Table IV reads exactly as III, the scores[37] being those made on all problems of the test in fundamentals. These two tables give some general help on the nature of the product of the first six years of arithmetic work. One very evident fact is the lack of uniformity among systems; another is the lack of correspondence of relative position among the systems in the two tables. With the exception of systems XXIII and XIV, no system occupies the same relative position in the two tables, e.g. system XXIV stands second from the lowest in reasoning and eighteenth from the lowest in fundamentals. This fact is more accurately summarized in the coefficients of correlation, table XV, p. 37.
As seen from its heading, table XXII gives the systems in order of achievements. These serial standings are derived from tables III and IV. Reading from the top, system XXIII has an average serial standing of one, being lowest in both reasoning and fundamentals; system XXV ranks three in average serial standing, being fourth from lowest in reasoning and second from lowest in fundamentals; the readings for the other systems are similar.
Column Heading Keys:
Sys = Systems
A = Average serial standing
B = Serial standing in reasoning
C = Serial standing in fundamentals
D = Serial standing in time expenditure
E = Week minutes devoted to arithmetic
F = Week minutes devoted to all subjects
G = % of time to arithmetic
TABLE XXII TABLE XXIII TABLE XXIV
.. = no time assigned.
Tables XXIII and XXIV keep the same order of systems and show the time expenditure. The first line of table XXIII reads,—system XXIII ranks fourteenth from the lowest in time expenditure, with 1150 week minutes devoted to arithmetic, 9675 week minutes devoted to all subjects, the 1150 week minutes devoted to arithmetic being 12 per cent of the 9675 week minutes devoted to all subjects. Similarly for the other systems, e.g. system XXV with a serial standing in abilities of three, and a serial standing in time expenditure of two, spends 722 week minutes on arithmetic, and 8700 week minutes on all subjects, arithmetic costing 8 per cent of all the school time. The reader will recognize that the third column, which gives the time devoted to all subjects for one week of each of the first six years, gives the only new data of this table, column two being the same as given in table XXI and the first and fourth columns being derived from the others.
Probably the first essential shown by this table is the lack of correspondence between the serial standing in time cost and the serial standing in abilities; e.g. the system with the lowest time cost is found by referring to table XIII to be system XXII, which is seen in table XXII to rank four and one-half in average abilities. Similarly, the system that ranks fifteenth in time cost, ranks fifth in abilities, etc. Another noticeable showing is the wide variability in the school time of the systems. It will be seen to vary from 7200 to 9900 week minutes. This time includes recesses, and it means that lengths of school days vary from an average of four hours to five and one-half hours. And if the names of the systems were given, it would be recognized that almost invariably the longer school hours are accompanied by the least amount of variation in program, such as physical education, field trips, assemblies, etc. Perhaps the other most striking fact of this table is the wide variation in the per cent of time devoted to arithmetic. It varies from 22 per cent for system IV to 7 per cent for system XXII, a difference of more than three to one.