The Psychology of Arithmetic

by Edward L. Thorndike

Abilities, arithmetical, nature of, [1 ff.];
measurement of, [27 ff.];
constitution of, [51 ff.];
organization of, [137 ff.]
Abstract numbers, [85 ff.]
Abstraction, [169 ff.]
Accuracy, in relation to speed, [31];
in fundamental operations, [102 ff.]
Addition, measurement of, [27 ff.], [34];
constitution of, [52 f.];
habit in relation to, [71 f.];
in the higher decades, [75 f.];
accuracy in, [108 f.];
amount of practice in, [122 ff.];
interest in [196 f.]
Aims of the teaching of arithmetic, [23 f.]
Ames, A. F., [89]
Analysis, learning by, [169 ff.];
systematic and opportunistic stimuli to, [178 f.];
gradual progress in, [180 ff.]
Area, [257 f.], [275]
Arithmetic, sociology of, [24 ff.]
Arithmetical abilities. See Abilities.
Arithmetical language, [8 f.], [19], [89 ff.], [94 ff.]
Arithmetical learning, before school, [199 ff.];
conditions of, [227 ff.];
in relation to time of day, [227 ff.];
in relation to time devoted to arithmetic, [228 ff.]
Arithmetical reasoning. See Reasoning.
Arithmetical terms, [8], [19]
Averages, [40 f.]; [135 f.]
Ballou, F. W., [34], [38]
Banking, [256 f.]
Binet, A., [201]
Bonds, selection of, [70 ff.];
strength of, [102 ff.];
for temporary service, [111 ff.];
order of formation of, [141 ff.]
See also Habits.
Brandell, G., [211]
Brandford, B., [198 f.]
Brown, J. C., [xvi], [103]
Burgerstein, L., [103]
Burnett, C. J., [202]
Burt, C., [286]
Cardinal and ordinal numbers confused, [206]
Catch problems, [21 ff.]
Chapman, J. C., [49]
Class, size of, in relation to arithmetical learning, [228];
variation within a, [289 ff.]
Cobb, M. V., [299]
Coffman, L. D., [xvi]
Collection meaning of numbers, [3 ff.]
Computation, measurements of, [33 ff.];
explanations of the processes in, [60 ff.];
accuracy in, [102 ff.]
See also Addition, Subtraction, Multiplication, Division, Fractions, Decimal numbers, Percents.
Concomitants, law of varying, [172 ff.];
law of contrasting, [173 ff.]
Concrete numbers, [85 ff.]
Concrete objects, use of, [253 ff.]
Conditions of arithmetical learning, [227 ff.]
Constitution of arithmetical abilities, [51 ff.]
Copying of numbers, eyestrain due to, [212 f.]
Correlations of arithmetical abilities, [295 ff.]
Courses of study, [232 f.]
Courtis, S. A., [28 ff.], [43 ff.], [49], [103], [291], [293], [299]
Crutches, [112 f.]
Culture-epoch theory, [198 f.]
Dairy records, [273]
Decimal numbers, uses of, [24 f.];
measurement of ability with, [36 ff.];
learning, [181 ff.];
division by, [270 f.]
De Croly, M., [205]
Deductive reasoning, [60 ff.], [185 ff.]
Degand, J., [205]
Denominate numbers, [141 f.], [147 f.]
Described problems, [10 ff.]
Development of knowledge of number, [205 ff.]

De Voss, J. C., [49]
Dewey, J., [3], [83], [150], [205], [207], [208], [219], [266], [277]
Differences in arithmetical ability, [285 ff.];
within a class, [289 ff.]
Difficulty as a stimulus, [277 ff.]
Drill, [102 ff.]
Discipline, mental, [20]
Distribution of practice, [156 ff.]
Division, measurement of, [35 f.], [37];
constitution of, [57 ff.];
deductive explanations of, [63], [64 f.];
inductive explanations of, [63 f.], [65 f.];
habit in relation to, [72];
with remainders, [76];
with fractions, [78 ff.];
amount of practice in, [122 ff.];
distribution of practice in, [167];
use of the problem attitude in teaching, [270 f.]
Donovan, M. E., [295]
Elements, responses to, [169 ff.]
Eleven, multiples of, [85]
Elliott, C. H., [228]
Equation form, importance of, [77 f.]
Explanations of the processes of computation, [60 ff.];
memory of, [115 f.];
time for giving, [154 ff.]
Eyestrain in arithmetical work, [212 ff.]
Facilitation, [143 ff.]
Figures, printing of, [235 ff.];
writing of, [214 f.], [241]
Flynn, F. J., [196]
Fractions, uses of, [24 f.];
measurement of ability with, [36 ff.];
knowledge of the meaning of, [54 ff.]
Freeman, F. N., [259], [261]
Friedrich, J., [103]
Generalization, [169 ff.]
Gilbert, J. A., [203]
Graded tests, [28 ff.], [36 ff.]
Greatest common divisor, [88 f.]
Habits, importance of, in arithmetical learning, [70 ff.];
now neglected, [75 ff.];
harmful or wasteful, [83 ff.]; [91 ff.];
propædeutic, [117 ff.];
organization of, [137 ff.];
arrangement of, [141 ff.]
Hahn, H. H., [295]
Hall, G. S., [200 f.]
Hartmann, B., [200 f.]
Heck, W. H., [227]
Heredity in arithmetical abilities, [293 ff.]
Highest common factor, [88 f.]
Hoke, K. J., [49]
Holmes, M. E., [103]
Howell, H. B., [259]
Hunt, C. W., [196]
Hygiene of arithmetic, [212 ff.], [234 ff.]
Individual differences, [285 ff.]
Inductive reasoning, [60 ff.], [169 ff.]
Insurance, [256]
Interest as a principle determining the order of topics, [150 ff.]
Interests, instinctive [195 ff.];
censuses of, [209 ff.];
neglect of childish, [226 ff.];
in self-management, [223 f.];
intrinsic, [224 ff.]
Interference, [143 ff.]
Inventories of arithmetical knowledge and skill, [199 ff.]
Jessup, W. A., [xvi]
Kelly, F. J., [49]
King, A. C., [103], [227]
Kirby, T. J., [76 f.], [104], [295]
Klapper, P., [xvi]
Kruse, P. J., [289], [293]
Ladder tests, [28 ff.], [36 ff.]
Language in arithmetic, [8 f.], [19], [89 ff.], [94 ff.]
Laser, H., [103]
Lay, W. A., [259], [261]
Learning, nature of arithmetical, [1 ff.]
Least common multiple, [88 f.]
Lewis, E. O., [210 f.]
Lobsien, M., [209 f.]
McCall, W. A., [49]
McDougle, E. C., [85 ff.]
McKnight, J. A., [210]
McLellan, J. A., [3], [83], [89], [205], [207]
Manipulation of numbers, [60 ff.]
Meaning, of numbers, [2 ff.], [171];
of a fraction, [54 ff.];
of decimals, [181 f.]
Measurement of arithmetical abilities, [27 ff.]
Mental arithmetic, [262 ff.]
Messenger, J. F., [202]
Metric system, [147]
Meumann, E., [261]
Mitchell, H. E., [24]

Monroe, W. S., [49]
Multiplication, measurement of, [35], [36];
constitution of, [51];
deductive explanations of, [61];
inductive explanations of, [61 f.];
with fractions, [78 ff.];
by eleven, [85];
amount of practice in, [122 ff.];
order of learning the elementary facts of, [144 f.];
distribution of practice in, [158 ff.];
use of the problem attitude in teaching, [267 ff.]
Nanu, H. A., [202]
National Intelligence Tests, [49 f.]
Negative reaction in intellectual life, [278 f.]
Number pictures, [259 ff.]
Numbers, meaning of, [2];
as measures of continuous quantities, [75];
abstract and concrete, [85 ff.];
denominate, [141 f.], [147 f.];
use of large, [145 f.];
perception of, [205 ff.];
early awareness of, [205 ff.];
confusion of cardinal and ordinal, [206].
See also Decimal numbers and Fractions.
Objective aids, used for verification, [154];
in general, [243 ff.]
Oral arithmetic, [262 ff.]
Order of topics, [141 ff.]
Ordinal numbers, confused with cardinal, [206]
Original tendencies and arithmetic, [195 ff.]
Overlearning, [134 ff.]
Percents, [80 f.]
Perception of number, [202 ff.]
Phillips, D. E., [3], [4], [205], [207]
Pictures, hygiene of, [246 ff.];
number, [259 ff.]
Pommer, O., [212]
Practice, amount of, [122 ff.];
distribution of, [156 ff.]
Precision in fundamental operations, [102 ff.]
Problem attitude, [266 ff.]
Problems, [9 ff.];
"catch," [21 ff.];
measurement of ability with, [42 ff.];
whose answer must be known in order to frame them, [93 f.];
verbal form of, [111 f.];
interest in, [220 ff.];
as introductions to arithmetical learning, [266 ff.]
Propædeutic bonds, [117 ff.]
Purposive thinking, [193 ff.]
Quantity, number and, [85 ff.];
perception of, [202 ff.]
Race, H., [295]
Rainfall, [272]
Ratio, [225 f.];
meaning of numbers, [3 ff.]
Reaction, negative, [278 f.]
Reality, in problems, [9 ff.]
Reasoning, arithmetical, nature of, [19 ff.];
measurement of ability in, [42 ff.];
derivation of tables by, [58 f.];
about the rationale of computations, [60 ff.];
habit in relation to, [73 f.], [190 ff.];
problems which provoke false, [100 f.];
the essentials of arithmetical, [185 ff.];
selection in, [187 ff.];
as the coöperation of organized habits, [190 ff.]
Recapitulation theory, [198 f.]
Recipes, [273 f.]
Rectangle, area of, [257 f.]
Rice, J. M., [228 ff.]
Rush, G. P., [49]
Seekel, E., [212]
Selkin, F. B., [196 f.]
Sequence of topics, [141 ff.]
Series meaning of numbers, [2 ff.]
Size of class in relation to arithmetical learning, [228]
Smith, D. E., [xvi], [224]
Social instincts, use of, [195 f.]
Sociology of arithmetic, [24 ff.]
Speed in relation to accuracy, [31], [108]
Speer, W. W., [3], [5], [83]
Spiral order, [141], [145]
Starch, D., [49], [295]
Stern, W., [210], [212]
Stone, C. W., [27 ff.], [42 ff.], [228 ff.]
Subtraction, measurement of, [34 f.];
constitution of, [57 f.];
amount of practice in, [122 ff.]
Supervision, [233 f.]
Suzzallo, H., [xvi]
Temporary bonds, [111 ff.]
Terms, [113 f.]
Tests of arithmetical abilities, [27 ff.]
Thorndike, E. L., [34], [38 ff.], [227], [294]
Time, devoted to arithmetic, [228 ff.];
of day, in relation to arithmetical learning, [227 f.]

Type, hygiene of, [235 ff.]
Underlearning, [134 ff.]
United States money, [148 ff.]
Units of measure, arbitrary, [5], [83 f.]
Variation, among individuals, [285 ff.]
Variety, in teaching, [153]
Verification, [81 f.];
aided by greater strength of the fundamental bonds, [107 ff.]
Walsh, J. H., [11]
Wells, F. L., [295]
White, E. E., [5]
Whitley, M. T., [295]
Wiederkehr, G., [212]
Wilson, G. M., [24], [49]
Woody, C., [29 ff.], [52], [287], [293]
Words. See Language and Terms.
Written arithmetic, [262 ff.]
Zero in multiplication, [179 f.]

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