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cation, but less than a few tenths of 1 percent of that per year, with the object in mind of enabling the pupils to run faster than they ever could run before they had the new learning aids.

The general guidelines of this kind of operation I think can be shown most easily with the aid of a chart that I drafted and sort of use to help keep some of the components clear in my own mind, but which I do not ever fill in.

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Dr. ZACHARIAS. Let me distribute some copies of this, although it is pedagogically very poor to let the class ever fumble with a piece. of paper while you are trying to talk.

Mr. THOMAS. If you will let me interrupt just a moment-Dr. Waterman is our distinguished guest the head of the Committee on the Science Textbooks?

Dr. WATERMAN. He has been head of the Physics Science Committee.

Mr. THOMAS. Didn't we have a fresh volume in here last fall? Dr. WATERMAN. Yes, sir.

Mr. THOMAS. Who was with the Doctor in that work?

Dr. WATERMAN. His associates have been a great many. They have changed over a period of time. I refer to the associates in the work of the Physical Science Study Committee.

Dr. ZACHARIAS. It depends on how restricted a view one is to take. If you are asking the question, "Who was involved in our trying to

change physics for American high schools?" my prime colleague was one man, Prof. Francis L. Friedman of MIT.

And, just in that same enterprise, we had the help of possibly a hundred assorted professors of physics, and a hundred or more assorted high school teachers over the 5-year period. In fact, Professor Purcell here has made two movies for us and has helped clarify our heads on numerous other parts of the subject matter.

Mr. THOMAS. It is great work. I just want to get that straight for the record.

PROJECTS FOR UPGRADING TEACHING

Dr. ZACHARIAS. However, what I should say is this: That there exist now a large number of different projects to upgrade the teaching of science and mathematics on a national scale. There are proj ects in biology, mathematics, chemistry, physics, and other sciences for the secondary school level, and there are several new programs underway to prepare improved instructional materials in science at the elementary school level. In addition, new materials for colleges are being worked out.

Mr. THOMAS. Begin at the high school teacher level. Are the institutes worth the money?

Dr. ZACHARIAS. They certainly are; there is just no question about that. But let me say a word about the items on the first page of my chart first, because I believe the support of high school teacher institutes, unrelated to the upgraded programs, is not the best way for us to spend our money. Let me pick the subject of teachers up in just a moment. If you will look at the chart that I just handed out, you will notice that down the left-hand column are a number of things that I call the learning aids. Ordinarily one thinks only of a textbook. But the first item to consider is subject matter. The subjects must be clear, and must be chosen for sound pedagogic

reasons.

Let me give a simple example of a piece of subject. Suppose somebody should ask you whether children should be taught square root— how to extract the square root of a number. You would say, "I don't see any reason for a child to learn square root."

On the other hand, if you said, "Is it worth while to give the students some good examples of the use of successive approximations?" the answer would be "Yes," because the nature of successive approximations is a mathematical or scientific method that everybody in the world uses in one way or another. You make a first cut. You say I get so far with that. You say, "Let me improve that, and so forth." The phrase "successive approximations," in fact, carries the whole idea. If you teach square root as an example of successive approximations, and if you include other examples of this powerful method, the student has really learned something. So, the subject that you want to include must be determined by a criterion which is other than just some kind of simple manipulative skill. In other words, you have really got to be very thoughtful in picking out subject matter.

If y you will look at the rest of that column where you see textbooks and laboratory-let me tarry a while on laboratory just a moment. Mr. THOMAS. Go ahead. Take your time.

Dr. ZACHARIAS. Many people do not really get to know what a subject is about until they start working with it with their hands. Without actually seeing and feeling devices, you do not know what the materials are or what a scientist really means when he uses his abstract notions. His abstract notions always refer to something that can be explained in very concrete form. There are many students, and for that matter grownups, who will never come to the abstractions without going through the clarification of concrete examples. Now, in addition, when you do have a school laboratory, it must be integrated with all of the other types of learning aids. The teacher must know how to exploit the tremendous power of learning through the hand.

Let me go to the next one: Films. In my opinion, educational movies are extremely difficult to produce. The movie, and especially the educational movie, must be regarded as a new art form, and cannot be properly made without a great deal of work. And, further, there is frequently a temptation to say, "Can't you replace a teacher by a film?" The answer always is "No." The film can set tone and set questions, and goad both students and teachers to heights that they would not otherwise reach, and make the whole educational process happen faster so that they can cover more material in less time.

EXAMINING AND TESTING

Let me go further-beyond demonstrations, displays, and examinations and tests. One ordinarily thinks of examinations and tests as something introduced to make the students' lives difficult, to make the teachers' lives a bore, and to evaluate children. Actually, an examination is a very important part of the learning process. You do not know what you are doing. You do not know how you have succeeded or what kind of thing you have succeeded in learning until you have set up first-class testing and examining procedures.

The whole Nation, in fact, I think the whole world is very backward in the whole business of examining and testing. If you turn to the next page-I won't read down the list-you will see television, programed aids, foreign adaptations, collateral reading, et cetera. You will notice I skipped over teacher training.

Mr. THOMAS. What about the examinations and tests? Give us a little rundown on that.

Dr. ZACHARIAS. What you would like to be able to do is to decide what you want to test and what you would like to test is not just somebody's memorization or rote learning. What you are trying to do with education is to give people tools with which to function later-to make people flexible enough so that they can adapt their skill and knowledge to do the kind of work that they want to do whenever they want to do it. Memorization is simply a part of the education process, but if examinations can be passed chiefly by memorizing, we will be failing to foster one of the major goals of education.

We are just beginning to learn how to test what the psychologists call travel in learning; we teach a student certain things. We teach him to know why he believes what he believes. We teach him with laboratory, films, et cetera, and then we ask him a question on a different subject-one in which he has not been specifically trained but one

that he can handle if he has learned his lesson, not just his lessons. He can handle new ideas just by the experience, the practice, the depth. the penetration of his original work.

Let me give an example. In our physics course we teach about light and we teach about waves, but we do not teach sound or acoustics. Now sound is carried by waves in the air so on the examinations we ask questions about sound which can be handled by any student if he has really understood what you were talking about when you were teaching light. On the other hand, if you give him a simple question about light, neither you nor her can tell whether he has merely memorized it or whether he has learned the subject in depth.

Mr. THOMAS. Doctor, may I interrupt you just a minute? The Federal Government on an annual basis holds or conducts, whatever term you want to use, through its various agencies and bureaus, in round numbers about 300,000 examinations a year. Have you had occasion to look into the course content of those examinations as to the value of them as a yardstick? Do they have the ability to measure a man or woman for a particular job to be performed?

Mr. OSTERTAG. You are referring to civil service examinations? Mr. THOMAS. Yes, sir.

Dr. ZACHARIAS. Off the record.

(Discussion off the record.)

Dr. ZACHARIAS. The truth is, I am sure that the Science Foundation in fact should be putting much more effort into all sorts of things associated with testing. I did not come here to try to advocate certain pieces of improvement in their program. I was just trying to lay out the general approach.

Mr. THOMAS. The science program has nothing to do with this. This is another agency of Government known as the Civil Service Commission.

Dr. ZACHARIAS. No. I think the Science Foundation-I beg your pardon-must learn to advance the art of examining and testing in its own right and for whatever purposes the Government or the educational system may want.

TEACHER INSTITUTES

Let me go back to your earlier question about the summer institutes. The question arises how many teachers are involved in these programs or should be. One of the smallest groups involved in these programs is the group teaching high school physics. There are only 12,000 teachers, total, in high school physics in this country. Biology has more by a factor of about four and high school mathematics has more by a factor of half a dozen.

The total number of teachers that one has to reach with new science and mathematics programs is some substantial fraction of a million teachers.

Teaching a few hundred thousand people is not easy nor cheap. When the summer institute program was initiated you very wisely distributed it over a large number of subjects, but in my view you have not let it grow fast enough nor have the summer institutes been specific enough on programs that have already been upgraded. A 6- or 8-week summer session can be extraordinarily valuable in helping a teacher to learn how to teach a specific course. Naturally, I

believe that the specific courses they should learn are the ones that are being upgraded. On the other hand, 8 weeks is not long enough o change the fundamental training of a teacher so that he can go head on his own. In short, I believe that the summer institute program should be expanded, but also the course curriculum content programs that make the summer institutes pay off.

Upgrading educational programs is a never-ending process. Peoɔle ask me, When are you going to finish this high school physics program? I say it will never finish. It will die if it finishes-and then his decade's new programs will be next decade's dead programs, unless we can keep them revised almost continuously.

Mr. THOMAS. You won't get any disagreement out of this committee, I am pretty sure on this. Go ahead.

Dr. ZACHARIAS. My feeling is that we must gradually increase the number of teacher institute programs to involve almost all of the eachers who are in science and mathematics programs. We must eventually increase the number of places available so that a hundred thousand teachers can take summer and inservice institutes. But the institutes must bear directly on the courses that the teachers will be teaching.

We must consider whether the bottleneck in running summer institutes is the availability of teachers to teach teachers, or whether it is the availability of finance. In my view, with the new upgraded science and mathematics program, what is holding us back is adequate financing of summer institutes, and adequate financing for preparation of course content materials for these institutes. For example, in our physics program, we are now up to about 20 percent of the students taking physics in this country.

Mr. THOMAS. I did not know it was that high.

Dr. ZACHARIAS. It is up to 20 percent. There are 2,000 teachers teaching it. There are now enough people who can teach teachers who have never taught it, so that the only thing that really limits the spread of any one of these upgraded programs in my view will eventually be money for teacher training.

That does not mean that the only important thing is teacher training, because the teacher must be provided with a whole kit of tools. This whole kit of tools must have gone through all of the indicated stages of planning, pilot production and feedback for correction leading to large-scale production with continuing feedback-and with adequate attention to the interrelations between the various kinds of aids. Only then can the teacher assist the student to go as rapidly as the student can go.

Maybe I ought to finish by saying one more thing: The American Association for the Advancement of Science has devoted a recent issue of a publication called Science Education News to a summary of current efforts to upgrade course content materials. It says something about every one of the major new science and mathematics

programs.

It seems to me that rather than try to comment in detail about each one-naturally they are all good, but naturally none is perfect, not even my own-I suggest that this publication be put into the record, or perhaps Dr. Waterman would just like to send copies to the committee.

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