The Infinite Cycle of Gladwell’s David and Goliath

I recently finished reading Malcolm Gladwell’sĀ David and Goliath: Underdogs, Misfits, and the Art of Battling Giants. The book is like most Gladwell books. It has a central thesis, and then interweaves studies and anecdotes to make the case. In this one, the thesis is fairly obvious: sometimes things we think of as disadvantages have hidden advantages and sometimes things we think of as advantages have hidden disadvantages.

The opening story makes the case from the Biblical story of David and Goliath. Read it for more details, but roughly he says that Goliath’s giant strength was a hidden disadvantage because it made him slow. David’s shepherding was a hidden advantage because it made him good with a sling. It looks like the underdog won that fight, but it was really Goliath who was at a disadvantage the whole time.

The main case I want to focus on is the chapter on education, since that is something I’ve talked a lot about here. The case he makes is both interesting and poses what I see as a big problem for the thesis. There is an infinite cycle of hidden advantages/disadvantages that makes it hard to tell if the apparent (dis)advantages are anything but a wash.

Gladwell tells the story of a girl who loves science. She does so well in school and is so motivated that she gets accepted to Brown University. Everyone thinks of an Ivy League education as being full of advantages. It’s hard to think of any way in which there would be a hidden disadvantage that wouldn’t be present in someplace like Small State CollegeĀ (sorry, I don’t remember what her actual “safety school” was).

It turns out that she ended up feeling like a complete inadequate failure despite being reasonably good. The people around her were so amazing that she got impostor syndrome and quit science. If she had gone to Small State College, she would have felt amazing, gotten a 4.0, and become a scientist like she wanted.

It turns out we have quite a bit of data on this subject, and this is a general trend. Gladwell then goes on to make just about the most compelling case against affirmative action I’ve ever heard. He points out that letting a minority into a college that they otherwise wouldn’t have gotten into is not an advantage. It’s a disadvantage. Instead of excelling at a smaller school and getting the degree they want, they’ll end up demoralized and quit.

At this point, I want to reiterate that this has nothing to do with actual ability. It is entirely a perception thing. Gladwell is not claiming the student can’t handle the work or some nonsense. The student might even end up an A student. But even the A students at these top schools quit STEM majors because they perceive themselves to be not good enough.

Gladwell implies that this hidden disadvantage is bad enough that the girl at Brown should have gone to Small State College. But if we take Gladwell’s thesis to heart, there’s an obvious hidden advantage within the hidden disadvantage. Girl at Brown was learning valuable lessons by coping with (perceived) failure that she wouldn’t have learned at Small State College.

It seems kind of insane to shelter yourself like this. Becoming good at something always means failing along the way. If girl at Brown had been a sheltered snowflake at Small State College and graduated with her 4.0 never being challenged, that seems like a hidden disadvantage within the hidden advantage of going to the “bad” school. The better plan is to go to the good school, feel like you suck at everything, and then have counselors to help students get over their perceived inadequacies.

As a thought experiment, would you rather have a surgeon who was a B student at the top med school in the country, constantly understanding their limitations, constantly challenged to get better, or the A student at nowhere college who was never challenged and now has an inflated sense of how good they are? The answer is really easy.

This gets us to the main issue I have with the thesis of the book. If every advantage has a hidden disadvantage and vice-versa, this creates an infinite cycle. We may as well throw up our hands and say the interactions of advantages and disadvantages is too complicated to ever tell if anyone is at a true (dis)advantage. I don’t think this is a fatal flaw for Gladwell’s thesis, but I do wish it had been addressed.


The Myth of a Great Seminar

Sometimes I peruse the debates at Intelligence Squared to see if any catch my eye. There was one this time that seemed really interesting to me. It was a debate on whether or not MOOCs are reasonable replacements for actual in-class and campus college experiences. You can see the full thing here.

This was interesting to me, because I’ve actually gone through a few MOOCs from start to finish and found them to be extremely good experiences. I was curious if there was research that would be mentioned about the effectiveness of one or the other. The debate was pretty disappointing in this regard. The main anti-MOOC argument was based around how wonderful small seminars are and that you can’t get this in a MOOC. That’s why I want to write a response to this mythical seminar.

Before talking about why I think such seminars don’t really exist in this Platonic, pristine state at any university, I want to first address the fact that the existence of seminars at all is pretty mythical. I decided to check the University of Washington’s Spring 2014 schedule. The senior level literature classes had a student range of 25-40, but most were about 30. Should I consider a 30 person class a “small seminar?” I get it. We’re a gigantic school, so I fully admit that small liberal arts colleges probably do have a lot of small seminars. But most students at most schools will graduate with few to no small seminars as their classes.

Even middle level courses like Introduction to the Theory of Literature at Ivy League schools are gigantic. That class probably has 100 students or more in it, and those are the types of courses that are offered as MOOCs. I think the comparison is a bit disingenuous when you take some capstone seminar and compare it to an “intro” MOOC. The MOOC side of the debate also responded to this criticism and pointed out that some MOOCs offer small group breakout sessions which actually do simulate small seminars. So the point doesn’t even stand.

Now that that rant is over, let’s pretend like the comparison is fair. Here are some of the myths I heard and why I think they are mostly myth (I’ll grant that maybe a few seminars run according to plan):

Let’s suppose for the sake of argument that the teacher is practically invisible in this mythical seminar and the students are all enraptured in high level critical conversation about Dostoevsky or some such nonsense. This seems to be the ideal the seminar aspires to. This is going to sound extremely cynical, but just how interesting can this conversation actually be? The seminar is going to be made up of an incredibly homogeneous group. Everyone is going to be about 20, never having had to make a living. They are all educated at the same school, which means they have roughly the same cultural experience, read the same books, and developed the same theories about how to analyze books.

What’s so great about this perfect conversation in comparison with a MOOC? When you take the exact same course as a MOOC, you will probably have a math professor in India, a farmer in the American midwest, a retired middle school teacher in Scotland, etc. The conversation about the same books is going to be infinitely more interesting and enlightening, because the perspectives will be so varied.

Now let’s back up a little from the perfect situation and get a little more realistic. We’ve all been to these seminar classes before. The free-flowing and enlightening conversation essentially never happens. You have some people who didn’t read the stuff. You have people who aren’t very good at articulating their thoughts on the spot. The whole thing usually turns into the professor calling on someone, a brief sentence or two is mumbled, and then the professor carries on along that point. The “conversation” is forced, and the student input is more like a prompt for the professor to riff on.

Depending on the day and material, the degree to which this is the case will vary, but I think the overall sentiment is what happens most days in most seminars. This is actually why I think a written discussion board in a MOOC is actually a far better method for discussion than a conversation in a seminar.

First off, there are hundreds of more topics and conversations going on at a discussion board than in class. This means that you can search around for conversations that you really want to participate in. Second, you have to write your thoughts down. This gives you time to figure out what you are going to say rather than awkwardly spewing out some muddled nonsense while everyone stares at you. It also gives you time to figure out what other people mean before responding to them.

It is amazing the number of times you start typing a response, and then when you go back to what was actually said you realize you misunderstood at first. Which brings me to my next point. A discussion board records all of it. You can continually return to conversations as your understanding of a topic develops. The conversation doesn’t end at the end of the hour. Once you leave the physical setting of a seminar, it probably only takes a few hours to forget most of what most people said. The discussion board allows you to go back whenever you want to recall certain parts of certain conversations.

To summarize, I think most courses most people take are not seminars, so it is pointless to use them as a main argument against MOOCs. I also think that the MOOC setup is actually a better platform for enlightening discussion in almost every respect than an actual seminar. That being said, I think the anti-MOOC side has a point when they say that communication skills are developed in class discussion. Unfortunately, even small seminars tend not to have real “discussions,” so I don’t find that compelling (along with the fact that some MOOCs are incorporating small group live chat sessions now).

Don’t get me wrong. I don’t think all university education should be relegated to the online setting. I’m just saying that using some idealized small seminar as the main argument is a highly flawed way to go about it.

Thoughts on Nicholson Baker’s Case Against Algebra II

The debate over standards in high school math has been going on for a very long time, but things seemed to come to a pretty nasty head last year when the New York Times ran the article Is Algebra Necessary? Bloggers and educators were outraged on both sides and started throwing mud. In the most recent issue of Harper’s (Sept 2013), Nicholson Baker wrote an essay basically reiterating the arguments from the NYT’s piece and responding to some of the criticisms.

I’ve been trying to stay out of this, because I honestly have no idea what high school is designed to do. The real argument here doesn’t seem to be whether or not algebra is “useful in the real world,” but rather about whether or not we should force students to learn things in high school that they are not interested in. Is the purpose of high school to teach students the basics in a broad range of topics so that they have some fundamental skills that will allow them to choose a career from there? Is the purpose to allow students to learn topics that are of interest to them? Something else?

I don’t know, and it is impossible to participate in this debate without clearly defining first what you think the purpose of making students go to high school is (of course, the arguments are muddied by the fact that no one actually defines this first).

Here is Baker’s main argument in a nutshell (he is a fantastic writer, so you should read the full thing yourself if this interests you). Algebra (II) is unnecessary for most people, i.e. the 70% of the population that do not go into a STEM field. It causes excessive stress and failure for basically no reason. Why not just have some survey course in ninth grade where some great ideas of math throughout history are presented and then have all future math courses be electives?

I assume for consistency this means that since English, foreign languages, history, and all other subjects taught in high school are also not directly applicable to most people’s daily lives that basically you’ll do ninth grade as a taste of what the subjects are about through survey courses, and then literally everything is an elective afterwards.

Honestly, I agree with Baker that this would probably make high school a lot more enjoyable and useful for everyone. A lot more learning would take place as well. It just boils back down to what you think the purpose of high school should be, and since I don’t know, I can’t say whether or not this is what should be done.

Here’s two thoughts I had that don’t seem to be raised in the main discussion.

1. How do you know whether or not taking algebra will be useful to you? Having core standards in some sense protects the high school student who isn’t equipped to make this type of decision from making a really bad decision. I’ll just give an anecdote about my own experience as someone who really loved all forms of learning and went into math and who still made a really bad decision when given a choice of electives.

When I was going into my senior year of high school, I knew I wanted to be a composer. I knew this so confidently that despite being advised against it, I decided to not take physics since it was an elective. My reasoning was that I would never, ever need it for my future career as a composer. Let’s ignore the fact that I didn’t realize that understanding the physics of sound is an extremely important skill for a composer to have and so made a poor decision for that reason. Let’s assume that physics really was useless for my intended career.

After my first year of undergrad I switched to a math major. I really regretted not taking physics at that point and ended up loving physics in college so much that I minored in it. Here’s the point. Almost no one in high school knows what they are going to do. So how in the world are the going to know if algebra is necessary for their career? Even if they know what they are going to do, they could still end up mistakenly thinking that it is unnecessary.

My guess is that if we switch to a system where practically everything is an elective, then when people get to college and their interests change they won’t have the basic skills to succeed. They’ll have to fill in this lacking knowledge on their own, because math departments definitely cannot offer more remedial classes. We have so many students and classes as it is we can barely find enough people to teach them all.

2. This seems much ado about nothing. What I’m about to say might seem harsh, but algebra II is not that hard. You don’t have to be good at it. You don’t have to like it. But it isn’t a good sign if you can’t at the very least pass it. Baker himself points out that Cardano in the 1500’s was able to do this stuff. Since then we’ve come up with much easier and better ways to think about it. The abstraction level is just not that high. We’re not talking about quantum mechanics or something. Students in other cultures don’t seem to struggle in the same way, and I don’t think we’re inherently dumber or anything.

Depending on where you look, 30%-50% of students fail algebra II. Let’s say it is closer to 30 because a large number of this statistic does not take into account that there are lazy/rebellious/apatethic/whatever students who can easily handle the abstraction, but just don’t put any work in and fail for that reason. I’d imagine the number of people who try really hard and still fail is pretty low (maybe 20% or less? I’m just making stuff up at this point, but probably way less if you count people who never pass it).

Is it too insensitive and politically incorrect for me to say that someone who can’t handle this level of abstraction probably isn’t cut out for college in any subject? Is college for everyone? I can’t remember what the proper response is to this anymore. What if the number who never pass is around 5%? Is saying this 5% isn’t cut out for college still too much? Sure, give them a high school diploma if they can’t do it, but college may not be the best fit. It seems a good litmus test.

What major won’t require abstraction at least at the level of algebra II? STEM is out. English? Definitely out, unless you somehow avoid all literary theory. Business? Most business degrees require some form of calculus. Music? I hope you can somehow get out of your post-tonal theory classes. History? There has been a recent surge of Bayesian methods in historical methods.

I guess the point is that if a high school diploma is meant to indicate some level of readiness for college, then algebra is probably a good indicator. This does not mean that you will use it, but will just point out that you have some ability to do some abstract things. I’m not saying it is the only way to test this, but it is probably a pretty good one.

Again, if a high school diploma isn’t meant to indicate readiness for college, then who cares what you do?

*Cringes and waits for backlash*