Learning and Teaching Crystallography

- A Personal View

My initiation into crystallography was a chance one. During my last year at Manchester Grammar School I was trying, like all my form mates, for scholarships at Cambridge and Oxford. During my interview in connection with the Cambridge examination, I was asked what subjects I would like to study if I came to that university. Like many young people at that stage, I suggested the three that I had studied in depth at school - chemistry, physics and maths. But for the Cambridge tripos I had to study four, and on enquiry about further possibilities, crystallography was mentioned as one. I had no idea then what the subject was about but, when it was explained, it sounded attractive and I agreed to it as the fourth subject. Well, I was not awarded a scholarship at Cambridge but succeeded at Oxford. I had been equally good at school at chemistry and physics but, at Oxford, I had to choose just one of them. I made the rather arbitrary choice of chemistry and, although that involved no additional full subjects, I was pleased to find that the course included lectures on crystallography and that it was also available for further study as an optional subsidiary subject.

The crystallography lectures in the first year of chemistry were given by Professor (then Mr) Powell in a rather eccentric way, which included rolling up his eyes until he was looking vertically upwards at the ceiling. However, at an early stage, he gave some most colourful demonstrations of optical properties, using a projection polarising microscope. These greatly impressed me and stimulated my interest. The subsidiary course involved a weekly two-hour practical, where I became fascinated by optical goniometer studies, stereographic projections and, eventually, solving structures from X-ray photographs. When it became clear that my fellow students who did not take the subsidiary course were finding the main course lectures barely comprehensible, whereas I found that the practicals made them not only understandable but interesting, I knew that this was the subject I must choose for my one year's research as part two of the degree. I was delighted when, towards the end of that year, Mr Powell invited me to stay on for research with him, to be funded by my becoming a departmental assistant.

One of my departmental duties was to act as a demonstrator in the practical class and to assist in rewriting some of the explanatory scripts. It is often said that there is no bettter way of learning a subject than to teach it, and that was certainly true for me as a demonstrator during my two years of research. Those two years in a small department also meant that I learned the subject as an apprentice, with easy access my to supervisor and to more experienced research students. Many structures were solved, in those days, by the trial structure method - usually with the aid of scale models - and that appealed to me as a form of detective process. The subsequent structure factor and Fourier calculations were a drag, having to be carried out using desk calculating machines and Beevers-Lipson strips and often taking several days, but one was sustained by the excitment of what the result might reveal.

From Oxford I went to Nottingham University as an Assistant Lecturer in Physical Chemistry. Before appointment, I had enquired of the head of department whether I should be able to continue my research in crystallo�graphy. He replied that it was a facility that he would like to have in the department but was it too expensive? I calculated that one could set up a basic unit for a thousand pounds, and so it turned out to be. That included an X-ray generator and tube, one X-ray camera, a polarising microscope, an electrical desk adding machine and a set of Beevers-Lipson strips.

At various times in my progress from Assistant Lecturer to Lecturer, Senior Lecturer and Reader, I was asked to do crystallography courses for the chemistry students of length varying from four to ten lectures. I soon discovered that chemistry students who, like me, had only a limited amount of mathematical training, were apprehensive about the apparent mathematical nature of crystallography. As I was teaching, I also had opportunities to continue learning crystallography by attending a number of excellent summer schools. At these, I shared the apprehension of my students and was occasionally overwhelmed by the mathematics - especially by vector and matrix algebra. But those summer schools taught me that understanding was enormously increased if one could have hands-on experience of applying new knowledge in the practical sessions, immediately after acquiring it in lectures (an echo of my Oxford undergraduate experience). I became convinced that this was the best way to teach and learn crystallography but I only had one opportunity of putting it into practice.

This was when I was asked to do ten three-hour sessions on crystallography for geology students. I could give a fifty-minute lecture and, after a ten minute break, conduct a two-hour practical and problem-solving class on the same material. The nearest I ever got to this with chemistry students was when programmed learning was becoming popular and I devised a set of programmed notes which set problems in a frame on one page and gave answers and notes on the next page, leading up to the next problem, and so on. With timetables and courses continually changing, these experiments in teaching lasted only for one trial each, and in any case they were not really suitable for a lecture room environment. As new material was added to physical chemistry courses, former topics were compressed into smaller numbers of lectures and demonstrations were reduced or eliminated. Remembering how I had been attracted by those on optical crystallography, but not having access to a projection microscope, I spent one long vacation making a colour film on this topic to show in lectures but it never had the impact of a live demonstration and was soon dropped.

This, however, revived another former Oxford interest in scientific films. (I had been a founder member and treasurer, then chairman, of the student Scientific Film Society.) I realised that a number of stimulating films were being made on crystallography and, for the X-ray Analysis Group (later the IOP and BCA Crystallography Group), I compiled a list of films on crystallography and used one occasionally in my lecture course. It was perhaps this list that led to my being invited to join, for a few years, the teaching commission of the IUCr. This was a very interesting experience which broadened my horizons concerning teaching methods. It also enabled me to attempt to mollify the mathematical bogey for less theoretically inclined students by contributing a pamphlet on the calculation of structure factors to the commission's series of teaching pamplets (a series which, though perhaps now dated, deserves to be better known). Being a chemist, I find it easier to understand visual analogues than mathematical formulae so addition of waves is shown diagrammatically in the pamphlet as well as by equations, and structure factors are illustrated by an Argand diagram.

Meanwhile, I was also putting into practice the apprenticeship method of teaching and learning, by training postgraduate research students, some of whom had had no previous formal training in crystallography. This was not only successful but enjoyable in that it developed personal friendships. Later, when Nottingham University Chemistry Department adopted the idea of having ten-week research projects in the third year of the undergraduate course, supervising these brought similar enjoyment in an apprenticeship environment. But it was also hard work, starting at the beginning again with every new project which, even if it did not precede the lecture course, demanded more detailed practical and theoretical knowledge than the course could provide.

Shortly before retirement, I was approached by the Royal Society of Chemistry, about the possibility of contributing a teaching audio cassette on crystallography to their series of Chemistry Cassettes. This opportunity I welcomed because, again, it provided a learning medium where each piece of newly acquired knowledge could be applied immediately afterwards by the student in the solving of problems. In line with my philosophy of keeping the mathematics to a minimum, the theory is shown diagrammatically as far as possible in the accompanying workbook (which also provides the problems and their answers). I was also determined not to gloss over aspects that I had found by experience often puzzled students (e.g. why is Bragg's Law usually quoted as n lambda = 2d sin theta but most often used in the form lambda = 2d sin theta In the event, this tape course spread over two C90 cassettes and two workbooks, even though it only purports to teach the basic principles of crystallography. It also took a long time to complete and Part 2 has only recently been issued by the RSC. The future for interactive learning of crystallography now lies, I am sure, with computers and I was pleased to see the results of a survey of educational software in the June 1995 issue of Crystallography News But as computer learning becomes more routine, care must be taken to ensure that crystallographic teaching retains those aspects that attract, and perhaps even thrill, learners.

In summary, then, I believe students are often attracted to crystallography as I was, by its visual aspects. Unless they are keen on mathematics, students may be put off unless that aspect can be reduced to a minimum and introduced gradually with hands-on experience of applying it. This is particularly true when crystallography is taught as an aspect of chemistry. I was interested to see, in the account of Max Perutz's address at Dorothy Hodgkin's memorial service ( Crystallography News No. 53, pp.10-16) that even she was very apprehensive at the start of her research at the amount of mathematics involved. And, in the June 1995 issue of Physics World (pp.17-18) attention is drawn to similar sentiments expressed by students of physics, and a plea is made for more explanation and less mathematics in teaching that subject. Perhaps teachers of crystallography would do well to ask their students what attracts them to the subject and what turns them off.

Stephen C. Wallwork.
August 1995
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