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