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 in196 f.Aims of the teaching of arithmetic,23 f.Ames, A. F.,89Analysis, learning by,169 ff.;systematic and opportunistic stimuli to,178 f.;gradual progress in,180 ff.Area,257 f.,275Arithmetic, sociology of,24 ff.Arithmetical abilities.SeeAbilities.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.SeeReasoning.Arithmetical terms,8,19Averages,40 f.;135 f.Ballou, F. W.,34,38Banking,256 f.Binet, A.,201Bonds, selection of,70 ff.;strength of,102 ff.;for temporary service,111 ff.;order of formation of,141 ff.See alsoHabits.Brandell, G.,211Brandford, B.,198 f.Brown, J. C.,xvi,103Burgerstein, L.,103Burnett, C. J.,202Burt, C.,286Cardinal and ordinal numbers confused,206Catch problems,21 ff.Chapman, J. C.,49Class, size of, in relation to arithmetical learning,228;variation within a,289 ff.Cobb, M. V.,299Coffman, L. D.,xviCollection meaning of numbers,3 ff.Computation, measurements of,33 ff.;explanations of the processes in,60 ff.;accuracy in,102 ff.See alsoAddition, 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.,49,103,291,293,299Crutches,112 f.Culture-epoch theory,198 f.Dairy records,273Decimal numbers, uses of,24 f.;measurement of ability with,36 ff.;learning,181 ff.;division by,270 f.De Croly, M.,205Deductive reasoning,60 ff.,185 ff.Degand, J.,205Denominate numbers,141 f.,147 f.Described problems,10 ff.Development of knowledge of number,205 ff.De Voss, J. C.,49Dewey, J.,3,83,150,205,207,208,219,266,277Differences in arithmetical ability,285 ff.;within a class,289 ff.Difficulty as a stimulus,277 ff.Drill,102 ff.Discipline, mental,20Distribution 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.,295Elements, responses to,169 ff.Eleven, multiples of,85Elliott, C. H.,228Equation 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.,241Flynn, F. J.,196Fractions, uses of,24 f.;measurement of ability with,36 ff.;knowledge of the meaning of,54 ff.Freeman, F. N.,259,261Friedrich, J.,103Generalization,169 ff.Gilbert, J. A.,203Graded 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.,295Hall, G. S.,200 f.Hartmann, B.,200 f.Heck, W. H.,227Heredity in arithmetical abilities,293 ff.Highest common factor,88 f.Hoke, K. J.,49Holmes, M. E.,103Howell, H. B.,259Hunt, C. W.,196Hygiene of arithmetic,212 ff.,234 ff.Individual differences,285 ff.Inductive reasoning,60 ff.,169 ff.Insurance,256Interest as a principle determining the order of topics,150 ff.Interests, instinctive195 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.,xviKelly, F. J.,49King, A. C.,103,227Kirby, T. J.,76 f.,104,295Klapper, P.,xviKruse, P. J.,289,293Ladder tests,28 ff.,36 ff.Language in arithmetic,8 f.,19,89 ff.,94 ff.Laser, H.,103Lay, W. A.,259,261Learning, nature of arithmetical,1 ff.Least common multiple,88 f.Lewis, E. O.,210 f.Lobsien, M.,209 f.McCall, W. A.,49McDougle, E. C.,85 ff.McKnight, J. A.,210McLellan, J. A.,3,83,89,205,207Manipulation 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.,202Metric system,147Meumann, E.,261Mitchell, H. E.,24Monroe, W. S.,49Multiplication, 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.,202National 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 alsoDecimal numbersandFractions.Objective aids, used for verification,154;in general,243 ff.Oral arithmetic,262 ff.Order of topics,141 ff.Ordinal numbers, confused with cardinal,206Original tendencies and arithmetic,195 ff.Overlearning,134 ff.Percents,80 f.Perception of number,202 ff.Phillips, D. E.,3,4,205,207Pictures, hygiene of,246 ff.;number,259 ff.Pommer, O.,212Practice, 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.,295Rainfall,272Ratio,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.,49Seekel, E.,212Selkin, F. B.,196 f.Sequence of topics,141 ff.Series meaning of numbers,2 ff.Size of class in relation to arithmetical learning,228Smith, D. E.,xvi,224Social instincts, use of,195 f.Sociology of arithmetic,24 ff.Speed in relation to accuracy,31,108Speer, W. W.,3,5,83Spiral order,141,145Starch, D.,49,295Stern, W.,210,212Stone, 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.,xviTemporary bonds,111 ff.Terms,113 f.Tests of arithmetical abilities,27 ff.Thorndike, E. L.,34,38 ff.,227,294Time, 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,153Verification,81 f.;aided by greater strength of the fundamental bonds,107 ff.Walsh, J. H.,11Wells, F. L.,295White, E. E.,5Whitley, M. T.,295Wiederkehr, G.,212Wilson, G. M.,24,49Woody, C.,29 ff.,52,287,293Words.SeeLanguageandTerms.Written arithmetic,262 ff.Zero in multiplication,179 f.
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 in196 f.Aims of the teaching of arithmetic,23 f.Ames, A. F.,89Analysis, learning by,169 ff.;systematic and opportunistic stimuli to,178 f.;gradual progress in,180 ff.Area,257 f.,275Arithmetic, sociology of,24 ff.Arithmetical abilities.SeeAbilities.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.SeeReasoning.Arithmetical terms,8,19Averages,40 f.;135 f.Ballou, F. W.,34,38Banking,256 f.Binet, A.,201Bonds, selection of,70 ff.;strength of,102 ff.;for temporary service,111 ff.;order of formation of,141 ff.See alsoHabits.Brandell, G.,211Brandford, B.,198 f.Brown, J. C.,xvi,103Burgerstein, L.,103Burnett, C. J.,202Burt, C.,286Cardinal and ordinal numbers confused,206Catch problems,21 ff.Chapman, J. C.,49Class, size of, in relation to arithmetical learning,228;variation within a,289 ff.Cobb, M. V.,299Coffman, L. D.,xviCollection meaning of numbers,3 ff.Computation, measurements of,33 ff.;explanations of the processes in,60 ff.;accuracy in,102 ff.See alsoAddition, 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.,49,103,291,293,299Crutches,112 f.Culture-epoch theory,198 f.Dairy records,273Decimal numbers, uses of,24 f.;measurement of ability with,36 ff.;learning,181 ff.;division by,270 f.De Croly, M.,205Deductive reasoning,60 ff.,185 ff.Degand, J.,205Denominate numbers,141 f.,147 f.Described problems,10 ff.Development of knowledge of number,205 ff.De Voss, J. C.,49Dewey, J.,3,83,150,205,207,208,219,266,277Differences in arithmetical ability,285 ff.;within a class,289 ff.Difficulty as a stimulus,277 ff.Drill,102 ff.Discipline, mental,20Distribution 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.,295Elements, responses to,169 ff.Eleven, multiples of,85Elliott, C. H.,228Equation 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.,241Flynn, F. J.,196Fractions, uses of,24 f.;measurement of ability with,36 ff.;knowledge of the meaning of,54 ff.Freeman, F. N.,259,261Friedrich, J.,103Generalization,169 ff.Gilbert, J. A.,203Graded 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.,295Hall, G. S.,200 f.Hartmann, B.,200 f.Heck, W. H.,227Heredity in arithmetical abilities,293 ff.Highest common factor,88 f.Hoke, K. J.,49Holmes, M. E.,103Howell, H. B.,259Hunt, C. W.,196Hygiene of arithmetic,212 ff.,234 ff.Individual differences,285 ff.Inductive reasoning,60 ff.,169 ff.Insurance,256Interest as a principle determining the order of topics,150 ff.Interests, instinctive195 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.,xviKelly, F. J.,49King, A. C.,103,227Kirby, T. J.,76 f.,104,295Klapper, P.,xviKruse, P. J.,289,293Ladder tests,28 ff.,36 ff.Language in arithmetic,8 f.,19,89 ff.,94 ff.Laser, H.,103Lay, W. A.,259,261Learning, nature of arithmetical,1 ff.Least common multiple,88 f.Lewis, E. O.,210 f.Lobsien, M.,209 f.McCall, W. A.,49McDougle, E. C.,85 ff.McKnight, J. A.,210McLellan, J. A.,3,83,89,205,207Manipulation 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.,202Metric system,147Meumann, E.,261Mitchell, H. E.,24Monroe, W. S.,49Multiplication, 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.,202National 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 alsoDecimal numbersandFractions.Objective aids, used for verification,154;in general,243 ff.Oral arithmetic,262 ff.Order of topics,141 ff.Ordinal numbers, confused with cardinal,206Original tendencies and arithmetic,195 ff.Overlearning,134 ff.Percents,80 f.Perception of number,202 ff.Phillips, D. E.,3,4,205,207Pictures, hygiene of,246 ff.;number,259 ff.Pommer, O.,212Practice, 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.,295Rainfall,272Ratio,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.,49Seekel, E.,212Selkin, F. B.,196 f.Sequence of topics,141 ff.Series meaning of numbers,2 ff.Size of class in relation to arithmetical learning,228Smith, D. E.,xvi,224Social instincts, use of,195 f.Sociology of arithmetic,24 ff.Speed in relation to accuracy,31,108Speer, W. W.,3,5,83Spiral order,141,145Starch, D.,49,295Stern, W.,210,212Stone, 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.,xviTemporary bonds,111 ff.Terms,113 f.Tests of arithmetical abilities,27 ff.Thorndike, E. L.,34,38 ff.,227,294Time, 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,153Verification,81 f.;aided by greater strength of the fundamental bonds,107 ff.Walsh, J. H.,11Wells, F. L.,295White, E. E.,5Whitley, M. T.,295Wiederkehr, G.,212Wilson, G. M.,24,49Woody, C.,29 ff.,52,287,293Words.SeeLanguageandTerms.Written arithmetic,262 ff.Zero in multiplication,179 f.