References
- Apostel , L. , Mays , W. , Morf , A. and Piaget , J. 1957 . “ Les liaisons analytiques et synthétiques dans les comportements du sujet ” . In Etudes d'épistémologie génétique , Vol. 4 , Paris : Presses Universitaires de France .
- Beard , R. M. 1963 . The order of concept development—Studies in two fields . Educ. Rev. , 15 : 105 – 117 .
- Beaumont , R. A. and Pierce , R. S. 1963 . The Algebraic Foundations of Mathematics , Reading, Mass. : Addison-Wesley .
- Beilin , H. 1970 . The training and acquisition of logical operations . Paper read at the Conference on Piaget-Type Research in Mathematics Education, Teachers College, Columbia University . October 1970 , New York.
- Brainerd , C. J. and Allen , T. W. 1971 . Experimental inductions of the conservation of “first-order” quantitative invariants . Psychol. Bull. , 75 : 128 – 144 .
- Brouwer , L. E. J. 1913 . Intuitionism and formalism . Bull. Amer. Math. Soc. , 20 : 81 – 96 .
- De Long , H. 1971 . Unsolved problems in arithmetic . Sci. Amer. , 224 ( 3 ) : 50 – 60 .
- Dodwell , P. C. 1960 . Children's understanding of number and related concepts . Canad. J. Psychol. , 14 : 191 – 205 .
- Dodwell , P. C. 1961 . Children's understanding of number concepts: Characteristics of an individual and of a group test . Canad. J. Psychol. , 15 : 29 – 36 .
- Dodwell , P. C. 1962 . Relations between the understanding of the logic of classes and of cardinal number in children . Canad. J. Psychol. , 16 : 152 – 160 .
- Flavell , J. H. 1963 . The Developmental Psychology of Jean Piaget , Princeton, N.J. : Van Nostrand .
- Flavell , J. H. 1970 . “ Concept development ” . In Charmichael's Manual of Child Psychology , Edited by: Mussen , P. H. New York : Wiley .
- Flavell , J. H. 1971 . Stage-related properties of cognitive development . Cognitive Psychol. , 2 : 421 – 453 .
- Flavell , J. H. 1972 . An analysis of cognitive-developmental sequences . Genet. Psychol. Monog. , 86 ( 2 ) : 279 – 350 .
- Frege , G. 1884 . Die Grundlagen der Arithmetik , Breslau : Marcus .
- Gibson , J. J. 1966 . The Senses Considered as Perceptual Systems , Boston : Houghton Mifflin .
- Gréco , P. 1962 . “ Une recherche sur la commutativité de l'addition ” . In Structures numériques élémentaires. Eludes d'épistémologie génétique , Edited by: Gréco , P. and Morf , A. Vol. 13 , Paris : Presses Universitaires de France .
- Green , B. F. 1954 . “ Attitude measurement ” . In Handbook of Social Psychology , Edited by: Lindzey , G. Vol. 1 , Cambridge, Mass. : Addison-Wesley .
- Griffiths , L. R. , Shantz , C. U. and Sigel , I. E. 1967 . A methodological problem in conservation studies: The use of relational terms . Child Devel. , 38 : 841 – 848 .
- Guilford , J. P. 1967 . The Nature of Human Intelligence , New York : McGraw-Hill .
- Heyting , A. 1964 . “ The intuitionist foundations of mathematics ” . In Philosophy of Mathematics , Edited by: Benacerraf , P. and Putnam , H. Englewood Cliffs, N. J. : Prentice-Hall .
- Hilbert , D. and Ackermann , W. 1928 . Grundzüge der Theoretischen Logik , Berlin : Springer .
- Hood , H. B. 1962 . An experimental study of Piaget's theory of the development of number in children . Brit. J. Psychol. , 53 : 273 – 286 .
- Inhelder , B. and Piaget , J. 1963 . “ De l'itération des actions à la récurrence élémentaire, Le formation des raisonements récurrentielles ” . In Etudes d'épistémologie génétique , Edited by: Gréco , P. , Inhelder , B. , Matalon , B. and Piaget , J. Vol. 17 , Paris : Presses Universitaires de France .
- Inhelder , B. and Piaget , J. 1964 . The Early Growth of Logic in the Child , London : Routledge & Kegan Paul .
- Katsoff , L. 1948 . A Philosophy of Mathematics , Ames, Iowa : Iowa State Coll. Press .
- Luchins , A. S. and Luchins , E. H. 1965 . Logical Foundations of Mathematics for Behavioral Scientists , New York : Holt, Rinehart & Winston .
- Matalon , B. 1963 . “ Recherches sur le nombre quelconque, Le formation des raisonements récurrentielles ” . In Etudes d'épistémologie génétique , Edited by: Gréco , P. , Inhelder , B. , Matalon , B. and Piaget , J. Vol. 17 , Paris : Presses Universitaires de France .
- Nelson , T. M. and Bartley , S. H. 1961 . Numerosity, arithmetization, measurement and psychology . Philos. Sci. , 28 : 178 – 203 .
- Peano , G. Formulaire de Mathématiques , Vols. 1–5 , 1894 – 1908 . Turin : Broca .
- Piaget , J. 1942 . Classes, Relations et Nombres: Essai sur les “Groupements” de la Logistique et al Réversibilité de la Pensée , Paris : Vrin .
- Piaget , J. 1949 . Traité de Logique , Paris : Colin .
- Piaget , J. 1952 . The Child's Conception of Number , New York : Humanities . (First published as La Genése du Nombre chez l'Enfant. Neuchâtel & Paris: Delachaux & Niestlé, 1941.)
- Piaget , J. 1970 . “ Piaget's theory ” . In Charmichael's Manual of Child Psychology , Edited by: Mussen , P. H. New York : Wiley .
- Piaget , J. 1970 . Genetic Epistemology , New York : Columbia Univ. Press .
- Piaget , J. 1970 . Structuralism , New York : Basic Books .
- Quine , W. V. O. 1961 . From a Logical Point of View , Cambridge, Mass. : Harvard Univ. Press .
- Quine , W. V. O. 1969 . Set Theory and Its Logic , Cambridge, Mass. : Belknap Press .
- Russell , B. 1903 . The Principles of Mathematics , Cambridge, , England : Cambridge Univ. Press .
- Russell , B. 1908 . Mathematical logic as based on a theory of types . Amer. J. Math. , 30 : 222 – 262 .
- Russell , B. 1919 . Introduction to Mathematical Philosophy , London : Allen & Unwin .
- Russell , B. 1937 . The Principles of Mathematics, , 2nd ed. , London : Allen & Unwin .
- Russell , B. 1948 . Human Knowledge: Its Scope and Limits , New York : Simon & Schuster .
- Sheffer , H. M. 1913 . A set of five independent postulates for Boolean algebras, with application to logical constants . Trans. Amer. Math. Soc. , 14 : 481 – 488 .
- Siegel , L. S. 1971 . The sequence of development of certain number concepts in preschool children . Devel. Psychol. , 5 : 357 – 361 .
- Siegel , L. S. 1971 . The development of the understanding of certain number concepts . Devel. Psychol. , : 362 – 363 .
- Stabler , E. R. 1953 . An Introduction to Mathematical Thought , Reading, Mass. : Addison-Wesley .
- van Heijenoort , J. , ed. 1967 . From Frege to Gödel: A Sourcebook in Mathematical Logic , Cambridge, Mass. : Harvard Univ. Press .
- von Neumann , J. 1923 . Zur einführung der transfiniten zahler . Acta Szeged. , 1 : 199 – 208 .
- Wang , M. C. , Resnick , L. B. and Boozer , R. F. 1971 . The sequence of development of some early mathematics behaviors . Child Devel. , 42 : 1767 – 1778 .
- Whitehead , A. N. and Russell , B. Principia Mathematica , Vols. 1–3 , 1910 – 1913 . Cambridge, , England : Cambridge Univ. Press .
- Whitehead , A. N. and Russell , B. 1927 . Principia Mathematica, , 2nd ed. , Cambridge, , England : Cambridge Univ. Press .
- Wohlwill , J. F. 1960 . A study of the development of the number concept by scalogram analysis . J. Genet. Psychol. , 97 : 345 – 377 .