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reason, there should be only one note-taker, a stenog rapher, who should afterwards make mimeographed copies of the lecture to be handed to each student. In general, it may be said that any lecture worth delivering at all is worth being duplicated by the mimeograph process, and then after it has been thoroughly revised, and possibly used for two or three years, it should be printed in pamphlet form, and finally, if it is the best possible statement of the subject, it should be bound in a book. A systematic course of study should have a textbook, and if there is no satisfactory textbook in existence in the professor's opinion, then he should make one. The course of study should also have numerous problems to be worked out arithmetically, or on a drawing board, or both. When a good problem is found which exercises strongly the thinking powers of the students, it should be printed and subsequent classes should be drilled on it. When possible, a series of problems all involving the same operations but with different numerical data should be used, so that each student gets a separate problem. The results may then be tabulated and errors in the solutions easily pointed out. I have found a good series of problems in elementary steamengine work to be the following:
“Required the mean effective pressure, the horsepower, and the probable steam-consumption of a single-cylinder engine under the following conditions: area of piston, 100 sq. in.; piston speed, 600 ft. a minute; steam pressure, 80, 100, 120, 140 and 160 pounds; cut-off, 0.15, 0.20, 0.25, 0.30, 0.40, 0.50, 0.75 of the stroke; back pressure, 3 pounds and 17 pounds absolute; compression in the non-condensing engine to one-half of the initial pressure; in the condensing engine, compression begins at 0.6 of the return stroke; clearance, 2, 5 and 10 per cent.; cylinder condensation considered as a percentage of the length of the stroke, 6, 7, 8, 9, 10, according to the initial pressure.” This series gives 5 X 7 X2 X3=210 separate problems, enough to give five or six to each member of a large class. When this set of problems was sprung on the students and they were asked to bring in after several days the complete solutions, it was found that the results which ought to plot in a series of smooth curves had no relation to any curves whatever, the errors being due to all sorts of mistakes in arithmetic. When these mistakes were corrected, a fine lot of curves resulted and they showed clearly the relation of probable economy to cut off, to clearance and to pressure.
The above remarks are offered merely as an introduction to the general subject of pedagogic methods and for the purpose of bringing out discussion on the definite question, “What is the best pedagogic method in each engineering course?” I submit that the best method will not be arrived at by mere discussion, but by actual experiment and the systematic recording of the results of such an experiment. One trouble with the subject now is that it has so many variables and that there is no satisfactory standard of measurement for any of the variables. I hope these remarks may lead some of our professors to make some experiments and to bring us the results in some such form as the results of the spelling class in Northwestern University, which I have quoted above.
JOINT DISCUSSION. DEAN WOODWARD: Professor Raymond said that he himself, in order to understand better the method of the individual instruction, took two of the subjects personally. I would like to ask if he also took two of the same subjects of the other section of the class so that his intellectuality and force of character would equally impress the two sections. Were the teachers equally competent, equally enthusiastic, equally hard at work? These are very important matters to consider before we can make anything like a comparison of results. If in individual instructions elaborate lectures were dispensed with, that would be a clear gain.
DEAN RAYMOND: I taught this section algebra and surveying, and I did not teach any other section algebra, but I have taught other sections in surveying. The instructor in mathematics, who covered the trigonometry and analytical geometry, is rated as one of our best instructors in mathematics. The instructor in drawing and descriptive geometry had also part of the rest of the freshman class. Owing to some irregularities in hours, I think the disadvantage of instruction was generally with this special section.
PROFESSOR WILLISTON: I would like to ask whether in this plan of individual instruction but one subject was studied at a time, or whether two or more subjects were studied at the same time, and if so, what was the maximum number of subjects studied during any one week?
DEAN RAYMOND: The maximum number was three. I would prefer to have two. Part of the year it was but two. When a student is studying a subject that is studied partly by text and partly by laboratory work, I would have but two, this one subject and English. The chemistry text was studied in the morning and the laboratory work done in the afternoon.
THE CHAIR: Were these two subjects under the direction of two different instructors ?
DEAN RAYMOND: Yes.
THE CHAIR: So you could have the student carry on the two subjects at a time with two instructors ?
PROFESSOR WILLISTON: In an earlier presentation of Professor Raymond's plan, I understood that it was his idea to have the student take up the subjects in an engineering course one at a time, finishing one before he was allowed to begin another. To follow that plan consistently would, I believe, lead to serious difficulties, and I am glad to know that Professor Raymond has not attempted it. I think, however, that he has made a very great gain by reducing the number of subjects which are usually carried at one time by engineering students. His arrangement limits the number of subjects on the program at any one time to three. I believe that there would be immeasurable gain if all engineering schools could approach the same limit.
I think that there is also an important advantage in Professor Raymond's plan which comes from frankly recognizing the fact that no two individuals are alike, and that no two men have the same capacities. I believe that we should attempt to meet the individual needs of our students, although I do not believe that it is absolutely necessary to have them taught entirely by the individual method in order to accomplish this. It is, however, necessary, in order to get the most efficient results, to recognize in one way or another the fact that the training and experience of different men before they enter college is apt to be very different. Their capacities are different, their tastes differ, and equally capable men grow and develop at different rates and in different ways. Enough individual attention and instruction therefore should always be given to allow for these differences of personality. In many places at the present time, I believe, too little attention is given to these, and the assumption is too often made that all students should acquire the same intelligence and information in the same time.
One more point I want to commend in Professor Raymond's plan. He has endeavored to make the atmosphere which surrounds the school work just as far as possible exactly like the atmosphere which his men will later find in practical work. The sooner young men become accustomed to the kind of requirements that will be made of them in real life the better; and in so far as the plan described in this paper accomplishes this result, there is real gain.
PROFESSOR HIGBEE: I taught a section in descriptive geometry in the regular way. I am confident that there were men in the special section who would have failed had they taken the subject in the regular way. And I am confident that there were men in the regular section who failed because they were in that section. They spent so long getting the elements of