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.