The best composition had the following beginning : 9.7 "What is the matter"? asked Miss Green, All this while they were drifting Enormous difference in quality between best and poorest compositions from a class. By careful scientific procedure Breed arranged the compositions upon a scale of merit in which the poorest one given above received a rank of .2, the second one a rank of 2.7, and the best a rank of 9.7. If these numerical values may be compared, we might say that the excellent composition is 48 times as good as the poorest and 3.6 times as good as the second one. However uncertain such precise comparisons of quality may be, the compositions illustrate the enormous disparity that exists between the poorest and brightest sixth-grade pupils in composition. While the brightest might write attractive stories with few suggestions from the teacher, the poorest would be barely able to compose a simple letter with great help. In class teaching, adapted to the average, the brightest pupil may mark time while the poorest drags or flunks. In our comparisons of rates and qualities of school work up to this point we have compared merely the extremes — the fast and the slow, or the excellent and the poor. More useful comparisons for the teacher to make are found in the answers to the following questions: If the pace of the instruction is adapted to the middle part of the class, 1. How much spare time will the brightest pupils have? 2. How much too fast will the pace be for the slowest pupils ? The general answers to these questions are as follows: 1. The brightest pupil may have from to of his time free to do as he pleases. 2. The pace will be about twice as fast as the pace of learning of the slowest pupils; that is, the slowest pupils will be dragged along at such a fast pace that they will fail in much of the work. As a result they come to be regarded as hopeless flunkers, whereas often they could make satisfactory progress with a slower pace and more careful instruction. Distribution of differences in ability. How many fast and how many slow pupils in each class? - The precise mathematical demonstration of such differences in capacities for learning has been the principal factor in bringing about the practical provisions for individual instruction for the slow and supplementary assignments for the fast which were described above on pages 280–286. In planning special provisions for these extremely fast and extemely slow pupils it is desirable for the teacher to understand what proportion of the class they are likely to comprise. This brings us to the question of the distribution of differences in capacity. This distribution may be illustrated by using the data in the Courtis arithmetic test given in the table on page 292 to make the picture on page 299. Graphic representation of distribution of pupils by piles of blocks; arithmetic scores. As a first step in our study of Courtis's table let us arrange it horizontally (as shown below), instead of vertically. Scorebased on number of problems done 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 The first numerical vertical column of this table reads, The second column reads, I pupil made a score of 2." "o pupils made a score of 3." reads, " 8 pupils made a score of 10," and the extreme righthand column reads, "I pupil made a score of 17." We may now represent these results in graphic or pictured form by the following device: Imagine the lower horizontal row to be written along the blackboard ledge, thus: Number of problems done 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Then place on the ledge, above each vertical column, one wooden block for each pupil who made the score indicated in the column. Thus, above the extreme left-hand column we would place I block; above the extreme right-hand column we would place I block; above the column for a score of IO we would pile 8 blocks, I for each pupil who made this score. After we had completed all the columns of blocks, the whole pile on the ledge would have the appearance shown in the figure on page 299. Rates of reading. We get a somewhat similar form of distribution if we pile blocks to represent the sixth-grade reading rates shown in the table on page 291. To carry out the process with these rates, first imagine the columns written horizontally, as follows: 151 176 201 Words per minute to to to to to to 175 200 225 250 275 300 325 350 375 400 226 251 276 301 326 351 376 to to to to Then imagine the lower row written along the blackboard ledge and above each vertical division on the ledge pile the BLOCKS PILED ON BLACK BOARD LEDGE TO REPRESENT The single block at the left indicates that I pupil made a score of 2. The block at the extreme right indicates that I pupil made a score of 17. The tallest column indicates that 8 pupils made a score of 10 number of blocks corresponding to the number of pupils that have read the amount indicated. This procedure gives the figure shown on page 300. Normal frequency surface; middle abilities frequent; extreme abilities infrequent. It appears that the piles of blocks (or distribution surfaces) for abilities in arithmetic and reading are similar in general form; that is, the middle abilities are piled high with several pupils, while the extremes are low-in other words, there are few bright pupils and few dull ones. If a larger number of pupils were tested (there were 48 in the arithmetic class and 26 in the reading class), the piles, or surfaces, would tend to assume the general form shown in the figure on page 301, which represents the heights of 1000 ten-year-old boys, distributed by a somewhat similar device, each boy being represented by a short horizontal line instead of a block. In general, measurements of BLOCKS PILED ON BLACKBOARD LEDGE TO INDICATE DISTRIBUTION OF READING RATES OF PUPILS IN GRADE 6 A The tall shaky column indicates that 10 pupils read from 226 to 250 words per minute. What do the 2 blocks at the extreme left indicate? The single block at the extreme right indicates what? any human trait, physical or mental, in a group of persons of the same type and age tend to show this form of distribution. It is known as the normal-frequency surface or, when shown in outline as at the bottom of page 301, as the normalfrequency curve or normal distribution curve. Only a few pupils need special attention and assignments in each subject. -With a knowledge of this form of distribution of abilities in spelling or arithmetic or reading or handwork, the teacher should form the habit of thinking |