained algebra into adulthood, and so that was prima facie evidence that algebra doesn’t pass the cost-benefit test. Then it’s true, he dealt with a possible retort from someone who would look at the same graph and claim, “Well if we just forced everyone to take calculus too, then it looks like they’d retain the algebra.” So yes, Caplan had an offhand remark that torturing students even more by forcing them to all learn calculus, would be dumb. But this was him dealing with a possible objection to the post itself, which was dedicated–as its title and Caplan over email personally confirmed–to the topic of whether algebra should continue to be taught to everybody.)

              • Ken B says:

                “I was actually joking Joe when I said that you wouldn’t even believe Caplan himself, telling you what his post was about. It will be hard for you to become wiser, if you absolutely refuse to admit when you are wrong about something.”

                I cannot resist pointing out Bob that you went ballistic when I made a similar joke to you imagining Jesus telling you he was not god.

              • joeftansey says:

                “It will be hard for you to become wiser, if you absolutely refuse to admit when you are wrong about something.”

                You distorted both your thesis, and my thesis in your e-mail to him.

                “To give you a hint: Caplan was saying that the results of that survey showed how few people retained algebra into adulthood, and so that was prima facie evidence that algebra doesn’t pass the cost-benefit test”

                No it isn’t. It is simply a description of benefit. There’s no commentary on whether it “passes” a CB test.

                “So yes, Caplan had an offhand remark that torturing students even more by forcing them to all learn calculus, would be dumb. But this was him dealing with a possible objection to the post itself,”

                Which, strangely, took up more volume than his title would suggest… Which is why I said “the bulk” of his post, rather than the “thesis”, “dedication”, or “thrust”.

                “But this was him dealing with a possible objection to the post itself, which was dedicated–as its title and Caplan over email personally confirmed–to the topic of whether algebra should continue to be taught to everybody.)”

                And this is different from what you said – namely that Caplan was arguing that algebra shouldn’t be taught at all.

                Doesn’t it bother you that you had to distort both our positions in the e-mail to Caplan? And that now you’ve abandoned the language of your OP in order to conform to the email?

              • Ken B says:

                Joe: If Bob distorted you how do you explain the comments directed at me that say the same thing Bob alleges?

              • joeftansey says:

                Can you rephrase that with less articles?

              • Ken B says:

                I can say it with fewer articles …

                What you said to me matches what Bob says you said. That suggests Bob isn’t distorting what you said.

                You’re a very cruel man, forcing me to side with Bob this way.
                🙂

              • joeftansey says:

                Is this what you’re talking about?

                “Caplan is talking about whether we should have weaker students pursue *calculus*. Bob is arguing that Caplan thinks students shouldn’t take *algebra*. ”

                Because it is true that Caplan talks about whether weaker students should take algebra, even if that isn’t the “dedication” of his post.

  8. Ken B says:

    Great point. And I think we can see the importance of it in many contexts. Modern society is getting better and better at filtering talented people to careers that suit their skills. The typical orchestra today for example is better than the typical orchestra 50 years ago. There are many factors but better catchment is surely amongst them.

  9. David R. Henderson says:

    Bob, Not a retired hockey player. I was one of the worst skaters in Canada.

    • Ken B says:

      Ohhhhh. A retired Maple Leafs player then.

      🙂

      • David R. Henderson says:

        Ooooh. Nasty Canadian in-joke, Ken B. 🙂

        • Jason B says:

          It had me laughing too, and then reminded me of the lockout. Damn you Ken B. He’s like the Newman of Bob’s blog.

          • Ken B says:

            I confess I don’t catch the reference. But Sarastro to Bob’s Papageno would be my reference, since we’re talking Mozart here.

  10. RPLong says:

    What I liked about Henderson’s post was that he pointed out that mathematics isn’t something unique that appeals to one set of people and not another. Rather, mathematics is any logical chain of thought carried through with a dedication to accuracy.

    I’ve always felt that math is logic and logic is math, and there’s no reason to differentiate the two (no pun intended). As such, people use math whether or not they choose to acknowledge that what they are doing happens to be math. That includes algebra.

    • Bob Murphy says:

      I couldn’t believe those guys took the time to write up that digression in a formal paper! (Right? That was in their paper, if you’re still reading David?) That was amazing.

      • David R. Henderson says:

        I am still reading, Bob. Yes, it was in the original 8-page paper. I loved the fact that they did that. I like the idea of even scholarly papers as conversation pieces. Some of my best lines have been edited out of academic papers by tight-assed journal editors. Well, one of my best lines, anyway.

    • Matt Tanous says:

      “I’ve always felt that math is logic and logic is math, and there’s no reason to differentiate the two (no pun intended).”

      Math is a form of logic. But I think to call all logic math is to make a logically fallacy. All birthday cakes are desserts, but not all desserts are birthday cakes.

      • RPLong says:

        I’ve yet to see any non-mathematical logic that could not also be demonstrated using mathematics, but I am always open to learning new things.

        • Ken B says:

          Whatever you do RP, don’t write “logic = math” over at Landsburg’s blog.

          You’ve been warned!

          🙂

  11. Neil says:

    Math is exercises in logic. Logic, as you know, is under attack in the Western world. It is an agenda. Remember this: http://www.nytimes.com/2000/04/27/nyregion/the-new-flexible-math-meets-parental-rebellion.html?pagewanted=all&src=pm

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