The Psychology of Arithmetic

by Edward L. Thorndike

The author long ago proposed that pupils be measured also with series like a to g shown below, in which the difficulty increases step by step.

a.	3	2	2	3	2	2	1	2
	2	3	1	2	4	5	5	1
	4	2	3	3	3	2	2	2
	—	—	—	—	—	—	—	—

b.	21	32	12	24	34	34	22	12
	23	12	52	31	33	12	23	13
	24	25	15	14	32	23	43	61
	—	—	—	—	—	—	—	—

c.	22	3	4	35	32	83	22	3
	3	31	3	2	33	11	3	21
	38	45	52	52	2	4	33	64
	—	—	—	—	—	—	—	—

d.	30	20	10	22	10	20	52	12
	20	50	40	43	30	4	6	22
	40	17	24	13	40	23	30	44
	—	—	—	—	—	—	—	—

e.		4	5	20	12	12	20	10
	20	30	3	40	4	11	20	20
	10	30	20	4	1	23	7	2
	20	2	40	23	40	11	10	30
	20	20	10	11	20	22	30	25
	—	—	—	—	—	—	—	—

f.			19	9			9
	14	2	19	24	9	4	13
	9	14	13	12	13	13	9	14
	17	23	13	15	15	34	12	25
	26	29	18	19	25	28	18	39
	—	—	—	—	—	—	—	—

g.						13
		13		9	14	12	9
		9		13	12	9	14	24
	23	19	19	29	9	9	13	21
	28	26	26	14	8	8	29	23
	29	16	15	19	17	19	19	22
	—	—	—	—	—	—	—	—

Woody ['16] has constructed his well-known tests on this principle, though he uses only one example at each step of difficulty instead of eight or ten as suggested above. His test, so far as addition of integers goes, is:—