W. E. Harris University of Alberta Edmonton, Aka., Canada
Analysis of Teaching
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It is not surprising that I should feel safe in choosing a title that includes the word ‘(analysis.”The word “teaching,” which to me means t o cause t o learn, is an equally unsurprising choice in view of the name of the award. Nevertheless, in presuming to talk about An Analysis of Teaching, I realize that I am daring to tread on hallowed ground. A common attitude is that teaching not only cannot be analyzed, but also that no one should pretend to do so. . Any analysis-chemical, educational, or other-comprises several operations that can be carried out on various scales and levels. The three principal operations are: to define the problem and identify the objectives or goals; to perform the appropriate functions; and to evaluate the results. Moreover, just as the operations of chemical analysis can be considered on a scale ranging from macro to micro, so also can we talk about the analysis of teaching on a scale ranging from that of university and national concerns to that of an individual instructor. Also, the analysis of teaching can be considered a t various levels ranging from kindergarten to postdoc1046 A
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Figure 1. Schematic representation of an analysis of teaching
toral study. If these three aspects of the analysis of teaching are combined, we can visualize their interrelations with the aid of the diagram in Figure 1. My objective in this presentation is to focus on the three operations at the undergraduate level and on the in-
ANALYTICAL CHEMISTRY, VOL. 47, NO. 12, OCTOBER 1975
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structor’s scale, emphasizing particularly the operation of evaluation. The restriction to these areas in no way implies that the other numerous aspects of the analysis are of lesser importance. For example, both preuniversity and postgraduate teaching are crucial, and by choosing to talk but little about them, I do not wish to downgrade their importance. I see no point in the platitude that teaching at the preuniversity level should be improved-this particular bromide is applicable to all levels. One of the frustrations and yet one of the challenges in teaching is that, no matter how much thought and effort may be expended, uncertainties concerning each of the three operations always persist. Anarchy would be inexcusable, but certainty is unattainable. Definition of Objectives To the extent possible, objectives should be defined in relatively broad terms to permit freedom in the area of instructional technique and in procedures used in the second operation. Some objectives are defined for an instructor by his department. Objectives
Chemical Education Award Address presented at t h e 58th Annual Chemical Conference of t h e Chemical Institute of Canada Toronto, M a y 1975
must be realistic as to limitations of time, manpower, and money. I am rapidly learning about the coercive power of a budget. In talking about objectives ( I ) in analytical chemistry, for example, such phrases as the following appear: “lay a foundation for becoming competent experimentalists,” “promote a sense of confidence and judgment respecting chemical measurements,” and “provide conditions for high-quality and satisfying work.” On the detailed level, one of my continuing and long-term objectives has been to reward competence and not to reward incompetence. This is a difficult goal to achieve. Often the highly motivated and competent student is clobbered; more frequently, the poorly motivated, incompetent student is bonused; and usually both of these are practiced. Teaching to Meet Objectives At the outset it should be recognized that, a t the university level, a superb teacher cannot exist in the absence of a basic interest in learning on the part of his students. A spark of interest can be fanned, but its absence can destroy a dedicated teacher and waste a good one. With positive feedback a good teacher and good students are mutually reinforced and strengthened. Students should have the interest, competence, and character to profit from what the superior teacher has to offer. With goals and objectives broadly defined, then as much leeway as possible should be allowed as to how these goals are to be implemented. Part of my philosophical approach to the performance of the teaching operation is summed up by the statement, “Live and let live.”
Both seasoned instructors and raw beginners are likely to have definite opinions about how to teach a subject and what should be included: it is all too easy to appear dogmatic and to give the impression that there is only one right way. At the same time, the uncertainties referred to earlier are probably most numerous in the teaching procedures used to meet the objectives. There are many ways of being an effective teacher, and there should be as much freedom as possible as t o choice of techniques of presentation; similarly, a t the departmental level there should be considerable freedom in matters of particular course and curriculum structures, with innovation and experimentation encouraged. The problems and the attempted solutions appear t o be eternal, but the language used to express them changes over the years. Teaching is an art, one that is developed and adapted from a knowledge of what has been revealed by research and experience in the subject. All of us can learn something from our colleagues, both those who are effective and those who are not. Interaction of the instructor with students on both the intellectual and personal levels is important. Qualities such as disturbing mannerisms and a voice too weak in volume or unattractive in quality are obstacles to successful teaching; a reasonable effort should be made to minimize them. Teaching is a science, which like the art cannot be ignored if excellence is to be achieved. Scientific and practical approaches are as important to the success of a highly effective teacher as are dedication, experience, and natural gifts. Thorough knowledge of subject matter is characteristic of good instructors. Sound planning and a
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sense of organization are also apparent and cannot be overemphasized. In a recent book by Sheffield ( 2 ) ,it is stated that outstanding teachers mostly use the lecture method, with a t least 3 hr of preparation for each 50-min lecture. A wise teacher also puts teaching aids in their proper perspective and recognizes the contributions they can make. Thus, teaching is both art and science, and in the discussion that follows, I make no attempt to delineate which is which. Also, my examples are mainly from the field of analytical chemistry, where I have had most of my experience. The content of a chemistry course clearly must bear an intelligent relation to what goes on in modern chemistry laboratories, and so courses must be modified as knowledge expands and needs of society change. Therefore, a second part of my philosophical approach is, “Seek change and modernization through evolution.” Almost all biological variations in nature are defective and are eliminated by natural selection. Similarly, virtually all new approaches to teaching are defective and need to undergo a process of selection and evolutionary adaptation. Proponents of so-called new approaches (genuinely new approaches being rare) are often able to report initial success because of the unusual interest aroused and the enthusiasm of the instructors for their ideas. This is called the Hawthorne effect ( 3 ) ,a powerful and useful effect. In less committed hands the same approaches may be anything but successful, and few are able to withstand the selection process. An answer is required to the question, “Is this a basically sound idea, or is it being carried beyond its intrinsic worth by an enthusiastic instructor and student condition-
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ing?” Furthermore, even a smoothly operating course may be hurt by introduction of too many changes too quickly. It seems important, therefore, to maintain the bulk of a course unchanged from the previous year and to introduce only a small amount of changed material at any one time. Special attention is then given to this new material, and the adaptation is proceeded with as quickly as possible. Recognize that much adaptation may be necessary or that an idea may have to be abandoned to cut your losses. In regard to selection of material, I have often said that no attempt should be made to teach anything because it is thought to be interesting-I regard interesting as a bad word in the context of teaching. Do not misunderstand. I believe that the beginnings of dedication cannot be instilled by frantic efforts to make a subject interesting through artificial approaches. For example, bandwagon use of. the discovery method of teaching often falls flat because situations contrived to stimulate interest are quickly recognized by the student as unrealistic. Beyond the Hawthorne effect, contrived approaches prove to be a waste of time. A rigorous and realistic course with carefully defined objectives should make no apology for its content. Competent, strongly motivated instructors can and should ignore innovations selected solely for the sake of presumed interest.
Evaluation and Improvement of Instructional Effectiveness Finally, let me focus on the last 1h7 of the cube in Figure 1,that of evaluation. This whole area is probably the most difficult for instructors to consider worth spending time on. Nonetheless, it is the weak link of the three analytical operations, especially if broadened to include feedback. Instructors are themselves evaluated by students, by other instructors, by administrators, and by the public. It is easy to become paranoid and look on any attempt at evaluation with unreasonable distrust. Nothing, however, contributes more handsomely to the goal of excellence than systematic and reasoned attempts at self-evaluation. Again, remember that certainty is not achievable. First, consider the meaning of the word “evaluate.” It has been defined as t o examine and judge. Evaluation can be visualized as including two stages: the gathering of data, which may involve making appropriate measurements, followed by a judgment process. A clear distinction should be recognized between the concepts of measurement and evaluation; measurement constitutes only one part of the process of evaluation. Whereas 1048 A
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many can be instructed in how to make measurements, only those with critical knowledge can be expected to make valid evaluations. Evaluation connotes value judgments; frequently, definition of scope, purpose, and context must be part of the process. A piece of wood can be measured easily, but it cannot be evaluated out of the context of purpose-proposed for a toothpick, its evaluation would be different than for a beam of a bridge. Evaluation can be on a broad or a detailed level. The most elementary broad-scale evaluation of a teaching contribution is simply related to the fundamental question of teaching load and class size. In one short study ( 4 ) an evaluation was arrived a t that is straightforward and indicates that, other things being equal, teaching load increases as the cube root of the number of students in a class. On the basis of this evaluation a section with 250 students would constitute a load twice that of a section with 30 students-a seemingly reasonable conclusion. The cube-root relation appears to be realistic and applicable over an extremely broad range of class sizes, from a single student to several hundred. Another broad-scale evaluation relates to overall effectiveness of teaching. One technique for obtaining such data involves a survey of student opinion. Opinion surveys composed and conducted by students are often slipshod, and the results should be used with discretion. Probably the most valid broad-scale evaluation of overall teaching effectiveness is reflected in the collective and independent judgments of several colleagues who themselves are recognized as able teachers. Whatever factors go into the making of a good teacher, such persons through their own competence can best weigh and judge the formal and informal input from the teacher, students, colleagues, and the university community in general. Such evaluations by superior teachers have proved to be remarkably consistent. Broad-scale evaluations are probably of only marginal value in helping an instructor toward the goal of excellence. They are important, but not enough. It does not take long for an instructor to recognize whether his teaching is generally effective. A simple yes or no answer is easy. Something of much more interest is whether it is better or worse than last yearwhether things are tending to improve or deteriorate, what changes show promise, and where special effort is needed. Here microscale evaluations are mandatory. Slow, long-term trends are not easily recognizable without systematic assessment of smaller segments of a subject. Most important, to keep any course alive, new ideas and
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changes should be continually explored and adapted; a t the same time, as I have stated, most changes are likely to be defective to some degree. Evaluations carried out on these small-scale items can be used as a means of accelerating positive evolutionary trends. One marginally useful measurement is that of average grade. It tells little about instructional effectiveness unless used with reference to some slippery absolute standard. An instructor can move a class average up or down a t will, not necessarily in relation to the level of students’ knowledge or to instructional merit. I t is no secret that, if an instructor wants to take an easy way out or does not want to be bothered with a new situation or one out of control, the assignment of high grades is a method of getting by. Thus, because the class average depends on arbitrary decisions of the instructor, it is of limited value in evaluating instructional effectiveness or change.
Discrimination Another quantity that can be measured is that of discrimination. It can be calculated without concern for its meaning or evaluation. However, I have found it, as have many others, to be the most important, useful, and efficient route to ascertaining trends in instructional effectiveness. Discrimination is a measure of the difference between the performance of the best and the poorest students in the class, for an item such as a test question or an experiment. With discrimination as a guide and sorting mechanism, the operation of a course can evolve systematically without preconceived notions. High discrimination correlates strongly with high student morale. But consistently high values of discrimination are not obtainable readily or by whim. They must be earned, and arbitrary actions by the instructor are of no avail. Every incremental increase requires effort, and instructional error has an adverse effect. Discrimination is calculated by the use of the top and bottom end fractions of a class. The size of the end fraction chosen is a compromise between including as many students as possible for statistical validity and maintaining as great a difference as possible between these fractions. The optimum end fraction has been shown ( 5 )mathematically to be 27%. Discrimination, 0 2 7 , is a value proportional to the difference in average grades of the top 27% of the class and the bottom 27%. (Select the top and bottom 27% using a base that is as broad as possible such as overall course grade or the grade for the en-
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tween grade and quality of results leads to high values of discrimination. Therefore, a pragmatic procedure I have adopted for year-to-year operation is that of doing everything and anything that appears to lead to higher values for the discrimination index.
Discrimination and the Laboratory Since discrimination for laboratory items can be calculated only once or twice per year, the opportunity for ongoing feedback is less than for written tests. Also, such calculations can lead to the largest bonuses. Figure 3 is a scatter diagram of overall discrimination values for the laboratory, final examinations, and term tests for a number of introductory analytical chemistry courses in Canadian universities in 1969. For the laboratory, discrimination was often significantly lower than that for the other two items shown. Probably most instructors are intuitively aware that the laboratory is often a weak link. The analytical laboratory is certainly discussed frequently, and it is the focus of innovative effort. In agreement with this diagram, I believe that properly directed effort on the laboratory is likely to yield the richest dividends when systematic and objective attempts are made to maintain or improve quality. If a laboratory is developed (8) along the lines that high discrimination indicates, many items can be tried on a small scale, with those having poor discrimination being either modified or replaced. With continual sorting and polishing, a superior and up-to-date instructional system can evolve without jeopardizing student response and acceptance, and evolution can proceed systematically without preconceived hypotheses. The use of discrimination guides the instructor to sources of error, instructional and other, and provides a medium for his sorting mechanism. I t is the key to the analytical approach to teaching-an approach I have used for more than two decades.
Discrimination and Written Examinations Calculation of discrimination and average-grade indices for detailed individual examination items takes little time-usually something like one additional hour after grading. By learning something about the quality of test items, the instructor can plan improvements for future tests, build up a Figure 2. Chart for assigning ratings to file of valid test items, and use the inexamination test items formation as feedback for instructional change. A combined evaluation of discrimination and average grade for individutire examination. Negative discrimina- al examination items can be obtained by use of an arbitrary chart such as in tion is clearly possible and is obtained Figure 2. In this chart, test items are on occasion. Avoid the mistake of seclassified into one of five groups: A, B, lecting the top and bottom 27% of the C, D, or E, to denote high to low desirstudents on that i t e m . ) Then ability. Both a high average and a high C top 27% - bottom 27% X value of discrimination are desirable. 0 2 1 = C maximum 27% This chart represents a compromise in 100 evaluation between the sometimes conflicting aspects of the two attriwhere maximum 27% is the maxibutes. mum total obtainable on that item by Oral examinations have low ability 27% of the class. to evaluate knowledge and underTo furnish a broad overview of instanding of subject matter; in my structional effectiveness, values of dismind their use is a questionable praccrimination and average can be calcutice. They are also highly inefficient. lated for several major items at the Ebel (6) has said, “It is possible to use completion of a course. Some recent oral examinations effectively, but it is values obtained for discrimination and almost always unattractively difficult average for several major items in a to do so.” The persistence of the use of quantitative analysis course were: oral examinations in the face of their final course grade, D27 = 34% and avlow validity must mean they serve a erage = 64%; final laboratory grade, 31 real need; of what it is, I am not cerand 70; December test, 30 and 62; (Continued on page 1054 A ) tain. first-term quizzes, 31 and 63; secondFlgure 3. Discrimination for examinations and laboratory grades in analytical term quizzes, 42 and 61; final examicourses for several universities (original figure adjusted to correspond to 0 2 7 ) [from nation, 39 and 56. Harris (7)] With 0 2 7 as an indicator of the overall quality of major items, a value of 10%or less indicates that something is third-rate. The general effect of the grades assigned under these conditions will be to batter the strongest students, generally lower the grades of the competent students, be about right for the middle students, and give massive bonuses to the weakest students. Morale is likely to be low and complaints numerous. An overall value for discrimination of about 20% can be considered adequate. The above effects remain, though to a less demoralizing extent. At discrimination values in excess of 30%, operations are likely to be highly satisfying for both students and staff. I stated earlier that one objective was that of assigning grades that reflect competence. High correlation be1050A
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ANALYTICAL CHEMISTRY, VOL. 47, NO. 12, OCTOBER 1975
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My experience has been that high discrimination and satisfying results cannot be expected until procedures have been refined, a set of adequate samples developed, and an optimized grading scale produced. Seeking excellence in the evolution of a laboratory, systematic effort must be spent concurrently in these three areas. First of all, students must be able to obtain high-quality results under the conditions provided for them. Essentially, no experimental procedure can be lifted directly from the literature with success, and only rarely can an experiment be introduced and be immediately acceptable. Usually too much background knowledge and technique are assumed. Appropriate parts of the enormous legacy of experimental knowledge must be selected and adapted to the capabilitiesand background knowledge of the students. This adaptation takes massive amounts of work, but as it proceeds, discrimination almost certainly will rise. To give an example, it took effort over a period of 6 years to adapt a procedure for the determination of glycol, even though it was carefully checked by a teaching assistant before its assignment to students. As adaptation proceeded, discrimination rose from 11%in the first year to better than 25%in the sixth and later years. Although few procedures take this long to become satisfactory, most do take several years of special attention. To cite a difficult case, it required 10 years to adapt and develop the practical test (9) that we use. I suspect the same type of experience would be found in other areas of chemistry or science generally. The second requirement is that of an adequate set of samples. Justified confidence by a student in his ability to gather reliable quantitative data is best attained through laboratory assignments based on unknown samples. The essence of reality and practicality of analysis is an obligation to come up with a reasonable estimate of the correct answer, which is not known to the analyst (here the student) beforehand but is known to the instructor. The socalled real samples assigned by some instructors fail in this vital respect. A high-quality set of samples is not easily obtained, but quality improves with continued effort (IO). The third requirement involves the development of rational and effective grading scales. This area is often neglected, and it is one of the most difficult to come to grips with. In the grading of experimental work, it is important that the scale be such that the grades accurately reflect the competence of the experimentalists. Without a rational and effective scale, progress made in the development of workable 1054 A
Figure 4. Relation between range assigned for grade of 5 in particular analysis and discrimination Curve 1: pass-fail or two-point grading scale (grades of 5 and 1 only); Curve 2: intermediate grading scale (broad distributionof grades, 1 through 5); Curve 3: nondifferentiatingscale (mostly grades of 3, few 1's and 5's).[Adapted from Harris and Kratochvil ( 7)]
procedures and valid samples can be nullified. It is essential that grades assigned to the results of analyses do not depend on procedures, samples, and grading scales that the instructor should, but does not, have under control. It may be profitable here to be more specific for a few minutes. In setting up a grading scale the first requirement is to consider the optimum number of levels. This may range from 2 (for a pass-fail scheme) up to 20 (for 0-10096 in 5% steps) or more. Several considerations influence the choice. One is that the average grade should be neither too low nor too high. Another is that the most competent should be able to earn the top grade most of the time. Another is how much credit to assign work that has resulted in totally inaccurate values. A two-point, or pass-fail, grading system is undesirable in that the wide range of answers to be graded "pass" provides attractive opportunities for guessing. Unless the pass range is broad, the number of failing grades must be demoralizingly high. But with a broad pass range, those who do superb work will receive the same grade as those who do only minimally acceptable work. A pass-fail grading scheme is an invitation to mediocrity. A five-point scale works well for grading experimental results. Arbitrarily, the top grade assigned is 5, and the bottom grade for completing the experiment no matter how inaccurate is 1. After a five-point system has been
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chosen, further decisions then need to be made. Although the average grade for an experiment can be arbitrarily chosen by the instructor, in principle, 60% can give the most reliable evaluation of performance when a one-to-five scale is used. Discrimination is the decisive quantity; a prudent choice of grading scale should maximize discrimination. Figure 4 shows three hypothetical and calculated curves for discrimination as a function of range for three types of grading scales, from carefully obtained data for carbonate analyses from highly motivated students. This figure illustrates that, in this hypothetical case, the highest obtainable discrimination is clearly for Curve 1,which corresponds to a twopoint grading scheme. However, since the curve rises slowly, the maximum corresponds to a wide range, and the probability of successful guessing would be high for a reasonable average grade. In my judgment, this hypothetical curve could not be achieved in practice. Morale would be low, both when the range was so wide as to permit successful guessing and when the range was narrow and the average grade low. Either would lead to low discrimination. In the nondifferentiating scale (Curve 3), few grades are allotted at either end of the scale. Here the requirements for a top grade are so demanding that even the work of a competent and experienced analyst might not qualify. In any case, the discrimination curve is unappealing. Curve 2 illustrates a grading scale that gives a broad distribution of grades 1through 5. The curve rises rapidly to a high value of discrimination and gives reasonable values of average grade without encompassing a broad range. Finally, in setting up a grading scale
Figure 5. Effect of varying degrees of skew (0.5, 1.0, 2.0) on relation between average grade and discrimination for chloride analysis
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that assigns informative and accurate grades, the permissible range for a 5 must be combined and optimized with a factor that takes into account skew, or bias, in the results obtained. In a real analysis, high and low results of the same magnitude are unlikely to occur with the same frequency. The resulting bias implies the presence of determinate errors in the analysis that have not been or cannot be eliminated. In fact, bias seems to be more and more clearly revealed ( 1 ) as the overall precision of the analysis improves and the procedures are debugged. Bias is instinctively difficult for many people to accept because, from a utopian view, a Gaussian distribution of errors is a persistently attractive model. In fact, it is so attractive that the term normal distribution is used. The use of “normal” as synonymous for Gaussian is unfortunate because of its misleading connotation. The graceful symmetry of the Gaussian curve unduly reassures and impresses the imagination of idealistic philosophers. Details cannot be given here, but the optimum skew factor ( 1 )is arrived a t by calculation of discrimination indices for various combinations of range and skew. To illust,rate the kind of data obtained in these optimization calculations, Figure 5 shows the relation between discrimination and average at various skew values for chloride analysis. In this case, use of skew values greater than unity (where unity = no skew) results in grades that less frequently penalize good students and help poor ones. Procedures, samples, and grading scales are monitored each year through calculation of discrimination indices and average grades for all experiments. Those experiments showing poor discrimination are reevaluated with a view to eliminating the causes for the unsatisfactory performance. Actually this is an efficient way for an instructor to spend his time, since his effort is focused on those items that yield the best returns for effort expended. As the closed-loop procedure is kept in operation, conditions keep getting better and better. Concluding Comment I have spoken on discrimination and similar matters at other times, and I have been attacked, or a t least roundly condemned, on idealistic or philosophical grounds for using it. In selfdefense, I feel I must state that (according to surveys carried out by our Students’ Union) this approach to the problem of teaching is acceptable to students (Figure 6). I have indicated that teaching is more than a science and more than an art. It is both. Those of us who teach 1056 A
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science are lucky in that we can use all the artistry available to our colleagues outside science, and our training enables us also to use science more easily and more efficiently. I have been doubly fortunate in having been associated with the teaching of analytical chemistry. Here is the best of all worlds in that the instructor has the tremendous built-in advantage that students can be motivated more positively than is probably possible in any other area. Since the time of Berzelius, the basic format of university chemical education has changed little. The volume of material is greater, the level of theory is more sophisticated, the lectures are supplemented by modern teaching aids, and the laboratory experiments and apparatus are more complex. Nevertheless, assuming interested students, the basic tools of professor, laboratory, and book continue to be an effective combination in all areas. Successful teachers owe much of their effectiveness to experience, dedication, and a natural gift, but it is also clear that a scientific and practical approach can augment these characteristics. Teaching requires creativity and innovation in both the scientific and artistic senses. Acknowledgment Discussions with my analytical colleagues at the University of Alberta, particularly, Professor Kratochvil, are gratefully acknowledged. Literature Cited (1) W. E. Harris and B. Kratochvil, “Teaching Analytical Chemistry,” Saunders, Philadelphia, Pa., 1974: (2) E. F. Sheffield, “Teaching in the Universities,’’ McGill-Queen’s Univ. Press, 1975. (3) D. A. Laird, E. C. Laird, R. T. Fruehling, and W. P. Swift, “Psychology,” p
ANALYTICAL CHEMISTRY, VOL. 47, NO. 12, OCTOBER 1975
Figure 6. Student opinion of laboratory work in analytical chemistry. From Students’ Union Course Guide, University of Alberta, 1968. [Adapted from Harris
380,5th ed., McGraw-Hill, New York, N.Y., 1975. (4) H. B. Dunford and W. E. Harris, in preparation. (5) T. L. Kelley, J . Educ. Psychol., 30,17 (1939). (6) R. L. Ebel, “Essentials of%ducational Measurement,” 2nd ed., Prentice-Hall, Englewood Cliffs, N.J., 1972. (7) W. E. Harris, Chem Can., 25 ( I ) , 18 (197.7) ~~- -,
(8) W. E. Harris, Anal. Chem., 42 (13), 53A (1970). (9) W. E. Harris and B. Kratochvil. J. Chem. Educ.. 48.543 (19711 (10) W. E. Harris and B.-Kratochvil, Anal. Chem , 46,313 (1974).
Walter E. Harris, chairman of the Department of Chemistry at the University of Alberta in Edmonton, was educated at Alberta (BS, MS) and studied under I. M. Kolthoff a t the University of Minnesota where he earned the PhD degree in 1944. He remained at Minnesota working on a US.government synthetic rubber program until 1946 when he joined the faculty a t the University of Alberta. His research interests have been in electrochemistry, hot atom chemistry, and, more recently, in chromatography. Dr. Harris received the Fisher Scientific Lecture Award, sponsored by the Chemical Institute of Canada, in 1969. He is a reviewer for ANALYTICAL CHEMISTRYand was a member of our Advisory Board from 1970 through 1972.
