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.
Explanations of the processes of computation, 60 ff.; memory of, 115 f.; time for giving, 154 ff.
Figures, printing of, 235 ff.; writing of, 214 f., 241
Fractions, uses of, 24 f.; measurement of ability with, 36 ff.; knowledge of the meaning of, 54 ff.
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.
Heredity in arithmetical abilities, 293 ff.
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.
Inventories of arithmetical knowledge and skill, 199 ff.
Language in arithmetic, 8 f., 19, 89 ff., 94 ff.
Meaning, of numbers, 2 ff., 171; of a fraction, 54 ff.; of decimals, 181 f.
Measurement of arithmetical abilities, 27 ff.
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.
Negative reaction in intellectual life, 278 f.
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.
Ordinal numbers, confused with cardinal, 206
Original tendencies and arithmetic, 195 ff.
Pictures, hygiene of, 246 ff.; number, 259 ff.
Practice, amount of, 122 ff.; distribution of, 156 ff.
Precision in fundamental operations, 102 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.