Chapter 22

Chapter 223,303 wordsPublic domain

A scale for measuring English composition in the eighth grade, which takes account of different types of composition, such as narration, description, and the like, has been developed by Dr. Frank W. Ballou, of Boston.[27] For those interested in the following up of the problem of English composition this scale will prove interesting and valuable.

Several scales have been developed for the measurement of the ability of children in reading. Among them may be mentioned the scale derived by Professor Thorndike for measuring the understanding of sentences.[28] This scale calls attention to that element in reading which is possibly the most important of them all, that is, the attempt to get meanings. We are all of us, for the most part, concerned not primarily with giving expression through oral reading, but, rather, in getting ideas from the printed page. A sample of this scale is given on the following page.

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SCALE ALPHA. FOR MEASURING THE UNDERSTANDING OF SENTENCES

Write your name here............................... Write your age.............years............months.

SET _a_

Read this and then write the answers. Read it again as often as you need to.

John had two brothers who were both tall. Their names were Will and Fred. John's sister, who was short, was named Mary. John liked Fred better than either of the others. All of these children except Will had red hair. He had brown hair.

1. Was John's sister tall or short?..................... 2. How many brothers had John?.......................... 3. What was his sister's name?..........................

SET _b_

Read this and then write the answers. Read it again as often as you need to.

Long after the sun had set, Tom was still waiting for Jim and Dick to come. "If they do not come before nine o'clock," he said to himself, "I will go on to Boston alone." At half past eight they came bringing two other boys with them. Tom was very glad to see them and gave each of them one of the apples he had kept. They ate these and he ate one too. Then all went on down the road.

1. When did Jim and Dick come?................................... 2. What did they do after eating the apples?..................... 3. Who else came besides Jim and Dick?........................... 4. How long did Tom say he would wait for them?.................. 5. What happened after the boys ate the apples?..................

SET _c_

Read this and then write the answers. Read it again as often as you need to.

It may seem at first thought that every boy and girl who goes to school ought to do all the work that the teacher wishes done. But sometimes other duties prevent even the best boy or girl from doing so. If a boy's or girl's father died and he had to work afternoons and evenings to earn money to help his mother, such might be the case. A good girl might let her lessons go undone in order to help her mother by taking care of the baby.

1. What are some conditions that might make even the best boy leave school work unfinished?............................................ ................................................................... 2. What might a boy do in the evenings to help his family?......... 3. How could a girl be of use to her mother?....................... 4. Look at these words: _idle, tribe, inch, it, ice, ivy, tide, true, tip, top, tit, tat, toe._

Cross out every one of them that has an _i_ and has not any _t_ (T) in it.

SET _d_

Read this and then write the answers. Read it again as often as you need to.

1. What is it that might seem at first thought to be true, but really is false? .......................................................................

2. What might be the effect of his father's death upon the way a boy spent his time?................................................................. 3. Who is mentioned in the paragraph as the person who desires to have all lessons completely done?.............................................. .......................................................................

4. In these two lines draw a line under every 5 that comes just after a 2, unless the 2 comes just after a 9. If that is the case, draw a line under the next figure after the 5:

5 3 6 2 5 4 1 7 4 2 5 7 6 5 4 9 2 5 3 8 6 1 2 5 4 7 3 5 2 3 9 2 5 8 4 7 9 2 5 6 1 2 5 7 4 8 5 6

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Many tests have been devised which have been thought to have more general application than those which have been mentioned above for the particular subjects. One of the most valuable of these tests, called technically a completion test, is that derived by Dr. M.R. Trabue.[29] In these tests the pupil is asked to supply words which are omitted from the printed sentences. It is really a test of his ability to complete the thought when only part of it is given. Dr. Trabue calls his scales language scales. It has been found, however, that ability of this sort is closely related to many of the traits which we consider desirable in school children. It would therefore be valuable, provided always that children have some ability in reading, to test them on the language scale as one of the means of differentiating among those who have more or less ability. The scores which may be expected from different grades appear in Dr. Trabue's monograph. Three separate scales follow.

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_Write only one word on each blank_ _Time Limit: Seven minutes_ NAME ..........................

TRABUE LANGUAGE SCALE B

1. We like good boys................girls. 6. The................is barking at the cat. 8. The stars and the................will shine tonight. 22. Time................often more valuable................money. 23. The poor baby................as if it.....................sick. 31. She................if she will. 35. Brothers and sisters ................ always ................ to help..............other and should................quarrel. 38. ................ weather usually................ a good effect ................ one's spirits. 48. It is very annoying to................................tooth-ache, ................often comes at the most................time imaginable. 54. To................friends is always................the........ it takes.

_Write only one word on each blank_ _Time Limit: Seven minutes_ NAME..........................

TRABUE LANGUAGE SCALE D

4. We are going................school. 76. I................to school each day. 11. The................plays................her dolls all day. 21. The rude child does not................many friends. 63. Hard................makes................tired. 27. It is good to hear................voice....................... ..........friend. 71. The happiest and................contented man is the one........ ........lives a busy and useful................. 42. The best advice................usually................obtained ................one's parents. 51.................things are................ satisfying to an ordinary ................than congenial friends. 84.................a rule one................association.......... friends.

_Write only one word on each blank_ _Time Limit: Five minutes_ NAME ............................

TRABUE LANGUAGE SCALE J

20. Boys and................soon become................and women. 61. The................are often more contented.............. the rich. 64. The rose is a favorite................ because of................ fragrance and................. 41. It is very................ to become................acquainted ................persons who................timid. 93. Extremely old..................sometimes..................almost as .................. care as ................... 87. One's................in life................upon so............ factors ................ it is not ................ to state any single................for................ failure. 89. The future................of the stars and the facts of............ history are................now once for all,................I like them................not.

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Other standard tests and scales of measurement have been derived and are being developed. The examples given above will, however, suffice to make clear the distinction between the ordinary type of examination and the more careful study of the achievements of children which may be accomplished by using these measuring sticks. It is important for any one who would attempt to apply these tests to know something of the technique of recording results.

In the first place, the measurement of a group is not expressed satisfactorily by giving the average score or rate of achievement of the class. It is true that this is one measure, but it is not one which tells enough, and it is not the one which is most significant for the teacher. It is important whenever we measure children to get as clear a view as we can of the whole situation. For this purpose we want not primarily to know what the average performance is, but, rather, how many children there are at each level of achievement. In arithmetic, for example, we want to know how many there are who can do none of the Courtis problems in addition, or how many there are who can do the first six on the Woody test, how many can do seven, eight, and so on. In penmanship we want to know how many children there are who write quality eight, or nine, or ten, or sixteen, or seventeen, as the case may be. The work of the teacher can never be accomplished economically except as he gives more attention to those who are less proficient, and provides more and harder work for those who are capable, or else relieves the able members of the class from further work in the field. It will be well, therefore, to prepare, for the sake of comparing grades within the same school or school system, or for the sake of preparing the work of a class at two different times during the year, a table which shows just how many children there are in the group who have reached each level of achievement. Such tables for work in composition for a class at two different times, six months apart, appear as follows:

DISTRIBUTION OF COMPOSITION SCORES FOR A SEVENTH GRADE

====================================== | NUMBER OF CHILDREN +----------------------- | NOVEMBER | FEBRUARY --------------+-----------+----------- Rated at 0 | 0 | 0 1.83 | 1 | 1 2.60 | 6 | 4 3.69 | 12 | 6 4.74 | 8 | 11 5.85 | 3 | 4 6.75 | 1 | 3 7.72 | 1 | 2 8.38 | 0 | 1 9.37 | 0 | 0 ======================================

A study of such a distribution would show not only that the average performance of the class has been raised, but also that those in the lower levels have, in considerable measure, been brought up; that is, that the teacher has been working with those who showed less ability, and not simply pushing ahead a few who had more than ordinary capacity. It would be possible to increase the average performance by working wholly with the upper half of the class while neglecting those who showed less ability. From a complete distribution, as has been given above, it has become evident that this has not been the method of the teacher. He has sought apparently to do everything that he could to improve the quality of work upon the part of all of the children in the class.

It is very interesting to note, when such complete distributions are given, how the achievement of children in various classes overlaps. For example, the distribution of the number of examples on the Courtis tests, correctly finished in a given time by pupils in the seventh grades, makes it clear that there are children in the fifth grade who do better than many in the eighth.

THE DISTRIBUTION OF THE NUMBER OF EXAMPLES CORRECTLY FINISHED IN THE GIVEN TIME BY PUPILS IN THE SEVERAL GRADES

=================================================================== ADDITION | SUBTRACTION No. OF |----------------------+ No. OF |------------------------ EXAMPLES| GRADES | EXAMPLES | GRADES FINISHED| 5 | 6 | 7 | 8 | FINISHED | 5 | 6 | 7 | 8 --------+----+-----+-----+-----+----------+----+-----+-----+------- 0 | 12 | 15 | 5 | 4 | 0 | 6 | 2 | 2 | -- 1 | 26 | 23 | 14 | 9 | 1 | 5 | 6 | 2 | 1 2 | 27 | 31 | 8 | 6 | 2 | 7 | 8 | 1 | -- 3 | 31 | 27 | 27 | 9 | 3 | 13 | 21 | 3 | 1 4 | 25 | 28 | 19 | 16 | 4 | 21 | 18 | 13 | 2 5 | 16 | 23 | 16 | 15 | 5 | 26 | 30 | 12 | 7 6 | 15 | 22 | 12 | 12 | 6 | 17 | 27 | 15 | 9 7 | 1 | 11 | 8 | 9 | 7 | 15 | 27 | 18 | 9 8 | 3 | 4 | 6 | 11 | 8 | 15 | 20 | 12 | 12 9 | 1 | 2 | 3 | 8 | 9 | 10 | 13 | 9 | 12 10 | -- | -- | -- | 6 | 10 | 8 | 6 | 13 | 11 11 | -- | -- | 1 | -- | 11 | 6 | 2 | 3 | 12 12 | -- | -- | 1 | 2 | 12 | 3 | 1 | 7 | 9 13 | -- | -- | -- | -- | 13 | 2 | 2 | 3 | 5 14 | -- | -- | -- | -- | 14 | 1 | 1 | 3 | 7 15 | -- | -- | -- | 2 | 15 | -- | -- | 2 | 3 16 | -- | -- | -- | 1 | 16 | -- | -- | 1 | 2 17 | -- | -- | -- | -- | 17 | -- | 1 | -- | 1 18 | -- | -- | -- | -- | 18 | -- | -- | -- | 1 19 | -- | -- | -- | -- | 19 | -- | -- | -- | 4 20 | -- | -- | -- | -- | 20 | -- | -- | -- | 2 21 | -- | -- | -- | -- | 21 | -- | -- | -- | 1 22 | -- | -- | -- | -- | 22 | -- | -- | -- | -- --------+----+-----+-----+-----+----------+----+-----+-----+------- Total | | | | | | | | | papers |157 | 86 | 119 | 111 | |155 | 185 | 119 | 111 ===================================================================

THE DISTRIBUTION OF THE NUMBER OF EXAMPLES CORRECTLY FINISHED IN THE GIVEN TIME BY PUPILS IN THE SEVERAL GRADES

======================================================================= MULTIPLICATION | DIVISION ------------------------------------|---------------------------------- No. of | GRADES |No. of | GRADES Examples|---------------------------|Examples|------------------------- Finished| 5 | 6 | 7 | 8 |Finished| 5 | 6 | 7 | 8 --------|------+-----+-----+--------|--------|------+-----+-----+------ 0 . . .| 10 | 4 | -- | -- | 0 . . .| 17 | 7 | 1 | -- 1 . . .| 10 | 4 | 3 | -- | 1 . . .| 19 | 17 | 2 | 1 2 . . .| 19 | 20 | 5 | 1 | 2 . . .| 18 | 22 | 8 | 4 3 . . .| 21 | 17 | 11 | 5 | 3 . . .| 21 | 26 | 6 | 2 4 . . .| 28 | 31 | 16 | 3 | 4 . . .| 25 | 27 | 8 | 6 5 . . .| 26 | 34 | 12 | 13 | 5 . . .| 21 | 27 | 11 | 7 6 . . .| 24 | 27 | 13 | 13 | 6 . . .| 9 | 15 | 12 | 4 7 . . .| 9 | 20 | 16 | 10 | 7 . . .| 10 | 15 | 16 | 18 8 . . .| 5 | 14 | 21 | 19 | 8 . . .| 6 | 7 | 20 | 9 9 . . .| 3 | 9 | 11 | 13 | 9 . . .| 4 | 7 | 11 | 6 10 . . .| -- | 4 | 6 | 10 |10 . . .| 4 | 9 | 7 | 13 11 . . .| 1 | -- | 2 | 9 |11 . . .| 1 | 3 | 3 | 7 12 . . .| -- | -- | 2 | 6 |12 . . .| -- | 2 | 10 | 10 13 . . .| -- | -- | 1 | 3 |13 . . .| -- | 2 | -- | 10 14 . . .| -- | -- | -- | 3 |14 . . .| 1 | -- | 1 | 4 15 . . .| -- | -- | -- | -- |15 . . .| -- | 1 | 2 | 9 16 . . .| -- | -- | -- | 1 |16 . . .| -- | -- | -- | 2 17 . . .| -- | -- | -- | -- |17 . . .| -- | -- | -- | 4 18 . . .| -- | -- | -- | 1 |18 . . .| -- | -- | -- | 2 19 . . .| -- | -- | -- | 1 |19 . . .| -- | -- | -- | 1 20 . . .| -- | -- | -- | -- |20 . . .| -- | -- | -- | 1 21 . . .| -- | -- | -- | -- |21 . . .| -- | -- | -- | 1 22 . . .| -- | -- | -- | -- |22 . . .| -- | -- | -- | -- --------+------+-----+-----+--------|--------|------+-----+-----+------- Total | | | | | | | | | Papers | 156 | 184 | 119 | 111 | | 156 | 187 | 118 | 111 =======================================================================

If the tests had been given in the fourth or the third grade, it would have been found that there were children, even as low as the third grade, who could do as well or better than some of the children in the eighth grade. Such comparisons of achievements among children in various subjects ought to lead at times to reorganizations of classes, to the grouping of children for special instruction, and to the rapid promotion of the more capable pupils.

In many of these measurements it will be found helpful to describe the group by naming the point above and below which half of the cases fall. This is called the median. Because of the very common use of this measure in the current literature of education, it may be worth while to discuss carefully the method of its derivation.[30]

[31]The _median point_ of any distribution of measures is that point on the scale which divides the distribution into two exactly equal parts, one half of the measures being greater than this point on the scale, and the other half being smaller. When the scales are very crude, or when small numbers of measurements are being considered, it is not worth while to locate this median point any more accurately than by indicating on what step of the scale it falls. If the measuring instrument has been carefully derived and accurately scaled, however, it is often desirable, especially where the group being considered is reasonably large, to locate the exact point within the step on which the median falls. If the unit of the scale is some measure of the variability of a defined group, as it is in the majority of our present educational scales, this median point may well be calculated to the nearest tenth of a unit, or, if there are two hundred or more individual measurements in the distribution, it may be found interesting to calculate the median point to the nearest hundredth of a scale unit. Very seldom will anything be gained by carrying the calculation beyond the second decimal place.

The best rule for locating the median point of a distribution is to _take as the median that point on the scale which is reached by counting out one half of the measures_, the measures being taken in the order of their magnitude. If we let _n_ stand for the number of measures in the distribution, we may express the rule as follows: Count into the distribution, from either end of the scale, a distance covered by *_n/2_ measures. For example, if the distribution contains 20 measures, the median is that point on the scale which marks the end of the 10th and the beginning of the 11th measure. If there are 39 measures in the distribution, the median point is reached by counting out 19-1/2 of the measures; in other words, the median of such a distribution is at the mid-point of that fraction of the scale assigned to the 20th measure.

The _median step_ of a distribution is the step which contains within it the median point. Similarly, the _median measure_ in any distribution is the measure which contains the median point. In a distribution containing 25 measures, the 13th measure is the median measure, because 12 measures are greater and 12 are less than the 13th, while the 13th measure is itself divided into halves by the median point. Where a distribution contains an even number of measures, there is in reality no median measure but only a median point between the two halves of the distribution. Where a distribution contains an uneven number of measures, the median measure is the (_n_+1)/2 measurement, at the mid-point of which measure is the median point of the distribution.

Much inaccurate calculation has resulted from misguided attempts to secure a _median point_ with the formula just given, which is applicable only to the location of the _median measure_. It will be found much more advantageous in dealing with educational statistics to consider only the median point, and to use only the _n_/2 formula given in a previous paragraph, for practically all educational scales are or may be thought of as continuous scales rather than scales composed of discrete steps.

The greatest danger to be guarded against in considering all scales as continuous rather than discrete, is that careless thinkers may refine their calculations far beyond the accuracy which their original measurements would warrant. One should be very careful not to make such unjustifiable refinements in his statement of results as are often made by young pupils when they multiply the diameter of a circle, which has been measured only to the nearest inch, by 3.1416 in order to find the circumference. Even in the ordinary calculation of the average point of a series of measures of length, the amateur is sometimes tempted, when the number of measures in the series is not contained an even number of times in the sum of their values, to carry the quotient out to a larger number of decimal places than the original measures would justify. Final results should usually not be refined far beyond the accuracy of the original measures.

It is of utmost importance in calculating medians and other measures of a distribution to keep constantly in mind the significance of each step on the scale. If the scale consists of tasks to be done or problems to be solved, then "doing 1 task correctly" means, when considered as part of a continuous scale, anywhere from doing 1.0 up to doing 2.0 tasks. A child receives credit for "2 problems correct" whether he has just barely solved 2.0 problems or has just barely fallen short of solving 3.0 problems. If, however, the scale consists of a series of productions graduated in quality from very poor to very good, with which series other productions of the same sort are to be compared, then each sample on the scale stands at the middle of its "step" rather than at the beginning.