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

SysComparative AchievementsComparative Time ExpenditureTime Distribution among Grades
Lower numbers show week minutes devoted to arithmetic; upper show % of school time devoted to arithmetic in each grade
ABCDEFGIIIIIIIVVVI
XXIII7612151515
111 14 1150 9675 12100100200250250250
XXV7910913
342272287008..100140155130197
XXII888711
54150772007..90909090147
XX71012141515
57315116182001480113210240265253
XVII21220202423
31221128375001727158250258300290
VIII21415151515
811518125896001325233250250250250
XV1115201718
897161173802515..147213292250271
III10911111216
91086944802512125125150150165229
XXIV14171717
102187950877511....200250250250
X712121418
101465921855011..88154184216279
I913141415
1113991068937511..130213238238249
IV282020242023
12420261854840022249300306361300338
II81214141516
131511171247990013121192217225233259
XXI81010121413
131610486576501180100100180210195
VI812181819
131214111126900013..127177266266290
XVI5813181716
14½62312112790001375113187263251238
XIII2623181919
151713251626847519..388350288300300
XVIII6515202019
168241912658700157575225300300290
IX131518181821
17½1916221559900017200225275275275309
XI1115181818
18½2215101130857513..157216250250257
XIV151618191919
18½1810231560885018225245270280270270
XII618161919
192117131148840014..81226255288298
XXVI71010131317
22½2322383772001280125125150150207
VII131922222217
22½2025241573780020175262300300300236
V81011121313
2325218971870011113154167175183179
XIX81017171320
252426201276900014125150250250250301

.. = 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.