Archive for the ‘Teaching’ Category

Teaching as inspiring

January 20, 2015

The post number 1379 of tomorrow’s professor is a must read:

As we go more and more toward class technology and a “facilitating” rather than an exemplary role for college teachers, the opportunity for students to be personally inspired by ennobling figures like Gullberg, Stebbins, and Eakin gets less and less. Not every teacher will or can be like those extraordinary people, but students in their first years of college need to be exposed to at least a few. Students may be able to understand the idea of DNA synthesis better with sophisticated graphics and a virtual teacher than with a mediocre live lecturer but no kid is going to say, “When I grow up, I want to be just like Dr. Macintosh here.” Things like TED and MOOCS are great for expanding the exposure of great teachers, but nobody watching those broadcasts has the feeling that the lecturer is talking to THEM. So, in the new world of large class college teaching where there is scant opportunity for students to be personally exposed to experienced, motivating teachers, how are we going to INSPIRE students, especially the non-traditional ones?

A great piece!

Worthiness apart from performance

January 17, 2015

A link I got thanks to Hariharan.

8 fantastic lessons

August 21, 2013

Doing the Stanford EDUC115N course and completing it is a truly transformative experience that I have had in a very long time. I believe I have completely changed in certain ways after doing the course. It is a true eye-opener. Strongly recommended!

Sometimes it is not scaling that is key

July 29, 2013

Say Paul Graham and Atul Gawande in two different contexts! When we discuss teaching methodologies and talk about scaling, I do feel that it is not scaling that is the key!

Teaching: for whom?

March 4, 2012

It may sometimes be rather deflating to discover that a well-prepared lesson did not really excite Johnny Smith’s interest, but, after all, the lesson was intended to benefit Johnny Smith, not his teacher; if it was uninteresting to him then the teacher must think again.

That is from E R Braithwaite‘s To Sir with love.

Competence: unconscious

October 5, 2011

Expertise, as the formula goes, requires going from unconscious incompetence to conscious incompetence to conscious competence and finally to unconscious competence.

That is Gawande at NewYorker. While I was thinking about teaching versus coaching problem with respect to students, Gawande talks about coaching teachers to teach. I do find lots of merit in the idea that experienced teachers can help novices better their teaching performance; in my own case, I have sat through lectures of colleagues to learn how they are teaching as well as had some of my colleagues sit in my class to tell me what I am doing right and what I am not doing right. Even without their presence in the classroom, just by discussions, some of my colleagues help me sort out problems that I face in the classroom. So, having a coach in the classroom might not be a bad idea — at least for undergraduate core courses, though, it is not clear where we would find the required number of personnel. One way this is done is by making instruction shared — some teach and others do tutorials but the instructors attend all sessions.

By the way, I liked the following section of Gawande’s post — because, that is what I like to be able to do in my classes with my students — make them think:

Year after year, the senior residents chose him for their annual teaching award. He was an unusual teacher. He never quite told you what to do. As an intern, I did my first splenectomy with him. He did not draw the skin incision to be made with the sterile marking pen the way the other professors did. He just stood there, waiting. Finally, I took the pen, put the felt tip on the skin somewhere, and looked up at him to see if I could make out a glimmer of approval or disapproval. He gave me nothing. I drew a line down the patient’s middle, from just below the sternum to just above the navel.

“Is that really where you want it?” he said. Osteen’s voice was a low, car-engine growl, tinged with the accent of his boyhood in Savannah, Georgia, and it took me a couple of years to realize that it was not his voice that scared me but his questions. He was invariably trying to get residents to think—to think like surgeons—and his questions exposed how much we had to learn.

“Yes,” I answered. We proceeded with the operation. Ten minutes into the case, it became obvious that I’d made the incision too small to expose the spleen. “I should have taken the incision down below the navel, huh?” He grunted in the affirmative, and we stopped to extend the incision.

A good post (as usual).

Exam structures

September 7, 2011

In core courses I teach, there is hardly any freedom for me to choose the method of examination. However, in my electives, I do try different methods; my favourite is a combined take-home and oral examination (in which, the students are asked to read a chapter, solve all problems and submit the same, and then come and teach that chapter to the other students). It works very well. So, I found this post at AMS graduate student blog quite interesting and useful.

Creativity and memory

March 8, 2011

Jim Holt at London Review of Books:

What do we really know about creativity? Very little. We know that creative genius is not the same thing as intelligence. In fact, beyond a certain minimum IQ threshold – about one standard deviation above average, or an IQ of 115 – there is no correlation at all between intelligence and creativity. We know that creativity is empirically correlated with mood-swing disorders. A couple of decades ago, Harvard researchers found that people showing ‘exceptional creativity’ – which they put at fewer than 1 per cent of the population – were more likely to suffer from manic-depression or to be near relatives of manic-depressives. As for the psychological mechanisms behind creative genius, those remain pretty much a mystery. About the only point generally agreed on is that, as Pinker put it, ‘Geniuses are wonks.’ They work hard; they immerse themselves in their genre.Could this immersion have something to do with stocking the memory? As an instructive case of creative genius, consider the French mathematician Henri Poincaré, who died in 1912. Poincaré’s genius was distinctive in that it embraced nearly the whole of mathematics, from pure (number theory) to applied (celestial mechanics). Along with his German coeval David Hilbert, Poincaré was the last of the universalists. His powers of intuition enabled him to see deep connections between seemingly remote branches of mathematics. He virtually created the modern field of topology, framing the ‘Poincaré conjecture’ for future generations to grapple with, and he beat Einstein to the mathematics of special relativity. Unlike many geniuses, Poincaré was a man of great practical prowess; as a young engineer he conducted on-the-spot diagnoses of mining disasters. He was also a lovely prose stylist who wrote bestselling works on the philosophy of science; he is the only mathematician ever inducted into the literary section of the Institut de France. What makes Poincaré such a compelling case is that his breakthroughs tended to come in moments of sudden illumination. One of the most remarkable of these was described in his essay ‘Mathematical Creation’. Poincaré had been struggling for some weeks with a deep issue in pure mathematics when he was obliged, in his capacity as mine inspector, to make a geological excursion. ‘The changes of travel made me forget my mathematical work,’ he recounted.

Having reached Coutances, we entered an omnibus to go some place or other. At the moment I put my foot on the step the idea came to me, without anything in my former thoughts seeming to have paved the way for it, that the transformations I had used to define the Fuchsian functions were identical with those of non-Euclidean geometry. I did not verify the idea; I should not have had time, as, upon taking my seat in the omnibus, I went on with a conversation already commenced, but I felt a perfect certainty. On my return to Caen, for conscience’s sake, I verified the result at my leisure.

How to account for the full-blown epiphany that struck Poincaré in the instant that his foot touched the step of the bus? His own conjecture was that it had arisen from unconscious activity in his memory. ‘The role of this unconscious work in mathematical invention appears to me incontestable,’ he wrote. ‘These sudden inspirations … never happen except after some days of voluntary effort which has appeared absolutely fruitless.’ The seemingly fruitless effort fills the memory banks with mathematical ideas – ideas that then become ‘mobilised atoms’ in the unconscious, arranging and rearranging themselves in endless combinations, until finally the ‘most beautiful’ of them makes it through a ‘delicate sieve’ into full consciousness, where it will then be refined and proved.

Poincaré was a modest man, not least about his memory, which he called ‘not bad’ in the essay. In fact, it was prodigious. ‘In retention and recall he exceeded even the fabulous Euler,’ one biographer declared. (Euler, the most prolific mathematician of all – the constant e takes his initial – was reputedly able to recite the Aeneid from memory.) Poincaré read with incredible speed, and his spatial memory was such that he could remember the exact page and line of a book where any particular statement had been made. His auditory memory was just as well developed, perhaps owing to his poor eyesight. In school, he was able to sit back and absorb lectures without taking notes despite being unable to see the blackboard.

It is the connection between memory and creativity, perhaps, which should make us most wary of the web. ‘As our use of the web makes it harder for us to lock information into our biological memory, we’re forced to rely more and more on the net’s capacious and easily searchable artificial memory,’ Carr observes. But conscious manipulation of externally stored information is not enough to yield the deepest of creative breakthroughs: this is what the example of Poincaré suggests. Human memory, unlike machine memory, is dynamic. Through some process we only crudely understand – Poincaré himself saw it as the collision and locking together of ideas into stable combinations – novel patterns are unconsciously detected, novel analogies discovered. And this is the process that Google, by seducing us into using it as a memory prosthesis, threatens to subvert.

Rethinking curriculum: some random thoughts

March 6, 2011

For the past one week or so, I have been reading Peter Medawar‘s The threat and the glory: reflections on science and scientists. While discussing the philosophy of Karl Popper, Medawar says the following:

No scientist thinks of himself as a man of facts and calculations. Popper puts it thus: “It is not his possession of knowledge that makes the man of science, but his persistent and relentlessly critical search for truth.”

That brings me to the question, namely, how about engineers? Are they men and women of facts and calculations? If so, in the age of Google and Watson, do we need such a training? If not, what are engineers for?

The above questions were also brought home to me by one of the students with whom we were chatting. He told us that his class (in general) thinks that since one can always google and find out, it is not important to remember

  • numbers (approximately, what is the melting point of aluminium or steel), or,
  • names (what is the instrument that converts mechanical energy into electrical energy in a power station), or,
  • sometimes even concepts (why should I know the definition of equilibrium melting point of a pure material? In my job, in future, I might never need to know; however, if I need it badly, I can google, find the relevant page, read it, and in an hour or so, I will know all that I need to know on the question).

If the student attitude is like this, I feel, we have an obligation either to convince them why these things are essential or to change our curriculum in ways in which it will reflect the “real world” scenario outside of the walls of the academia.

Explaining the curriculum

One reason why students have viewpoints like this is because they have never been told the philosophy behind the curriculum. Take an English Literature course; the students might be asked to read a novel, say, The English Teacher of R K Narayan.  Even before they begin reading the novel, the students do know that their reading is different from that of a lay (non-literary) person’s reading of the novel. They also know that reading the novel is not to train them in reading but to train them in other things. Similarly, when students of mathematics are taught proofs, they know that learning the proofs is only one part of their mathematical training. You might know all the proofs and still not be a mathematician.

I feel, that in engineering courses such meta-learning goals (which are sort of obvious in literature and mathematics courses) are not clear to our students. They do not know what is it that they are learning when they learn, say, the equilibrium melting point of a pure material and things of the sort. Thus, I feel that explaining them the meta-learning goals will help them appreciate what they are being taught as well as evaluate by themselves along the way as to how much of the meta-learning is happening.

If we need to explain the meta-learning goal, of course, it means that we know what they are. The prime question is, are we? For example, what is the meta-learning objectives in a materials engineering curriculum where the students are asked to learn structure, thermodynamics, kinetics, transport phenomena, phase transformations, properties (mechanical, electrical, magnetic), and processing? And, how much of these meta-learning goals will be of use to the students even if they decide not to stick to the materials engineering field after their graduation? I think we need to think more along these lines and collectively come up with some answers (which, at the moment at least, seem to be muddled or not known in my mind — one reason why I am writing this post — to get my ideas cleared on the issue).

Knowing names and numbers

Once students know of the importance of learning the concepts, the naming of them and the numbers automatically follow. As Feynman observes in one of his interviews (available on YouTube — I think here, or one of the other parts), just by knowing the name, we may not know anything; however, knowing the name comes very handy for discussions and effective communication. Similarly, even though one might not know the exact number (and, may have to look it up), the orders of magnitudes of quantities is part of the understanding — much like a mathematicians way of learning a proof; they do not memorise it but build it up from first principles every time, and after several such exercises know it by heart). So, our emphasis in our teaching for knowing the names and numbers should be secondary to concepts and their understanding.

Engineering is becoming more science-like

Finally, I feel that there are good reasons to believe that current engineering training lays more emphasis on engineering sciences. Some of our students who come from the industry, have told me a change that has taken place in the shop floor. More and more of routine jobs, which  would have been carried out by an engineer or technician in the past, have been taken over by machines these days. So, the engineer is called only  when there is a hiccup. This means that the engineers job description on the shop floor sounds more and more like that of a scientist in the R&D division. Further, as a discipline, Materials Engineering itself is at that edge where engineering meets science; unlike other engineers, we do not take any property for granted and make our engineering solutions based on them; instead, we generally try to find the means of changing the property itself; this, generally gives a feeling to other engineers that we are not engineers but more science oriented people at best and artisans at worst; on the other hand scientists have difficulty in accepting materials engineers as one among them because of the emphasis that these engineers put on applications than on the basic underlying phenomena; in the end, the net effect of all this is to make the possession of exact knowledge of numbers important only to the extent that it also helps in our understanding the underlying phenomena as far as materials engineering goes — once again making the learning of concepts the primary goal of our engineering curriculum.

The teaching triangle or pyramid?

February 23, 2011

Jay Parini, in his Art of teaching, says, that for instruction, all you need is a student, a teacher and some log to sit on. Generalizing the log, and calling it the tools, one sees that the teaching triangle has for its vertices the tools, the teacher and the student. All three are essential for teaching to happen. However, what ties together all these three vertices is the subject of discussion. Thus, it is more of a pyramid with the subject of discussion forming the fourth vertex.

So, what happens, if any of the vertices disentangle from any other? Obviously, the pyramid collapses. When I am teaching and/or preparing to teach, I continuously worry about my holding on to the vertices of students, subject and tools. While I have control (or, at least I tend to think that I have control) over the subject end and tools end, sometimes, I tend to lose the students — individually or, worse still, as a group. Of course, this might be due to the fact that I have not yet mastered the tools and the subject well enough to make students stick to the task of instruction and sharing. But, the feeling that in spite of your best efforts students get disentangled from the process for reasons outside of your purview and control does pop up occasionally; and, it is quite frustrating when I get such a feeling.

ArunN points to a piece in Chronicle which talks about the problem of students disentangling from the other vertices, the possible reasons and causes for this disentanglement (some of which do lie outside the college campus) and some hints as to what helps in preventing such disentanglement:

Arum and Roksa point out that students in math, science, humanities, and social sciences—rather than those in more directly career-oriented fields—tend to show the most growth in the areas measured by the Collegiate Learning Assessment, the primary tool used in their study. Also, students learn more from professors with high expectations who interact with them outside of the classroom. If you do more reading, writing, and thinking, you tend to get better at those things, particularly if you have a lot of support from your teachers.

The piece seems to be the first in a series; may be it is worth while to follow it up and think on some of the issues discussed!

Update: Another piece about teaching; I can see one difference though; unlike patients who do want to be cured of their current ailments, students might be happy with their current status, or, might want something else which is not part of the mandate!