The Calculus Bottleneck

What if someone told you that learners in high-school don’t actually need calculus as a compulsory subject for a career in STEM? Surely I would disagree. After all, without calculus how will they understand many of the topics in the STEM. For example basic Newtonian mechanics? Another line of thought that might be put forth is that calculus allows learners to develop an interest in mathematics and pursue it as a career. But swell, nothing could be farther from truth. From what I have experienced there are two major categories of students who take calculus in high school. The first category would be students who are just out of wits about calculus, its purpose and meaning. They just see it as another infliction upon them without any significance. They struggle with remembering the formulae and will just barely pass the course (and many times don’t). These students hate mathematics, calculus makes it worse. Integration is opposite of differentiation: but why teach it to us?

The other major category of students is the one who take on calculus but with a caveat. They are the ones who will score in the 80s and 90s in the examination, but they have cracked the exam system per se. And might not have any foundational knowledge of calculus. But someone might ask how can one score 95/100 and still not have foundational knowledge of the subject matter? This is the way to beat the system. These learners are usually drilled in solving problems of a particular type. It is no different than chug and slug. They see a particular problem – they apply a rote learned method to solve it and bingo there is a solution. I have seen students labour “problem sets” — typically hundreds of problems of a given type — to score in the 90s in the papers. This just gives them the ability to solve typical problems which are usually asked in the examinations. Since the examination does not ask for questions based on conceptual knowledge – it never gets tested. Perhaps even their teachers if asked conceptual questions will not be able to handle them — it will be treated like a radioactive waste and thrown out — since it will be out of syllabus.

There is a third minority (a real minority, and may not be real!, this might just be wishful thinking) who will actually understand the meaning and significance of the conceptual knowledge, and they might not score in the 90s. They might take a fancy for the subject due to calculus but the way syllabus is structured it is astonishing that any students have any fascination left for mathematics. Like someone had said: the fascination for mathematics cannot be taught it must be caught. And this is exactly what MAA and NCTM have said in their statement about dropping calculus from high-school.

What the members of the mathematical community—especially those in the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM)—have known for a long time is that the pump that is pushing more students into more advanced mathematics ever earlier is not just ineffective: It is counter-productive. Too many students are moving too fast through preliminary courses so that they can get calculus onto their high school transcripts. The result is that even if they are able to pass high school calculus, they have established an inadequate foundation on which to build the mathematical knowledge required for a STEM career. (emphasis added)

The problem stems from the fact that the foundational topics which are prerequisites for calculus are on shaky grounds. No wonder anything build on top of them is not solid. I remember having very rudimentary calculus in college chemistry, when it was not needed and high-flying into physical meaning of derivatives in physics which was not covered enough earlier. There is a certain mismatch between the expectations from the students and their actual knowledge of the discipline as they come to college from high-school.

Too many students are being accelerated, short-changing their preparation in and knowledge of algebra, geometry, trigonometry, and other precalculus topics. Too many students experience a secondary school calculus course that drills on the techniques and procedures that will enable them to successfully answer standard problems, but are never challenged to encounter and understand the conceptual foundations of calculus. Too many students arrive at college Calculus I and see a course that looks like a review of what they learned the year before. By the time they realize that the expectations of this course are very different from what they had previously experienced, it is often too late to get up to speed.

Though they conclude that with enough solid conceptual background in these prerequisites it might be beneficial for the students to have a calculus course in the highschool.

The problem with what is taught in schools

Many people have written on the problem of what is taught in schools and why children don’t like what they study. One of the major issue seems to be there is no direct relevance to what children are taught in the school and their own personal and social lives. The content in the school textbooks has been dissected of any meaningful connections that the children could make in their real lives. The school tasks are decontextualised so that they become insulated from the real world. The quote below very nicely captures what I wanted to say on this issue.

These kinds of situated-learning tasks are different from most school tasks, because school tasks are decontextualized. Imagine learning tennis by being told the rules and practicing the forehand, backhand, and serve without ever playing or seeing a tennis match. If tennis were taught that way, it would be hard to see the point of what you were learning. But in school, students are taught algebra and Shakespeare without cognitive apprenticeship being given any idea of how they might be useful in their lives. That is not how a coach would teach you to play tennis. A coach might first show you how to grip and swing the racket, but very soon you would be hitting the ball and playing games. A good coach would have you go back and forth between playing games and working on particular skills – combining global and situated learning with focused local knowledge.

Allan Collins – Cognitive Apprenticeship (The Cambridge Handbook of the Learning Sciences)

Papert too has some nice metaphors for this, and constructionism hence includes problems or projects which are personally meaningful to the learner so that they are contextualised withing the lives of the learners..

Conditioning hatred for books

INFANT NURSERIES. NEO-PAVLOVIAN CONDITIONING ROOMS, announced the notice board.

The Director opened a door. They were in a large bare room, very bright and sunny; for the whole of the southern wall was a single win-dow. Half a dozen nurses, trousered and jacketed in the regulation white viscose-linen uniform, their hair aseptically hidden under white caps, were engaged in setting out bowls of roses in a long row across the floor. Big bowls, packed tight with blossom. Thousands of petals, ripe-blown and silkily smooth, like the cheeks of innumerable little cherubs, but of cherubs, in that bright light, not exclusively pink and Aryan, but also luminously Chinese, also Mexican, also apoplectic with too much blowing of celestial trumpets, also pale as death, pale with the posthumous whiteness of marble.

The nurses stiffened to attention as the D.H.C. came in.

“Set out the books,” he said curtly.

In silence the nurses obeyed his command. Between the rose bowls the books were duly set out-a row of nursery quartos opened invitingly each at some gaily coloured image of beast or fish or bird.

“Now bring in the children.”

They hurried out of the room and returned in a minute or two, each
pushing a kind of tall dumb-waiter laden, on all its four wire-netted
shelves, with eight-month-old babies, all exactly alike (a Bokanovsky
Group, it was evident) and all (since their caste was Delta) dressed in
khaki.

“Put them down on the floor.” The infants were unloaded.

“Now turn them so that they can see the flowers and books.”

Turned, the babies at once fell silent, then began to crawl towards those clusters of sleek colours, those shapes so gay and brilliant on the white pages. As they approached, the sun came out of a momentary eclipse behind a cloud. The roses flamed up as though with a sudden passion from within; a new and profound significance seemed to suffuse the shining pages of the books. From the ranks of the crawling babies came little squeals of excitement, gurgles and twitterings of pleasure.

The Director rubbed his hands. “Excellent!” he said. “It might almost have been done on purpose.”

The swiftest crawlers were already at their goal. Small hands reached out uncertainly, touched, grasped, unpetaling the transfigured roses, crumpling the illuminated pages of the books. The Director waited until all were happily busy. Then, “Watch carefully,” he said. And, lifting his hand, he gave the signal.

The Head Nurse, who was standing by a switchboard at the other end of the room, pressed down a little lever.

There was a violent explosion. Shriller and ever shriller, a siren shrieked. Alarm bells maddeningly sounded.

The children started, screamed; their faces were distorted with terror.

“And now,” the Director shouted (for the noise was deafening), “now we proceed to rub in the lesson with a mild electric shock.”

He waved his hand again, and the Head Nurse pressed a second lever. The screaming of the babies suddenly changed its tone. There was something desperate, almost insane, about the sharp spasmodic yelps to which they now gave utterance. Their little bodies twitched and stiffened; their limbs moved jerkily as if to the tug of unseen wires.

“We can electrify that whole strip of floor,” bawled the Director in explanation. “But that’s enough,” he signalled to the nurse.

The explosions ceased, the bells stopped ringing, the shriek of the siren died down from tone to tone into silence. The stiffly twitching bodies relaxed, and what had become the sob and yelp of infant maniacs broadened out once more into a normal howl of ordinary terror.

“Offer them the flowers and the books again.”

The nurses obeyed; but at the approach of the roses, at the mere sight of those gaily-coloured images of pussy and cock-a-doodle-doo and baa-baa black sheep, the infants shrank away in horror, the volume of their howling suddenly increased.

“Observe,” said the Director triumphantly, “observe.”

Books and loud noises, flowers and electric shocks-already in the infant mind these couples were compromisingly linked; and after two hundred repetitions of the same or a similar lesson would be wedded indissolubly. What man has joined, nature is powerless to put asunder.

“They’ll grow up with what the psychologists used to call an ‘instinctive’ hatred of books and flowers. Reflexes unalterably conditioned. They’ll be safe from books and botany all their lives.” The Director turned to his nurses. “Take them away again.”

Aldous Huxley, Brave New World

Though fictionalised the above passages capture what makes people hate books in general. The conditioning happens in reality in a more subtle manner. The conditioning laboratory is the school. In school children are made to engage with the books, textbooks in most cases, in the most artificial and dishonest matter. Another problem is the quality of textbooks themselves. Though the school has a “textbook culture”, not enough effort is put in by the writers and designers of the textbooks to make the best that they can offer. Instead cheap, copy-paste techniques, and a mix-and-match fashioned content is crammed and printed onto those pages glued together called as textbooks. No wonder, people when they grow up don’t like books or run away at the sight of them. Its just behaviorism at work with Pavlov portrait in the background.

Schooled and unschooled education

It is difficult now to challenge the school as a system because we are
so used to it. Our industrial categories tend to define results as
products of specialized institutions and instruments, Armies produce
defence for countries. Churches procure salvation in an
afterlife. Binet defined intelligence as that which his tests
test. Why not, then, conceive of education as the product of schools?
Once this tag has been accepted, unschooled education gives the
impression of something spurious, illegitimate and certainly
unaccredited.

– Ivan Illich (Celebration of Awareness)

Einstein on his school experience

One had to cram all this stuff into one’s mind, whether one liked it or not. This coercion had such a deterring effect that, after I had passed the final examination, I found the consideration of any scientific problems distasteful to me for an entire year … is in fact nothing short of a miracle that the modern methods of instruction have not yet entirely strangled the holy curiosity of inquiry; for this delicate little plant, aside from stimulation, stands mainly in need of freedom; without this it goes to wreck and ruin without fail. It is a very grave mistake to think that the enjoyment of seeing and searching can be promoted by means of coercion and a sense of duty. To the contrary, I believe that it would be possible to rob even a healthy beast of prey of its voraciousness, if it were possible, with the aid of a whip, to force the beast to devour continuously, even when not hungry – especially if the food, handed out under such coercion, were to be selected accordingly.

Seeing that even almost a hundred years later it is almost unchanged gives one an idea of how little effort has gone into changing how we learn.

On respect in the classroom

If you are a teacher (of any sort) and teach young people, don’t be disheartened if the students in your class don’t respect you or listen to you or maintain discipline. Even great philosophers like Socrates and Aristotle has a tough time dealing with their students

Socrates grumbled that he don’t get no respect: his pupils “fail to rise when their elders enter the room. They chatter before company, gobble up dainties at the table, and tyrannize over their teachers.” Aristotle was similarly pissed off by his stu­dents’ attitude: “They regard themselves as omniscient and are positive in their assertions; this is, in fact, the reason for their carrying everything too far.”Their jokes left the philosopher unamused: “They are fond of laughter and conse­quently facetious, facetiousness being disciplined insolence.”

– Judith Harris The Nurture Assumption

That being said, the students are also very perceptive about the knowledge of the teachers, and know who is trying to be a cosmetic intellectual.

Cosmetic Intellectuals (+ IYI)

In the last few years, the very connotation of the term intellectual has seen a downward slope. Such are the times that we are living in that calling someone an “intellectual” has become more like an insult rather than a compliment: it means an idiot who doesn’t understand or see things clearly. Now as the title of the post suggests it is this meaning, not the other meaning intellectuals who know about cosmetics. Almost two decades back Alan Sokal wrote a book titled Intellectual Impostures, which described quite a few of them. In this book, Sokal exposed the posturing done by people of certain academic disciplines who were attacking science from a radical postmodernist perspective. What Sokal showed convincingly through his famous hoax, is that many of these disciplines are peddling out bullshit with no control over the meaning contained. Only the form was important not the meaning. And in the book, he takes it a step forward, showing that this was not an isolated case. He exposes the misuse of the technical terms (which often have precise and operational meanings) as loose metaphors or even worse completely neglecting the accepted meaning of those terms. The examples given are typical, and you cannot make sense of what is being written. You can read, but cannot understand. It makes no sensible meaning. At this point, you start to doubt your own intelligence and intellectual competence, perhaps you have not read enough to understand this complex piece of knowledge. It was after all written by an intellectual. Perhaps you are not aware of the meaning of the jargon or their context, hence you are not able to understand it. After all there are university departments and journals dedicated to such topics. Does it not legitimise such disciplines as academic and its proponents/followers as intellectuals? Sokal answered it empirically by testing if presented with nonsense whether it makes any difference to the discipline. You are not able to make sense of these texts because they are indeed nonsensical. To expect any semblance of logic and rationality in them is to expect too much.

Nassim Taleb has devised the term Intellectual Yet Idiots (the IYI in the title) in his Incerto series. He minces no words and takes no bullshit. Sokal appears very charitable in comparison. Taleb sets the bar even higher. Sokal made a point to attack mostly the postmodernists, but Taleb bells the cats who by some are even considered proper academics, for example, Richard Dawkins and Steven Pinker. He considers entire disciplines as shams, which are otherwise considered academic, like economics, but has equal if not more disdain to several others also, for example, psychology and gender studies. Taleb has at times extreme views on several issues and he is not afraid to speak of his mind on matters that matter to him. His writings are arrogant, but his content is rigorous and mathematically sound.

they aren’t intelligent enough to define intelligence, hence fall into circularities—their main skill is a capacity to pass exams written by people like them, or to write papers read by people like them.

But there are people who are like IYIs, but don’t even have the depth of the content or knowledge of IYIs. They are wannabe IYIs, all form no conent. They are a level below IYIs. I term such people as cosmetic intellectuals (cosint). We have met them before: they are the envious mediocre and the ones who excel in meetings. The term cosmetic is used in two senses both as adjectives. The first sense is the Loreal/Lakme/Revlon fashion sense as given from the dictionary entry below:

cosmetic

  • relating to treatment intended to restore or improve a person’s appearance
  • affecting only the appearance of something rather than its substance

It is the second sense that I mean in this post. It is rather the substance of these individuals that is only present in the appearance. And as we know appearance can be deceiving. Cosints appear intellectuals, but only in appearance, hence the term cosmetic. So how does one become a Cosint? Here is a non-exhaustive list that can be an indicator (learn here is not used in the deeper sense of the word, but more like as in rote-learn):

  1. Learn the buzzwords: Basically they rote learn the buzzwords or the jargon of the field that they are in. One doesn’t need to understand the deeper significance or meaning of such words, in many cases just knowing the words works. In the case of education, some of these are (non-comprehensive): constructivism, teaching-learning process, milieu, constructivist approaches, behaviorism, classroom setting, 21st-century skills, discovery method, inquiry method, student-centered, blended learning, assessments, holistic, organic, ethnography, pedagogy, curriculum, TLMs. ZPD, TPD, NCF, RTE, (the more complicated the acronyms, the better). More complicated it sounds the better. They learn by association that certain buzzwords have a positive value (for example, constructivism) and other a negative one (for example, behaviorism) in the social spaces where they usually operate in, for example, in education departments of universities and colleges. Not that the Cosints are aware of the deeper meaning of there concepts, still they make a point of using them whenever possible. They make a buzz using the buzzwords. If you ask them about Piaget, they know the very rudimentary stuff, anything deeper and they are like rabbits in front of flashlight. They may talk about p-values, 𝛘2 tests, 98.5 % statistical significances, but when asked will not be able to distinguish between dependent and independent variables.
  2. Learn the people: The CosInts are also aware of the names of the people in their trade. And they associate the name to a concept or of a classic work. They are good associating. For example, (bad) behaviorism with Burrhus F. Skinner or Watson, hence Skinner bad. Or Jean Piaget with constructivism and stages (good). Vygotsky: social constructivism, ZPD. Or John Dewey and his work. So they have a list of people and concepts. Gandhi: Nayi Taleem.  Macauley: brought the English academic slavery on India (bad).
  3. Learn the classics: They will know by heart all the titles of the relevant classics and some modern ones (you have to appear well-read after all). Here just remembering the names is enough. No one is going to ask you what was said in section 1.2 of Kothari Commission. Similarly, they will rote learn the names of all the books that you are supposed to have read, better still carry a copy of these books and show off in a class. Rote learn a few sentences, and spew it out like a magic trick in front of awestruck students. Items #1 through #3 don’t work very well when they have real intellectual in front of them. A person with a good understanding of basics will immediately discover the fishiness of the facade they put up. But that doesn’t matter most of the time, as we see in the next point.
  4. Know the (local) powerful and the famous: This is an absolute must to thrive with these limitations. Elaborated earlier.
  5. Learn the language aka Appear academic (literally not metaphorically): There is a stereotype of academic individuals. They will dress in a particular manner (FabIndia?, pyor cotton wonly, put a big Bindi, wear a Bongali kurta etc, carry ethnic items, conference bags (especially the international ones), even conference stationery), carry themselves in a particular manner, talk in a particular manner (academese). This is also true of wannabe CosInt who are still students, they learn to imitate as soon as they enter The Matrix. Somehow they will find ways of using names and concepts from #1 #2 #3 in their talk, even if they are not needed. Show off in front of the students, especially in front of the students. With little practice one can make an entire classroom full of students believe that you are indeed learned, very learned. Any untoward questions should be shooed off, or given so tangential an answer that students are more confused than they were earlier.
  6. Attend conferences, seminars and lectures: The primary purpose is network building and making sure that others register you as an academic. Also, make sure that you ask a question or better make a tangential comment after the seminar so that everyone notices you. Ask the question for the sake of asking the question (even especially if you don’t have any real questions). Sometimes the questions devolve into verbal diarrhea and don’t remain questions and don’t also have any meaning that can be derived from them (I don’t have a proper word to describe this state of affairs, but it is like those things which you know when you see it). But you have to open your mouth at these events, especially when you have nothing substantial/meaningful to say. This is how you get recognition. Over a decade of attending various conferences on education in India, I have come to realise that it is akin to a cartel. You go to any conference, you will see a fixed set of people who are common to these conferences. Many of these participants are the cosints (both the established and the wannabes). After spending some time in the system they become organisers of such conferences, seminars and lectures definitely get other CosInts to these conferences. These are physical citation rings, I call you to my conference you call me to yours. Year after year, I see the same patterns, so much so I can predict, like while watching a badly written and cliche movie, what is going to happen when they are around. That person has to ask a question and must use a particular buzzword. (I myself don’t ask or comment, unless I think I have something substantial to add. Perhaps they think in same manner, just that their definition of substantial is different than mine.) Also, see #5, use the terms in #1, #2 and #3. Make sure to make a personal connection with all the powerful and famous you find there, also see #4.
  7. Pedigree matters: Over the years, I have seen the same type of cosints coming from particular institutions. Just like you can predict certain traits of a dog when you know its breed, similarly one can predict certain traits of individuals coming from certain institutions. Almost without exception, one can do this, but certain institutions have a greater frequency of cosints. Perhaps because the teachers who are in those places are themselves IYI+cosints. Teaching strictly from a  prescribed curriculum and rote-learning the jargon: most students just repeat what they see and the cycle continues. Sometimes I think these are the very institutions that are responsible for the sorry state of affairs in the country. They are filled to the brim with IYIs, who do not have any skin in the game and hence it doesn’t matter what they do. Also, being stamped as a product of certain institution gives you some credibility automatically, “She must be talking some sense, after all he is from DU/IIT/IIM/JNU/”
  8. Quantity not quality: Most of us are not going to create work which will be recognised the world over (Claude Shannon published very infrequently, but when he did it changed the world). Yet were are in publish or perish world. CosInts know this, so they publish a lot. It doesn’t matter what is the quality is (also #4 and #5 help a lot). They truly are environmentalists. They will recycle/reuse the same material with slight changes for different papers and conferences, and surprisingly they also get it there (also #4 and #5 help a lot). So, at times, you will find a publication list which even a toilet paper roll may not be able to contain. Pages after pages of publications! Taleb’s thoughts regarding this are somewhat reassuring, so is the Sokal’s hoax, that just when someone has publications (a lot of them) it is not automatic that they are meaningful.
  9. Empathisers and hypocrites: Cosints are excellent pseudo-emphatisers. They will find something to emphathise with. Maybe a class of people, a class of gender (dog only knows how many). Top of the list are marginalised, poor low socio-economic status, underprivileged, rural schools, government students, school teachers, etc. You get the picture.  They will use the buzz words in the context of these entities they emphathise with. Perhaps, once in their lifetimes, they might have visited those whom they want to give their empathy, but otherwise, it is just an abstract entity/concept.(I somehow can’t shake image of Arshad Warsi in MunnaBhai MBBS “Poor hungry people” while writing about this.) It is easier to work with abstract entities than with real ones, you don’t have to get your hands (or other body parts) dirty. The abstract teacher will do this, will behave in this way: they will write a 2000 word assignment on a terse subject. This is all good when designing things because abstract concepts don’t react in unwanted ways. But when things don’t go as planned in real world, teachers don’t react at all! The blame is on everyone else except the cosints. Perhaps they are too dumb to understand that it is they are at fault. Also, since they don’t have skin in the game, they will tell and advise whatever they have heard or think to be good, when it is implemented on others. For example, if you talk to people especially from villages, they will want to learn English as it is seen as the language which will give them upward mobility. But cosints, typically in IYI style, some researchers found that it is indeed the mother tongue which is better for students to learn, it should be implemented everywhere. The desires and hopes of those who will be learning be damned, they are too “uneducated” to understand what they need. It is the tyranny of fake experts at work here.

    He thinks people should act according to their best interests and he knows their interests… When plebeians do something that makes sense to themselves, but not to him, the IYI uses the term “uneducated.” (SITG Taleb)

    Now one would naturally want to know under what conditions that research was done? was there any ideological bias of the researchers? whether it is applicable in as diverse a country as India? What do we do of local “dialects”? But they don’t do any of this. Instead, they will attack anyone who raises these doubts, especially in #6. They want to work only with the government schools: poor kids, poor teachers no infrastructure. But ask them where their own children study: they do in private schools! But their medium must be their mother tongue right? No way, it is completely English medium, they even learn Hindi in English. But at least the state board? No CBSE, or still better ICSE. Thus we see the hypocrisy of the cosint, when they have the skin in the game. But do they see it themselves? Perhaps not, hence they don’t feel any conflict in what they do.

So we see that IYI /cosint are not what they seem or consider themselves. Over the last decade or so, with the rise of the right across the world is indicating to everyone that something is wrong when cosints tell us what to do. The tyranny of pseudo-experts has to go.  But why it has come to that the “intellectuals” who are supposed to be the cream of the human civilisation, the thinkers, the ideators, so why the downfall? Let us first look at the meaning of the term, so as to be not wrong about that:

 The intellectual person is one who applies critical thinking and reason in either a professional or a personal capacity, and so has authority in the public sphere of their society; the term intellectual identifies three types of person, one who:

  1. is erudite, and develops abstract ideas and theories;
  2. a professional who produces cultural capital, as in philosophy, literary criticism, sociology, law, medicine, science; and
  3. an artist who writes, composes, paints and so on.

Intellectual (emphasis mine)

Now, see in the light of the above definition, it indeed seems that it must be requiring someone to be intelligent and/or well-cultured individual. So why the change in the tones now? The reasons are that the actual intellectual class has degraded and cosints have replaced them, also too much theory and no connect with the real world has made them live in a simulacrum which is inhabited and endorsed by other cosints. And as we have seen above it is a perpetuating cycle, running especially in the universities (remember Taleb’s qualification). They theorize and jargonise (remember the buzzwords) simple concepts so much that no one who has got that special glossary will understand it). And cosints think it is how things should be. They write papers in education, supposedly for the betterment of the classroom teaching by the teachers, in such a manner that if you give it to a teacher, they will not be able to make any sense of it, leave alone finding something useful. Why? Because other cosints/IYI demand it! If you don’t write a paper in a prescribed format it is rejected, if it doesnt have enough statistics it is rejected, if it doesn’t give enough jargon in the form of theoretical review, and back scratching in the form of citations it is rejected. So what good are such papers which don’t lead to practice? And why should the teachers listen to you if you don’t have anything meaningful to tell them or something they don’t know already?

The noun to describe them:

sciolist – (noun) – One who engages in pretentious display of superficial knowledge.

Technologies in the classroom

ict-satellite-education

How to modernise education? How to make use of new technological developments that are around us to make learning in schools better? These are some of the questions that we will look at in the current post. In particular, we will be looking at the so-called satellite education as being implemented in some schools.

In many discussions regarding education, the teachers are usually blamed for not doing their assigned jobs correctly. There is some truth in these accusations. Having worked with teachers at different levels (primary to university) and in different settings (govt schools, private elite schools, teacher training institutes, colleges, and universities) I have come to the conclusion that teachers are part of the problem. This will be elaborated in another post and before you draw out your pitchforks the disclaimer: of course there are good teachers, who do their jobs well.

So one of the solutions is to take these good teachers to all the classrooms. Of course, it cannot be done in a physical way. This is where the technological advance pitches in. We take the good teachers to classrooms via satellites. The TV in the classroom becomes the blackboard, which allows the students to get the best of experiences that the system can offer. Now, this is not just limited to schools but also colleges, some of the best institutes in the country are offering “distance-education” courses like this. The government has invested a large sum in higher education in the form of Swayam channels. These channels are running lectures by various faculties of institutes across India 24×7. Mind you most of these are not specially produced lectures for the TV, they are recordings of usual lectures that these faculties give to their classes. Most are boring af, with them reading out the powerless-pointless slides one after other. They cram as much text as possible on these slides. Making them dense in terms of ink ratio, but unfathomable in terms of learning from them. Anyways this is a subject for another post.

Imagination and philosophies

Our sense of imagination is limited by what we know, and the
philosophies that we subscribe to. For some, it is clear about what their assumptions are for others it is not. They think that this is how it should be, completely ignorant of the notion that some of their concepts are based on assumptions. For some people, this is something that they are aware of, for most of us, we are not aware of this. Many
times we think of finding solace in things which are traditional. Since it has stood the test of time, it must have some inherent value they say. It is our ignorance and arrogance that we are not seeing any value in it. Hence people resist change. Why try something new which might or might work, or work equally well when we have something which is tried and tested? Of course, stability is important, but then stability does not lead to change. Yet when people change things, they try to replicate the models that they have found to work, and hence reducing the risk.

If we apply the same idea with regards to education, we also come across many such examples. The satellite television used in the classroom is one such case. The idea is not new. As soon as television technology became commonly feasible in the 50s and 60s, immediately some pedagogues of the era jumped to the idea of using them for education. This ideally suited the “transmission model” of education which was in vogue at that time with behaviorism ruling the roost of psychology in general and education in particular. In a way, learning via television is the ultimate epitome of the transmission model. In a regular classroom, there is at least a scope for the teacher and student to interact. But in this case, the entire flow of information is in one direction. The transmission is the transmission of learning. No wonder for many decades, and even now television was seen as a game-changer and harbinger of technological learning. Television was also seen as non-invasive technology, as it is passive which works for everyone involved, except perhaps for the most important stakeholders the learner. The television didn’t and doesn’t challenge the traditional “transmission model” of education, which most teachers and stakeholders (including parents) do believe in. The values which enlightened pedagogues worship, find a very low priority with most other stakeholders.

The central mindset in education

The term “centralised mindset” refers to the idea that in complex systems there has to be a controlling agent who overseas all executions.  The centralised mindset refers to a belief that any system which works well must have a system or authority (in the form of a person or a group) which must somehow control the mechanism. The belief in the centralised mindset is that the individuals in a complex system are too unintelligent to behave in a coordinated, complex manner. For example, for a long time, it was believed that the “V” formation that one sees in the flying birds is due to a “leader” in the group. This supposed leader will make the group fall in the “V” patterns by organising the other group members. This is a very intuitive model that appeals to common sense. Whenever we see some patterns, we assume there must be an inherent design or a designer. In the case of the birds in “V” shape the same logic applies. There must be a leader who makes sure such a pattern is created. But such a view, however intuitive and correct it may seem is incorrect. As it happens with most of the other principles in science, in this case too the correct explanation is counter-intuitive. There is no leader in the case of the birds. The “V” pattern that we see is an example of what is known as an emergent phenomenon. It arises from the interaction of the birds which are flying together. When all the individuals follow simple rules in interacting with their neighbours, the “V” pattern emerges. The people who believe in a central leader are wrong in this case. It is a fiction that makes things that we observe easy to accept. But it is not correct. For many such examples and deeper discussions, see Turtles, Termites, and Traffic Jams by Mitchel Resnick.

There are several natural and artificial phenomena where earlier we (including the experts who propose such explanations) though that there was a central control involved in creating patterns, but in most cases, we have discovered otherwise. The counter-intuitive explanation that there is no central control or mechanism just doesn’t appeal to people. How can it be that there is no central control and yet the thing works on its own? Do we always need a centralised control? People argue that without a centralised control there will be chaos or anarchy. Stable patterns of behaviour or observations cannot emerge, it is assumed if there is no central control. Examples are given of a central governing that we are used to so much.

Now you might be wondering what has this to do with education? The general bureaucracy in the educational field is seen as centralised. For example, the creation of a textbook or syllabus or curriculum and assessment is always a centralised process. Think of the board exams.

Why cannot a school or a teacher decide upon textbooks and curriculum?

Why this is so? Because that is how it was in the other government departments. This is what the tradition says. A bunch of experts (preferably with a prefix of a Dr. or Prof.) will decide for everyone what they should learn and more importantly how they should learn it and most importantly how will this learning be assessed. This triumvirate or what to learn, how to learn and how to assess is assumed to be too complex and too important to be left to the plebs. This is where centralised mindset in the form of centralised expert committees is brought in.

The power of the teacher in the classroom is reduced to
a mere executioner ( a meek dictator if you will, as per Krishna Kumar) of all the algorithms set for them to follow. Some good teachers would improvise on this little elbow room that the classroom did offer. But now in an effort to make it
more central in discourse and execution, a centralised teacher and
teaching is needed. Indeed this is the idea behind the satellite television in the
classrooms. To ensure that quality (standardised) education reaches all learners. This also reduces the load on the local teachers, who just have to shepherd the learners to the AV room, and their job is done. The parents are happy as their children are supposed to be learning from the best teacher. And this happens live in some cases, I witnessed this entire process in Rajasthan. Seeing it from the studio being recorded and transmitted live via the satellite, and also saw (at another time) how it is received and executed in the schools. In some cases for interactivity and feedback, a Whatsapp number is provided where the teachers or the learners can reach out to the teacher in the studio. This teacher at the studio genuinely believed that he was being helpful to the students and the system worked. The proof for this was not some study but the messages he received from the school teachers thanking him for taking their class. Real interactivity which might happen in an actual classroom was found to be missing.

Just like the illustration on the top of the post shows, the core idea in the satellite television in the classroom is to centrally repeat the process of transmission of knowledge to all the learners with an added bonus of synchronicity. One act can be used at multiple locations. But this creates inhibitions for interactivity. Constructivism of the experts can go for a toss. Why do we need to create a custom curriculum for each child, when one expert in one manner can teach them all at the same time?

 

Genetics and human nature

Usually, in the discussion regarding human nature, there is a group of academics who would like to put all the differences amongst humans to non-genetic components. That is to say, the cultural heritage plays a much more important or the only important role in the transfer of characteristics. In the case of education, this is one of the most contested topics. The nature-nurture debate as it is known goes to the heart of many theories of human behaviour, learning and cognition. The behaviourist school was very strong until the mid 20th century. This school strongly believed that the entirety of human learning is dependent only on the environment with the genes or (traits inherited from the parents) playing little or no role. This view was seriously challenged on multiple fronts with attacks from at least six fields of academic inquiry: linguists, psychology, philosophy, artificial intelligence, anthropology, and neuroscience. The advances in these fields and the results of the studies strongly countered the core aspects of behaviourism. Though the main thrust of the behaviourist ideas seems to be lost, but the spirit still persists.  This is in the form of academics who still deny any role for genes, or even shun at the possibility of genes having any effect on human behaviour. They say it is all the “environment” or nurture as they name it. Any attempt to study the genetic effects are immediately classified as fascist, Nazi or equated to social Darwinism and eugenics. But over several decades now, studies which look at these aspects have given us a mounting mountain of evidence to lay the idea to rest. The genes do play a definitive role and what we are learning is that the home environment may not be playing any role at all or a very little role in determining how we turn out. Estimates range from 0 to 10%. The genes, on the other hand, have been found to have about 50% estimate, the rest 40% being attributed to a “unique”  environment that the individual experiences.   Though typically, some of the individuals in academia argue strongly against the use of genetics or even mention of the word associated with education or any other parameters related to education. But this has to do more with their ideological positions, which they do not want to change, than actual science. This is Kuhnian drama of a changing science at work. The old scientists do not want to give up on their pet theories even in the case of evidence against them. This is not a unique case, the history of science is full of such episodes.

Arthur Jensen, was one of the pioneers of studying the effect of genetic heritability in learning. And he lived through the behaviourist and the strong nurture phases of it. This quote of his summarises his stand very well.

Racism and social elitism fundamentally arise from identification of individuals with their genetic ancestry; they ignore individuality in favor of group characteristics; they emphasize pride in group characteristics, not individual accomplishment; they are more concerned with who belongs to what, and with head-counting and percentages and quotas than with respecting the characteristics of individuals in their own right. This kind of thinking is contradicted by genetics; it is anti-Mendelian. And even if you profess to abhor racism and social elitism and are joined in battle against them, you can only remain in a miserable quandary if at the same time you continue to think, explicitly or implicitly, in terms of non-genetic or antigenetic theories of human differences. Wrong theories exact their own penalties from those who believe them. Unfortunately, among many of my critics and among many students I repeatedly encounter lines of argument which reveal disturbing thought-blocks to distinguishing individuals from statistical characteristics (usually the mean) of the groups with which they are historically or socially identified.

–  Arthur Jensen, Educability and Group Differences 1973

As the highlighted sentence in the quote remarks, the theories which are wrong or are proven to be wrong do certainly exact penalties from their believers. One case from history of science being the rise and rise of Lysenkoism in the erstwhile USSR. The current bunch of academics who strongly deny any involvement of genes in the theories of human learning are no different.

The logician, the mathematician, the physicist, and the engineer

The logician, the mathematician, the physicist, and the engineer. “Look at this mathematician,” said the logician. “He observes that the first ninety-nine numbers are less than hundred and infers hence, by what he calls induction, that all numbers are less than a hundred.”

“A physicist believes,” said the mathematician, “that 60 is divisible by all numbers. He observes that 60 is divisible by 1, 2, 3, 4, 5, and 6. He examines a few more cases, as 10, 20, and 30, taken at random as he says. Since 60 is divisible also by these, he considers the experimental evidence sufficient.”

“Yes, but look at the engineers,” said the physicist. “An engineer suspected that all odd numbers are prime numbers. At any rate, 1 can be considered as a prime number, he argued. Then there come 3, 5, and 7, all indubitably primes. Then there comes 9; an awkward case, it does not seem to be a prime number. Yet 11 and 13 are certainly primes. ‘Coming back to 9’ he said, ‘I conclude that 9 must be an experimental error.'”

George Polya (Induction and Analogy – Mathematics of Plausible Reasoning – Vol. 1, 1954)

On mathematics

Mathematics is regarded as a demonstrative science. Yet this is only one of its aspects. Finished mathematics presented in a finished form appears as purely demonstrative, consisting of proofs only. Yet mathematics in the making resembles any other human knowledge in the making. You have to guess a mathematical theorem before you prove it; you have to guess the idea of the proof before you carry through the details. You have to combine observations and follow analogies; you have to try and try again. The result of the mathematician’s creative work is demonstrative reasoning, a proof; but the proof is discovered by plausible reasoning, by guessing. If the learning of mathematics reflects to any degree the invention of mathematics, it must have a place for guessing, for plausible inference.

George Polya (Induction and Analogy – Mathematics of Plausible Reasoning – Vol. 1, 1954)

Unreal and Useless Problems

We had previously talked about problem with contexts given in mathematics problems. This is not new, Thorndike in 1926 made similar observations.

Unreal and Useless Problems

In a previous chapter it was shown that about half of the verbal problems given in standard courses were not genuine, since in real life the answer would not be needed. Obviously we should not, except for reasons of weight, thus connect algebraic work with futility. Similarly we should not teach the pupil to solve by algebra problems which in reality are better solved otherwise, for example, by actual counting or measuring. Similarly we should not set him to solve problems which are silly or trivial, connecting algebra in his mind with pettiness and folly, unless there is some clear, counterbalancing gain.
This may seem beside the point to some teachers, ”A problem is just a problem to the children,” they will say,

“The children don’t know or care whether it is about men or fairies, ball games or consecutive numbers.” This may be largely true in some classes, but it strengthens our criticism. For, if pupils^do not know what the problem is about, they are forming the extremely bad habit of solving problems by considering only the numbers, conjunctions, etc., regardless of the situation described. If they do not care what it is about, it is probably because the problems encountered have not on the average been worth caring about save as corpora vilia for practice in thinking.

Another objection to our criticism may be that great mathematicians have been interested in problems which are admittedly silly or trivial. So Bhaskara addresses a young woman as follows: ”The square root of half the number of a swarm of bees is gone to a shrub of jasmine; and so are eight-ninths of the swarm: a female is buzzing to one remaining male that is humming within a lotus, in which he is confined, having been allured to it by its fragrance at night. Say, lovely woman, the number of bees.” Euclid is the reputed author of: ”A mule and a donkey were going to market laden with wheat. The mule said,’If you gave me one measure I should carry twice as much as you, but if I gave you one we should bear equal burdens.’ Tell me, learned geometrician, what were their burdens.” Diophantus is said to have included in his preparations for death the composition of this for his epitaph : ” Diophantus passed one-sixth of his life in childhood one-twelfth in youth, and one-seventh more as a bachelor. Five years after his marriage was born a son, who died four years before his father at half his father’s age.”

My answer to this is that pupils of great mathematical interest and ability to whom the mathematical aspects of these problems outweigh all else about them will also be interested in such problems, but the rank and file of pupils will react primarily to the silliness and triviality. If all they experience of algebra is that it solves such problems they will think it a folly; if all they know of Euclid or Diophantus is that he put such problems, they will think him a fool. Such enjoyment of these problems as they do have is indeed compounded in part of a feeling of superiority.

– From Thorndike et al. The Psychology of Algebra 1926

School as a manufacturing process

Over most of this century, school has been conceived as a manufacturing process in which raw materials (youngsters) are operated upon by the educational process (machinery), some for a longer period than others, and turned into finished products. Youngsters learn in lockstep or not at all (frequently not at all) in an assembly line of workers (teachers) who run the instructional machinery. A curriculum of mostly factual knowledge is poured into the products to the degree they can absorb it, using mostly expository teaching methods. The bosses (school administrators) tell the workers how to make the products under rigid work rules that give them little or no stake in the process.
– (Rubba, et al. Science Education in the United States: Editors Reflections. 1991)

Thomas Kuhn on the role of textbooks in science education

The single most striking feature of this [science] education is that, to an extent wholly unknown in other fields, it is conducted entirely through textbooks. Typically, undergraduate and graduate students of chemistry, physics, astronomy, geology, or biology acquire the substance of their fields from books written especially for students.

Thomas Kuhn The Essential Tension

Here Kuhn is trying to show us the nature of science education which is usually divergent from the historical processes and events which led to the currently accepted theories. Most of the textbooks rather show the content matter which makes sense conceptually in a rationally organised manner. Of course, the ideal goal, at least in the physical sciences, is to create a hypothetico-deductive model in which a given theory, its predictions, explanations and implications can be derived from some basic definitions and axioms. For example, an introductory text on motion in physics usually starts with definitions and assumptions usually of a mass point, and/or operations that are defined on it. The text does not describe the historical conditions in which this conceptual approach arose, rather it adapts a very pragmatic pedagogical approach. It defines the term and ends it there, but in this process, it redefines the conceptual history. This approach assumes that there is no pedagogical merit or role in introducing a concept in its historical context. This perhaps is also linked to Poppers distinction of the context of discovery and the context of justification. What we see is a rational reconstruction of historical processes to make sense of them in a straightforward manner.

 

 

On not learning or con in the context

We will, we will, fail you by testing what you do not know…

We live in a rather strange world. Or is it that we assume the world
to be non-strange in a normative way, but the descriptive world has
always been strange? Anyways, why I say this is to start a rant to
about some obviously missed points in the area of my work. Namely,
educational research, particularly science and mathematics education
research.

In many cases the zeal to show that the students have
‘misunderstandings’ or are simply wrong, and then do a hair-splitting
(micro-genetic) exercise on the test the students were inflicted
with. Using terse jargon and unconsequential statistics, making the
study reports as impossible to read as possible, seem to be the norm.

But I have seen another pattern in many of the studies, particularly
in mathematics education. The so-called researchers spent countless
nights in order to dream up situations as abstract as possible (the
further far away from real-life scenarios the better), then devise
problems around them. Now, these problems are put in research studies,
which aim to reveal (almost in evangelical sense) the problems that
plague our education. Unsuspecting students are rounded, with
appropriate backgrounds. As a general rule, the weaker socio-economic
background your students come from, the more exotic is your study. So
choose wisely. Then these problems are inflicted upon these poor,
mathematically challenged students. The problems will be in situations
that the students were never in or never will be. The unreal nature of
these problems (for example, 6 packets of milk in a cup of coffee! I
mean who in real life does that? The milk will just spill over, the
problem isn’t there. This is just a pseudo-problem created for satisfying the research question of the researcher. There is no context, but only con.

Or finding out a real-life example for some weird fractions) puts many off. The fewer students perform correctly happier the researcher is. It just adds to the data statistic that so many % students cannot perform even this elementary task well. Elementary for
that age group, so to speak. The situation is hopeless. We need a
remedy, they say. And remedy they have. Using some revised strategy,
which they will now inflict on students. Then either they will observe
a few students as if they are some exotic specimens from an
uncontacted tribe as they go on explaining what they are doing or why
they are doing it. Or the researcher will inflict a test (or is it
taste) in wholesale on the lot. This gives another data
statistic. This is then analysed within a ‘framework’, (of course it
needs support) of theoretical constructs!

Then the researcher armed with this data will do a hair-splitting
analysis on why, why on Earth student did what they did (or didn’t
do). In this analysis, they will use the work of other researchers before
them who did almost the same thing. Unwieldy, exotic and esoteric
jargons will be used profusely, to persuade any untrained person to
giveup on reading it immediately. (The mundane, exoteric and
understandable and humane is out of the box if you write in that
style it is not considered ‘academic’.) Of course writing this way,
supported by the statistics that are there will get it published in
the leading journals in the field. Getting a statistically significant
result is like getting a license to assert truthfulness of the
result. What is not clear in these mostly concocted and highly
artificial studies is that what does one make of this significance
outside of the experimental setup? As anyone in education research
would agree two setups cannot be the same, then what is t

Testing students in this way is akin to learners who are learning a
new language being subjected to and exotic and terse vocabulary
test. Of course, we are going to perform badly on such a test. The
point of a test should be to know what students know, not what they
don’t know. And if at all, they don’t know something, it is treated as
if is the fault of the individual student. After all, there would be
/some/ students in each study (with a sufficiently large sample) that
would perform as expected. In case the student does not perform as
expected we can have many possible causes. It might be the case that
the student is not able to cognitively process and solve the problem,
that is inspite of having sufficient background knowledge to solve the
problem at hand the student is unable to perform as expected. It might
be the case that the student is capable, but was never told about the
ways in which to solve the given problem (ZPD anyone?). In this case, it might be that the curricular materials that the student has access
to are simply not dealing with concepts in an amenable way. Or it
might be that the test itself is missing out on some crucial aspects
and is flawed, as we have seen in the example above. The problem is
systemic, yet we tend to focus on the individual. This is perhaps
because we have a normative structure to follow an ideal student at
that age group. This normative, ideal student is given by the so-called /standards of learning/. These standards decide, that at xx age
a student should be able to do multiplication of three digit
numbers. The entire curricula are based on these standards. Who and
what decides this? Most of the times, the standards are wayyy above
the actual level of the students. This apparent chasm between the
descriptive and the normative could not be more. We set unreal
expectations from the students, in the most de-contextualised and
uninteresting manner, and when they do not fulfil we lament the lack
of educational practices, resources and infrastructure.

The Textbook League

I came across this site while reading an article, there are interesting reviews of textbooks used in schools. And some of these reviews are gory, splitting out the blood and guts of the textbooks and their inaneness. Hopefully, many people will find it useful, though the latest book that is reviewed is from about 2002. Perhaps one should do a similar thing for books in the Indian context, basically performing a post-mortem on the zombiesque textbooks that flood our schools.

The Web site of The Textbook League is a resource for middle-school and high-school educators. It provides commentaries on some 200 items, including textbooks, curriculum manuals, videos and reference books. Most of the commentaries appeared originally in the League’s bulletin, The Textbook Letter.

http://www.textbookleague.org/ttlindex.htm

Uberization of Education

An Uberized education is when…

An Uberized education is when – as in antiquity – one goes to a specific teacher to get lectures, bypassing the university. The students and the teachers are thus matched. If a piece of paper is necessary, it would be given by that teacher, or a group of teachers. It is not too different from the decentralized apprentice model. This already works well for executive “education”. I give short workshops in my specialty of applied probability (I have given a few with PW, YBY and RD, though only lasting 1-2 days), limited to professionals. An Uberization would consist in making longer workshops, say of 2-3 week duration, after which the attendees would be getting a piece of paper of sorts. From my experience, both students and lecturers are more sincere when they bypass institutions. And, as with other Uberizations, it would be much, much efficient economically. A full education would be a collection of such micro-diplomas, which can be done on top of a conventional one. Finally I would personally like to attend such workshops in disciplines outside my specialty. After my experience with Aramaic/Syriac last summer, I have a list of subjects I would be hungry to learn outside university systems…

Source: The Black Swan Report › An Uberized education is when…

Implicit cognition in the visual mode

Images become iconified, with the image representing an object or
phenomena, but this happens by enculturation rather by training. An
example to elaborate this notion is the painting Treachery of
Images by Belgian surrealist artist René Magritte. The painting is
also sometimes called This is not a pipe. The picture shows a
pipe, and below it, Magritte painted, “Ceci n’est pas une pipe.”,
French for “This is not a pipe.”

176

When one looks at the painting, one
exclaims “Of course, it is a pipe! What is the painter trying to say
here? We can all see that it is indeed a pipe, only a fool will claim
otherwise!” But then this is what Magritte has to say:

The famous pipe. How people reproached me for it! And yet, could you
stuff my pipe? No, it’s just a representation, is it not? So if I had
written on my picture `This is a pipe’, I’d have been lying!

Aha! Yess! Of course!! you say. “Of course it is not a pipe! Of
course it is a representation of the pipe. We all know that! Is this
all the painter was trying to say? Its a sort of let down, we were
expecting more abstract thing from the surrealist.” We see that the
idea or concept that the painting is a \emph{representation} is so
deeply embedded in our mental conceptual construct that we take it for
granted all the time. It has become so basic to our everyday social
discourse and intercourse that by default we assume it to be so. Hence
the confusion about the image of the pipe. Magritte exposes this
simple assumption, that we so often ignore. This is true for all the
graphics that we see around us. The assumption is implicit in all the
things we experience in the society. The representation becomes the
thing itself, for it is implicit in the way we talk and communicate.

Big B and D

When you look at a photo of something or someone, you recognize
it. “This is Big B!” you say looking at the painting! But then you
have already implicitly assumed that the representation of Big B is Big B. This implicit assumption comes from years of implicit training from being submerged in  the sea of the visual artefacts that surround and drown us. This association between the visual representation and the reality it represents had become the central theme of the visual culture that we live in. The training that we need for such an association comes from the peers and mentors that surround us from the childhood. The meaning and the association of the images is taught/caught over the years, so much so that we assume the abstract association is the normal way things are. In this way it becomes the implicit truth, though when one is pressed, the explicit connections are brought out.

Yet when it comes to understanding images in science and mathematics, the same thing doesn’t happen. There is no enculturation of children into understand the implicit meaning in these images. Hardly there are no peers or mentors whose actions and practices can be imitated by the young impressible learners. The practice which comes so naturally in other domains (identifying actor with a picture of the actor, or identifying a physical space with a photo) doesn’t happen in science and mathematics classrooms. The notion of practice is dissociated from the what is done to imbibe this understanding in the children. A practice based approach where the images become synonymous with their implied meaning is used in vocabulary might one very positive way out, this is after all practitioners of science and mathematics learn their trade.

The True Purpose Of Graphic Display – J. W. Tukey

John Wilder Tukey, one of the greatest Statistician of the last century points to what the purpose of a graphic display should be:

  1.  Graphics are for the qualitative/descriptive – conceivably the semi quantitative – never for the carefully quantitative (tables do that better).
  2. Graphics are for comparison – comparison of one kind or another – not for access to individual amounts.
  3. Graphics are for impact – interocular impact if possible, swinging-finger impact if that is the best one can do, or impact for the unexpected as a minimum – but almost never for something that has to be worked at hard to be perceived.
  4. Finally, graphics should report the results of careful data analysis – rather than be an attempt to replace it. (Exploration-to guide data analysis – can make essential interim use of graphics, but unless we are describing the exploration process rather than its results, the final graphic should build on the data analysis rather than the reverse.)

From:

Tukey, J. W. (1993). Graphic comparisons of several linked aspects: Alternatives and suggested principles. Journal of Computational and Graphical Statistics, 2(1), 1-33.

Reflections on Liping Ma’s Work

Liping Ma’s book Knowing and teaching elementary mathematics has been very influential in Mathematics Education circles. This is a short summary of the book and my reflections on it.

Introduction

Liping Ma in her work  compares the teaching of mathematics in the American and the Chinese schools. Typically it is found that the American students are out performed by their Chinese counterparts in mathematical exams. This fact would lead us to believe that the Chinese teachers are better `educated’ than the U.S. teachers and the better performance is a straight result of this fact. But when we see at the actual schooling the teachers undergo in the two countries we find a large difference. Whereas the U.S. teachers are typically graduates with 16-18 years of formal schooling, the typical Chinese maths teacher has about only 11-12 years of schooling. So how can a lower `educated’ teacher produce better results than a more educated one? This is sort of the gist of Ma’s work which has been described in the book. The book after exposing the in-competencies of the U.S. teachers also gives the remedies that can lift their performance.

In the course of her work Ma identifies the deeper mathematical and procedural understanding present, called the profound understanding of fundamental mathematics [PUFM] in the Chinese teachers, which is mostly absent in the American teachers. Also the “pedagogical content knowledge” of the Chinese teachers is different and better than that of the U.S. teachers. A teacher with PUFM “is not only aware of the conceptual structure and the basic attitudes of mathematics inherent in elementary mathematics, but is able to teach them to students.” The situation of the two teacher is that the U.S. teachers have a shallow understanding of a large number of mathematical structures including the advanced ones, but the Chinese teachers have a deeper understanding of the elementary concepts involved in mathematics. The point where the PUFM is attained in the Chinese teachers is addressed. this Also the Chinese education system so structured that it allows cooperation and interaction among the junior and senior teachers.

Methodology

The study was conducted by using the interview questions in Teacher Education and Learning to Teach Study [TELT] developed by Deborah Ball. These questions were designed to probe teacher’s knowledge of mathematics in the context of common things that teachers do in course of teaching. The four common topics that were tested for by the TELT were: subtraction, multiplication, division by fractions and the relationship between area and perimeter. Due to these diverse topics in the questionnaire the teachers subject knowledge at both conceptual and procedural levels at the elementary level could be judged quite comprehensively. The teacher’s response to a particular question could be used to judge the level of understanding the teacher has on the given subject topic.

Sample

The sample for this study was composed of two set of teachers. One from the U.S., and another from China. There were 23 U.S. teachers, who were supposed to be above average. Out of these 23, 12 had an experience of 1 year of teaching, and the rest 11 had average teaching experience of 11 years. In China 72 teachers were selected, who came from diverse nature of schools.In these 72, 40 had experience of less than 5 years of teaching, 24 had more than 5 years of teaching experience, and the remaining 8 had taught for more than 18 years average. Each teacher was interviewed for the conceptual and procedural understanding for the four topics mentioned.

We now take a look at the various problems posed to the teachers and their typical responses.

Subtraction with Regrouping

The problem posed to the teachers in this topic was:

Lets spend some time thinking about one particular topic that you may work with when you teach, subtraction and regrouping. Look at these questions:
62
– 49
= 13

How would you approach these problems if you were teaching second grade? What would you say pupils would need to understand or be able to do before they could start learning subtraction with regrouping?

Response

Although this problem appears to be simple and very elementary not all teachers were aware of the conceptual scheme behind subtraction by regrouping. Seventy seven percent of the U.S. teachers and 14% of U.S. teacher had only the procedural knowledge of the topic. The understanding of these teachers was limited to just taking and changing steps. This limitation was evident in their capacity to promote conceptual learning in the class room. Also the various levels of conceptual understanding were also displayed. Whereas the U.S. teachers explained the procedure as regrouping the minuend and told that during the teaching they would point out the “exchanging” aspect underlying the “changing” step. On the other hand the Chinese teachers used subtraction in computations as decomposing a higher value unit, and many of them also used non-standard methods of regrouping and their relations with standard methods.

Also most of the Chinese teachers mentioned that after teaching this to students they would like to have a class discussion, so as to clarify the concepts.

Multidigit Multiplication

The problem posed to the teachers in this topic was:

Some sixth-grade teachers noticed that several of their students were making the same mistake in multiplying large numbers. In trying to calculate:
123
x 645
13

the students were forgetting to “move the numbers” (i.e. the partial products) over each line.}
They were doing this Instead of this
123 123
x 64 x 64
615 615
492 492
738 738
1845 79335

While these teachers agreed that this was a problem, they did not agree on what to do about it. What would you do if you were teaching the sixth grade and you noticed that several of your students were doing this?}

Response

Most of the teachers agreed that this was a genuine problem in students understanding than just careless shifting of digits, meant for addition. But different teachers had different views about the error made by the student. The problem in the students understanding as seen by the teachers were reflections of their own knowledge of the subject matter. For most of the U.S. teachers the knowledge was procedural, so they reflected on them on similar lines when they were asked to. On the other hand the Chinese teachers displayed a conceptual understanding of the multidigit multiplication. The explanation and the algorithm used by the Chinese teachers were thorough and many times novel.

Division by Fractions

The problem posed to the teachers in this topic was:

People seem to have different approaches to solving problems involving division with fractions. How do you solve a problem like this one?

1/(3/4) / 1/2 = ??

Imagine that you are teaching division with fractions. To make this meaningful for kids, sometimes many teachers try to do is relate mathematics to other things. Sometimes they try to come up with real-world situations or story-problems to show the application of some particular piece of content. What would you say would be good story or model for 1/(3/4) / 1/2 ?

Response

As in the previous two cases the U.S. teachers had a very weak knowledge of the subject matter. Only 43% of the U.S. teachers were able to calculate the fraction correctly and none of them showed the understanding of the rationale underlying their calculations. Only one teacher was successful in generating an illustration for the correct representation of the given problem. On the other hand all the Chinese teachers did the computational part correctly, and a few teachers were also able to explain the rationale behind the calculations. Also in addition to this most of the Chinese teachers were able to generate at least one correct representation of the problem. In addition to this the Chinese teachers were able to generate representational problems with a variety of subjects and ideas, which in turn were based on their through understanding of the subject matter.

Division by Fractions

The problem posed to the teachers in this topic was:

Imagine that one of your students comes to the class very excited. She tells you that she has figured out a theory that you never told to the class. She explains that she has discovered the perimeter of a closed figure increases, the area also increases. She shows you a picture to prove what she is doing:

Example of the student:

How would you respond to this student?

Response

In this problem task there were two aspects of the subject matter knowledge which contributed substantially to successful approach; knowledge of topics related to the idea and mathematical attitudes. The absence or presence of attitudes was a major factor in success

The problems given to the teachers are of the elementary, but to understand them and explain them [what Ma is asking] one needs a profound understanding of basic principles that underly these elementary mathematical operations. This very fact is reflected in the response of the Chinese and the U.S. teachers. The same pattern of Chinese teachers outperforming U.S. teachers is repeated in all four topics. The reason for the better performance of the Chinese teachers is their profound understanding of fundamental mathematics or PUFM. We now turn to the topic of PUFM and explore what is meant by it and when it is attained.

PUFM

According to Ma PUFM is “more than a sound conceptual understanding of elementary mathematics — it is the awareness of the conceptual structure and the basic attitudes of mathematics inherent in elementary mathematics and the ability to provide a foundation for that conceptual structure and instill those basic attitudes in students. A profound understanding of mathematics has breadth, depth, and thoroughness. Breadth of understanding is the capacity to connect topic with topics of similar or less conceptual power. Depth of the understanding is the capacity to connect a topic with those of greater conceptual power. Thoroughness is the capacity to connect all these topics.”

The teacher who possesses PUFM has connectedness, knows multiple ways of expressing same thing, revisits and reinforces same ideas and has a longitudinal coherence. We will elaborate on these key ideas of PUFM in brief.

Connectedness: By connectedness being present in a teacher it is meant that there is an intention in the teacher to connect mathematical procedures and concepts. When this is used in teaching it will enable students to learn a unified body of knowledge, instead of learning isolated topics.

Multiple Perspectives: In order to have a flexible understanding of the concepts involved, one must be able to analyze and solve problems in multiple ways, and to provide explanations of various approaches to a problem. A teacher with PUFM will provide multiple ways to solve and understand a given problem, so that the understanding in the students is deeper.

Basic Ideas: The teachers having PUFM display mathematical attitudes and are particularly aware of the powerful and simple concepts of mathematics. By revisiting these ideas again and again they are reinforced. But focusing on this students are not merely encouraged to approach the problems, but are guided to conduct real mathematical activity.

Longitudinal Coherence: By longitudinal coherence in the teachers having PUFM it is meant that the teacher has a complete markup of the syllabus and the content for the various grades of the elementary mathematics. If one does have an idea of what the students have already learnt in the earlier grades, then that knowledge of the students can be used effectively. On the other hand if it is known what the students will be learning in the higher grades, the treatment in the lower grades can be such that it is suitable and effective later.

PUFM – Attainment

Since the presence of PUFM in the Chinese teachers makes them different from their U.S. counterparts, it is essential to have a knowledge of how the PUFM is developed and attained in the Chinese teachers. For this Ma did survey of two additional groups. One was ninth grade students, and the other was that of pre-service teachers. Both groups has conceptual understanding of the four problems. The preservice teachers also showed a concern for teaching and learning, but both groups did not show PUFM. Ma also interviewed the Chinese teachers who had PUFM, and explored their acquisition of mathematical knowledge. The teachers with PUFM mentioned several factors for their acquisition of mathematical knowledge. These factors include:

  • Learning from colleagues
  • Learning mathematics from students.
  • Learning mathematics by doing problems.
  • Teaching
  • Teaching round by round.
  • Studying teaching materials extensively.

The Chinese teachers during the summers and at the beginning of the school terms , studied the Teaching and Learning Framework document thoroughly. The text book to be followed is the most studied by the teachers. The text book is also studied and discussed during the school year. Comparatively little time is devoted to studying teacher’s manuals. So the conclusion of the study is that the Chinese teachers have a base for PUFM from their school education itself. But the PUFM matures and develops during their actual teaching driven by a concern of what to teach and how to teach it. This development of PUFM is well supported by their colleagues and the study materials that they have. Thus the cultural difference in the Chinese and U.S. educational systems also plays a part in this.

Conclusions

One of the most obvious outcomes of this study is the fact that the Chinese elementary teachers are much better equipped conceptually than their U.S. counterparts to teach mathematics at that level. The Chinese teachers show a deeper understanding of the subject matter and have a flexible understanding of the subject. But Ma has attempted to give the plausible explanations for this difference in terms of the PUFM, which is developed and matured in the Chinese teachers, but almost absent in the U.S. teachers. This difference in the respective teachers of the two countries is reflected in the performance of students at any given level. So that if one really wants to improve the mathematics learning for the students, the teachers also need to be well equipped with the knowledge of fundamental and elementary mathematics. The problems of teacher’s knowledge development and that of student learning are thus related.

In China when the perspective teachers are still students, they achieve the mathematical competence. When they attain the teacher learning programs, this mathematical competence is connected to primary concern about teaching and learning school mathematics. The final phase in this is when the teachers actually teach, it is here where they develop teacher’s subject knowledge.  Thus we see that good elementary education of the perspective teachers themselves heralds their growth as teachers with PUFM. Thus in China good teachers at the elementary level, make good students, who in turn can become good teachers themselves, and a cycle is formed. In case of U.S. it seems the opposite is true, poor elementary mathematics education, provided by low-quality teachers hinders likely development of mathematical competence in students at the elementary level. Also most of the teacher education programs in the U.S. focus on How to teach mathematics? rather than on the mathematics itself. After the training the teachers are expected to know how to teach and what to teach, they are also not expected to study anymore. All this leads to formation of a teacher who is bound in the given framework, not being able to develop PUFM as required.

Also the fact that is commonly believed that elementary mathematics is basic, superficial and commonly understood is denied by this study. The study definitively shows that elementary mathematics is not superficial at all, and anyone who teaches it has to study it in a comprehensive way. So for the attainment of PUFM in the U.S. teachers and to improve the mathematics education their Ma has given some suggestions which need to be implemented.

Ma suggests that the two problems of improving the teacher knowledge and student learning are interdependent, so that they both should be addressed simultaneously. This is a way to enter the cyclic process of development of mathematical competencies in the teachers. In the U.S. there is a lack of interaction between study of mathematics taught and study of how to teach it. The text books should be also read, studied and discussed by the teachers themselves as they will be using it in teaching in the class room. This will enable the U.S. teachers to have clear idea of what to teach and how to teach it thoughtfully. The perspective teachers can develop PUFM at the college level, and this can be used as the entry point in the cycle of developing the mathematical competency in them. Teachers should use text books and teachers manuals in an effective way. For this the teacher should recognize its significance and have time and energy for the careful study of manuals. The class room practice of the Chinese teachers is text book based, but not confined to text books. Again here the emphasis is laid on the teacher’s understanding of the subject matter. A teacher with PUFM will be able to choose materials from a text book and present them in intelligible ways in the class room. To put the conclusions in a compact form we can say that the content knowledge of the teachers makes the difference.

Reflections

The study done by Ma and its results have created a huge following in the U.S. Mathematics Education circles and has been termed as `enlightening’. The study diagnoses the problems in the U.S. treatment of elementary mathematics vis-a-vis Chinese one. In the work Ma glorifies the Chinese teachers and educational system as against `low quality’ American teachers and educational system. As said in the foreword of the book by Shulman the work is cited by the people on both sides of the math wars. This book has done the same thing to the U.S. Mathematics Education circles what the Sputnik in the late 1950’s to the U.S. policies on science education. During that time the Russians who were supposed to be technically inferior to the U.S. suddenly launched the Sputnik, there by creating a wave of disgust in the U.S. This was peaked in the Kennedy’s announcement of sending an American on moon before the 1970’s. The aftermath of this was to create `Scientific Americans’, with efforts directed at creating a scientific base in the U.S. right from the school. Similarly the case of Ma’s study is another expos\’e, this time in terms of elementary mathematics. It might not have mattered so much if the study was performed entirely with U.S. teachers [Have not studies of this kind ever done before?]. But the very fact that the Americans are apparently behind the Chinese is a matter of worry. This is a situation that needs to be rectified. This fame of this book is more about politics and funding about education than about math. So no wonder that all the people involved in Mathematics Education in the U.S. [and others elsewhere following them] are citing Ma’s work for changing the situation. Citing work of which shows the Americans on lower grounds may also be able to get you you funds which otherwise probably you would not have got. Now the guess is that the aim is to create `Mathematical Americans’ this time so as to overcome the Chinese challenge.

Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum Associates.

Millions of Computers for Millions of Children

Yesterday ( it should be now read “a couple of years back”)while giving a talk, I was asked this rhetorical question (not verbatim, but close):

“What did you say was the sample size of your study?”

“Two. This was a case study.”

“So, considering that the activity that you have designed requires a computer and expeyes (a hardware for collecting data). How can you scale it up to schools which have millions of children?”

It seems that the person who was asking the question, for lack of any other question asked this. In seminars and academic institutes, there are always people like this, who will ask the question for sake of it. Just to make their presence felt. Anyways, it was good for me. I was expecting that this question would be asked. And I was very happy that it was asked.

The short answer that I gave was:

“You give a million computers to a million children!”

one-computer-per-child

Some people thought, this was a rhetoric answer to a rhetoric question, which incidentally was also humorous, as it also generated a lot of laughter, but this was not the case. In this post, I would like to elaborate on the short answer that I gave.

Of course, most of these ideas have come from reading and hearing Seymour Papert (who has recently demised, the article was started before that, but due to my lethargy never seen completion). The memes have been transferred, and now I am trying to make sense and adapt them to my own experience. And I would like to assert again that reading Papert has been an immensely rewarding and enriching experience for me. His are perhaps few books which I do not mind reading again and again. I like his writing style of giving parables to explain points in his arguments because the points he wants to make do not need a backbone of statistics to survive. Here also I will give a hypothetical example (derived from Papert) to explain what I meant.

The technological tools that children are using now mainly in the traditional school system are the pencil and the book. In this case, almost all educationalists would agree that every child would require to have one pencil to write and book for study. Even then there are some children who do use computers, some because their parents have them, some because the school has them, some have both. Now we consider a time 50 years back. Computers were almost non-existent, as we know them now. Computers were one of the most complicated and expensive technological artefacts that humans produced. But the enormous amount of money and efforts were put in the miniaturization of computers. So finally now we have computers that have become devices that we now know. In the last 50 years, the computer technology has grown exponentially, while the prices for the memory and computing power that one gets are falling, their usage.

Consider a classroom of 50 years back. Though there were computers they were something to be wondered about, something like very very expensive toys. The computers were not mature enough that children could handle them. In the classroom, the only available technological artefacts were used. The technology in the classroom was the pencil
and the printed book and a notebook to write with the pencil and of course, there was the blackboard.

Wait, you might be thinking we are in a digital age technology by default means computers, be it in your smart-phone, laptop or a desktop or at least a projector for god’s sake. But here I would like you to think about somethings which are very deeply embedded in our cultural psyche. The very fact that many things which we take for granted are
all technologies. For example, the writing instruments that you have to be it a pencil or a chalk are all technologies. But most of us don’t think of them as such because they are so common and most of us have had our experience with them. The mystery is lost. As the Arthur C. Clarke once said about technology and magic as his Third Law:

Any sufficiently advanced technology is indistinguishable from magic.

So deeply embedded this image is that we define it as the normal for our learners to be able to use this technology. Rather the entire edifice of our educational system rests on it. For example, your educational achievement is more or less based on the fact how much you can “write” in a limited time, from memory. And this we call assessment, examination and the like. Also the written text, from the time of Gutenberg, has more
or less complete hold over our intellectual activities. The text formed the basis of our discourse and analysis of the world. Why do children use to write with a pencil on piece of paper in order to learn. The drill typically starts with the children trying to
recreate elegant fonts in some shape or form which is decipherable for the teacher. You have to write “A” 500 times to get it right, ok? How would you write words when you cannot write alphabets? How would write sentences when you cannot write words? How will you write examinations if you cannot write sentences?

Is it the only way in which we can learn language? If we observe this in detail we see that only reason we ask them to write “a” 500 times in a notebook is because it comes from an era when there was no other technology to write. And this is the same learner who can converse well and answer questions, but yet we need them to write it down with their hands. It was the only possible solution. And generations of humans were trained using this method. So much so that most of us still think this is the only method for education. Any deviation from hand-written text is seen as a abomination. But typing on a computer provides us, and especially, young learners with cognitive offloading of immense task of holding a writing instrument and shaping an alphabet, a word, a sentence out of it. Children learn to type much much faster than they learn to write with a pen. And what is even more important is that the written text is in electronic form, which can be revised and shared with their peers and teachers. In hand written text there is no question of revision, the original takes too much effort to produce so there is no question of revising it.

one-pencil-per-child

Considering the amount of cognitive load the child has to undergo to produce decipherable alphabets, words and sentences in order to “write”, a thing which he can perfectly do orally, are the results worth the effort? Are there any studies which show that this is an efficient method? Yet is used everywhere without exceptions and we accept it meekly without challenge because this is how it was done in the past and someone in the past must have had good reason to use this hence, we should also use this. Papert calls this as “QWERTY Phenomena”. Somethings just get culturally embedded because the are
suited for an bygone era, the are like relics in the current era. And writing with pencil and paper is just one of them.

Now consider the question that was asked at the beginning of the post. Replace the computer with a pencil. The question then becomes,

“So, considering that the activity that you have designed requires a
pencil and a notebook. How can you scale it up to schools which have
millions of children?”

one-pencil-per-1000-child-cyan

Suddenly question seems rather bizzare and at the same time sotrivial. Of course you might say but the pencil and notebook is so much cheaper than the computer. Yes. It. Is. But if you consider that a well designed laptop like OLPC, can serve a learners for 5-6 years and can remain with them through the schooling years. Then calculations show the investment that we seek is rather modest. In general when something becomes more
common, it also becomes cheaper. Mobile phones provide an excellent proof for this argument. And it is not happening in some first world country but in our own. What has promoted a rapid growth in the number of mobile users? How do tariff plans compare
from 15 years back to now? How come something which was something exclusive for the rich and the famous, just a few years back, is now so common? It is hard to find a person without a phone these days. Even people who do not have access to electricity have a
phone, they get it charged from some place else. Now if some sociologist would have done some study regarding usefulness of mobile phones for communication, perhaps 20 years earlier, they might have had some statistics to show, but critics would have said,

“but the cost is too prohibitive; this is perhaps ok for a case study you seriously
think all (or most) of the people can have this; and people who cannot
read and write will be able to use this; people do not have
electricity and food to eat and you want to give them mobile phone?”

But look at where we are, because people found contextual and personal value in using a mobile, it became their personal assistant in communicating with others, an inherent human trait, they got it. With proliferation of the mobiles, the cost of hardware came down, the cost of tariffs came down, almost everyone could afford one now.

It is sensationalist to compare a pencil and laptop in terms of cost, but when you consider the kinds of learning that can happen over a computer there is simple no match. They are not different in degree but in kind. Note that I have used “can happen” instead of will happen. This is for a reason, a laptop can be used in a variety of ways in learning. Some of the ways can be subversive, disruptive of the traditional education system, and redefine radically the ways our children learn. But in most cases its subversion is tamed and is made submissive to the existing educational system. And computers are made to do what a teacher or a textbook will do in a traditional context. So it is blunted and made part of a system which the computer has the potential to alter radically.

Some people then cite “research studies” done with “computers”. These studies will typically groups “with” computers and “without” computers. Some tasks are given and then there are pre and post tests. They are looking at the submissive action set in a highly conservative educational system. Even if such studies show the use of computers in a positive light, all these studies are missing the point. They are just flogging a dead horse. The point that computers when used in the right way, the constructionist way, can change the way we learn in a fundamental way. There are many studies which “prove” the counter-point. That computers don’t improve “learning”. Typically children will have limited access both in terms of time and sharing it with more people. One computer shared by three people, one hour in a week. Even then children learn, with computers if
used correctly. Continuing with out example of the pencil, consider this: one pencil shared among three children, once a week! Seems absurd isn’t it? But this is what typically happens in the schools, children are not allowed to develop a personal relationship with one of the most powerful learning ideas that they can have access to. Access is limited and in most cases uninformed involving trivialisation of the learning ideas that can redefine learning.

one-computer-per-1000-child

Politics Science Education or Science Education Politics or Science Politics Education

I am rather not sure what should be the exact title of this
post. Apart from the two options above it could have been any other
combination of these three words. Because I would be talking about all
three of them in interdependent manner.

If someone tells you that education is or should be independent of politics they, I would say they are very naive in their view about society. Education in general and formalised education in particular, which is supported and implemented by state is about political ideology that we want our next generation to have. One of the Marxian critique of state formalised education is that it keeps the current hierarchical structures untouched in its approach and thus sustains them. Now when we come to science education we get a bit more involved about ideas.

Science by itself was at one point of time assumed to be value-neutral. This line of though can be seen in the essays that some of us wrote in the schools with titles like “Science: good or bad”. Typically the line of argument in such is that by itself science is neither good or bad, but how we put it to use is what determines whether it is good or bad. Examples to substantiate the arguments typically involve some horrific incidents like the atomic bomb on one hand and life saving drugs on the other hand. But by itself, science is not about good or bad values. It is assumed to be neutral in that sense (there are other notions of value-neutrality of science which we will consider later). Scientific thought and its products are considered above petty issues of society and indiduals, it seemed to be an quest for eternal truth. No one questioned the processes or products of science which were assumed to be the most noble, rational, logical and superior way of doing things. But this pretty picture about scientific enterprise was broken by Thomas Kuhn. What we were looking at so far is the “normative” idea of science. That is we create some ideals about science and work under the assumption that this is how actual science is or ought to be. What Kuhn in his seminal work titled The Structure of Scientific Revolution was to challenge such a normative view, instead he did a historical analysis of how science is actually done ans gave us a “descriptive” picture about science, which was based on historical facts. Keeping up the name of the book, it actually revolutionised the way we look at science.

Now keeping in mind this disctinction between “normative” and “descriptive” views is very important. This is not only true for science but also for all other forms of human endeavours. People often tend to confuse or combine the two or many times are not even aware of the difference.

After Kuhn’s groundbreaking work entire new view about science its processes and products emerged. Various aspects of the scientific enterprise which were initially thought about outside purview of science or not affecting science came in to spotlight. Science was dissected and deconstructed from various points of view. Over the next few decades these ideas emerged into full fledged disciplies on their own. Some very valid criticisms of the scientific enterprise were developed and agreed upon. For example, the idea that there exists “the scientific method” was serisously looked into and was found to be too naive. A modified view was adopted in this regard and most of philosophers of science agreed that this is too restrictive a view. Added to this the post-modernist views about science may seem strange and bizzare at times to the uninitiated. This led to what many call as the “science-wars” between scientific realists and postmodernists. The scientific realists who believe that the world described by science is the real world as it is, independent of what it might be. So in this view it implies that there is objective truth in science and the world it describes is real. This view also implies that there is something like “scientific method” and it role in creating true knowledge about the world is paramount. On the other hand postmodernist critics don’t necessarily agree with this view of the world. For example they question the very idea of objectivity of the scientific world-view. Deriving their own meaning into writings of Kuhn (which he didn’t agree to) they claimed that science itself is a social construct and has nothing to do with the real world. The apparent supremacy of “scientific-method” in creating knowledge or presenting us about the world-views is questioned. The entire scientific enterprise from processes to products was deciphered from dimensions of gender, sexual orientation, race and class. Now, when you are teaching about science to learners there should be an awareness about these issues. Some of the issues are usually overlooked or have a logical positivist nature in them. Many philosophers lament that though considerable change has happened in ideas regarding scientific enterprise especially in philosophy of science, it seems corresponding ideas in science education are not up to date. And this can be seen when you look at the science textbook with a critical focus.

With this background I will go into the reasons that made me write this post and the peculiar multi-title. It seems for post-modernists and some others that learning about politics of science is more important than learning science itself. And they feel this is the neutral view and there is nothing political about it. They look at science as an hierarchical enterprise where gender, class and race play the decisive role, hence everyone should know about it. I am not against sharing the fact with learners of science that there are other world-views, what I am against is to share only a peculiar world view which is shaped completely by one’s ideology and politcal stance rather than by actual contents. Many of the people don’t actually know science, yet they feel that they are fully justified to criticise it. And most of these people would fall on the left side of the political spectrum (at least that is what their self-image is). But the way I see it is that these same people are no different from the right-wingers who burn books without reading them. The pomos may think of themselves as intellectually superior to the tilak-sporting people but they are not. Such is the state of intellectuals that they feel threatened by exclusion of certain articles or inclusion of certain other ones in reading courses. They then use all their might to restore the “balance”. At the same time they also tell us only they have some esoteric knowledge about these issues which people like me cannot have. And no matter what I do I will never be able to do what they can. Perhaps they have super powers which I don’t know about, perhaps in their subjective world view the pigs can fly and this fact can be proven by using other methods than the scientific ones. Last point I want to make in this is inspite of all the criticims of science and its products it doesn’t stop these people from refraining use of these products and technologies! This is hypocrisy, they will curse the phone or the computer if it doesn’t work, what they perhaps don’t realise is that it might be working just that the pomos are not able to see it in their worldview.

Main purpose of the educational sector

The main purpose of the health sector is not to provide other sectors with workers in good health. By the same token, the main purpose of the educational sector is not to prepare students to take up an occupation in some other sector of the economy. In all human societies, health and education have an intrinsic value: the ability to enjoy years of good health, like the ability to acquire knowledge and culture, is one of the fundamental purposes of civilization.

via Thomas Piketty’s Capital in the 21st Century

Gandhi on Textbooks

M. K. Gandhi

Harijan Vol VII, No. 31 pg. 1, 9 September 1939

Text Books

The craze for ever-changing text books is hardly a healthy sign from
the educational standpoint. If text books are treated as a vehicle for
education, the living word of the teacher has very little value. A
teacher who teaches from text books does not impart originality to his
pupils. He himself becomes a slave of the text books and has no
opportunity or occasion to be original. It therefore seems that the
less text books there are the better it is for the teacher and his
pupils. Text books seem to have become an article of commerce. Authors
and publishers who make writing and publishing a means of making money
are interested in frequent change of text books. In many cases
teachers and examiners are themselves authors of text books. It is
naturally to their interest to have their books sold. The selection
board is again naturally composed of such people. And so the vicious
circle becomes complete. And it becomes very difficult for parents to
find money for new books every year. It is a pathetic sight to see
boys and girls going to school loaded with books which they are ill
able to carry. The whole system requires to be thoroughly
examined. The commercial spirit needs to be entirely eliminated and
the question approached in the interest of the scholars. It will then
probably be found that 75 per cent of the text books will have to be
consigned to scrap-heap. If I had it my way, I would have books
largely as aids to teachers rather than for the scholars. Such
textbooks as are found to be absolutely necessary for the scholars
should circulate among them for a number of years os that the cost can
be easily borne by middle class families. The first step in this
direction is perhaps for the State to won and organize the printing
and publishing of text books. This will act as an automatic check on
their unnecessary multiplication.

Equity Over Excellence

There is an interesting piece in The Atlantic by Sergey Ivanov on the education system in Finland. Though the article is written from a viewpoint of an American, there are a lot of take home points for everyone and particularly for India. In this post I am trying to make sense of this article from an Indian standpoint. Through out the post if you just insert India for America (which I have done at places), it at once catches. For the problems Indians are facing are also the problems of the Americans, as we have more or less tried to follow their model of education. The basic theme that underlies the article
is this:

The Scandinavian country is an education superpower because 
 it values equality more than excellence.

To many in the Indian context who believe that excellence must be given priority over equity this might be surprising. Surprising because it undermines a basic premise in their logic: that to excel in science and technology the only way is to promote excellence. In India there have been two distinct approaches to education, there is a clear stratification of the students based on standardized tests, and it is these tests which filter out students. But as the Finnish experience shows us that this need not be the case.

The newly found fame for Finland’s educational system comes after excellence of their students in the PISA scores since 2000. This seems paradoxical when we learn more about the educational system. The tried and trusted formulae of instructionism and rote-learning, which many people swear by, have almost no place there. The Finnish educational system seems like an educational philosophers utopian materialized in the real world.

To understand why it is working, the way it is, Indians will have to give away their long cherished beliefs about educational system. This would make the government more accountable towards education of the people. This is not just cosmetic school reform, but a revamping of the complete educational philosophy with which we are running the show.

One of the most intriguing (at least for me) things to notice is:

“Oh,” he mentioned at one point, “and there are no private schools in
Finland.”

This notion may seem difficult for an American (Indian?) to digest, but it’s true. Only a small number of independent schools exist in Finland, and even they are all publicly financed. None is allowed to charge tuition fees. There are no private universities, either. This means that practically every person in Finland attends public school, whether for pre-K or a Ph.D.

(emphasis added)

Now, this is interesting. What can we say about India? In fact over the years there has been general trend that we are seeing, that the number of private schools is increasing. And then there are branded schools which are spreading their networks across the country. Not to tell that they charge really hefty fees, and are meant for the elite. And so is the case with the colleges, each professional degree has a price tag, only people who can afford it, get those degrees. The haves not, the non-elites, who are mostly from the deprived classes, remain with almost no education. The government keeps on talking about reaching out to people, and by allowing the private schools colleges to exist, it is actually preventing people from joining in. Another aspect about this is that since there are alternatives to the government schools, the government schools themselves have no pressure to perform. And as any intelligent parents will tell you, it is better to put your child in a private school than a government one. Most of the parents who are in a financial position to put their children in private schools, do so.

How many parents do you know who have enrolled their children in government schools, even when they can afford private schools?

There was yet another interesting piece If You Send Your Kid to Private School, You Are a Bad Person in which the author makes a case that it is parents who are driving the change of declining government schools. If the educated parents make a sustained effort of challenging and helping government schools to improve, they will surely improve. The parents adopt the path of least effort, and send their children to private schools, which are supposed to be better. This automatically creates a class divide without asking.

Even among the private schools there is an hierarchy. There are international schools, convent schools etc. So the social stratification that exists, is just reflected in the school system. Seen from this perspective, one can understand why are the government schools neglected. They are neglected because the people who are influential and who are amongst the rich and powerful are never affected by the dismal state of the government schools. They have an alternate avenue for their children where these schools never come into picture.

There is another thing that is striking in the Indian system, that is of the coaching classes. I do not know if they are present in Finland or even anywhere in the world. But in India, the coaching classes have a complete parallel system of cracking the educational system. The amount money that the coaching classes do attract must be comparable to the amount Government of India spends on education. This is another avenue where the class divide comes in. Only people with enough finances can afford to send their children to the best coaching classes. But the more fundamental question to ask is:

Why do coaching classes exist in the first place?

The answer to this question is not easy and it related closely to the way in which Indians look at education and its practices. The coaching classes exist because there is a demand for them. And what do coaching classes achieve. Most of the coaching classes are aimed at helping students crack some standardized test or the other. But why do you need standardized tests? Some of the rhetorical questions that one might ask against this question are:

From his (Sasi’s) point of view, Americans (Indians) are consistently obsessed
with certain questions:

+ How can you keep track of students’ performance if you don’t test
them constantly?
+ How can you improve teaching if you have no accountability for bad
teachers or merit pay for good teachers?
+ How do you foster competition and engage the private sector?
+ How do you provide school choice?

The answers Finland provides seem to run counter to just about everything America’s (India’s) school reformers are trying to do. For example the introduction of CCE or Continuous and Comprehensive Examination introduced as part of NCF 2005 is one such reform. Similarly we have incentives in forms of awards for best teachers, and of course the best students get rewards like getting admission to the best colleges. Their parents are proud, schools are proud, and their coaching classes are also proud. This can be seen by the number of advertisements the coaching classes put up. But all the exams like IIT-JEE, AIEEE, Medical Exams, Olympiads, etc. are standardized tests. These are the parameters of excellence in the country. Similar tests are also found in the US, like GRE, TOEFL, SAT etc. One would assume the standardized tests in Finland would be of very great quality, but in reality they don’t exist there.

For starters, Finland has no standardized tests. The only exception is what’s called the National Matriculation Exam, which everyone takes at the end of a voluntary upper-secondary school, roughly the equivalent of American high school.

The very idea of standardized tests emerged in the shadow of the Second World War. The mass recruitment of troops required a mass approach, which resulted in production of tests. In his book The Tyranny of Testing physicist Banesh Hoffman, criticises the standardized tests that were prevalent in the US, and takes to task the leading makers of these tests on the fundamental premise of their objectivity. Similarly one can, question the fundamentals of the standardized tests in the country.

Can any standardized test be really objective?

Personally, I do not think so. None of the standardized tests, take into account multiple factors that a student has skills in. These tests make the process of filtering students easier for the administrators. But do they help students at all (except for getting admission to a desired institute)? Do they really test the understanding of the subject matter? Do they take into account various social factors that is part of the mileu of the students? As Banesh Hoffman says the only thing objective about these tests is that once, the students fills in the answer sheet, the grading is objective. But why is that the teachers who are actually teaching the students cannot test them? Why do we need standardized tests to test the students?

And here comes in the idea of academic flexibility in the schools. In India even most university department do not have academic flexibility. There is a central committee which decides, what is to be taught and a committee sets a test with which we grade the students. This creates a definite goal in form of “completing the syllabus” for the teachers. This is a malice which pervades the educational system of India from primary schools to university departments. The teachers are in a race to reach the finish line of the syllabus, because if they do not, the students might face questions which they were not taught.

Though the teacher is the representative of the entire educational system in the classroom, they are nothing more than, to use a term by Krishna Kumar, “meek dictators” in the classroom. The real dictators are adminitrators and decision makers sitting at the top of the educational system. This perhaps is a colonial mentality which has been deeply embodied in the Indian psyche. But in Finland what happens:

Instead, the public school system’s teachers are trained to assess children in classrooms using independent tests they create themselves. All children receive a report card at the end of each semester, but these reports are based on individualized grading by each teacher. Periodically, the Ministry of Education tracks national progress by testing a few sample groups across a range of different schools.

People say that then the teachers cannot be trusted that they will grade their students correctly. So how will they be held accountable?

As for accountability of teachers and administrators, Sahlberg shrugs. “There’s no word for accountability in Finnish,” he later told
an audience at the Teachers College of Columbia University. “Accountability is something that is left when responsibility has been subtracted.”

For Sahlberg what matters is that in Finland all teachers and administrators are given prestige, decent pay, and a lot of responsibility. A master’s degree is required to enter the profession, and teacher training programs are among the most selective professional schools in the country. If a teacher is bad, it is the principal’s responsibility to notice and deal with it.

This is where the responsibility of the Government comes in. Goverment slowly is trying to distance itself from its role in providing education to all its citizens. But if teachers are themselves left unsatisfied both monetarily and ideologically??, what results one can
expect. In this way the Government is indirectly encouraging the private schools and coaching classes, and thus making the class divide even more striking.

And while Americans (Indians) love to talk about competition, Sahlberg points out that nothing makes Finns more uncomfortable. In his book Sahlberg quotes a line from Finnish writer named Samuli Paronen: “Real winners do not compete.” It’s hard to think of a more un-American (Indian) idea, but when it comes to education, Finland’s success shows that the Finnish attitude might have merits. There are no lists of best schools or teachers in Finland. The main driver of education policy is not competition between teachers and between schools, but cooperation.

Compare this with the Indian attitude. Competition seems to be the key to everything and especially education. Where does collaboration of
cooperation enter in Indian educational scenario?

Finally, in Finland, school choice is noticeably not a priority, nor is engaging the private sector at all. Which brings us back to the silence after Sahlberg’s comment at the Dwight School that schools like Dwight don’t exist in Finland.

“Here in America (India), parents can choose to take their kids to private schools. It’s the same idea of a marketplace that applies to, say, shops. Schools are a shop and parents can buy what ever they want. In Finland parents can also choose. But the options are all the same.”

And in India there are coaching classes which prepare students to get into better coaching classes. With both private schools and the coaching class industry around the education and related services have been commercialised to furthest extent possible. This just works in the favour of the already existing class divide. Parents do choose best for their children, and thus do perpetuate the divide as they have no other choices.

Decades ago, when the Finnish school system was badly in need of reform, the goal of the program that Finland instituted, resulting in so much success today, was never excellence. It was equity.

This is the state of the educational system in India now. And with the over emphasis on the excellence part which addresses a small set of mostly elite students, the goal should be creating equal opportunities for equity. The idea of equity in the academic circles is unfortunately equated with that of sub-standard or below average. There are people who will tell you, that “Look, there are bright students, and they need special coaching.” The government has to spend the money of bright students, so as to make the country excel in education. This is done at the expense of the average students. One may ask the question, how in the first place do you know a student is bright? The answer comes from scores of the standardized tests, which are the root cause of many problems that the educational system in India is facing now. If one is serious about changing the educational scenario in the country this has to be addressed. Though there are champions of the standardized tests, in India as in the US of Amerika, they are the ones whose existence is based on such tests. Without these tests their existence becomes meaningless. It will certainly increase the workload of lot many people a lot many times. But the problems of magnitude of changing educational system in India is no mean problem and will require solutions of these magnitudes.

Since the 1980s, the main driver of Finnish education policy has been the idea that every child should have exactly the same opportunity to
learn, regardless of family background, income, or geographic location.

In the Indian scenario this seems to have been forgotten. And one of the main reasons for this is the presence of private schools and coaching classes where parents can shop for education.

Education has been seen first and foremost not as a way to produce star performers, but as an instrument to even out social inequality.

This particular quote is exactly opposite of what the Indian
educational system does by promoting academic excellence over equity.
And this also relates to the qualities that Indians cherish. If good
education is equated with chances of making good money, then we know
where we are wrong. With private schools and coaching classes the
education of a student becomes a balance sheet, which will be brought
to green from red by the money that student will make after
completing education.

In the Finnish view, as Sahlberg describes it, this means that schools should be healthy, safe environments for children. This starts with
the basics. Finland offers all pupils free school meals, easy access to health care, psychological counseling, and individualized student
guidance.

In case of India we have seen implementation of the mid-day meal scheme. But does it extend to the other domains?

In fact, since academic excellence wasn’t a particular priority on the Finnish to-do list, when Finland’s students scored so high on the
first PISA survey in 2001, many Finns thought the results must be a mistake. But subsequent PISA tests confirmed that Finland — unlike,
say, very similar countries such as Norway — was producing academic excellence through its particular policy focus on equity.

And with so much emphasis on coming on top of the class in India, we are getting what we are sowing. Surveys will tell you that students,
including even those from the best private schools in the country do fail in simple evaluation. But is this unexpected? If the entire
focus of the educational system is to pass standardized tests, why should we expect our students to be better in something else?

That this point is almost always ignored or brushed aside in the U.S. (India) seems especially poignant at the moment, after the financial crisis and Occupy Wall Street movement have brought the problems of inequality in America into such sharp focus. The chasm between those who can afford $35,000 in tuition per child per year — or even just the price of a house in a good public school district — and the other “99 percent” is painfully plain to see.

Though India is yet to undergo Occupy BSE protests, it is not long before this happens.

Some people may point out that Finland is a developed nation. It is much more homogeneous as compared to India. Here it might become more complicated than in the US, but the central argument should hold through.

Yet Sahlberg doesn’t think that questions of size or homogeneity should give Americans (Indians) reason to dismiss the Finnish example. Finland is a relatively homogeneous country — as of 2010, just 4.6 percent of Finnish residents had been born in another country, compared with 12.7 percent in the United States. But the number of foreign-born residents in Finland doubled during the decade leading up to 2010, and the country didn’t lose its edge in education. Immigrants tended to concentrate in certain areas, causing some schools to become much more mixed than others, yet there has not been much change in the remarkable lack of variation between Finnish schools in the PISA surveys across the same period.

The social conditions in India do not match those in Finland. We have many factors like, caste and religion, which do strongly affect our educational policies in practice, if not in theory. So is this comparison valid? But comparing Finland with an country whose demographics are similar, namely Norway, we find different results. Which shows it is the educational policy which determines the outcome, and not the demographics.

Like Finland, Norway is small and not especially diverse overall, but unlike Finland it has taken an approach to education that is more American than Finnish. The result? Mediocre performance in the PISA survey. Educational policy, Abrams suggests, is probably more important to the success of a country’s school system than the nation’s size or ethnic makeup.

And time and again it is said that India does not have enough money to spend on its enormous population. Looking at the amount of GDP that is spent on education India ranks spends 3.1% of GDP on education (2006), while the US spends 5.5% (2007) and Finland 5.9% (2007). A more updated list shows this hasn’t changed much in the intervening years. A look at the graph below from the World Bank Data on these matters makes the picture clear. Though Norway spends more than Finland on education, the results are poor. So if we assume that this is the control then it clearly shows it is not the amount of money you spend or your socio-economic status of the people that matter. What matters most is the way in which you have planned for education and its spending.

gdp-educationPeople tell you that most problems in Indian education system will go away if we have enough teachers! But why are not there enough teachers one may ask? Isn’t it funny that in a country which has second largest population in the world, we do not have enough government teachers? It is surely not a problem of human resources, but of will, both political and social. We do not want to spend more on education, and yet we expect the things to be better. And somehow government is willing to spend on private partners for education, a sort of outsourcing if you want. And with more and more Public Private Partnerships for education, government is just abdicating its responsibility, in the field of education as in other fields.

Finland’s experience suggests that to win at that game, a country has to prepare not just some of its population well, but all of its population well, for the new economy. To possess some of the best schools in the world might still not be good enough if there are children being left behind.

Problem in India is manifold.

“Finland’s dream was that we want to have a good public education for every child regardless of where they go to school or what kind of families they come from, and many even in Finland said it couldn’t be done.”

Clearly, many were wrong. It is possible to create equality. And perhaps even more important — as a challenge to the American (Indian) way of thinking about education reform — Finland’s experience shows that it is possible to achieve excellence by focusing not on competition, but on cooperation, and not on choice, but on equity.

(emphasis added)

The problem facing education in America (India) isn’t the ethnic diversity of the population but the economic inequality of society, and this is precisely the problem that Finnish education reform addressed. More equity at home might just be what America (India) needs to be more competitive abroad.

Most of us think that utopian ideas are not practicable. The talk about equity in education is essentially seen with that attitude. But the Finland example has just shown us that this is possible. Though it is definitely not to say that we blindly follow that model. But it seems that utopian things are possible, just that we will have to give up on long cherished notions of what we consider excellence as.

Cram, don’t think

The message from 15 years of education in my country – first at a top-notch school and then at one of the best known colleges in India – was:

Facts are more important than thought and imagination; that it’s more important to know the answers than think critically; that exams are more important than knowledge itself. Some may say that in college the majority of us chose the convenient way out and they are right.Our system of education, even at the undergraduate level, does not encourage us – in fact, gives us every opportunity not to think independently, critically, creatively or analytically.

via The Hindu

JEE and school system

“The old JEE (is?) destroying school system, leading to rampant coaching industry, biased in favour of urban areas and boys.”

“IITs cannot pursue excellence at the cost of the school system. They must also have a stake in Board exams.”

via Firstpost.

What Kapil Sibbal says is maybe true. But the damage is already done. Lets see what is the outcome of this.

… तर मराठी शाळा बंद पडतील

मैदाने आहेत , पण क्रीडा साहित्य नाही .. प्रयोगशाळेत प्रयोगाचे साहित्य नाही .. तुटके बेंच आणि गळकी छपरे .. अशा दारुण स्थितीत असलेल्या मराठी शाळांना संजीवनी मिळावी , यासाठी वेतनेतर अनुदान तातडीने सुरु करावे , अशी मागणी राज्य शिक्षक परिषदेने केली आहे . हे अनुदान न मिलाल्यास राज्यातील शेकडो मराठी शाळा बंद पडतील अशी भीती परिषदेने व्यक्त केली आहे .

via Maharashtra Times.

आता आपण काही केले नाही तर मग कोण करणार? आमच्या खैरात शाळे मध्ये विज बिल भरायची काही तरतुदच नाही आहे. त्यामुळे तिथला विज पुरवठा खंडित पण करण्यात आला होता.

Max Planck – on scientific truth

A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it.

via Max Planck – Wikiquote.

This I think in general applies to the state of educational system in general. All the people who are opposing the use of technology in the classrooms, will never see the light, but instead will just die and the newer generation will induced to teach with use of technology.

Mahatma Phooley’s Thoughts on Education

In this post I will reproduce the letter written by Joteerao Phooley (मराठी: जोतीराव फुले ) (in the modern times his name is written as Phule instead of Phooley as he himself wrote) one of the great reformers in India. The letter was written to the Hunter Education Commission for “opinion as to the system and personnel employed in the lower schools of the Educational Department” in 1882. Though the suggestions were largely ignored by the commission they give us an insight to the state of education and its possible remedies during that era. But when one reads the letter, one can relate immediately to the present state of education in the country, all the possible issues that one will think of are covered: the overarching presence of divisions in the society (caste, religion, gender), teacher training or rather lack of it, textbooks, syllabus, scholarships for the needy, school drop-outs, school inspections, school management, structure of fees, distance learning, privatisation of education etc.

This reminds of of a quote from Seymour Papert in Children’s Machine: Rethink of School in Age of Computers which suits very well what I am going to describe.

Imagine a party of time travelers from an earlier century, among them one group of surgeons and another of school- teachers, each group eager to see how much things have changed in their profession a hundred or more years into the future. Imagine the bewilderment of the surgeons finding themselves in the operating room of a modern hospital. Although they would know that an operation of some sort was being performed, and might even be able to guess at the target organ, they would in almost all cases be unable to figure out what the surgeon was trying to accomplish or what was the purpose of the many strange devices he and the surgical staff were employing. The rituals of antisepsis and anesthesia, the beeping electronics, and even the bright lights, all so familiar to television audiences, would be utterly unfamiliar to them.

The time-traveling teachers would respond very differently to a modern elementary school classroom. They might be puzzled by a few strange objects. They might notice that some standard techniques had changed and would likely disagree among themselves about whether the changes they saw were for the better or the worse but they would fully see the point of most of what was being attempted and could quite easily take over the class. I use this parable to provide a rough-and-ready measure of the unevennes progress across the broad front of historical change. In the wake of the startling growth of science and technology in our recent past, some areas of human activity have undergone megachange. Telecommunications, entertainment, and transportation, as well as medicine, are among them. School is a notable example of an area that has not. One cannot say that there has been no change at all in the way we dish out education to our students. Of course there has; the parable gives me a way of pointing out what most of us know about our system of schooling: Yes, it has changed, but not in ways that have substantially altered its nature. The parable sets up the question: Why, through a period when so much human activity has been revolutionized, have we not seen comparable change in the way we help our children learn? (emphasis mine)

In this letter one gets a window in the past, regarding the practices of education in that era. It is as if we are time-travelling to the past, and we can indeed relate to most of things that Phooley says. If one were to write a diagnosis and possible solutions for the problems of education present in India, many of the sentences from the letter can be taken as they are, and they will fit in the current scenario. This letter presents shows that Phooley had a deep understanding of the educational system that he was trying so hard to reform. The educational experience that Phooley had was wide ranging, as he started the first indigenous school for girls, then went on to open the first “an indigenous mixed school for the lower classes, especially the Mahars and Mangs”, along with these he was “also been a teacher for some years in a mission female boarding school.”

In the first part of the letter he quotes extensively from Slavery (मराठी: गुलामगिरी). And sets a stage upon which the systemic way in which “Brahmin thraldom” is in place. I do not know if he is talking about Marx when he says:

A well-informed English writer states that our income is derived, not from surplus pro ts, but from capital; not from luxuries, but from the poorest necessaries. It is the product of sin and tears.

He questions the policy of the Government

Upon what grounds is it asserted that the best way to advance the moral and intellectual welfare of the people is to raise the standard of instruction among the higher classes?

And at times becomes very dramatic to describe the dire situation at hand!

I sincerely hope that Government will ere long see the error of their ways, trust less to writers or men who look through highclass spectacles, and take the glory into their own hands of emancipating my Shudra brethren from the trammels of bondage which the Brahmins have woven around them like the coils of a serpent.

The next section is in particular about the state of primary education in Bombay Presidency. Joteerao has hold of relevant statistics in this regard. He laments the absence of schools for the lower classes in general and identifies in general the cause of misery as the general lack of education.

A good deal of their poverty, their want of self-reliance, their entire dependence upon the learned and intelligent classes, is attributable to this deplorable state of education among thepeasantry.

About village he says that

In villages also most of the cultivating classes hold aloof owing to extreme poverty, and also because they require their children to tend cattle and look after their fields.

And makes a recommendation that:

… primary education of the masses should be made compulsory up to a certain age, say at least 12 years.

Citing statistics he says:

Under the promise of the Queen’s Proclamation I beg to urge that Mahars, Mangs, and other lower classes, where their number is large enough, should have separate schools for them, as they are not allowed to attend the other schools owing to caste prejudices.

As regarding the actual suggestions that he makes for the Commission, are worthy to take note of:

With regard to the few Government primary schools that exist in the Presidency, I beg to observe that the primary education imparted in them is not at all placed on a satisfactory or sound basis. The system is imperfect in so far as it does not prove practical, and useful in the future career of the pupils.

Further he has particular suggestions regarding the remodelling of the system. First of all he talks about the almost complete occupation of teacher’s posts by Brahmins and that too untrained ones. These issues particularly relate to teacher professional development. I do not know anything about the colleges for training teachers which were present then. Also he suggests the minimum salary for the teachers “To secure a better class of teachers and to improve their position,”

As to the actual content which is to be taught to the students he is very practical.

The course of instruction should consist of reading, writing Modi and Balbodh and accounts, and a rudimentary knowledge of, general history, general geography, and grammar, also an elementary
knowledge of agriculture and a few lessons on moral duties and sanitation.

And for the villages he says (a studio approach to education!)

The studies in the village schools might be fewer than those in larger villages and towns, but not the less practical. In connection with lessons in agriculture, a small model farm, where practical instruction to the pupils can be given, would be a decided advantage and, if really eciently managed, would be productive of the greatest good to the country.

The textbooks which are lamented about in almost all educational surveys find a mention here:

The text-book in use, both in the primary and Anglo-vernacular schools, require revision and recasting as much as they are not practical or progressive in their scope. Lessons on technical education and morality, sanitation and agriculture, and some useful arts,. should be interspersed among them in progressive series.

As regards to the fees paid by the students he suggests that: “fees in the primary schools should be as 1 to 2 from the children of cess-payers and non-cess payers.” And on important note he also advises on placing a quality control over the schools by inspection, but at the same time mentioning “advisability of visiting these schools at other times and without any intimation being given.” It seems the schools then as they are now are only dressed up when they are being inspected. Also he says

No reliance can be placed on the district or village officers owing to the multifarious duties devolving on them, as they seldom find time to visit them, and when they do, their examination is necessarily very super ficial and imperfect.

Further he says that the number of primary schools need to be increased and provides ways in which these schools can be funded. Though he is very much for the municipalities providing the funding for the schools, but he is totally against the management being transferred to them.

The Municipalities in large towns should be asked to contribute whole share of the expenses incurred on primary schools within the municipal area. But in no case ought the management of the same to be entirely made over to them, They should be under the supervision of the Educational Department.

Also he is particular about the handling of funds as regards to primary education.

The administration of the funds for primary education should ordinarily be in the hands of the Director of Public Instruction.

In the next section he describes the state of Indigenous Schools in the Bombay Presidency.

Indigenous schools exist a good deal in cities, towns and some large villages, especially where there is a Brahmin population. From the latest reports of Public Instruction in this presidency, it is found that there are 1,049 indigenous schools with about 27,694 pupils in them.

And this is what he has to say as regards to the content in these schools

They are conducted on the old village system. The boys are generally taught the multiplication table by heart, a little Modi writing and reading, and, to recite a few religious pieces.

And is particularly harsh on the quality of teachers in these schools:

The teachers, as a rule, are not capable of effecting any improvements, as they are not initiated in the art of teaching. … The teachers generally come from the dregs of Brahminical society. Their qualifi cations hardly go beyond reading and writing Marathi very indi fferently, and casting accounts up to the rule of three or so. They set, up as teachers as the last resource of getting a livelihood. Their failure or unfi tness in other callings of life obliges them to open schools.

This we can say is true for many teachers in our own era. There are a very few who will choose to become teachers, usually it is the last choice, when all other choices are gone. And further Phooley adds for the training of the teachers:

No arrangements exist in the country to train up teachers for indigenous schools. The indigenous schools could not be turned to any good account, unless the present teachers are replaced by men from the training colleges and by those who pass the 6th standard in the vernaculars. The present teachers will willingly accept State aid but money thus spent will be thrown away.

The next section he describes the state of Higher Education in his times.

The cry over the whole country has been for some time past that Government have amply provided for higher education, whereas that of the masses has been neglected. To some extent this cry is justified, although the classes directly benefitted by the higher education may not readily admit it. But for all this no well-wisher of his country would desire that Government should, at the present time, withdraw its aid from higher education. All that they would wish is, that as one class of the body politic has been neglected, its advancement should form as anxious a concern as that of the other.

About the general education in India he says:

Education in India is still in its infancy. Any withdrawal of State aid from higher education cannot but be injurious to the spread of education generally.

He furthers this by adding that the withdrawal may be partial.

A taste for education among the higher and wealthy classes, such as the Brahmins and Purbhoos, especially those classes who live by the pen, has been created, and a gradual withdrawal of State aid may be possible so far as these classes are concerned; but in the middle and lower classes, among whom higher education has made no perceptible progress, such a withdrawal would be a great hardship. In the event of such withdrawal, boys will be obliged to have recourse to inefficient and sectarian schools much against their wish, and the cause of education cannot but suffer.

Phooley also has concerns regarding privatisation of education, which we are facing now.

Nor could any part of such education be entrusted to private agency. For a long time to come the entire educational machinery, both ministerial and executive, must be in the hands of Government. Both the higher and primary education require all the fostering care and attention which Government can bestow on it.The withdrawal of Government from schools or colleges would not only tend to check the spread of education, but would seriously endanger that spirit of neutrality which has all along been the aim of Government to foster, owing to the different nationalities and religious creeds prevalent in India. This withdrawal may, to a certain extent, create a spirit of self-reliance for local purposes in the higher and wealthy classes, but the cause of education would be so far injured that the spirit of self-reliance would take years to remedy that evil.

He says that the Government schools are much superior to the private ones, one does not know whether this claim will hold in the current times, though for Higher Education this may be generally true as to get admitted to Government run colleges and institutions is much harder than private ones. But whether the reason is same for that one does not know, comparing the salaries that are paid in international schools as opposed to the Government schools the balance is upturned.

The superiority of Government schools is mainly owing to the richly paid staff of teachers and professors
which it is not possible for a private schools to maintain.

The content of what is taught in these schools is again brought under scanner as in the case of primary education:

The character of instruction given in the Government higher schools, is not at all practical, or such as is required for the necessities of ordinary life. It is only good to turn out so many clerks and schoolmasters.

And one wouldn’t agree more with what he says about the matriculation exam:

The Matriculation examination unduly engrosses the attention of the teachers and pupils, and the course of studies prescribed has no practical element in it, so as to fit the pupil for his future career in independent life.

Also he is very much for printing of textbooks by the Government, which will encourage “private studies”, thus opening up possibilities for distance education and lead to “diffusion of knowledge in country”:

The higher education should be so arranged as to be within easy reach of all, and the books on the subjects for the Matriculation examination should be published in the Government Gazette, as is done in Madras and Bengal. Such a course will encourage private studies and secure larger diffusion of knowledge in the country. It is a boon to the people that the Bombay University recognises private studies in the case of those presenting for the entrance examination. I hope, the University authorities will be pleased to extend the same boon to higher examinations. If private studies were recognised by the University in granting the degrees of B.A., M.A. &c., many young men will devote their time to private studies.

Further he has to say regarding the scholarships being granted to the students

The system of Government scholarships, at present followed in the Government schools, is also defective, as much as it gives undue encouragement to those classes only, who have already acquired a taste for education to the detriment of the other classes. The system might, be so arranged that some of these scholarships should be awarded to such classes amongst whom education has made no progress.

On this issue he further adds:

The system of awarding them by competition, although abstractedly equitable, does not tend to the spread of education among other classes.

In the final section he mentions the state in which “educated natives” are left who are not able to find public service, as most of the education that they are imparted with is “not of a technical or practical nature”.

The present number of educated men is very small in relation to the country at large, and we trust that the day may notbe far distant when we shall have the present number multiplied a hundred-fold and all betaking themselves to useful and remunerative occupations and not be looking after service.

Also in the last lines of the letter he recommends the spread of female education.

In conclusion, I beg to request the Education Commission to be kind enough to sanction measures for the spread of female primary education on a more liberal scale.

Thus the letter ends and Phooley states his status as:

Merchant and Cultivator and
Municipal Commissioner

To read the letter in retrospect about 130 years later, one cannot but help to relate to the status quo in many aspects of education in general which Phooley describes, thus reminding one of the time-travellers of Papert. One theme which runs through the entire letter is that the people who are already on the higher class of the society, are the ones who benefit most from the educational reforms, and this is detrimental to diffusion of knowledge in all strata of the society. As regards to the content of what is actually taught in schools, absence of practical knowledge, quality and quantity of teachers, prospective jobs, the quality of textbooks one would recommend almost the same things even today.

The complete letter is reproduced below. A PDF version of the letter is available here.

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