Blake's Development of the Number Words “One,” “Two,” and “Three”

REFERENCES

• Anderson , A. 1991 . Learning mathematics at home: A case study . Canadian Children , 16 ( 2 ) : 47 – 58 .
   Google Scholar
• Ansari , D. , Donlan , C. , Thomas , M. , Ewing , S. and Karmiloff-Smith , A. 2003 . What makes counting count? Verbal and visuo-spatial contributions to typical and atypical number development . Journal of Experimental Child Psychology , 85 : 50 – 62 .
   PubMed Web of Science ®Google Scholar
• Balaban , M. T. and Waxman , S. R. 1997 . Do words facilitate object categorization in 9-month-old infants? . Journal of Experimental Child Psychology , 64 : 3 – 26 .
   PubMed Web of Science ®Google Scholar
• Baroody , A. J. 1987 . Children's mathematical thinking: A developmental framework for preschool, primary, and special education teachers , New York, NY : Teachers College Press .
   Google Scholar
• Baroody , A. J. 1999 . “ The development of basic counting, number, and arithmetic knowledge among children classified as mentally retarded ” . In International review of research in mental retardation, vol. 22 , Edited by: Glidden , L. M. 51 – 103 . New York, NY : Academic Press .
   Google Scholar
• Baroody , A. J. 2002, May . The developmental foundations of number and operation sense , Arlington, VA : Poster presented at the EHR/REC (NSF) Principal Investigators’ Meeting (“Learning and Education: Building Knowledge, Understanding Its Implications”) .
   Google Scholar
• Baroody , A. J. 2008, March . Fostering early number sense , Banff, , Alberta : Invited keynote speech presented at the Banff International Conference on Behavioural Science .
   Google Scholar
• Baroody , A. J. , Benson , A. P. and Lai , M. L. Paper presented at the biennial meeting of the Society for Research in Child Development . Tampa, FL. Early number and arithmetic sense: A summary of three studies ,
   Google Scholar
• Baroody , A. J. , Lai , M. and Mix , K. Paper presented at the annual conference of the National Association for the Education of Young Children . Washington, DC. Changing views of young children's numerical and arithmetic competencies ,
   Google Scholar
• Baroody , A. J. , Lai , M.-L. and Mix , K. S. 2006 . “ The development of young children's number and operation sense and its implications for early childhood education ” . In Handbook of research on the education of young children , Edited by: Spodek , B. and Saracho , O. 187 – 221 . Mahwah, NJ : Erlbaum .
   Google Scholar
• Baroody , A. J. , Li , X. and Lai , M.-L. 2008 . Toddlers’ spontaneous attention to number . Mathematics Thinking and Learning , 10 : 1 – 31 .
   Google Scholar
• Baroody , A. J. and Mason , C. A. 1984 . “ The case of Brian: An additional explanation for production deficiencies ” . In Proceedings of the Sixth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education , Edited by: Moser , J. 2 – 8 . Madison, WI : Wisconsin Center for Educational Research .
   Google Scholar
• Baroody , A. J. and Price , J. 1983 . The development of number word sequence in the counting of three-year-olds . Journal for Research in Mathematics Education , 14 : 361 – 368 .
   Google Scholar
• Beilin , H. 1975 . Studies in the cognitive basis of language development , New York, NY : Academic Press .
   Google Scholar
• Beilin , H. and Kagan , J. 1969 . Pluralization rules and the conceptualization of number . Developmental Psychology , 1 : 697 – 706 .
   Web of Science ®Google Scholar
• Benson , A. P. and Baroody , A. J. Paper presented at the annual meeting of the Society for Research in Child Development . Tampa, FL. Where does non-verbal production fit in the evergence of children's mental models? ,
   Google Scholar
• Blevins-Knabe , B. and Musun-Miller , L. 1996 . Number use at home by children and their parents and its relationship to early mathematical performance . Early Development and Parenting , 5 ( 1 ) : 35 – 45 .
   Web of Science ®Google Scholar
• Bloom , P. and Wynn , K. 1997 . Linguistic cues in the acquisition of number words . Journal of Child Language , 24 : 511 – 533 .
   PubMed Web of Science ®Google Scholar
• Brownell , W. A. 1935 . “ Psychological considerations in the learning and the teaching of arithmetic ” . In The teaching of arithmetic (Tenth yearbook, National Council of Teachers of Mathematics , Edited by: Reeve , D. W. 1 – 50 . New York, NY : Bureau of Publications, Teachers College, Columbia University .
   Google Scholar
• Carey , S. 2004 . Bootstrapping and the origin of concepts . Daedalus , 133 : 59 – 68 .
   Web of Science ®Google Scholar
• Carey , S. and Sarnecka , B. W. 2006 . “ The development of human conceptual representations ” . In Processes of change in brain and cognitive development: Attention and performance XXI , Edited by: Johnson , M. and Munakata , Y. 473 – 496 . New York, NY : Oxford Press .
   Google Scholar
• Condry , K. F. and Spelke , E. S. 2008 . The development of language and abstract concepts: The case of natural number . Journal of Experimental Psychology: General , 137 : 22 – 38 .
   PubMed Web of Science ®Google Scholar
• Dantzig , T. 1954 . Number: The language of science , New York, NY : The Free Press. (Original work published in 1933) .
   Google Scholar
• Dueker , G. and Needham , A. Poster presented at the annual meeting of the Society for Research in Child Development . Tampa, FL. Labeling facilitates 5-month-old infants’ category formation ,
   Google Scholar
• Durkin , K. , Shire , B. , Riem , R. , Crowther , R. D. and Rutter , D. R. 1986 . The social and linguistic context of early number word use . British Journal of Developmental Psychology , 4 : 269 – 288 .
   Web of Science ®Google Scholar
• Fuson , K. C. 1988 . Children's counting and concepts of number , New York, NY : Springer-Verlag .
   Google Scholar
• Gallistel , C. R. 2007 . Commentary on Le Corre & Carey . Cognition , 105 : 439 – 445 .
   Web of Science ®Google Scholar
• Gallistel , C. R. and Gelman , R. 1992 . Preverbal and verbal counting and computation . Cognition , 44 : 43 – 74 .
   PubMed Web of Science ®Google Scholar
• Geary , D. C. 1994 . Children's mathematical development: Research and practical applications , Washington, DC : American Psychological Association .
   Google Scholar
• Gelman , R. and Gallistel , C. R. 1978 . The child's understanding of number , Cambridge, MA : Harvard University Press .
   Google Scholar
• Gibson , D. J. and Shusterman , A. Poster presented at the biennial meeting of the Society for Child Development . Denver, CO. Evidence for very early understanding that “two” means “a pair.” ,
   Google Scholar
• Ginsburg , H. P. 1977 . Children's arithmetic , New York, NY : D. Van Nostrand .
   Google Scholar
• Huttenlocher , J. , Jordan , N. C. and Levine , S. C. 1994 . A mental model for early arithmetic . Journal of Experimental Psychology: General , 123 : 284 – 296 .
   PubMed Web of Science ®Google Scholar
• Klahr , D. and Wallace , J. G. 1973 . The role of quantification operators in the development of conservation of quantity . Cognitive Psychology , 4 : 301 – 327 .
   Web of Science ®Google Scholar
• Klahr , D. and Wallace , J. G. 1976 . Cognitive development: An information-processing view , Hillsdale, NJ : Erlbaum .
   Google Scholar
• Langer , J. 2000 . Response to peer commentaries . Developmental Science , 3 ( 4 ) : 385 – 388 .
   Web of Science ®Google Scholar
• Lawler , R. 1981 . The progressive construction of mind . Cognitive Science , 5 : 1 – 30 .
   Web of Science ®Google Scholar
• Le Corre , M. and Carey , S. 2007 . One, two, three, four, nothing more: An investigation of the conceptual sources of the verbal counting principles . Cognition , 105 : 395 – 438 .
   PubMed Web of Science ®Google Scholar
• Le Corre , M. and Carey , S. 2008 . Why the verbal counting principles are constructed out of representations of small sets of individuals: A reply to Gallistel . Cognition , 107 : 650 – 662 .
   PubMed Web of Science ®Google Scholar
• Le Corre , M. , Van de Walle , G. , Brannon , E. M. and Carey , S. 2006 . Re-visiting the competence/performance debate in the acquisition of the counting principles . Cognitive Psychology , 52 : 130 – 169 .
   PubMed Web of Science ®Google Scholar
• Mix , K. S. 1999a . Preschoolers’ recognition of numerical equivalence: Sequential sets . Journal of Experimental Child Psychology , 74 : 309 – 332 .
   PubMed Web of Science ®Google Scholar
• Mix , K. S. 1999b . Similarity and numerical equivalence: Appearances count . Cognitive Development , 14 : 269 – 297 .
   Web of Science ®Google Scholar
• Mix , K. S. 2002 . The construction of number concepts . Cognitive Development , 17 : 1345 – 1363 .
   Web of Science ®Google Scholar
• Mix , K. S. 2009 . How Spencer made number: First uses of the number words . Journal of Experimental Child Psychology , 102 : 427 – 444 .
   PubMed Web of Science ®Google Scholar
• Mix , K. S. , Huttenlocher , J. and Levine , S. C. 1996 . Do preschool children recognize auditory-visual numerical correspondences? . Child Development , 67 : 1592 – 1608 .
   PubMed Web of Science ®Google Scholar
• Mix , K. S. , Huttenlocher , J. and Levine , S. C. 2002 . Quantitative development in infancy and early childhood , New York, NY : Oxford University Press .
   Google Scholar
• Mix , K. S. , Sandhofer , C. M. and Baroody , A. J. 2005 . “ Number words and number concepts: The interplay of verbal and nonverbal processes in early quantitative development ” . In Advances in child development and behavior, Vol. 33 , Edited by: Kail , R. New York, NY : Academic Press .
   Google Scholar
• Piaget , J. 1965 . The child's conception of number , New York, NY : Norton .
   Google Scholar
• Piaget , J. and Inhelder , B. 1969 . The psychology of the child , New York, NY : Basic Books .
   Google Scholar
• Resnick , L. B. 1992 . “ From protoquantities to operators: Building mathematical competence on a foundation of everyday knowledge ” . In Analysis of arithmetic for mathematics teaching , Edited by: Leinhardt , G. , Putnam , R. and Hattrup , R. A. 373 – 425 . Hillsdale, NJ : Erlbaum .
   Google Scholar
• Resnick , L. B. and Ford , W. W. 1981 . The psychology of mathematics for instruction , Hillsdale, NJ : Erlbaum .
   Google Scholar
• Rice , M. 1980 . Cognition to language: Categories, word meanings, and training , Baltimore, MD : University Park Press .
   Google Scholar
• Sandhofer , C. M. and Smith , L. B. 1999 . Learning color words involves learning a system of mappings . Developmental Psychology , 35 : 668 – 679 .
   PubMed Web of Science ®Google Scholar
• Sarnecka , B. W. and Carey , S. 2008 . How counting represents number: What children must learn and when they learn it . Cognition , 108 : 662 – 674 .
   PubMed Web of Science ®Google Scholar
• Sarnecka , B. W. , Kamenskaya , V. G. , Yamana , Y. , Ogura , T. and Yudovina , J. B. 2007 . From grammatical number to exact numbers: Early meanings of “one,” “two,” and “three” in English, Russian, and Japanese . Cognitive Psychology , 55 : 136 – 168 .
   PubMed Web of Science ®Google Scholar
• Sarnecka , B. W. and Lee , M. D. 2009 . Levels of number knowledge during early childhood . Journal of Experimental Child Psychology , 103 : 325 – 337 .
   PubMed Web of Science ®Google Scholar
• Saxe , G. B. , Guberman , S. and Gearhart , M. 1987 . Social processes in early number development . Monographs of the Society for Research in Child Development , 52 (Serial No. 2)
   PubMed Web of Science ®Google Scholar
• Schaeffer , B. , Eggleston , V. H. and Scott , J. L. 1974 . Number development in young children . Cognitive Psychology , 6 : 357 – 379 .
   Web of Science ®Google Scholar
• Simon , T. J. 1997 . Reconceptualizing the origins of numerical knowledge: A “nonnumerical” account . Cognitive Development , 12 : 349 – 372 .
   Web of Science ®Google Scholar
• Smith , L. 2002 . “ Reasoning by mathematical induction in children's arithmetic ” . Boston, MA : Pergamon .
   Google Scholar
• Sophian , C. 1992 . “ Learning about numbers: Lessons for mathematics education from preschool number development ” . In Pathways to number , Edited by: Bideaud , J. and Meljac , C. 19 – 40 . Hillsdale, NJ : Erlbaum .
   Google Scholar
• Spelke , E. 2003 . “ What makes us smart? Core knowledge and natural language ” . In Language in mind , Edited by: Genter , D. and Goldin-Meadow , S. Cambridge, MA : MIT Press .
   Google Scholar
• Starkey , P. and Cooper , R. G. 1995 . The development of subitizing in young children . British Journal of Developmental Psychology , 13 : 399 – 420 .
   Web of Science ®Google Scholar
• Starkey , P. , Spelke , E. S. and Gelman , R. 1990 . Numerical abstraction by human infants . Cognition , 36 : 97 – 127 .
   PubMed Web of Science ®Google Scholar
• Steffe , L. and Cobb , P. 1988 . Construction of arithmetical meanings and strategies , New York, NY : Springer-Verlag .
   Google Scholar
• von Glasersfeld , E. 1982 . Subitizing: The role of figural patterns in the development of numerical concepts . Archives de Psychologie , 50 : 191 – 218 .
   Google Scholar
• von Glasersfeld , E. 1991 . “ Abstraction, re-presentation, and reflection: An interpretation of experience and Piaget's approach ” . In Epistemological foundations of mathematical experience , Edited by: Steffe , L. P. 46 – 67 . New York, NY : Springer-Verlag .
   Google Scholar
• Wagner , S. H. and Walters , J. A. 1982 . “ A longitudinal analysis of early number concepts ” . In Action and thought: From sensorimotor schemes to symbolic operations , Edited by: Forman , G. 137 – 161 . New York, NY : Academic Press .
   Google Scholar
• Walkerdine , V. 1988 . The mastery of reason: Cognitive development and the production of rationality , New York, NY : Routledge .
   Google Scholar
• Waxman , S. R. and Markow , D. B. 1995 . Words as invitations to form categories: Evidence from 12- to 13-month-old infants . Cognitive Psychology , 29 : 257 – 302 .
   PubMed Web of Science ®Google Scholar
• Wilkins , J. L. M. and Baroody , A. J. 2000 . “ An additional explanation for production deficiencies ” . In Proceedings of the Twenty-Second Annual Meeting North American Chapter of the International Group for the Psychology of Mathematics Education , Edited by: Fernández , M. L. Vol. 2 , 740 Columbus, OH : The Eric Clearinghouse for Science, Mathematics, and Environment Education .
   Google Scholar
• Wynn , K. 1990 . Children's understanding of counting . Cognition , 36 : 155 – 193 .
   PubMed Web of Science ®Google Scholar
• Wynn , K. 1992 . Children's acquisition of the counting words in the number system . Cognitive Psychology , 24 : 220 – 251 .
   Web of Science ®Google Scholar
• Wynroth , L. 1986 . Wynroth math program—The natural numbers sequence , Ithaca, NY : Wynroth Math Program (Original work published in 1975) .
   Google Scholar