Rational numbers: Componential versus holistic representation of fractions in a magnitude comparison task

REFERENCES

• Behr , M. J. , Harel , G. , Post , T. and Lesh , R. 1992 . “ Rational number, ratio, and proportion ” . In Handbook of research on mathematics teaching and learning. A project of the national council of teachers of mathematics , Edited by: Grouws , D. A. 296 – 333 . New York : Simon and Schuster Macmillan .
   Google Scholar
• Bonato , M. , Fabbri , S. , Umiltà , C. and Zorzi , M. 2007 . The mental representation of numerical fractions: Real or integer? . Journal of Experimental Psychology: Human Perception and Performance , 33 : 1410 – 1419 .
   PubMed Web of Science ®Google Scholar
• Dehaene , S. , Bossini , S. and Giraux , P. 1993 . The mental representation of parity and number magnitude . Journal of Experimental Psychology: General , 122 : 371 – 396 .
   Web of Science ®Google Scholar
• Dehaene , S. , Dupoux , E. and Mehler , J. 1990 . Is numerical comparison digital? Analogical and symbolic effects in two-digit number comparison . Journal of Experimental Psychology: Human Perception and Performance , 16 : 626 – 641 .
   PubMed Web of Science ®Google Scholar
• English , L. D. and Halford , G. S. 1995 . Mathematics education: Models and processes , Mahwah, NJ : Lawrence Erlbaum Associates, Inc. .
   Google Scholar
• Field , A. 2005 . Discovering statistics using SPSS , London : Sage .
   Google Scholar
• Fischer , M. H. and Rottmann , J. 2005 . Do negative numbers have a place on the mental number line? . Psychology Science , 47 : 22 – 32 .
   Google Scholar
• Gallistel , C. R. and Gelman , R. 2000 . Non-verbal numerical cognition: From reals to integers . Trends in Cognitive Sciences , 4 : 59 – 65 .
   PubMed Web of Science ®Google Scholar
• Gallistel , C. R. , Gelman , R. and Cordes , S. The cultural and evolutionary history of the real numbers . Culture and evolution: A Fyssen Foundation symposium . Cambridge, MA. Edited by: Jaisson , P. and Levinson , S. C. pp. 247 – 274 . MIT Press .
   Google Scholar
• Gevers , W. and Lammertyn , J. 2005 . The hunt for SNARC . Psychology Science , 47 : 10 – 21 .
   Google Scholar
• Grégoire , J. and Meert , G. 2005 . “ L'apprentissage des nombres rationnels et ses obstacles [Rational number learning and its obstacles] ” . In La dyscalculie. Trouble du développement numérique chez l'enfant , Edited by: Noël , M. P. 223 – 251 . Marseille, , France : Solal .
   Google Scholar
• Hair , J. F. , Anderson , R. E. , Tatham , R. L. and Black , W. C. 1998 . Multivariate data analysis , Upper Saddle River, NJ : Prentice Hall .
   Google Scholar
• Hartnett , P. and Gelman , R. 1998 . Early understandings of numbers: Paths or barriers to the construction of new understandings? . Learning and Instruction , 8 : 341 – 374 .
   Web of Science ®Google Scholar
• Howell , D. C. 1998 . Méthodes statistiques en sciences humaines , Bruxelles : De Boeck . [Statistical methods for psychology] (M. Rogier, Trans.) (Original work published 1997.)
   Google Scholar
• Hubbard , E. M. , Piazza , M. , Pinel , P. and Dehaene , S. 2005 . Interactions between number and space in parietal cortex . Nature Reviews Neuroscience , 6 : 435 – 448 .
   PubMed Web of Science ®Google Scholar
• Mack , N. K. 1993 . “ Learning rational numbers with understanding: The case of informal knowledge ” . In Rational numbers. An integration of research , Edited by: Carpenter , T. P. , Fennema , E. and Romberg , T. A. 85 – 105 . Hillsdale, NJ : Lawrence Erlbaum Associates, Inc. .
   Google Scholar
• Moyer , R. S. and Landauer , T. K. 1967 . Time required for judgements of numerical inequality . Nature , 215 : 1519 – 1520 .
   PubMed Web of Science ®Google Scholar
• Ni , Y. and Zhou , Y. D. 2005 . Teaching and learning fraction and rational numbers: The origins and implications of whole number bias . Educational Psychologist , 40 : 27 – 52 .
   Web of Science ®Google Scholar
• Nuerk , H. C. , Iversen , W. and Willmes , K. 2004 . Notational modulation of the SNARC and the MARC (linguistic markedness of response codes) effect . Quarterly Journal of Experimental Psychology , 57A : 835 – 863 .
   Web of Science ®Google Scholar
• Nuerk , H. C. , Weger , U. and Willmes , K. 2001 . Decade breaks in the mental number line? Putting the tens and units back in different bins . Cognition , 82 : B25 – B33 .
   PubMed Web of Science ®Google Scholar
• Nuerk , H. C. and Willmes , K. 2005 . On the magnitude representations of two-digit numbers . Psychology Science , 47 : 52 – 72 .
   Google Scholar
• Ratinckx , E. , Brysbaert , M. and Fias , W. 2005 . Naming two-digit Arabic numerals: Evidence from masked priming studies . Journal of Experimental Psychology: Human Perception and Performance , 31 : 1150 – 1163 .
   PubMed Web of Science ®Google Scholar
• Reynvoet , B. and Brysbaert , M. 1999 . Single-digit and two-digit Arabic numerals address the same semantic number line . Cognition , 72 : 191 – 201 .
   PubMed Web of Science ®Google Scholar
• Shaki , S. and Petrusic , W. M. 2005 . On the mental representation of negative numbers: Context-dependent SNARC effects with comparative judgments . Psychonomic Bulletin and Review , 12 : 931 – 937 .
   PubMed Web of Science ®Google Scholar
• Sophian , C. 1996 . Children's numbers , Boulder, CO : Westview Press .
   Google Scholar
• Stafylidou , S. and Vosniadou , S. 2004 . The development of students' understanding of the numerical value of fractions . Learning and Instruction , 14 : 503 – 518 .
   Web of Science ®Google Scholar
• Tzelgov , J. and Henik , A. 1991 . Suppression situations in psychological research: Definitions, implications, and applications . Psychological Bulletin , 109 : 524 – 536 .
   Web of Science ®Google Scholar
• Verguts , T. and De Moor , W. 2005 . Two-digit comparison: Decomposed, holistic, or hybrid? . Experimental Psychology , 52 : 195 – 200 .
   PubMed Web of Science ®Google Scholar
• Whalen , J. , Gallistel , C. R. and Gelman , R. 1999 . Nonverbal counting in humans: The psychophysics of number representation . Psychological Science , 10 : 130 – 137 .
   Web of Science ®Google Scholar
• Zhang , J. and Wang , H. 2005 . The effect of external representations on numeric tasks . Quarterly Journal of Experimental Psychology , 58A : 817 – 838 .
   Google Scholar
• Zhou , X. , Chen , C. , Chen , L. and Dong , R. 2008 . Holistic or compositional representation of two-digit numbers? Evidence from the distance, magnitude, and SNARC effects in a number-matching task . Cognition , 106 : 1525 – 1536 .
   PubMed Web of Science ®Google Scholar