The metaphor of 'difference between rotation and revolution'- III

Many parents  are not very concerned  about whether their children learn anything or not so long as they score marks in exams. For instance, a child solved a problem by the wrong method but got the right answer by fluke because of the particular combination of numbers used. I wanted to correct the error but the mother was happy that her son had got the correct answer and moved on to the next problem. The tragedy is that exactly the same problem from the textbook will come for the exam, the child will solve it using the wrong method, get full marks and everyone will be happy. So the child will never learn what the error was. This will have consequences in higher classes.

The topics covered seem to be a lot lesser than what I seem to remember. Of course one must remember what one professor told his students when they asked him what he  would cover during the term - 'It is not about what I cover but about what you discover.' But with the methods of teaching and learning that I see, I am not sure how much students discover. For example, students are asked to memorise the scientific names of various creatures or the atomic numbers of various elements. Parrots could do that. ( Actual exam questions: 1.The scientific name for saffron is___ 2.An element with 15 protons, 15 electrons and 16 neutrons is_______) Hardly any time is spent explaining the Scientific Method.  Most Indians graduating from their 12th standard in the high schools of India don’t know what science is.

Studying to learn  and studying to score marks in exams are two different things. In an ideal world the two approaches should coincide but we live in a messy world. The good schools achieve a decent balance between the two objectives. But in the majority of schools (especially in Tamil Nadu from what I can see) the emphasis seems to be on maximizing the marks scored in tests irrespective of whether the student has actually learnt something.

Over the years, there has been considerable marks inflation. I often hear about absurd cut-off marks for admission in various colleges. I studied with many super-brains at various levels and I keep wondering whether so many of these students are so much better than them. It seems improbable.

The libaral marking may havee been an effort to reduce stress on students but it may be having the opposite effect because in spite of doing well in the exams, they have to sweat over college admmission. I have heard students say that it is no use studying hard because they are still not sure of getting admission in good colleges. (Again the conflation of studies and marks.) The liberal marking may be detrimental to students. In this interesting course introduction, a professor at Yale University explains why he is strict in awarding grades.

Whenever multifaceted, amorphous concepts are sought to be measured along a linear scale, some information is sure to be lost. This problem happens when there is excessive focus on marks. For example, the ability to write grammatically correct sentences and arrange them properly so as to express one's thoughts clearly is an important skill which the marks don't tell you anything about.I don't think enough attention is being paid to developing the writing abilities of students.

However highly qualified you are, it is an advantage to to be able to write clearly in the language that the person at the receiving end is able to understand. In many bussines situations, this happens to be English due to historical reasons, what economists call a path dependant process. (Here is an account of an attempt to create the perfect language. I am sure it handles these emotions better than English.) I was surprised to see that in the previous school Sujit studied in, the students were asked to memorise some essays that had been dictated to them and the students were asked to vomit out one of these essays during the exams.

It seems to be a fashion these days for students to attend tuitions. When I was a student, only the weak students went for tuitions but now everybody goes for tuitions. It seems to have got into the heads of students that attending tuitions is essential for scoring marks in exams. (Again the conflation of marks with learning.)

These tuition centres know the patterns of questions in various exam papers and they make the students do just those types of questions. The students score well in the exams and both they and the parents are happy. Little actual learning takes place. If you ask the students the same questions in a different form, they will struggle to answer.

PS: Here is a chat with Salman Khan of Khan Academies at Google and here is an earlier talk he gave at Google.

PPS:  Finnish education system. 

The metaphor of 'difference between rotation and revolution'- II

A couple of students who were going to write their Board exams told me that their teacher told them that they should write matter relevant to the question at the beginning and the end and they can write any story they want inbetween in order to make the answer lengthy! It seems that the person correcting the paper will only read the beginning and end of the answer. All that needs to be ensured is that the answer is long. One doesn't expect all teachers to be like Sanderson of Oundle but at least one doesn't expect such an advice. The general idea among students seems to be that  to get more marks one should make the answers as long as possible. What is actually written seems to be less important. There seems to be more emphasis on form rather than content.

Students seem to be encouraged to learn some formula to some problem rather than think about the process. For eg.,  for finding out the area of a pathway, the students were not told the general approach of subtracting the area of the inner shape from the area of the outer shape. Instead students had to learn one formula for a rectangular  pathway and another for a circular pathway which was also the approach followed in the textbook. They didn't know that the same logic was used for deriving both formulas. Using generalisations seems to be out of fashion. While discussing misconceptions about mathematics, John Allen Paulos writes in A Mathematician Reads the Newspaper:

Probably the most harmful misconception is that mathematics is essentially a matter of computation. Believing this is roughly equivalent to believing that writing essays is the same as typing them. Or, to vary the analogy, imagine the interest in literature that would be engendered if every English class focused exclusively on punctuation.

There also seems to be the fear that one has to write exactly what the teacher has dictated else it will marked wrong.  In his textbook, one student had written the answer '8 min.' for the question 'What is the speed of light?' and  for the next question, 'How long does it take for light from the sun to reach the earth?', he had written the answer '300,0000 km/s'. It was obvious that the teacher had dictated the correct answers but the boy had written them the wrong way around. I told him to correct the error but he was reluctant saying that the teacher would mark him wrong if he wrote a different answer. It should have been obvious from the units that the answers were looking weird. I managed to make him change the the answers but I am quite sure that if the questions came for the exam, he would have written his original incorrect answers.  Bertrand Russell said:

Passive acceptance of the teacher's wisdom is easy to most boys and girls. It involves no effort of independent thought, and seems rational because the teacher knows more than his pupils; it is moreover the way to win the favour of the teacher unless he is a very exceptional man. Yet the habit of passive acceptance is a disastrous one in later life. It causes man to seek and to accept a leader, and to accept as a leader whoever is established in that position.

In this video, Noam Chomsky outlines two approaches to education: one which emphasises critical thinking and gaining knowledge or one that is used for indoctrination and ensuring conformity. I think  that the education  system as currently structured leans more towards the latter approach. For instance, take educational loans. Making them freely available sounds a good idea but I think there are issues.

People will flock to the highest paid jobs initially, If it is thought that they can easily switch to a job more to their liking after they paid back their loans, it is easier said than done. By that time, they would have got used to their lifestyles, they may have a family of their own  which reduces risk-taking ability and there will be considerable peer and family pressure against taking a lower paying job in a lower position which will be hard to ignore. It is hard to know how to address this problem but I think the bigger problem is that the-powers -that-be don't think that it is a problem.

Some months ago there was An Open Letter to India’s Graduating Classes written by an employer which drew varied reactions. I can't comment on all the points since I have been out of the loop for a while but the following comment could be true in a large number of cases:

You are also unduly impressed by titles and perceived hierarchy. While there is a strong cultural bias of deference and subservience to titles in India, it is as much your responsibility as it is ours to challenge this view.

This is not an easy problem to solve since deference to authority is ingrained in everyone since childhood. The educational system just perpetuates the system justification bias and many end up making choices like Vera in Chekhov's short story, At Home.In this video, where Alain de Button talks about Socrates, he says that there are many similarities between humans and sheep. This tendency is accentuated by the increasing debt burden students have to bear which makes it important for them to hold on to their jobs.

PS:I was shocked by this account of how nerds are treated in many US schools as also by this post.

PPS: This cartoon reminded me of 'arbit c.p.' (arbitrary class participation) at IIMA.

The metaphor of 'difference between rotation and revolution'- I

I was told sometime back that some toppers of the matriculation Board may not know the difference between rotation and revolution. I don't know whether to believe this or not but it is a good metaphor for how learning takes place in many schools. The matriculation Board is no longer there but the teaching and learning methods are not going to change overnight. In The Greatest Show on Earth, Richard Dawkins relates a similar tale:

It is with horrified fascination that I return,  as if scratching an itch or pressing a toothache, to the poll, documented in the Appendix, suggesting that 19% of British people don’t know what a year is, and think the Earth orbits the sun once per month. Even of those who understand what a year is, a larger percentage has no understanding of what causes seasons, presuming, with rampant Northern Hemisphere chauvinism, that we are closest to the sun in June and furthest away in December.

I wouldn't have been surprised if these figures (or even higher), were for India because of widespread illiteracy but in Britain? (According to this TED talk, the illiteracy may be much higher in India because of the way in which literacy is measured.)

Apparently, in the Matriculation Board, you had to write exactly as given in text book. If you write in your words, there is a good possibility that you may be marked wrong. Children are not encouraged to refer to other books and write things that are not in the the text books. And what about those text books? One cannot expect them to be as gripping as Robert Krulwich would like them to be but at least one expects them to be free of blunders like the following:

1. Revolution of the earth causes seasons. 
2. Fungi are plants.
3. Some two land masses separated over thousands of years. (You could say that millions is made up of many thousands but it gives an erroneous idea of the  scales of time involved in these processes.)
4. Aryabhatta knew about Pythagoras theorem before Pythagoras did.(The problem is that Pythagoras lived about a millennium  before Aryabhatta. But that is nothing compared to a textbook like this.)
5. The atomic number of an element is 6 therefore its mass number is 14.

Another problem in many schools is that the students are required to learn only the answers to the questions given at the end of the chapter. They can get good marks in the subject even if they don't read the chapter because the questions will come from the back of the the chapter. It is quite possible that the difference between rotation  and revolution would have been discussed in the chapter but would not have been a question at the end of the the chapter so the students would never have learnt it.

I think all noise over academic pressure is a bit exaggerated or perhaps the correction has moved too far in the other direction. I  was surprised to learn  that Sujit had only one chapter each in physics and chemistry in Std. VIII in the final exam. In Maths, only the portion taught in the third term was included for the final exam. Since algebra  was taught in previous terms, it was not included. Algebra is a useful topic to know so this is not doing the students any favours. All this seems to be part of a dumbing down process that seems to be mistaken for simplification. A similar dumbing down process also seems to be taking place in the US.

PS: People  often ask children what they want to become when they grow up. Some know  that these keep changing but some people take them seriously and start advising them about what they have to do. In this commencement speech, Robert Krulwich describes how people typically stumble on to their final career. (This is the second awesome Krulwich speech in this post.)

Travelling to another dot

(The world did not end on 21st December as widely expected so you are condemned to read more of my posts. My commiserations. But don't lose hope.)

In the Wodehouse novel 'Mike and Psmith', while  explaining the benefits of not getting up early in the morning, Psmith tells Mike:

"One of the Georges," said Psmith, "I forget which, once said that a certain number of hours' sleep a day - I cannot recall for the moment how many - made a man something, which for the time being  has slipped my memory. However, there you are. I've given you the main idea of the thing.

I find myself in the Psmith situation. I had read an article (I don't think it was by a George but then, it could have been one.) which had been about some people who had lived for some days (or weeks or months) in isolation, having no contact with the rest of the world during that period, and the psychological problems this produced. There you are. I've given you the main idea of the thing. I was reminded of this article when I read Packing for Mars: The Curious Science of Life in the Void by Mary Roach which is about the technological, political and psychological challenges involved in sending a manned mission to Mars. Mary Roach writes:

To the rocket scientist, you are a problem.  You are the most irritating piece of machinery he or she will ever have to deal with. You and your fluctuating metabolism, your puny memory, your frame that comes in a million different configurations. You are unpredictable. You're inconstant. You take weeks to fix.  The engineer must worry about the water and oxygen and food you'll need in space, about how much extra fuel it will take to launch your shrimp cocktail and irradiated beef tacos.  A solar cell or a thruster nozzle is stable and undemanding. It does not excrete or panic or fall in love with the mission commander. It has no ego.  Its structural elements don't start to break down without gravity, and it works just fine without sleep.

People have been fascinated by Mars (including Mohammad Ali) for a long time but space travel is not the fun adventure that it is portrayed as in PR videos. There are plans to send 80,000 people to Mars but that is easier said than done. Apart from the various psychological problems, you have to deal with things like motion sickness, vomiting in helmets, excess gravity, low gravity, worry about the impact tolerance of the human body, deal with body odour and how to carry out many mundane activities.

Food for space has to be light and compact - every extra pound costs thousands of dollars to launch. It should not be crumbly because in anti-gravity, crumbs clog the controls or may get into some one's eyes. Astronauts have to drink recycled urine. They have to be specially toilet trained. If not careful, faeces may float around the spacecraft which is not a pleasant experience.Even the simple act of urination can, in the absence of gravity, become a medical emergency. And then there is religion:

Religious observations are even tougher in a real spacecraft.  Launch weight limitations forced Buzz Aldrin to pack a "tiny Host" and thimble-sized wine chalice for his DIY Communion on the moon.  Zero gravity and a ninety minute orbital day created so many questions for Muslim astronauts that a "Guideline of Performing Ibadah at the International Space Station" was drafted. Rather than require Muslim astronauts to pray five times during each ninety minute orbit of Earth, the guidelines allowed them to go by the twenty-four-hour cycle of the launch location.  Wipes ("not less than 3 pieces") could be used for preprayer cleansing. And since the orbiting Muslim who began his prayer while facing Mecca was likely, by prayer's end, to be mooning Mecca, provisions were made allowing him to simply face the Earth or "wherever." Lastly, instead of lowering the face to the ground, a trying manoeuvre in zero gravity, prostrating oneself could be approximated by "bringing down the chin closer to the knee," "using the eye lid as an indicator of the changing of posture" or - in the vein of "wherever" - simply "imagining" the sequence of movements.

The most interesting part of the book for me was a chapter describing an experiment where NASA observes volunteers who were asked to spend 3 months 24*7 lying on a bed. This was because during a trip to Mars, astronauts would have to spend about 6 months in a cramped space without much movement. For a couple of years after my stroke, I used to lie most of the time on the bed watching TV. I was aware that prolonged periods of inactivity causes some deterioration in bones and muscles but I didn't know that it could be so bad.

In 2 years, a paraplegic person could lose 1/3 to 1/2 the bone mass in the lower limbs,about the same amount that an astronaut could expect to lose on a 2 year mission to Mars. There is a very real danger that the bones of the astronaut may snap on returning to Earth's gravity. The best method for preventing bone loss is weight bearing exercise. In spite of the various ideas that have been tried over the years for dealing with bone and muscle loss, the best methods remain those that were available 40 years ago.

In spite of the perils, some astronauts are willing to go on a one-way trip to Mars with no possibility of return.These folks have incredible guts. The very thought of living in a cramped space for months on end far away from the earth gives me the heebie jeebies. (Does it have something to do with the DRD4-7R gene?) There have been suggestions of trying to see if humans can hibernate (like the folks of 'B'Ark) but the idea has never been pursued seriously because of ethical issues.

Finally, should so much resources be spent on sending a manned mission to Mars? Many reasons have been given in favour of space exploration. Neil deGrasse Tyson puts costs in perspective. As Mary Roach says:

The nobility of the human spirit grows harder for me to believe in.  War, zealotry, greed, malls, narcissism.  I see a backhanded nobility in excessive, impractical outlays of cash prompted by nothing loftier than a species joining hands and saying "I bet we can do this. "Yes, the money could be better spent on Earth.  But would it? Since when has money saved by government red-lining been spent on education and cancer research? It is always squandered.  Let's squander some on Mars.  Let's go out and play. 

Here is Mary Roach talking about her book at Google.

PS: A documentary on the case for Mars.

PPS: Bizarre space cases

O judgment! Thou art fled to brutish beasts

Things Fall Apart. Check out this TED Talk.

The dark side of superstition

This is about a time about an year after my stroke. At that time I used to lie on the bed most of the day watching T.V.  I was not reading any books and there was no computer at home.I had no idea what I could do. I was thinking more along the lines of an Amitabh Bachchan quip in this song - 'Arre yeh jeena bhi koi jeena hai, lallu?' (This is immediately followed by one of my favourite songs which conveys a very different mood.)

There is a Malayalam movie on Asianet every afternoon which  I used to keep.This was not because I was particularly keen on watching it but I knew that the nurse would be interested in watching it. This would keep her awake so I would not have to strain too much to call her if I wanted to pass urine. Cunning devil, no?

One afternoon there was a movie starring the Malayalam super star Mammooty. I was not paying much attention to the movie initially. After some time I started becoming interested in the plot and started watching more earnestly. The story was as follows:

The Mammooty character (let us call him Kumar) was a respected school teacher in a typical Kerala village. He lived a normal life in a joint family and had a wife and 2 kids. The family had some hereditary disease like Huntington's Chorea. The family belief was that some goddess had put a curse on them which meant that 1 member of the family in every generation will go mad.

In this generation, it was the turn of an elderly uncle to go mad. He was kept in chains in a separate room. One day he suddenly died. After the cremation, the family waited and wondered who the goddess would choose as her next victim.

One night, Kumar had a bad dream and screamed in his sleep. Everyone rushed to his room to find out what the matter was. He assured them that he just had a bad dream and he was all right. Everyone looked at him suspiciously. They suspected that he had been chosen by the goddess to go mad. By the next morning the news had spread through the grapevine to the whole village. Kumar was blissfully unaware of all these developments as he made his way to the school the next day.

He was puzzled when the owner of a tea-stall where he used to stop regularly seemed to be in a hurry to get rid of him. The people he used to regularly chat with seemed to be keen to avoid him. In school, the students passed mocking remarks which he could not understand and his colleagues were avoiding eye contact. This strange behaviour went on for some days and Kumar began to suspect what the problem was.

His father-in-law heard the stories, decided that he cannot let his daughter and grand kids stay with a mad man and took them away in spite of his protests that there was nothing wrong with him. This broke him completely and he stopped caring about anything. He stopped talking to anybody and just stared silently when anybody asked him anything. He looked dishevelled and roamed around like a zombie. Eventually, he was kept in chains in a separate room like the uncle who had died. After many days, his mother took pity on him, mixed poison in his food and killed him.

I could picture myself in the shoes  of the Mammooty character. Jaya has been an indefatigable gatekeeper keeping out many superstitious beliefs which she knows irritates me, as also the suggestions of those who read nothing but know everything. I live among liberal believers and my heretical views don't provoke the kind of ostracizing seen in the Bible belt of the US. Jaya has also been able to ignore the various emotional blackmails that came her way.

I kept a watch out for the movie in various channels because I wanted to check if I remembered the facts right before writing this post but I never saw the movie again. I still don't know its title.

PS: It is not just about superstitions, it could be about something as simple as signing a piece of paper. Once, an Ayurvedic doctor gave some powder and said that a little bit of it should be mixed with milk and given to me everyday. He said that it contained silver and proceeded to extoll the virtues of silver as a curative agent for various neurological problems. Jaya asked him to write the prescription on his letterhead with his signature on it. He brushed this off as unimportant so his suggestion was ignored.

What they conceal is vital - II

In this list of Carl Sagan quotes, I saw the following quote:

"I'm often asked the question, "Do you think there is extraterrestrial intelligence?" I give the standard arguments -- there are a lot of places out there, and use the word *billions*, and so on. And then I say it would be astonishing to me if there weren't extraterrestrial intelligence, but of course there is as yet no compelling evidence for it. And then I'm asked, "Yeah, but what do you really think?" I say, "I just told you what I really think." "Yeah, but what's your gut feeling?" But I try not to think with my gut. Really, it's okay to reserve judgment until the evidence is in.

But people often rely on gut feel for making decisions. When news reports have a lot of numbers, eyes typically glaze over so people in power get away with saying anything.What Steven Pinker calls 'failure of statistical thinking' has made it difficult for Facts to survive. In this video, Daniel Kahneman distinguishes two types of thinking: System 1 and System 2.System 1 represents what we call intuition. It tirelessly provides us with quick impressions, intentions and feelings. System 2, on the other hand, represents reason, self-control and considered decision making.

System  1 is fast and does not require much effort. System 2 is slow and requires effort. We rely most of the time on System 1 for our regular activities and it does fine.Occasionally, this causes problems. There are times when some statistical thinking using System 2 would have been beneficial but we often skip it since it requires time and effort. Advertising, political, nationalistic and religious messages target System 1 which is why they are so effective.

Some years back, I had read a book called How to Lie with Statistics by  Darrell Huff, the most widely read statistics book in the history of the world.  You can read it online here, Written almost 60 years ago, it gives many ways in which people present statistics in order to favour their biases. He says that the book sounds like a how-to manual for crooks for which his justification is - "the crooks already know these tricks; honest men must learn them in self-defence." Some of the techniques that he discusses are:

1. Using a sample with built-in bias. Examples are TV and Internet polls.
2. Using any of mean, median or mode as the 'average' depending on which one best represents your bias. Since most people won't know the difference between them ,you will generally be safe. For example, to depict the average income of the inhabitants of a country, the median is more informative than the mean. There is a joke that when Bill Gates visits an old age home, all inhabitants are millionaires on average.
3. Failing to mention some numbers like sample size, confidence intervals etc. This is especially a problem on TV  because the screen changes so fast that you don't have time to read everything and only the shape of the image stays  in your mind.
4. Misleading graphs - An example
5. Misleading  figures - An example.
6. Comparing  wrong percentages - An example
7. Correlation is not causation - An example
8. Post hoc ergo propter hoc
9. Using impressively precise figures - Saying that the monthly expenditure of an average family is Rs. 12436 sounds more authoritative than saying it is around Rs. 12,000.
10. Beware of extrapolations.

Darrell Huff says that there are 5 questions that one must ask when one sees any statistic:

1. Who Says So?
2. How Does He Know?
3. What's Missing?
4. Did Somebody Change the Subject?
5. Does It Make Sense? 

Whenever one political party levels an accusation against a member of  another party, the latter responds by saying something like, 'People will not believe such wild allegations. They know better.' Want to bet? Initial reports tend to persist and myths are remarkably easy to spread because we use System  1 much more than System 2. This makes us us more enamoured of superficial things as depicted in Chekhov's short story, The First-Class Passenger. This is a difficult trap to avoid.

PS: There are many examples of statical machinations dissected at Ben  Goldacre's blog.