Wednesday, April 7, 2010

Math-phobia, pedagogy and the choice of occupations

The general question that I am interested in is this: how does the pedagogy of science (and mathematics) influence a student's choice of occupation i.e. whether she decides to become an engineer, a doctor or even a lawyer? In particular, I am interested in understanding why the best and the brightest high school students in the United States usually choose not to become engineers or scientists while those in India choose the technical professions in overwhelming numbers, even though the style of science pedagogy is roughly the same in both countries. My hunch is that while the style of science pedagogy remains the same, the style in which other subjects are taught is drastically different and this, in turn, is responsible for the difference in the number of students who opt for technical careers.

But I want to develop this answer a bit more. So here goes.

How do styles of pedagogy influence the choice of a career/major? In a sense, the answer is trivial. An "internalist" account would go as follows: students develop an interest in a subject depending on how it is taught to them. This, in turn, depends on the pedagogical style used. Their like (or dislike) for certain subjects will typically determine the occupation they end up in. Reasonable. So, for instance, a student who likes science and mathematics in high school, is more likely to be an engineer or choose a technical occupation. A student who dislikes mathematics intensely ("math-phobia") is more likely to want to be a journalist, writer or lawyer.

The reason I call this an "internalist" account is that it ignores all the "external" factors that go into choosing a career. Jobs have values associated with them: some pay more than others (law, medicine); others have cultural prestige (academia, research), yet others offer you the possibility of being influential (journalism, politics). These values (and a lot of chance: the job market, familial obligations) often determine an occupation a person ends up in.

For the purposes of this post, I am going to ignore the these external factors (or only bring them up when needed) and concentrate on the "internalist" account that assigns a student's like or dislike for a certain subject as the main reason for her choice of occupation. But this account itself is too vague and non-explanatory if the issue at stake is choosing an occupation out of all possible occupations; e.g. it gives almost no understanding of why someone goes into journalism rather than law. It does, however, have a certain power if the issue in question is the choice between a technical occupation (i.e. being an engineer, a doctor, a computer programmer, or a researcher in science and technology) and a non-technical occupation.

So far, so good. Let me now restate the internalist account with a focus on the choice between technical and non-technical occupations. Students who experience some kind of aversion to science and mathematics in high school (a.k.a. "math-phobia") will typically not choose to go into technical occupations. The ones who don't feel math-phobic are more likely to become, say, engineers.

What causes this math-phobia in high school? Mostly, it is attributed to the "authoritarian" way that mathematics and science (especially physics) are taught. (Note that from now on, when I use the word "science", it means "mathematics and the mathematical sciences".) The use of an adjective, often used to describe hated regimes, being used to describe science education often surprises people. The metaphor is largely correct, I think but it has some slightly different connotations while describing a style of pedagogy.

Consider how we learn Newton's laws of motion. The laws are first, of course, taught to us and explained. But explaining the law and expressing it in symbolic form (e.g. F=ma for the Second Law) is only the first step. The most important thing in learning the laws of motion is to be able to use them to solve problems. It turns out that most students can't solve problems on their own just by learning the laws because the symbolic forms of the law used in these equations (e.g. mg = d2s/dt2 for problems dealing with free fall and gravity) bear little resemblance to the canonical F=ma. Students need to learn to transform F=ma so that it applies to a variety of scenarios. And the way they learn this is by solving practice problems, scores of them. There is no other way of mastering Newton's laws of motions without solving practice problems.

You can see why students can often find the procedure authoritarian. They are being asked to do something (solve problems) without really "understanding" it. But of course, as more problems are solved, students do understand, which, in this context, means that they learn to inductively apply the laws of motion to a variety of scenarios (free fall, motion on an inclined plane, etc.) on their own. Understanding in science means to understand in practice.

But solving problems can often be a frustrating experience, especially when one is learning them because an active construction process is involved. The current problem has to be seen in terms of previously solved problems, that too in a certain way. Note that, in this scenario, the teacher can only do so much: she can demonstrate more solved problems in class, teach the students certain tricks of the trade, she can arrange the problems in the textbook in a very precise order of difficulty so that progressing from one problem to the next is more orderly, she can help a student when he gets stuck. But that's really about it. It is finally the student who has to grind through the unsolved problems in order to master a concept -- and one can see easily why students get turned off.

In order to see how limited the actions of the science teacher are, consider a teacher of history teaching, say, the Great Depression. She can show a movie about the Depression, read extracts from novels set in that time, look at photographs or she can ask her students to write short stories set in the Depression highlighting some aspect of it. The pedagogical possibilities are endless (and "creative"). But if you compare this to the possibilities existing for a science teacher, who has to get her students to solve problems and thereby master the concept, and you will see how rigidly structured the teaching of science is.

The interesting thing to note here is that science pedagogy is pretty much the same across countries and cultures (which makes sense, because science is a relatively autonomous culture). Of course, there are differences: the class size may be smaller or larger, the teacher may have more time or less to demonstrate solved problems, the textbooks may be better or worse or more easily available. But the end objective is the same: in some way or the other, the teacher has to make the students solve the practice problems, which in turn means that the students have mastered a concept.

And yet -- and this is where we come to the main point of this post -- if the style of pedagogy influences the choice of college majors and/or occupations, and if the style of science pedagogy is still the same i.e. authoritarian, then why do so few students opt for engineering/technical majors in the US while so many of them do in India? To make the point a little more narrow and precise, why do the "best and brightest" students in the US choose non-technical professions (law, business) while those in India opt in overwhelming numbers for engineering and medicine? (For now, assume that this category of the "best and brightest" just exists.)

Obviously this claim needs to be substantiated. Without going into too many details (and honestly, I don't really have the statistics), let's take the admissions figures of an elite US university.

Admissions statistics for Columbia University show that there were 21273 applicants for Columbia College (CC) but only 4154 applicants to the School of Engineering (SEAS). Assuming that this is a fair sampling of the best and the brightest, it's clear that the number of CC applicants is almost 4 times the SEAS applicants! Now it is possible that a lot of CC graduates major in Mathematics or Physics but if this (and this) data is any indication, I would say that most common major would be Psychology.

Contrast this with some figures from 2007 of the Joint Entrance Examination (JEE) to the elite Indian Institutes of Technology (IITs). "Over 240,000 candidates took the exam, and "7,209 (almost 3 percent) are eligible to seek admission to 5,537 seats" in the seven IITs, IT-BHU and ISMU-Dhanbad." Clearly the best and the brightest in India prefer the technical professions (and majors) to the non-technical ones.

Why the discrepancy?

I am not going to argue that the "external" factors don't matter here. Clearly, they do, perhaps overwhelmingly so. Getting into an elite engineering college in India is sometimes the only sure-shot way of guaranteeing oneself a pretty decent job straight out of campus. And engineers and doctors in India are well-regarded socially too.

But I am going to argue that the "internal" factors (a student's interest in science and technology, i.e. whether or not a student suffers from math-phobia, which in turn depends on the styles of pedagogy) matter too. Here's why. Clearly someone who is math-phobic and has an aversion to mathematics will not opt for an engineering degree in college. So at the very least, something must happen that makes the best and the brightest in India less prone to math-phobia. Clearly that something cannot be the style of science pedagogy, which, if anything, is even more authoritarian in India.

The difference, I will argue, lies in the way that other subjects -- the non-technical ones -- are taught in India. In these subjects, students are asked to learn a lot of things by heart (a.k.a. rote learning) and there is an emphasis on facts rather than method. When compared with this, the best and the brightest often find the problem-solving methods of mathematics and science strangely appealing.

Consider my own experience. I went to a fairly good private school for middle and lower-middle class students. Our school did not have too many resources; the library was practically non-existent, there was hardly any equipment in class beyond chalk and blackboard (no projectors, no computers, no DVD players) and we rarely used any other books besides the state-printed textbooks. Our teachers did the best they could under the circumstances. But the limited time per week devoted to a subject, the amount of material that needed to be covered in that time (and our teachers were pretty scrupulous and covered everything they would put on the exam), and the structure of the exam itself (regurgitating facts that one had memorized) meant that they couldn't do much.

Consequently, non-technical subjects like history, geography, civics, the languages, and part of the sciences (that did not involve problem-solving, like biology or parts of chemistry) become exercises in teaching "facts". Meaning that they never became "interesting" to any of the students, and certainly not to the best and the brightest. My point is this: non-technical subjects were taught as "facts", not "methods." Mathematics and the mathematical sciences, on the other hand, despite the authoritarian way they were taught, were still taught as "methods".

Consider, say, a subject like history. This was taught from a state-sanctioned textbook. E.g. our 10th grade textbook had chapters on World Wars I and II, and then multiple chapters on India's freedom movement. Each chapter would be 6/8 pages and therefore fact-packed. Exams would be filled with questions like: "What were the immediate causes of World War I?" "What were the provisions of the Morley-Minto reforms of 1909?" And so on. Consequently (to me) school history became a compendium of facts to be memorized but the idea that history is also a method, an analytic tool came to me much later, when I started reading other books on history.

What's my point? My point is that I could never conceive of what a historian did because history seemed to me to be a body of well-defined facts without any idea of what methods a historian uses. I had no idea that there was even a science called sociology (beyond school, my reading consisted of voraciously reading pulp novels. Since access to good books in India is limited, I didn't come into contact with it in my outside reading either). But on the other hand, I was well-aware of the "methods" of mathematics and the mathematical sciences. It was easy to imagine what scientists, mathematicians or engineers do: they solve problems! It wasn't so easy to imagine what historians or sociologists did. (I probably I thought they had to master a lot of facts in order to be historians -- and who wanted to do that??!)

Consider exams. History exams (to take one example) were dreadfully tense affairs, the day before the exam particularly so as I had to revise and remember all the facts. Mathematics and physics exams, on the other hand, were not so much work. The method to solve problems had already been learned (and once learned, couldn't be forgotten). I think that exams (and their difficulty/easiness) have a lot to do with how a discipline is perceived by students. The conservative and authoritarian nature of science education meant that if one had solved all the problems before-hand, the exam itself would be a breeze. On the other hand, attending all the history lectures did not mean that one had memorized all the facts, so preparing for the exam was a hot and excruciating affair, full of memorizing and swotting. Was it any wonder that most students (or at the very least, the best and the brightest) preferred science to the other disciplines?

To sum up, my point in this post was to posit an "internal" explanation, rooted in styles of pedagogy, for why the best and the brightest high school students in the US do not opt for technical majors/careers in college, while those in India do so overwhelmingly. My explanation for this was that, in the US, it is the authoritarian nature of science education, especially when compared with the "creative" way other disciplines (like history or literature) are taught, that is responsible for the math-phobia. On the other hand, in India, the cultural logic of the same authoritarian style of science education works out differently because students can discern a "method" in it, and they can discern no such method in the other disciplines, just a series of facts. Consequently, the best and the brightest high school students in India are less likely to suffer from math-phobia.

[Note: There is probably a deeper sociological explanation of this and I am hoping that the sociology of Pierre Bourdieu can help me in this.

If you have any comments, notes, suggestions, disagreements, please post them in the comments below. I'd love to hear what you think of this. Also if you know any prior research on this, please do post it below. Thanks!]


Merritt said...

"... why the best and the brightest high school students in the United States usually choose not to become engineers or scientists..."

Sort of vague, but I was pretty much missing in action in high school...

Just like to give a shout out to Matt Damon. Handsome!

kevinjbutler said...

Earning potential.


Ian said...

Interesting thesis about how the general teaching style in Indian secondary schooling molds the learner.

a point to make:
The IITs are India's premier engineering universities-perhaps a better comparison would be against a US school like MIT? Some people in the US looking for a high-reputation engineering education might not consider a degree from Columbia.

An anecdote: at my public high school in the United States physics classes were not a requirement to graduate, thus a large chuck of graduates wouldn't even know what Newton's laws were.

Sudarshan P said...

Return on Investment!!!

No of years of study(Medicine takes much longer and is costlier)...

If u r an engineer u make abt 2X or more compared to other desciplines... no particular capability needed especially to get a comp sci engg degree from a not so reputed institute... just perseverence + average intelligince is more than enough.

If u r an engineer in india u sell ur time to MNCs while staying/spending the cash in India which translates into a huge monetary gain due to currency conversion peculiarities...

A Common Entrance Exam is conducted for admission to all courses. The highest scorers end up with the most sought after engineering seats which produces maximum salaries... Simple n boring ;-)...

Doctors, Lawyers, Writers, Accountants etc would find it harder to benefit as
much as engineering from outsourcing boom. BPO jobs are also sought after these days but not by the brightest... We also produce a lot of MBAs... so it is just not engineers... An IIM MBA is as sought after or probably more than even an IIT B.Tech by some I guess. Also there are a number of engineers who then get an MBA. ;-) But for most people it is just the dough. education is generally uninspiring... if in doubt compare lectures of Prof.Lwein's Physics from MIT v/s indian institutions and u 'll know that US edn is far more exciting... Also Professors in india get worse salaries than industry. So education is generally dry... and students rarely opt for teaching as a career...

As an indian I would say we r second to none in IQ... but it is pure quest for wealth that drives the decision in most cases. One chooses science while moving out of 10th. And the decision is usually strongly co-erced with parental and peer pressure. arts and commerce r for the losers(or so most believe). The best among the arts and commerce stream choose MBAs/Chartered Accountancy,Law,Journalism and so on...

FYI, I am a software engineer from a respected local college in bangalore.

Pierre said...

First of all, this is a fascinating thesis! There is a lot of material for thought in here. I think a lot of people in the US think that Indian (and Japanese and Chinese) education systems are great because their students are good at math/science. But there is perhaps no real understanding of the wider context, which you so neatly addressed. I’ve talked to someone who taught in Japan for three years and who is absolutely caustic about the Japanese education system, that same system so many Americans want to laud. His comments about it were very similar to your comments about how humanities are taught in India.

You make some good antidotal/heuristic arguments that the pedagogy of science/math based courses in India and the US are the same, or at least similar; can that be verified in any sort of a quantifiable manner? What are the metrics you are using? It would be interesting to look at the education systems of the major global cultures, India, Japan, China, Europe, and Latin America. (And maybe even the Middle East!) Providing a good analysis of this alone would be quite interesting, though it is possible that such an analysis has already been done. Doing something similar for how humanities are taught would be even more interesting, and would provide some great insights along the lines that you are currently looking at. That would probably in and of itself make a rich PhD dissertation!)

Next, why does “Internalist” approach give a certain power if the issue is a choice between technical occupations? I really don’t buy it or understand your reasoning behind it.

Until I read your rational, I’d have said that the vast majority of the reason why engineering is popular in India and not the US was for “externalist” reasons. I still think it is, but you have brought up some very interesting questions. Answering what the real causes are would require an in depth understanding of how humanities and sciences are taught, a great deal of data, and some powerful statistical techniques. (Those techniques are out there, quantitative psychology uses them a lot! You could talk to Michael Hoyt about them.)

But, that aside, let’s look at the Japanese. At a first approximation I’d guess that the Japanese educational system is more similar to India’s than to the US’s. Are the same effects being seen there? How many engineers are produced in Japan (as a percent of population) verses in the US or India? What about in China? What about Russia and Europe? I think you have to have quantifiable metrics of the educational systems of all of these places and data on majors/careers choices for all of them if you ‘d want to do a real analysis of this question. While looking at the stats of Columbia and the IITs is a first start, and okay for a little blog like this, it doesn’t hold water for anything more.

Anyway, the gist of what I am saying is that I actually do, at least to some extent, buy what you are saying; it is a very interesting theory and one which warrants a much closer look.

scritic said...

Thanks, all, for the comments.

Ian, the MIT comparison would be far more valid, I'm going to modify the post and put that in.

I do agree that external factors far outweigh the internal factors but I'm sort of interested in the relationship between them. At the very least, I am thinking that this difference in pedagogical styles in India allows students to remain indifferent to science (rather than hating it or fearing it as in the US).

But yes, certainly more work is needed! Thanks again!

Johanna Marion said...

Math-phobia has been instilled with the minds of the students who are not taught well enough how to solve and compute math problems. If one can't understand how to solve an algebra problem, he'll start to give some 'hate' to the subject, right? The best solution for Math-phobia, probably, is to teach students on how to love the subject. Math may not be easy, but it can be enjoyed still. :)