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THE PSYCHOLOGY OF
ARITHMETIC
BY
EDWARD L. THORNDIKE
TEACHERS COLLEGE, COLUMBIA
UNIVERSITY
New York
THE MACMILLAN COMPANY
1929
All rights reserved
Copyright, 1922,
By THE MACMILLAN COMPANY.
Set up and electrotyped. Published January, 1922.
Reprinted October, 1924; May, 1926; August, 1927; October, 1929.
· PRINTED IN THE UNITED STATES OF AMERICA ·
[Pg v]
PREFACE
Within recent years there have been three lines of advancein psychology which are of notable significance for teaching.The first is the new point of view concerning thegeneral process of learning. We now understand thatlearning is essentially the formation of connections orbonds between situations and responses, that the satisfyingnessof the result is the chief force that forms them, andthat habit rules in the realm of thought as truly and asfully as in the realm of action.
The second is the great increase in knowledge of theamount, rate, and conditions of improvement in thoseorganized groups or hierarchies of habits which we callabilities, such as ability to add or ability to read. Practiceand improvement are no longer vague generalities, butconcern changes which are definable and measurable bystandard tests and scales.
The third is the better understanding of the so-called"higher processes" of analysis, abstraction, the formationof general notions, and reasoning. The older view of amental chemistry whereby sensations were compoundedinto percepts, percepts were duplicated by images, perceptsand images were amalgamated into abstractions and concepts,and these were manipulated by reasoning, has givenway to the understanding of the laws of response to elementsor aspects of situations and to many situations or elementsthereof in combination. James' view of reasoning as"selection of essentials" and "thinking things together"[Pg vi]in a revised and clarified form has important applicationsin the teaching of all the school subjects.
This book presents the applications of this newer dynamicpsychology to the teaching of arithmetic. Its contents aresubstantially what have been included in a course of lectureson the psychology of the elementary school subjects givenby the author for some years to students of elementaryeducation at Teachers College. Many of these formerstudents, now in supervisory charge of elementary schools,have urged that these lectures be made available to teachersin general. So they are now published in spite of theauthor's desire to clarify and reinforce certain matters byfurther researches.
A word of explanation is necessary concerning the exercisesand problems cited to illustrate various matters, especiallyerroneous pedagogy. These are all genuine, havingtheir source in actual textbooks, courses of study, stateexaminations, and the like. To