Teaching: Experience, interests and philosophy

Rafi Blumenfeld

My experience

As a Teaching Assistant at Tel Aviv University I taught laboratory courses to undergraduates, problem-solving in statistical mechanics and electrodynamics to physics graduates, and general physics, classical mechanics, thermal physics and electromagnetic theory to undergraduates. This involved frontal teaching, supervision during experiments, clarification of lectures (sometimes to the point of completely re-lecturing the course if the lecturer gave a particularly impenetrable course, which happened all too often those days), demonstrations of problem solution, homework assignment, homework marking, and the marking of exams and course work. Most of the students I dealt with came from physics and engineering but there was a fair amount of classes given to students from biology and medicine. The official surveys of teaching and instructing quality among students ranked me among the top 10% so my approach must have found some favour with them.
At the Cavendish Laboratory I supervised undergraduates from all years in a range of subjects: Classical Physics, Thermodynamics and Statistical Mechanics, Dynamical Systems, Properties of Condensed Matter, and recently Soft Condensed Matter Systems. At Princeton University I gave lectures to students on Fractals and Percolation Theory in a course on heterogeneous materials - a course that proved to be surprisingly popular.

At Los Alamos National Laboratory there were no academic studies but postgraduates from other universities usually came to do research work for a few months at a time. I have had one such a student, Yi Jiang from Notre Dame University, who worked with me on evolution of two dimensional interfaces and on a systematic coarse-graining procedure for inhomogeneous media. She did very well and went on to become a postdoc and then staff member in Los Alamos.

When my sons started to go through the UK education system I got somewhat alarmed by the education of Science and Maths in their schools. Trying to help them with these subjects was so successful that the word spread and ever since I have had a steady trickle of GCSE and A-level students coming for tutoring. Some of my happiest moments have been reading Thank-you notes from students who passed their exams with flying colours.

My philosophy

In general I like teaching and I derive great satisfaction from observing the face of a student when the penny drops. From early days I recognised that allowing students time to gain fundamental understanding through patient explanation and problem practice is more useful than drills in problem sonlving relying only on memory and formulae. Moreover, I believe that this principle holds not only at the higher-education level but also at primary and secondary school education. To my mind this is the main problem with the current education in the UK.
I have found in my limited teaching how to approach problems systematically, remembering as few formulae as possible, is the most effective way to produce basic understanding and successful students. By relying less on memory and more on insight students gain confidence and grow to experiment with the application of the analysis and reasoning 'tools' that they acquire. It is evident that for most science graduates who intend to stay in the academia this is the only viable approach - after all, the essence of their career will be to solve problems that no one has solved before. However, I am convinced that taking this approach and combining it with emphasis on independent research projects, is also essential at the undergraduate level. By and large, independent projects and practical work get students excited about research and the taste of that excitement is more than half way toward the production of a good graduate.
Having said that, one has to keep in mind that the university is not an extension of high school in the sense that students must be encouraged to independence. Success in higher education is more in producing students who can ask good questions rather than give good answers. This means that students should be encouraged to become independent in searching for, and obtaining, relevant material and on working hard on problem solving. Without these skills theoretical understanding would not be of much use. I fear that education to independent thinking and research is not a very high priority in universities these days.
A particularly important aspect of education at the higher education level is that, in addition to in-depth knowledge on their particular projects, students should get a broad knowledge of the state of the art in science in general. In today's world there is a need to produce scientists at all levels who know how to apply their expertise flexibly and practically, sometimes in unexpected directions. Nevertheless, a good education system must be able to identify students showing the inclination and appetite for pure and applied research. Such students should be provided with the opportunity to pursue their own ideas, even at the expense of reducing some conventional studies. As the history of science shows time and again, it is very difficult to predict where the next breakthrough will come from. What is certain is that such breakthroughs are often the result of original thinking and alert minds, not necessarily familiarity with the body of existing knowledge. In fact, one of Yakir Aharononv's favourite stories was that had he read the literature thoroughly as a student he would have never come up with the famous Aharonov-Bohm effect. He believes that the paradigm at the time that such an effect is impossible classically, would have put him off and that his lack of familiarity with the literature was a blessing in disguise.
So, there is a delicate balance that has to be struck between the teaching of current knowledge and the nurturing of creativity. Giving students the freedom to follow their interests would encourage original thinking and is bound to prove a better educational strategy in today's society.

Personally I regard teaching and supervision as paying my debt to those who educated me to become a creative physicist. I will elaborate on my personal views regarding student-advisor relations below. I believe in leaving the door open to students to discuss anything from clarifications of the lectures (mine and others'!) to any new ideas that they might have. More importantly, I believe in encouraging students to think about the ramifications of the subjects discussed in class and implications regarding any issue. To my mind, one of the signatures of a potentially good student is the ability to ask questions whose answers may not be clear even to the teacher. And there are plenty of those around. I believe that acknowledging the large gaps in our understanding of the universe around us tends to attract students. One of the worst things that an educator of science can do is pretend that s/he knows something s/he does not. We tell students of all levels that there are no silly questions, but we should also tell teachers and lecturers that there are no embarrassing questions. Mankind still has only little understanding of the world around us. A seemingly embarrassing question should be not only be acknowledged but also students asking such questions should be rewarded. Whatever the approach, such questions definitely should not be quenched by refering to existing formulae, if only because those are usually limited by implicit simplifying assumptions.

On student - advisor relations:

My principal advisor throughout my graduate studies at Tel Aviv University was professor Amnon Aharony, whose approach to advisorship was probably not too common. His main goal was that a student finishing a Ph.D. with him would be in the best possible position to when getting out into the scientific arena. This means that he not only guided me in learning the necessary technical skills but also made an effort to expose me to all the top-ranking scientists in my, and related, fields so that I get connected. Eminent visitors to the department would be faced with a unique experience. Amnon would collect all his students in his far-from-spacious office (and at times there were quite a few of us) and in this cramped atmosphere the visitor would have to present his work and discuss it with all of us (in fact, sometimes even defend it against all of us). Amnon would usually lead the discussion but would later retreat and let the students take over. What a learning experience for the students, possibly even for the visitor.
He sent me to as many conferences as possible, selecting (under budget constraints) the conferences that maximised exposure and interaction, naturally, those were usually the most prestigious ones. A memorable example for me is the following. One day, as Amnon and I were discussing something in his office, he got a call from Mandelbrot. He listened for a couple of minutes and then turned to me and asked off-handedly "would you like to go to Benoit for a couple of months?" "Yes", I said, "When?". "Next week" he replied matter-of-factly. I did set off only slightly more than a week later for about four months to what proved to be a very educational experience. Amnon also put a lot of effort in teaching me to write clear manuscripts. A draft manuscript would come back to me completely covered with red ink at least 15-20 times before he was satisfied. I remember my first ever paper by myself. I had an idea and I did some calculations and came to Amnon who discussed it with me at length and suggested that I start writing a paper. I did, with him as a coauthor. As usual the paper went between us back and forth many a time but at the last iteration it came back to me with only one red mark - his name was lined over in red. I asked why is that and whether he thought the paper was so bad he would rather not be on it. His reply was that he acted only as an editor and therefore did not deserve to be on it. That incident quite impressed me and taught me a code of conduct that is still with me.

When Amnon went abroad on a sabbatical I approached Professor David Bergman who agreed to be my second advisor. (Interestingly, he took a sabbatical the following semester. The administration, astutely making the connection, warned me in advance that I could not take a third advisor even if I tried for fear that he takes off too!). Having been exposed to two different approaches to doing science was a quite a bonus for my education. David's style was completely different from Amnon's: He was very methodic, doing every calculation to the last iota. In retrospect, this was not as much because he distrusted the student but because he was almost obsessive about not making any errors. He would make sure every possible detail is absolutely correct before publishing anything. In contrast, Amnon would cut quickly straight to the heart of a problem and then organise the plan of attack to resolve it and publish the result. Amnon's approach was more like Sir Sam Edwards' - an approach that later on was named by Edwards' students 'stealing the gold' (see the book for Sir Sam's 75th birthday with that name). David would play with one problem for a long time until he was sure that we haven't missed any detail. He also made a point of educating me in many facets in the etiquette of science. He used to repeat to me that one GOOD paper a year is worth more than five half-baked ones and that therefore I should put a lot of time and effort in making the paper good even if I believe I solved the problem. He recognised my tendency to get the essence of a problem, write a sketchy solution and be off to the next trail and warned me to keep it in check. Consequently, he came across as one of the most critical persons I have ever met. The collaboration with both of them produced a good list of papers, some of which were real gems from my perspective.
All this, however, was one level of my relationship with them. The relationship had an emotional undercurrent, of which I became aware as my postgraduate years went on. The only parallel I can see for this layer, and it is quite a good parallel, is parenthood. The advisor receives a raw student and moulds him into a scientist according to his or her perception of what a scientist should be. Isn't this what parents do with children? The student first looks up to his advisor, thirstily drinking everything that is said, not too differently than the way toddlers do. Then the student works hard to prove himself to the advisor. Gradually, however, as the student becomes more involved in his field, he starts to notice that there are some things that he knows better than the advisor. This is normal since the student is absorbed in one problem while the advisor has many. This is where the 'teen-age'-like period sets in and the budding feeling that he can eventually surpass the advisor. In due course the student leaves the nest to make do on his own, and, looking back, starts to appreciate the values and education that he received. All this process is not dissociated from emotions that resemble those between children and parents: Devotion, love, disappointment and feeling of being abandonned at times. Talking to quite a few colleagues on this subject, I found that I am not alone in this view and quite a few felt a child-parent sort of relationship with their advisors.

I absorbed much from my advisors and the standards that they set are with me to stay. Whatever I have been given in this respect I regard as a debt that I need to repay to other students, inasmuch as my debt to my parents I repay to my children. Hopefully, I will be able to follow and continue the line of good mentorship that my advisors exemplified.

Raphael Blumenfeld
Cavendish Laboratory
Madingley Road, Cambridge CB3 0HE, UK
Tel: +44 (1223) 337-001, Fax: +44 (1223) 337-000
Email: rbb11@phy.cam.ac.uk

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