440
Views
17
CrossRef citations to date
0
Altmetric
Regular articles

The mental representation of the magnitude of symbolic and nonsymbolic ratios in adults

, , &
Pages 702-724 | Received 02 Jun 2010, Published online: 05 Jan 2012

REFERENCES

  • Ansari , D. , Donlan , C. and Karmiloff-Smith , A. K. 2007 . Typical and atypical development of visual estimation abilities . Cortex , 43 : 758 – 768 .
  • Balci , F. and Gallistel , C. R. 2006 . Cross-domain transfer of quantitative discriminations: Is it all a matter of proportion? . Psychonomic Bulletin & Review , 13 : 636 – 642 .
  • Barth , H. , Baron , A. , Spelke , E. and Carey , S. 2009 . Children's multiplicative transformations of discrete and continuous quantities . Journal of Experimental Child Psychology , 103 : 441 – 454 .
  • Barth , H. , La Mont , K. , Lipton , J. , Dehaene , S. , Kanwisher , N. and Spelke , E. 2006 . Non-symbolic arithmetic in adults and young children . Cognition , 98 : 199 – 222 .
  • Barth , H. and Paladino , A. M. 2011 . The development of numerical estimation: Evidence against a representational shift . Developmental Science , 14 : 125 – 135 .
  • 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 .
  • Boyer , T. W. , Levine , S. C. and Huttenlocher , J. 2008 . Development of proportional reasoning: Where young children go wrong . Developmental Psychology , 44 : 1478 – 1490 .
  • Butterworth , B. 2007 . Why frequencies are natural . Behavioral and Brain Sciences , 30 : 259 – 260 .
  • Cohen , D. and Blanc-Goldhammer , D. 2011 . Numerical bias in bounded and unbounded number line tasks . Psychonomic Bulletin & Review , 18 : 331 – 338 .
  • Cordes , S. , Gallistel , C. R. , Gelman , R. and Latham , P. 2007 . Nonverbal arithmetic in humans: Light from noise . Perception & Psychophysics , 69 : 1185 – 1203 .
  • Dehaene , S. 1992 . Varieties of numerical abilities . Cognition , 44 : 1 – 42 .
  • Dehaene , S. 2003 . The neural basis of the Weber–Fechner law: A logarithmic mental number . Trends in Cognitive Sciences , 7 : 145 – 147 .
  • Dehaene , S. , Piazza , M. , Pinel , P. and Cohen , L. 2003 . Three parietal circuits for number processing . Cognitive Neuropsychology , 20 : 487 – 506 .
  • Fias , W. , Lammertyn , J. , Reynvoet , B. , Dupont , P. and Orban , G. A. 2003 . Parietal representation of symbolic and nonsymbolic magnitude . Journal of Cognitive Neuroscience , 15 : 47 – 56 .
  • Gallistel , C. R. 1990 . Organization of learning , Cambridge , MA : MIT Press .
  • Gallistel , C. R. and Gelman , R. 1992 . Preverbal and verbal counting and computation . Cognition , 44 : 43 – 74 .
  • Gallistel , C. R. and Gelman , R. 2000 . Non-verbal numerical cognition: From reals to integers . Trends in Cognitive Sciences , 4 : 59 – 65 .
  • Gallistel , C. R. , Gelman , R. and Cordes , S. 2006 . “ The cultural and evolutionary history of the real numbers ” . In Evolution and culture: A Fyssen Foundation symposium , Edited by: Jaisson , P. and Levinson , S. C. Vol. XVII , 247 – 274 . Cambridge , MA : MIT Press .
  • Hollands , J. G. and Dyre , B. P. 2000 . Bias in proportion judgments: The cyclical power model . Psychological Review , 107 : 500 – 524 .
  • Hollands , J. G. , Tanaka , T. and Dyre , B. P. 2002 . Understanding bias in proportion production . Journal of Experimental Psychology: Human Perception and Performance , 28 : 563 – 574 .
  • Ischebeck , A. K. , Schocke , M. and Delazer , M. 2009 . The processing and representation of fractions within the brain. An fMRI investigation . NeuroImage , 47 : 403 – 413 .
  • Jacob , S. N. and Nieder , A. 2009a . Notation-independent representation of fractions in the human parietal cortex . The Journal of Neuroscience , 29 : 4652 – 4657 .
  • Jacob , S. N. and Nieder , A. 2009b . Tuning to non-symbolic proportions in the human frontoparietal cortex . European Journal of Neuroscience , 30 : 1432 – 1442 .
  • Jeong , Y. , Levine , S. C. and Huttenlocher , J. 2007 . The development of proportional reasoning: Effect of continuous versus discrete quantities . Journal of Cognition and Development , 8 : 237 – 256 .
  • Kallai , A. Y. and Tzelgov , J. 2009 . A generalized fraction: An entity smaller than one on the mental number line . Journal of Experimental Psychology: Human Perception and Performance , 35 : 1845 – 1864 .
  • Kaufman , E. L. , Lord , M. W. , Reese , T. W. and Volkmann , J. 1949 . The discrimination of visual number . The American Journal of Psychology , 62 : 498 – 525 .
  • Knops , A. , Viarouge , A. and Dehaene , S. 2009 . Dynamic representations underlying symbolic and nonsymbolic calculation: Evidence from the operational momentum effect . Attention, Perception & Psychophysics , 71 : 803 – 821 .
  • Mandler , G. and Shebo , B. J. 1982 . Subitizing—An analysis of its component processes . Journal of Experimental Psychology: General , 111 : 1 – 22 .
  • McCrink , K. , Dehaene , S. and Dehaene-Lambertz , G. 2007 . Moving along the number line: Operational momentum in nonsymbolic arithmetic . Perception & Psychophysics , 69 : 1324 – 1333 .
  • McCrink , K. and Spelke , E. S. 2010 . Core multiplication in childhood . Cognition , 116 : 204 – 216 .
  • McCrink , K. and Wynn , K. 2007 . Ratio abstraction by 6-month-old infants . Psychological Science , 18 : 740 – 745 .
  • Meert , G. , Grégoire , J. and Noël , M. P. 2009 . Rational numbers: Componential versus holistic representation of fractions in a magnitude comparison task . The Quarterly Journal of Experimental Psychology , 62 : 1598 – 1616 .
  • Meert , G. , Grégoire , J. and Noël , M. P. 2010a . Comparing 5/7 and 2/9: Adults can do it by accessing the magnitude of the whole fractions . Acta Psychologica , 135 : 284 – 292 .
  • Meert , G. , Grégoire , J. and Noël , M. P. 2010b . Comparing the magnitude of two fractions with common components: Which representations are used by 10- and 12-year-olds? . Journal of Experimental Child Psychology , 107 : 244 – 259 .
  • Mix , K. S. , Levine , S. C. and Huttenlocher , J. 1999 . Early fraction calculation ability . Developmental Psychology , 35 : 164 – 174 .
  • Morton , A. and Hollands , J. G. 2003 . Effects of response method on error and cyclical bias in proportion judgments . Proceedings of the Human Factors and Ergonomics Society 47th Annual Meeting , (pp. 1654–1658). Santa Monica, CA: Human Factors and Ergonomics Society
  • Moyer , R. S. and Landauer , T. K. 1967 . Time required for judgements of numerical inequality . Nature , 215 : 1519 – 1520 .
  • 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 .
  • Norusis , M. J. 2008 . SPSS 16.0 advanced statistical procedures companion , Upper Saddle River , NJ : Prentice Hall .
  • Opfer , J. E. , Siegler , R. S. and Young , C. J. 2011 . The powers of noise-fitting: Reply to Barth and Paladino . Developmental Science , 14 : 1194 – 1204 .
  • Schneider , M. and Siegler , R. S. 2010 . Representations of the magnitudes of fractions . Journal of Experimental Psychology: Human Perception and Performance , 36 : 1227 – 1238 .
  • Siegler , R. S. and Booth , J. L. 2005 . “ Development of numerical estimation. A review ” . In Handbook of mathematical cognition , Edited by: Campbell , J. I. D. 197 – 212 . New York , NY : Psychology Press .
  • Siegler , R. S. and Opfer , J. E. 2003 . The development of numerical estimation: Evidence for multiple representations of numerical quantity . Psychological Science , 14 : 237 – 243 .
  • Singer-Freeman , K. E. and Goswami , U. 2001 . Does half a pizza equal half a box of chocolates? Proportional matching in an analogy task . Cognitive Development , 16 : 811 – 829 .
  • Sophian , C. 2000 . Perceptions of proportionality in young children: Matching spatial ratios . Cognition , 75 : 145 – 170 .
  • Spence , I. 1990 . Visual psychophysics of simple graphical elements . Journal of Experimental Psychology: Human Perception and Performance , 16 : 683 – 692 .
  • Spinillo , A. G. 2002 . Children's use of part–part comparisons to estimate probability . The Journal of Mathematical Behavior , 21 : 357 – 369 .
  • Stafylidou , S. and Vosniadou , S. 2004 . The development of students' understanding of the numerical value of fractions . Learning and Instruction , 14 : 503 – 518 .
  • Trick , L. M. and Pylyshyn , Z. W. 1994 . Why are small and large numbers enumerated differently—A limited-capacity preattentive stage in vision . Psychological Review , 101 : 80 – 102 .
  • Vallentin , D. and Nieder , A. 2008 . Behavioral and prefrontal representation of spatial proportions in the monkey . Current Biology , 18 : 1420 – 1425 .
  • Van den Noortgate , W. and Onghena , P. 2006 . Analysing repeated measures data in cognitive research: A comment on regression coefficient analyses . European Journal of Cognitive Psychology , 18 : 937 – 952 .
  • Varey , C. A. , Mellers , B. A. and Birnbaum , M. H. 1990 . Judgments of proportions . Journal of Experimental Psychology: Human Perception and Performance , 16 : 613 – 625 .
  • Verguts , T. and Fias , W. 2004 . Representation of number in animals and humans: A neural model . Journal of Cognitive Neuroscience , 16 : 1493 – 1504 .
  • Whalen , J. , Gallistel , C. R. and Gelman , R. 1999 . Nonverbal counting in humans: The psychophysics of number representation . Psychological Science , 10 : 130 – 137 .
  • Xu , F. and Spelke , E. S. 2000 . Large number discrimination in 6-month-old infants . Cognition , 74 : B1 – B11 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.