JEE coaching and high school learning

One reason I’m not as good at machine learning as I can possibly be is because I suck at linear algebra. I totally completely suck at it. Seven years of usage of R has meant that at least I no longer get spooked out by the very sight of vectors or matrices, and I understand the concept of matrix multiplication (an operator rotating a vector), but I just don’t get linear algebra.

For example, when I see terms such as “singular value decomposition” I almost faint. Multiple repeated attempts at learning the concept have utterly failed. Don’t even get me started on the more complicated stuff – and machine learning is full of them.

My inability to understand linear algebra runs deep, and it’s mainly due to a complete inability to imagine vectors and matrices and matrix operations. As far back as I remember, I have hated matrices and have tried to run away from it.

For a long time, I had placed the blame for this on IIT Madras, whose mathematics department in its infinite wisdom had decided to get its brilliant Graph Theory expert to teach us matrices. Thinking back, though, I remember going in to MA102 (Vectors, Matrices and Differential Equations) already spooked. The rot had set in even earlier – in school.

The problem with class 11 in my school (a fairly high-profile school which was full of studmax characters) was that most people harboured ambitions of going to IIT, and had consequently enrolled themselves in formal coaching “factories”. As a result, these worthies always came to maths, physics and chemistry classes “ahead” of people like me who didn’t go for such classes (I’d decided to chill for a year after a rather hectic class 10 when I’d been under immense pressure to get my school a “centum”).

Because a large majority of the class already knew what was to be taught, teachers had an incentive to slack. Also the fact that most students were studmax had meant that people preferred to mug on their own rather than display their ignorance in class. And so jai happened.

I remember the class when vectors and matrices were introduced (it was in class 11). While I don’t remember too many details, I do remember that a vocal majority already knew about “dot product” and “cross product”. It was similar a few days later when the vocal majority knew matrix multiplication.

And so these concepts were glossed over, and lacking a grounding in fundamentals, I somehow never “got” the concept.

In my year (2000), CBSE decided to change format for its maths examination – everyone had to attempt “Part A” (worth 70 marks) and then had a choice between “Part B” (vectors, matrices, etc.) and “Part C” (introductory statistics). Most science students were expected to opt for Part B (Part C had been introduced for the benefit of commerce students studying maths since they had little to gain from reading about vectors). For me and one other guy from my class, though, it was a rather obvious choice to do Part C.

I remember the invigilator (who was from another school) being positively surprised during my board exam when I mentioned that I was going to attempt Part C instead of Part B. He muttered something to the extent of “isn’t that for commerce students?” but to his credit permitted us to do the paper in whatever way we wanted (I fail to remember why I had to mention to him I was doing Part C – maybe I needed log tables to do that).

Seventeen odd years down the line, I continue to suck at linear algebra and be stud at statistics. And it is all down to the way the two subjects were introduced to me in school (JEE statistics wasn’t up to the same standard as Part C so the school teachers did a great job of teaching that).

Deresiewicz, Pinker and the IIT JEE

A few months back, William Deresiewicz, formerly of Yale, wrote a long piece advising people why they should not send their kids to Ivy League schools. He talked about students in Ivy League schools becoming single dimensioned, hyper-competitive, and less appreciative of the finer things in life. He spoke of the Ivy League system being broken, and not close to what it used to be once upon a time.

Now, Steven Pinker (he of the Stuff of Thought and Language Instinct fame) of Harvard has responded, and he has the opposite problem with Ivy League students. Halfway though the semester, the class is half-empty, he cribs, with students more involved in extra curricular activities rather than attending class. This implies that all the effort the university puts in building world-class libraries and laboratories and other facilities go waste. Pinker’s diagnosis is different – he blames the “well roundedness” criteria that universities use for admissions (supposedly initially put in place to restrict the number of jewish students, and then kept in place to restrict the number of asians).

I’m about halfway through Pinker’s article, and I remember reading Deresiewicz’s article in full, and my reaction to both is the same – “IIT JEE rocks”. By having a standardised exam to admit students, the IITs actually take pressure off high school students rather than imposing more pressure – since the criteria for admission are clear – that one examination, a student of class 11 or 12 has her objectives clear in front of her in case she wants to go to IIT – single-minded mugging of Maths, Physics and Chemistry.

With a more “well-rounded” criterion – say one that includes social service and extra curricular activities and sport and all such, the objective function is not that clear, and the student needs to slog towards an uncertain objective function, which is significantly inferior to slogging towards a known objective function.

Some of the cribs that Pinker puts in his post is true of IITs as well – I’ve had several professors lecture to me about the lack of seriousness on the part of IIT students, and how they would prefer students who might be less brilliant but more serious about their learning (an oft touted solution to this was to jack up the fees and make students dependent on education loans they had to repay. Not sure if the IITs have implemented this, but the IIMs have, for sure).

But then IIT Madras, where I studied for four years, and where everyone had come in after passing a rigorous standardised test, had no shortage of characters. While everyone who was in had necessarily shown single-minded devotion to mugging maths physics and chemistry in the preceding year or two, a large number of students there had interests that went much beyond those three scientific subjects. In that sense, if the Ivy League schools want to see a system where standardised admissions process actually lead to a fairly diverse class, they need not look beyond the IITs (a system they are no doubt familiar with since the IITs contribute generously to the grad student population of the Ivy League schools).

One of the frequent criticisms of the IIT JEE is that it can easily be gamed – rather than selecting the “brightest” students or those that have the best understanding of maths, physics and chemistry, the IITs end up selecting students who are best prepared for the standardised exam. An oft-touted solution to this is to make the entry process more “holistic” (in India that means including board exam marks (??!!) ), to make it less game-able. However, evidence from the Deresiewicz and Pinker pieces suggests that even the “holistic” admissions process that the Ivy League schools follow are easily gamed, and that the gaming of those systems is in fact biased towards kids with rich parents.

A while back I was looking at the admissions process of some Ivy League schools – both undergrad and MBA programs. Now, all these schools tout diversity as one of their drawing criteria. But if you look a little deeper, you will notice that this purported diversity is only skin-deep (literally!). While these schools might do a fantastic job of getting students from different nationalities, skin colour, undergraduate backgrounds and work experience, the way their essays are structured implies that the students they get are largely similar in thought – students should have done some social work, they should have exhibited a particular kind of leadership, they should be politically correct, and so forth.

The reason I mention this is that “holistic” admissions criteria need not actually produce a student body that is necessarily more diverse than that produced by a standardised test – it all depends upon the axis that you look along!

PS: I happened to have a good day on 7th May 2000, when I wrote the IIT JEE and did rather well, so this post might be biased by that. I don’t know if I would have taken such a charitable view towards standardised tests if I hadn’t done so well in them.

Relationships and IIT

So the basic premise of this post is that being in a romantic relationship is like studying at IIT.

Everyone wants to get into IIT. They do thipparlaaga to try and get in. They join expensive coaching classes. Some of them even move cities. They wait for several years giving multiple attempts. People work extremely hard. Still, success is not guaranteed. There is that luck factor. There is the day’s performance that matters. Some days are important than others. Cracking the JEE is a “discrete” job.

While preparing for JEE, everyone thinks that if they clear the exam, their life is made. They come under the impression that after JEE, life will become smooth. That they won’t need to put any fight for the rest of their lives. That all that matters for their future is their cracking the JEE. And so forth.

It’s only after people come to IIT that they realize that life is not the cakewalk they assumed it to be. It is only after they get there that they realize that life after JEE is quite hard. That it is necessary to work hard. That if they don’t work hard, they will do very badly, and might flunk. It is only when they get to IIT that it hits them. Some learn quickly but others get disillusioned and give up in life. Several people do badly. Some even drop out.

So it’s similar with a romantic relationship. Everyone wants to get into a romantic relationship. Everyone looks only about the “entrance examination”. Everyone believes (before they get in) that life ban jaayegi after they get into a relationship. And getting into a relationship is a “discrete” job. It’s about how you “perform” during those blading sessions. It takes that bit of luck. It takes those set of fateful events to happen together in that precise coincidence.

And it is only when you get into a relationship that you realize how hard it is (provided you haven’t been there before). It is like being in IIT all over again. You know that you will need to work really hard to keep it going (applies to both parties). It is a continuous job, and you need to continuously “perform”. The randomness is much smaller than it is during the “relationship acquisition” phase.  However, you necessarily need to work hard. There is no “stud way out”. Some people give up when they find this out and break up (drop out). Others understand and put in the requisite effort and sustain the relationship. And continue to work hard.

The thing with arranged marriages is that you are typically forced to commit as soon as you’re done with “evaluating” the other person. You don’t get to test the counterparty on their ability to work hard and keep things going. It is like offering someone a job as soon as he has cleared the JEE.

And I wonder if one can draw an analogy between marriage and (academic) tenure.