Chapter IX: Part 9

3. Why may we not consider the several "steps" of the inductive lesson as occurring in a definite and mutually exclusive sequence?

4. In what respect is the procedure in a deductive lesson like that which you follow in an inductive lesson?

5. Show how verification is an important element in both inductive and deductive lessons.

6. Give illustrations of successful drill lessons and make clear the reason for the degree of success achieved.

7. What measures have you found most advantageous in securing speed in drill work?

8. What are the elements which make for success in an appreciation lesson?

9. Upon what grounds and to what extent can lecturing be defended as a method of instruction?

10. What may be the relation between a good recitation lesson and the solution of a problem? Growth in power of appreciation?

11. For what purposes should examinations be given? When should examinations be given?

12. When are questions which call for facts justified?

13. Why are questions which call for comparisons to be considered important?

14. Why is it important to phrase questions carefully?

15. Why should a teacher ask some questions which cannot be answered immediately?

16. What criteria would you apply in testing the questions which you put to your class?

17. Write five questions which in your judgment will demand thinking upon some topic which you plan to teach to your class.

* * * * *

XIV. HOW TO STUDY

The term study has been used very loosely by both teachers and children. As used by teachers it frequently meant something very different from what children had in mind when they used it. Further, teachers themselves have often used the term in connection with mental activities which, technically speaking, could not possibly come under that head. Much confusion and lack of efficient work has been the result. Recently various attempts have been made to give the term study a more exact meaning. McMurry defines it as "the work that is necessary in the assimilation of ideas"--"the vigorous application of the mind to a subject for the satisfaction of a felt need." In other words, study is thinking. Psychologically, what makes for good thinking makes for good study. Study is controlled mental activity working towards the realization of a goal. It is the adaptation of means to end, in the attempt to satisfy a felt need. It involves a definite purpose or goal, which is problematic, the selection and rejection of suggestions, tentative judgments, and conclusion. The mind of the one who studies is active, vigorously active, not in an aimless fashion, but along sharply defined lines. This is the essential characteristic of all study.

There are, however, various types of study which differ materially from each other according to the subject matter or to the type of response required. Some study involves comparatively little thinking. The directed activity must be present, but the choice, the judgment, may need to be exercised only in the beginning when methods of procedure need to be selected, and later on, perhaps, when successes or failures need to be noted and changes made in the methods accordingly. Another type of study needs continual thinking of the most active sort all the way through the period. Just the proportion of the various factors involved in thinking which is present at any given study period must be determined by the response. A type of study which would be completely satisfactory for one subject needing one response, would be entirely inadequate for another subject needing another response. To illustrate, in some cases the study must deal with habit formation. The need felt is to learn a mechanical response of a very definite nature to this situation; the problem is to get that response. The thinking would come in in deciding upon the method, in watching for successes, in criticizing progress, and in judging when the end was obtained. A large part of the time spent in study would, however, need to be spent in repetition, in drill. Of such character is study of spelling, of vocabularies, of dates; study in order to gain skill in adding, or speed in reading, or to improve in writing or sewing. Much of habit formation goes on without study--in fact, to some it may seem to be ludicrous to use the word "study" in connection with the formation of habits. It is just because the study elements in connection with responses of this type have been omitted that there has been such a tremendous waste of time in teaching children to form right habits. This omission also explains the poor results, for the process has been mechanical and blind on the part of the student. At the other extreme in types of study is that which can be used in science and mathematics, in geography and history, when the major part of the time is given to selecting and rejecting suggestions and seems required by the goal. In this type the habituation, the fixing of the material, comes largely as a by-product of the factors used in the thinking.

Study may, then, be classified according as the response required is physical habit, memory, appreciation, or judgment. These types overlap, no one of them can exist absolutely alone, but it is possible to name them according to the response. Study may also be classified into supervised study, or unsupervised study, into individual or group study. We might also classify study as it has to do with books, with people, or with materials. The term has been rather arbitrarily applied to activities that dealt with books, but surely much study is accomplished when people are consulted instead of books, and also when the sources of information or the standards are flowers, or rocks, or textiles.

Study, then, is a big term, including many different varieties of activities, of varying degrees of difficulty and responsibility. It cannot possibly be taught all at once, according to one method, at one spot in the school curriculum. Power to study is of very gradual growth. It must proceed slowly, from simple to complex types. From easy to difficult problems, from situations where there is close supervision and direction to situations where the student assumes full responsibility. Knowing how to study is not an inborn gift--it does not come as a matter of intuition, nor does it come in some mysterious way when the child is of high school age. It is governed by the laws of learning, or readiness, exercise, and effect, just as truly as any other ability is. If adults are to know how to study, if they are to use the technique of the various kinds of study efficiently, children must be taught how. Nor can we expect the upper grammar grade or the high school teachers to do this. Habits of study must be formed just as soon as the responses to which it leads are needed. Beginning down in the kindergarten with study in connection with physical and mental habits, the child should be taught how to study. The type must gradually become more complex; he must pass from group to individual study, from supervised to unsupervised, but it must all come logically, from step to step. True, it is not easy to teach how to study. A careful analysis of the various types with their peculiar elements should be a help. First, however, there are some general principles that underlie all study which must be discussed.

Study must have, as has already been stated, a purpose. The individual, in order to exercise his mind in a controlled way, must have an aim. The clearer and more definite the aim, whether it be little or big, the better the study will be. From the beginning, then, children must be taught to make sure they know what they are going to do before beginning to study. It may be necessary to teach them in the early grades to say to themselves or to the class just what they are going to accomplish in the study. Teach them when the lesson is assigned to write down in their books just what the problem for study is. Warn them never to begin study without definitely knowing the aim--if they don't know it, make them realize that the first thing to do is to find out the purpose by asking some one else. Better no study at all than aimless or misdirected activity, because of lack of purpose.

No study worthy of the name can be carried on without interest. The child who studies well must be brought to realize this. The value of interest can be brought home to him by having him compare the work he does, the time he spends, and how he feels when studying something in which he has a vital interest with the results when the topic is uninteresting. Of course, as will be pointed out later, much of the gaining of interest lies in the hands of the teacher necessarily, but if the child realizes the need of it in efficient study, some responsibility will rest on him to find an interest if it is not already there. No matter how expert the teacher may be, because of individual differences no problem will be equally interesting to all pupils in itself, and no incentive will have an equal appeal to all children. Therefore children should be taught to find interest for themselves. Certain devices can be suggested, such as working with another child and competing with him, "making believe" in study, and finding some connection with something in which he is interested, working against his own score, and the like.

Not only do the demands of economy require that the topic of study receive concentrated attention, but the results themselves are better when such is the case. Half an hour of concentrated work gives much better results than an hour of study with scattered attention. An hour spent when half an hour would do is thus not only wasteful of time, but is productive of poorer results and bad habits of study as well. Children need to be taught this from the beginning. Much time is wasted even by mature university students when they suppose themselves to be studying. Children can be taught to ignore distractions--to train themselves to keep their eyes on the book, despite the fact that the door is opened, or a seat mate is looking for a book. They should be encouraged to set themselves time limits in various subjects and adhere to them. It is economical to follow a regular schedule in study--either in the school or at home. Let each child make out his study schedule and keep to it. Teach children that the best work is done when they are calm and steady. That either excitement or worry is a hindrance. Therefore they should avoid doing their studying under those conditions, and should do all they can to remove such conditions. Training children to do their best and then not to worry would not only improve the health of many upper grammar grade and high school children, but would also improve their work.

Study requires a certain critical attitude, a checking up of results against the problem set. In order to be efficient in study a child should know when he has reached the solution, when the means have been adapted to the end, when he has reached the goal. This checking up, of course, means habits of self-criticism and standards. Sometimes all that is necessary is for the child to be made conscious of this fact so that he can test himself, for instance, in memory work, or in solving a problem in mathematics. On the other hand, sometimes he will have to compare his work with definite standards, such as the Thorndike Handwriting Scale, or the Hillegas Composition Scale.[19] In other instances, he will have to search for standards. He will need to know what his classmates have accomplished, what other people think, what other text-books say, and so on. Gradually he must be made conscious that study is a controlled activity, and unless it reaches the goal, and the correct one, it is useless. He must be made to feel that the responsibility to see that such results are reached rests on him.

These, then, are the general factors involved in all types of study, and therefore are fundamental to good habits of study: a clear purpose; vital interest of some kind; concentrated attention, and a critical attitude. There are further additional suggestions which are peculiar to the special type of study.

In study which is directed to habit formation, the student should be taught the danger of allowing exceptions. He should know the possibility of undoing much good work through a little carelessness. Preaching won't bring this home to him--it must come through having his attention attracted to such an occurrence in his own work or in that of his mates. After that knowledge of the actual experiences of others, athletes, musicians, and others will help to intensify the impression. The value of repetition as one of the chief factors in habit formation must be emphasized. The child should be encouraged to make opportunities for practice both in free minutes during the school program, and outside of school. He must be taught in habit formation to practice the new habit in the way it is to be used: practicing the sounds of letters in words, the writing movements in writing words, swimming movements in the water, and so on. Practicing the whole movements, not trying to gain perfection in parts of it and then putting it together. It is important also that the learner be taught to keep his attention on the result to be obtained, instead of the movements. He should attend to the swing of the club, the lightness of the song, the cut the saw is making, the words he is writing, instead of the muscle movements involved. In breaking up bad habits it is sometimes necessary to concentrate on a part or a movement, when that is the crux of the error, but in general it is a bad practice when forming a new habit. The child must also learn to watch the habit of skill he is forming for signs of improvement and then to try to find out the reason for it. It has been proved experimentally that much of the improvement in habits of skill comes unconsciously to the learner, and necessarily so, but that in order for the improvement to continue and be effective, it must become conscious. Of course, at the beginning and for a long time it must be the teacher's duty to point out the improvement and to help the child to think out the reasons for it, but if he is to learn to study by himself the child must finally come to habits of self-criticism which will enable him to recognize success or failure in his own work. In all this discussion of teaching children to study it must be constantly borne in mind that it is a gradual process--and only very slowly does the child become conscious of the technique. Which elements can be made conscious, how much he can be left to himself, must depend on his maturity and previous training. In time, however, he should be able to apply them all--for only by so doing will he become capable of independent study.

When the study is primarily concerned with memory responses, all the elements which have just been discussed in connection with habit apply, for, after all, memory is but mental habit. There are other factors which enter into and which should be used in this type of study. First, the child should realize the need for understanding the material that is to be learned, before beginning to memorize it. He will then be taught to read the entire assignment through--look up difficult words and references, master the content, whether prose or poetry, whether the learning is to be verbatim or not, before doing anything further. Second, he will need to know the value of the modified whole method of learning, as well as its difficulties. If in the supervised periods of study and in class work, this method has been followed, it is very easy to make him conscious of it and willing to adopt it when he comes to do independent study. Third, he must be taught to distribute his time so that he does not devote too long a stretch to one subject. The value of going over work in the morning, after having studied the night or two nights before, should be emphasized. Also the value of beginning on assignments some time ahead, even if there is not time to finish them. Fourth, the child should be taught not to stop his work the minute he can give it perfectly. The need for overlearning, for permanent retention, must be made clear. How much overlearning is necessary, each child should find out for himself. Fifth, the value of outlining material as a means of aiding memory must be stressed. Sixth, the child should be taught to search for associations, connections of all types, in order to help himself remember facts. He might even be encouraged to make up some mnemonic device as an aid if these measures fail. If instead of simply trying to hammer material in by mere repetition children had been taught in their study to consciously make use of the other elements in a good memory, much time would be saved. But the responsibility should rest finally on the child to make use of these helps. The teacher must make him conscious of them, sometimes from their value by experiment, and then teach him to use them himself.

Much less can be done as a matter of conscious technique when the occasion of study is to further appreciation. A few suggestions might be offered. First, the child should be taught the value of associating with those who do appreciate in the line in which he is striving for improvement. He should be encouraged to consciously associate with them when opportunities for appreciation come. Second, he should know the need for coming in contact with the objects of appreciation if true feeling is to be developed. It is only by mingling with people, reading books, listening to music, that appreciation in those fields can be developed. Third, the value of concrete imagery and of connections with personal experience in arousing emotional tone should be emphasized. The child might be encouraged to consciously call up images and make connections with his own experience during study.

Study, when the object is to arrive at responses of judgment, is the type which has received most attention. This type of study includes within itself several possibilities. Although judgment is the only response that can solve the problem, still the problem may be one of giving the best expression in art or music or drama. It may be the analysis of a course of action or of a chemical compound. It may be the comparison of various opinions. It may be the arriving at a new law or principle. It is to one of these types of thinking that the term "study" is usually applied. Important as it is, the other three types already discussed cannot be neglected. If children are taught to study in connection with the simpler situations provided by the first two types, they will be the better prepared to deal with this complex type, for this highest type of study involves habit formation often and memory work always.

In the type of study involving reasoning, because of its complexity, and because the individual must work more independently, the child must learn the danger of following the first suggestion which offers itself. He must learn to weigh each suggestion offered with reference to the goal aimed at. Each step in the process must be tested and weighed in this manner. To go blindly ahead, following out a line of suggestions until the end is reached, which is then found to be the wrong one, wastes much time and is extremely discouraging. No suggestion of the way to adapt means to end should be accepted without careful criticism. The pupil should gradually be made conscious of the technique of reasoning, analysis, comparison, and abstraction. He must know that the first thing to do is to analyze the problem and see just what it requires. He must know that the abstraction depends upon the goal. The learner should be taught the sources of some of the commonest mistakes in judgment. For instance, if he knows of the tendency to respond in terms of analogy, and sees some of the errors to which accepting a minor likeness between two situations as identity lead, he will be much more apt to avoid such mistakes than would otherwise be true. If he knows how unsafe it is to form a judgment on limited data,--if from his own and his classmates' thinking first, and later from the history of science, illustrations are drawn of the disastrous effect of such thinking, he will see the value of seeking sources of information and several points of view before forming his own judgment. In his study the child should be taught not to be satisfied until he has tested the correctness of his judgment by verifying the result. This is a very necessary part of studying. He should check up his own thinking by finding out through appeal to facts if it is so; by putting the judgment into execution; by consulting the opinion of others, and so on.

Study may be considered from the point of view of the type of material which is used in the process. The student may be engaged on a problem which involves the use of apparatus or specimens of various kinds, or he may need to consult people, or he may have to use books. So far as the first type is concerned, it is obviously unwise to have a student at work on a problem which involves the use of material, unless the technique of method of use is well known. Until he can handle the material with some degree of facility it is waste of time for him to be struggling with problems which necessitate such use. Such practice results in divided attention, poor results from the study, and often bad habits in technique as well. Gaining the technique must be in itself a problem for separate study.

Children should be taught to ask questions which bear directly on the point they wish to know. If they in working out some problem are dependent on getting some information from the janitor, or the postman, or a mason, they must be able to ask questions which will bring them what they want to know. Much practice in framing questions, having them criticized, having them answered just as they are asked, is necessary. Children should be aware of the question as a tool in their study and therefore they must know how to handle it. In connection with this second type of material, the problem of the best source of information will arise. Children must then be made conscious of the relative values of various persons as sources of a particular piece of information. Training in choice of the source of information is very important both when that source is people and also when it is books.

Teaching children to use books in their study is one of the big tasks of the teacher. They must learn that books are written in answer to questions. In order to thoroughly understand a book, students must seek to frame the questions which it answers. They must also know how to use books to answer their own questions. This means they must know how to turn from part to part, gleaning here or there what they need. It means training in the ability to skim, omitting unessentials and picking out essentials. It means the ability to recognize major points, minor points, and illustrative material. Children must be taught to use the table of contents, the index, and paragraph headings. They must, in their search for fuller information or criticism, be able to interpret different authors, use different language, and attack from different angles, even when treating the same object. Children must in their studying be taught to use books as a means to an end--not an infallible means, but one which needs continual criticism, modification, and amplification.

Study may be supervised study, or unsupervised study. To some people the requirements in learning to study may seem too difficult to be possible, but it should be remembered that the process is gradual--that one by one these elements in study are taught to the children in their supervised study periods. These periods should begin in the primary grades, and require from the teacher quite as much preparation as any other period. Many teachers have taught subjects, but not how to study subjects. The latter is the more important. The matter of distributed learning periods, of search for motive, of asking questions, of criticizing achievement, of use of books; each element is a topic for class discussion before it is accepted as an element in study. Even after it is accepted, it may be raised by some child as a source of particular difficulty and fresh suggestions added. Very often with little children it is necessary for the teacher to study the lesson with them. Teachers need much more practice in doing this, for one of the best ways to teach a child to study is to study with him. Not to tell him, and do the work for him, but to really study with him. Later on the supervised study period is one in which each child is silently engaged upon his own work and the teacher passes from one to the other. In order to do this well, the teacher needs to be able to do two things. First, to find out when the child is in difficulty and to locate it, and second, to help him over the trouble without giving too much assistance. Adequate questioning is needed in both cases. It is probably true that comparatively little new work should be given for unsupervised study. There is too much danger of error as well as lack of interest unless a start is given under supervision.

Studying, especially unsupervised, may be done in groups or individually. The former is a stepping-stone to the latter. There is a greater chance for suggestions, for getting the problem worded, for arousing interest and checking results, when a group of children are working together than when a child is by himself. Two things must be looked after. First, that the children in the group be taught not to waste time, and second, that the personnel of the group be right. It is not very helpful if one child does all the work, nor if one is so far below the level of the group that he is always tagging along behind. More opportunities for group study in the grammar grades would be advantageous.

When it comes to individual study, the student then assumes all responsibility for his methods of study. He should be taught the influence of physical conditions or mental reactions. He will therefore be responsible for choosing in the home and in the school the best possible conditions for his study. He will see to it that, in so far as possible, the air and light are good, that there are no unnecessary distractions, and that he is as comfortable bodily as can be. He must think not only in terms of the goal to be reached, but also with respect to the methods to be employed. He should be asked by the teacher to report his methods of work as well as his results.

QUESTIONS

1. Are children always primarily engaged in thinking when they study?

2. What type of study is involved in learning a multiplication table, a list of words in spelling, a conjugation in French?

3. How would you teach a pupil to study his spelling lesson?

4. In what sense may one study in learning to write? In acquiring skill in swimming?

5. How would you teach your pupils to memorize?

6. Show how ability to study may be developed over a period of years in some subject with which you are familiar. Reading? Geography? History? Latin translation?

7. Is the boy who reads over and over again his lesson necessarily studying?

8. Can one study a subject even though he may dislike it? Can one study without interest?

9. How can you teach children what is meant by concentration of attention?

10. How have you found it possible to develop a critical attitude toward their work upon the part of children?

11. Of what factors in habit formation must children become conscious, if they are to study to best advantage in this field?

12. How may we hope to have children learn to study in the fields requiring judgment? Why will not consciousness of the technique of study make pupils equally able in studying?

13. What exercises can you conduct which will help children to learn how to use books?

14. How can a teacher study with a pupil and yet help him to develop independence in this field?

15. How may small groups of children work together advantageously in studying?

* * * * *

XV. MEASURING THE ACHIEVEMENTS OF CHILDREN

The success or failure of the teacher in applying the principles which have been discussed in the preceding chapters is measured by the achievements of the children. Of course, it is also possible that the validity of the principle which we have sought to establish may be called in question by the same sort of measurement. We cannot be sure that our methods of work are sound, or that we are making the best use of the time during which we work with children, except as we discover the results of our instruction. Teaching is after all the adaptation of our methods to the normal development of boys and girls, and their education can be measured only in terms of the changes which we are able to bring about in knowledge, skill, appreciation, reasoning, and the like.

Any attempt to measure the achievements of children should result in a discovery of the progress which is being made from week to week, or month to month, or year to year. It would often be found quite advantageous to note the deficiencies as well as the achievements at one period as compared with the work done two or three months later. It will always be profitable to get as clearly in mind as is possible the variation among members of the same class, and for those who are interested in the supervision of schools, the variation from class to class, from school to school, or from school system to school system. For the teacher a study of the variability in achievement among the members of his own class ought to result in special attention to those who need special help, especially a kind of teaching which will remove particular difficulties. There should also be offered unusual opportunity and more than the ordinary demand be made of those who show themselves to be more capable than the ordinary pupils.

The type of measurement which we wish to discuss is something more than the ordinary examination. The difficulties with examinations, as we have commonly organized them, has* been their unreliability, either from the standpoint of discovering to us the deficiencies of children, or their achievements. Of ten problems in arithmetic or of twenty words in spelling given in the ordinary examination, there are very great differences in difficulty. We do not have an adequate measure of the achievements of children when we assign to each of the problems or words a value of ten or of five per cent and proceed to determine the mark to be given on the examination paper. If we are wise in setting our examinations, we usually give one problem or one word which we expect practically everybody to be able to get right. On the other hand, if we really measure the achievements of children, we must give some problems or some words that are too hard for any one to get right. Otherwise, we do not know the limit or extent of ability possessed by the abler pupils. It is safe to say that in many examinations one question may actually be four or five times as hard as some other to which an equal value is assigned.

Another difficulty that we have to meet in the ordinary examination is the variability among teachers in marking papers. We do not commonly assign the same values to the same result. Indeed, if a set of papers is given to a group of capable teachers and marked as conscientiously as may be by each of them, it is not uncommon to find a variation among the marks assigned to the same paper which may be as great as twenty-five per cent of the highest mark given. Even more interesting is the fact that upon re-marking these same papers individual teachers will vary from their own first mark by almost as great an amount.

Still another difficulty with the ordinary examination is the tendency among teachers to derive their standards of achievement from the group itself, rather than from any objective standard by which all are measured. It is possible, for example, for children in English composition to write very poorly for their grade and still to find the teacher giving relatively high marks to those who happen to belong to the upper group in the class. As a result of the establishment of such a standard, the teacher may not be conscious of the fact that children should be spurred to greater effort, and that possibly he himself should seek to improve his methods of work.

Out of the situation described above, which includes on the one hand the necessity for measurement as a means of testing the success of our theories and of our practice, and on the other hand of having objective standards, has grown the movement for measurement by means of standard tests and scales. A standard test which has been given to some thousands of children classified by grades or by ages, if given to another group of children of the same grade or age group will enable the teacher to compare the achievement of his children with that which is found elsewhere. For example, the Courtis tests in arithmetic, which consist of series of problems of equal difficulty in addition, subtraction, multiplication, and division may be used to discover how far facility in these fields has been accomplished by children of any particular group as compared with the achievements of children in other school systems throughout the country. In these tests each of the problems is of equal difficulty. The measure is made by discovering how many of these separate problems can be solved in a given number of minutes.[20]

A scale for measuring the achievements of children in the fundamental operations of addition, subtraction, multiplication, and division has been derived by Dr. Clifford Woody,[21] which differs from the Courtis tests in that it affords opportunity to discover what children can achieve from the simplest problem in each of these fields to a problem which is in each case approximately twice as difficult as the problems appearing on the Courtis tests. The great value of this type of test is in discovering to teachers and to pupils, as well, their particular difficulties. A pupil must be able to do fairly acceptable work in addition before he can solve one problem on the Courtis tests. Considerable facility can be measured on the Woody tests before an ability sufficient to be registered on the Courtis tests has been acquired. In his monograph on the derivation of these tests Mr. Woody gives results which will enable the teacher to compare his class with children already tested in other school systems. In the case of all of these standard tests, school surveys and superintendents' reports are available which will make it possible to institute comparisons among different classes and different school systems. One form of the Woody tests is as follows:

* * * * *

SERIES A
ADDITION SCALE
BY CLIFFORD WOODY

Name......................
When is your next birthday?...... How old will you be?.....
Are you a boy or girl?....... In what grade are you?......

(1) (3) (5) (7) (9) (10) (11) (12) (13) (15) (16)
2 17 72 3+1= 20 21 32 43 23 100 9
3 2 26 10 33 59 1 25 33 24
-- -- -- 2 35 17 2 16 45 12
30 -- -- 13 -- 201 15
(2) (4) (6) (8) 25 -- 46 19
2 53 60 2+5+1= -- --- --
4 45 37 (14)
3 -- -- 25+42=
--

(17) (19) (21) (22) (23) (26) (29)
199 $ .75 $8.00 547 1/3+1/3= 121/2 4 3/4
194 1.25 5.75 197 621/2 2 1/4
295 .49 2.33 685 (24) 121/2 5 1/4
156 ----- 4.16 678 4.0125 371/2 -----
--- .94 456 1.5907 ---
6.32 393 4.10 (30)
(18) (20) ----- 525 8.673 (27) 2 1/2
2563 $12.50 240 ------ 1/8+1/4+1/2= 6 3/8
1387 16.75 152 3 3/4
4954 15.75 --- -----
2065 ------ (25) (28)
---- 3/8+5/8+7/8+1/8= 3/4+1/4=

(31) (33) (34) (35) (36) (37)
113.46 .49 1/6+3/8= 2ft. 6in. 2yr. 5mo. 16 1/3
49.6097 .28 3ft. 5in. 3yr. 6mo. 12 1/8
19.9 .63 4ft. 9in. 4yr. 9mo. 21 1/2
9.87 .95 --------- 5yr. 2mo. 32 3/4
.0086 1.69 6yr. 7mo. ------
18.253 .22 ---------
6.04 .33
-------- .36 (38)
1.01 25.091+100.4+25+98.28+19.3614=
(32) .56
3/4+1/2+1/4= .88
.75
.56
1.10
.18
.56
----

* * * * *

SERIES A
SUBTRACTION SCALE
BY CLIFFORD WOODY

Name......................
When is your next birthday?......How old will you be?.....
Are you a boy or girl?.......In what grade are you?.......

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11)
8 6 2 9 4 11 13 59 78 7-4= 76
5 0 1 3 4 7 8 12 37 60
-- -- -- -- -- -- -- -- -- --

(12) (13) (14) (15) (16) (17) (18) (19) (20)
27 16 50 21 270 393 1000 567482 2 3/4-1=
3 9 25 9 190 178 537 106493
-- -- -- -- --- --- ---- ------

(21) (22) (23) (24) (25) (26)
10.00 3 1/2-1/2= 80836465 8 7/8 27 4yd. 1ft. 6in.
3.49 49178036 5 3/4 12 5/8 2yd. 2ft. 3in.
----- -------- ----- ------ --------------

(27) (28) (29) (30)
5yd. 1ft. 4in. 10-6.25 75 3/4 9.8063-9.019=
2yd. 2ft. 8in. 52 1/4
-------------- ------

(31) (32) (33) (34) (35)
7.3-3.00081= 1912 6mo. 8da. 5/12-2/10= 6 1/8 3 7/8-1 5/8=
1910 7mo. 15da. 2 7/8
--------------- -----

* * * * *

SERIES A
DIVISION SCALE
BY CLIFFORD WOODY

Name...............................
When is your next birthday?....... How old will you be?......
Are you a boy or girl?.......... In what grade are you?......

(1) (2) (3) (4) (5) (6)
__ ___ ___ __ ___ ___
3)6 9)27 4)28 1)5 9)36 3)39

(7) (8) (9) (10) (11) (12)
4 ÷ 2 = __ __ 6 × __ = 30 ___ 2 ÷ 2 =
9)0 1)1 2)13

(13) (14) (15) (16) (17)
______________ _____ 1/4 of 128= _____ 50 ÷ 7 =
4)24 lbs. 8 oz. 8)5856 68)2108

(18) (19) (20) (21) (22)
______ 248 ÷ 7 = _____ _____ ______
13)65065 2.1)25.2 25)9750 2)13.50

(23) (24) (25) (26)
____ ________ _______ _____
23)469 75)2250300 2400)504000 12)2.76

(27) (28) (29) (30)
7/8 of 624 = ______ 3 1/2 ÷ 9 = 3/4 ÷ 5 =
.003).0936

(31) (32) (33)
5/4 ÷ 3/5 = 9 5/8 ÷ 3 3/4 = _____
52)3756

(34) (35) (36)
62.50 ÷ 1 1/4 = ______ ______________
531)37722 9)69 lbs. 9 oz.

* * * * *

SERIES A
MULTIPLICATION SCALE
BY CLIFFORD WOODY

Name......................
When is your next birthday?...... How old will you be?.....
Are you a boy or girl?....... In what grade are you?.......

(1) (2) (3) (4) (5) (6) (7)
3 × 7 = 5 × 1 = 2 × 3 = 4 × 8 = 23 310 7 × 9 =
3 4
-- ---
(8) (9) (10) (11) (12) (13) (14) (15)
50 254 623 1036 5096 8754 165 235
3 6 7 8 6 8 40 23
-- --- --- ---- ---- ---- --- ---

(16) (17) (18) (19) (20) (21) (22)
7898 145 24 9.6 287 24 8 × 53/4
9 206 234 4 .05 21/2
---- --- --- --- --- --

(23) (24) (25) (26) (27) (28) (29)
11/4 × 8 = 16 7/8 × 3/4 = 9742 6.25 .0123 1/8 × 2 =
2 5/8 59 3.2 9.8
------ ---- ---- -----
(30) (31) (32) (33) (34)
2.49 12 15 6 dollars 49 cents 2-1/2 × 3-1/2 = 1/2 × 1/2 =
36 -- × -- 8
---- 25 32 ------------------

(35) (36) (37) (38) (39)
9873/4 3ft. 5in. 21/4 × 41/2 × 11/2 = .0963 1/8 8ft. 91/2in.
25 5 .084 9
---- --------- --------- ----------

* * * * *

A series of problems in reasoning in arithmetic which were given in twenty-six school systems by Dr. C.W. Stone furnish a valuable test in this field, as well as an opportunity for comparison with other schools in which these problems have been used.[22] A list of problems follows.

Solve as many of the following problems as you have time for;
work them in order as numbered:

1. If you buy 2 tablets at 7 cents each and a book for 65
cents, how much change should you receive from a two-dollar
bill?

2. John sold 4 Saturday Evening Posts at 5 cents each. He kept
1/2 the money and with the other 1/2 he bought Sunday papers
at 2 cents each. How many did he buy?

3. If James had 4 times as much money as George, he would have
$16. How much money has George?

4. How many pencils can you buy for 50 cents at the rate of 2
for 5 cents?

5. The uniforms for a baseball nine cost $2.50 each. The shoes
cost $2 a pair. What was the total cost of uniforms and shoes
for the nine?

6. In the schools of a certain city there are 2200 pupils; 1/2
are in the primary grades, 1/4 in the grammar grades, 1/8 in
the High School, and the rest in the night school. How many
pupils are there in the night school?

7. If 3-1/2 tons of coal cost $21, what will 5-1/2 tons cost?

8. A news dealer bought some magazines for $1. He sold them
for $1.20, gaining 5 cents on each magazine. How many
magazines were there?

9. A girl spent 1/8 of her money for car fare, and three times
as much for clothes. Half of what she had left was 80 cents.
How much money did she have at first?

10. Two girls receive $2.10 for making buttonholes. One makes
42, the other 28. How shall they divide the money?

11. Mr. Brown paid one third of the cost of a building; Mr.
Johnson paid 1/2 the cost. Mr. Johnson received $500 more
annual rent than Mr. Brown. How much did each receive?

12. A freight train left Albany for New York at 6 o'clock. An
express left on the same track at 8 o'clock. It went at the
rate of 40 miles an hour. At what time of day will it overtake
the freight train if the freight train stops after it has gone
56 miles?

A different type of measurement is accomplished by using Thorndike's scale for measuring the quality of handwriting.[23] A typical distribution of the scores which children receive on the handwriting scale reads as follows: For a fourth grade one child writes quality four, two quality six, five quality seven, seven quality eight, eight quality nine, three quality ten, two quality eleven, two quality twelve, one quality thirteen, one quality fourteen. In a table the distributions of scores in penmanship for a large number of papers selected at random show the following results:

============================================================
| GRADES
SCORES +------+------+------+------+------+------+-----
| 2 | 3 | 4 | 5 | 6 | 7 | 8
------------+-------------+------+------+------+------+-----
0 | -- | -- | -- | -- | -- | -- | --
1 | -- | -- | -- | -- | -- | -- | --
2 | -- | -- | -- | -- | -- | -- | --
3 | -- | -- | -- | -- | -- | -- | --
4 | 5 | 2 | -- | -- | -- | -- | --
5 | 22 | 2 | 3 | 3 | -- | 1 | --
6 | 21 | 21 | 16 | 3 | 2 | -- | 1
7 | 29 | 44 | 24 | 12 | 1 | 3 | 3
8 | 28 | 86 | 42 | 56 | 20 | 15 | 7
9 | 42 | 41 | 55 | 61 | 25 | 29 | 11
10 | 7 | 8 | 20 | 16 | 9 | 11 | 1
11 | 29 | 13 | 21 | 17 | 32 | 25 | 23
12 | 5 | 2 | 15 | 15 | 44 | 12 | 21
13 | 7 | 2 | 2 | 6 | 17 | 19 | 9
14 | -- | -- | 3 | 4 | 10 | 16 | 9
15 | -- | -- | 1 | -- | 9 | 6 | 15
16 | 1 | -- | -- | 1 | 10 | 12 | 17
17 | -- | -- | -- | -- | 6 | 2 | 3
18 | -- | -- | -- | -- | 3 | 1 | --
------------+------+------+------+------+------+------+-----
Total papers| 196 | 221 | 202 | 194 | 188 | 152 | 124
============================================================

* * * * *

A SCALE FOR HANDWRITING OF CHILDREN IN GRADES 5-8

The Unit of the Scale Equals approximately One-Tenth of the Difference between the Best and Worst of the Formal Writings of 1,000 Children in Grades 5-8. The Differences 16-15, 15-14, 14-13, etc., represent Equal Fractions of the Combined Mental Scale of Merit of from 23-55 Competent Judges.

Sample 140, representing zero merit in handwriting. Zero merit is arbitrarily defined as that of a handwriting, recognizable as such, but yet not legible at all and possessed of no beauty.

Quality 4.

Quality 5.

Quality 6.

Quality 7.

Quality 8.

Quality 9.

Quality 10.

Quality 11.

Quality 12.

Quality 13.

Quality 14.

Quality 15.

Quality 16.

Quality 17.

Quality 18.

* * * * *

This table reads as follows: Quality four was written by five children in the second grade and two in the third grade, quality five was written by twenty-two children in the second grade, two children in the third grade, three in the fourth grade, three in the fifth grade, none in the sixth grade, one in the seventh grade, and none in the eighth grade, and so on for the whole table.[24]

A scale for measuring ability in spelling prepared by Dr. Leonard P. Ayres arranges the thousand words most commonly used in the order of their difficulty. From this sheet it is possible to discover words of approximately the same difficulty for each grade. A test could therefore be derived from this scale for each of the grades with the expectation that they would all do about equally well. There would also be the possibility of determining how well the spelling was done in the particular school system in which these words were given as compared with the ability of children as measured by an aggregate of more than a million spellings by seventy thousand children in eighty-four cities throughout the United States. Such a list could be taken from the scale for the second grade, which includes words which have proved to be of a difficulty represented by a seventy-three percent correct spelling for the class. Such a list might be composed of the following words: north, white, spent, block, river, winter, Sunday, letter, thank, and best. A similar list could be taken from the scale for a third, fourth, fifth, sixth, seventh, or eighth grade. For example, the words which have approximately the same difficulty,--seventy-three percent to be spelled correctly by the class for the sixth grade,--read as follows: often, stopped, motion, theater, improvement, century, total, mansion, arrive, supply. The great value of such a measuring scale, including as it does the thousand words most commonly used, is to be found not only in the opportunity for comparing the achievements of children in one class or school with another, but also in the focusing of the attention of teachers and pupils upon the words most commonly used.[25]

One of the fields in which there is greatest need for measurement is English composition. Teachers have too often thought of English composition as consisting of spelling, punctuation, capitalization, and the like, and have ignored the quality of the composition itself in their attention to these formal elements. A scale for measuring English composition derived by Dr. M.B. Hillegas,[26] consisting of sample compositions of values ranging from 0 to 9.37, will enable the teacher to tell just how many pupils in the class are writing each different quality of composition. The use of such a scale will tend to make both teacher and pupil critical of the work which is being done not only with respect to the formal elements, but also with respect to the style or adequacy of the expression of the ideas which the writer seeks to convey. Probably in no other field has the teacher been so apt to derive his standard from the performance of the class as in work in composition. Even though some teachers find it difficult to evaluate the work of their pupils in terms of the sample compositions given on the scale, much good must come, it seems to the writer, from the attempt to grade compositions by such an objective scale. If such measurements are made two or three times during the year, the performance of individual pupils and of the class will be indicated much more certainly than is the case when teachers feel that they are getting along well without any definite assurance of the amount of their improvement.

In one large school system in which the writer was permitted to have the principals measure compositions collected from the sixth and the eighth grades, it was discovered that almost no progress in the quality of composition had been accomplished during these two years. This lack of achievement upon the part of children was not, in the opinion of the writer, due to any lack of conscientious work upon the part of teachers, but, rather, developed out of a situation in which the whole of composition was thought of in terms of the formal elements mentioned above. The Hillegas scale, together with the values assigned to each of the samples, is given below.

A SCALE FOR THE MEASUREMENT OF THE QUALITY OF ENGLISH
COMPOSITION

BY MILO B. HILLEGAS

VALUE 0. Artificial sample

_Letter_

Dear Sir: I write to say that it aint a square deal Schools is
I say they is I went to a school. red and gree green and brown
aint it hito bit I say he don't know his business not today
nor yeaterday and you know it and I want Jennie to get me out.

VALUE 183. Artificial sample

_My Favorite Book_

the book I refer to read is Ichabod Crane, it is an grate book
and I like to rede it. Ichabod Crame was a man and a man wrote
a book and it is called Ichabod Crane i like it because the
man called it ichabod crane when I read it for it is such a
great book.

VALUE 260. Artificial sample

_The Advantage of Tyranny_

Advantage evils are things of tyranny and there are many
advantage evils. One thing is that when they opress the people
they suffer awful I think it is a terrible thing when they say
that you can be hanged down or trodden down without mercy and
the tyranny does what they want there was tyrans in the
revolutionary war and so they throwed off the yok.

VALUE 369. Written by a boy in the second year of the high
school, aged 14 years

_Sulla as a Tyrant_

When Sulla came back from his conquest Marius had put himself
consul so sulla with the army he had with him in his conquest
siezed the government from Marius and put himself in consul
and had a list of his enemys printy and the men whoes names
were on this list we beheaded.

VALUE 474. Written by a girl in the third year of the high
school, aged 17 years

_De Quincy_

First: De Quincys mother was a beautiful women and through her
De Quincy inhereted much of his genius.

His running away from school enfluenced him much as he roamed
through the woods, valleys and his mind became very
meditative.

The greatest enfluence of De Quincy's life was the opium
habit. If it was not for this habit it is doubtful whether we
would now be reading his writings.