The Mental Representation of Numerical Fractions: Real or Integer?

Journal of Experimental Psychology: Human Perception and Performance

Volumn 33, Issue 6, 2007, Pages 1410-1419

  Bonato, Mario ^a   Fabbri, Sara ^a   Umiltà, Carlo ^a   Zorzi, Marco ^a  

^a UNIVERSITY OF PADOVA   (Italy)

Author keywords

distance effect; fractions; magnitude representation; SNARC effect; whole number bias

Indexed keywords

ADULT; ANALYSIS OF VARIANCE; APTITUDE; ARTICLE; ATTENTION; AWARENESS; COMPREHENSION; FEMALE; HUMAN; LEARNING; MALE; MATHEMATICS; PROBLEM SOLVING; REACTION TIME;

ADULT; ANALYSIS OF VARIANCE; APTITUDE; ATTENTION; AWARENESS; COMPREHENSION; FEMALE; HUMANS; MALE; MATHEMATICS; PRACTICE (PSYCHOLOGY); PROBLEM SOLVING; REACTION TIME;

EID: 38349120491     PISSN: 00961523     EISSN: None     Source Type: Journal    
DOI: 10.1037/0096-1523.33.6.1410     Document Type: Article

References (34)

1. Barth H., La Monta K., Lipton J., Dehaene S., Kanwisher N., and Spelke E. Non-symbolic arithmetic in adults and young children. Cognition 98 (2006) 199-222
2. Bell E.T. Men of mathematics (1937), Simon and Schuster, New York
3. Bright G.W., Behr M.J., Post T.R., and Wachsmuth I. Identifying fractions on number lines. Journal for Research in Mathematics Education 19 (1998) 215-232
4. Butterworth B. Statistics: What seems natural?. Science 292 (2001) 853-855
5. Dehaene S., Bossini S., and Giraux P. The mental representation of parity and number magnitude. Journal of Experimental Psychology: General 122 (1993) 371-396
6. Dehaene S., Dehaene-Lambertz G., and Cohen L. Abstract representation of numbers in the animal and human brain. Trends in Neurosciences 21 (1998) 355-361
7. Dehaene S., Dupoux E., and Mehler J. Is numerical comparison digital? Analogical and symbolic effects in two-digit number comparison. Journal of Experimental Psychology: Human Perception and Performance 16 (1990) 626-641
8. Feigenson L., Dehaene S., and Spelke E. Core systems of number. Trends in Cognitive Sciences 8 (2004) 307-314
9. Fias W., Brysbaert M., Geypens F., and d'Ydewalle G. The importance of magnitude information in numerical processing: Evidence from the SNARC effect. Mathematical Cognition 2 (1996) 95-110
10. Fias W., and Fischer M.H. Spatial representation of numbers. In: Campbell J.I.D. (Ed). Handbook of mathematical cognition (2005), Psychology Press, New York 43-54
11. Fischer M.H. Cognitive representation of negative numbers. Psychological Science 14 (2003) 278-282
12. Fischer M.H., and Rottmann J. Do negative numbers have a place on the mental number line?. Psychology Science 47 (2005) 22-32
13. Fuson K.C., and Abrahamson D. Understanding ratio and proportion as an example of the apprehending zone and conceptual-phase problem-solving models. In: Campbell J.I.D. (Ed). Handbook of mathematical cognition (2005), Psychology Press, New York 213-233
14. Gallistel C.R., and Gelman R. Non-verbal numerical cognition: From reals to integers. Trends in Cognitive Sciences 4 (2000) 59-65
15. Gevers W., Verguts T., Reynvoet B., Caessens B., and Fias W. Numbers and space: A computational model of the SNARC effect. Journal of Experimental Psychology: Human Perception and Performance 32 (2006) 1197-1207
16. Gigerenzer G., and Hoffrage U. Overcoming difficulties in Bayesian reasoning: A reply to Lewis and Keren (1999) and Mellers and McGraw (1999). Psychological Review 106 (1999) 425-430
17. Hartnett P., and Gelman R. Early understandings of numbers: Paths or barriers to the construction of new understandings?. Learning and Instruction 8 (1998) 341-374
18. Lemaire P., and Siegler R.S. Four aspects of strategic change: Contributions to children's learning of multiplication. Journal of Experimental Psychology: General 124 (1995) 83-97
19. Lorch Jr. R.F., and Myers J.L. Regression analyses of repeated measures data in cognitive research: A comparison of three different methods. Journal of Experimental Psychology: Learning, Memory, and Cognition 16 (1990) 149-157
20. Mack N. Confounding whole-number and fraction concepts when building on informal knowledge. Journal for Research in Mathematics Education 26 (1995) 422-441
21. Mix K., Levine S., and Huttenlocher J. Early fraction calculation ability. Developmental Psychology 35 (1999) 164-174
22. Moyer R.S., and Landauer T.K. Time required for judgements of numerical inequality. Nature 215 (1967) 1519-1520
23. Ni Y., and Zhou Y. Teaching and learning fraction and rational numbers: The origins and implications of whole number bias. Educational Psychologist 40 (2005) 27-52
24. Nuerk H.C., Weger U., and Willmes K. Decade breaks in the mental number line? Putting the tens and units back in different bins. Cognition 82 (2001) 25-33
25. Piazza M., Izard V., Pinel P., Le Bihan D., and Dehaene S. Tuning curves for approximate numerosity in the human intraparietal sulcus. Neuron 44 (2004) 547-555
26. Smith C.L., Solomon G.E.A., and Carey S. Never getting to zero: Elementary school students' understanding of the infinite divisibility of number and matter. Cognitive Psychology 51 (2005) 101-140
27. Sophian C., Garyantes D., and Chang C. When three is less than two: Early developments in children's understanding of fractional quantities. Developmental Psychology 33 (1997) 731-744
28. Stafylidou S., and Vosniadou S. The development of student's understanding of the numerical value of fractions. Learning and Instruction 14 (2004) 508-518
29. Wu Z. Multiplying fractions. Teaching Children Mathematics 8 (2001) 174-177
30. Zorzi M., and Butterworth B. On the representation of number concepts. In: Shafto M.G., and Langley P. (Eds). Ninth annual conference of the Cognitive Science Society (1997), Erlbaum, Mahwah, NJ
31. Zorzi, M., & Butterworth, B. (1999). A computational model of number comparison. In M. Hahn & S. C. Stoness (Eds.), Proceedings of the twenty first annual conference of the Cognitive Science Society (pp. 778-783). Mahwah, NJ: Erlbaum.
32. Zorzi M., Priftis K., and Umiltà C. Brain damage: Neglect disrupts the mental number line. Nature 417 (2002) 138-139
33. Zorzi, M., Stoianov, I., Becker, S., Umiltà, C., & Butterworth, B. (2006). The numerosity code for the representation of numerical magnitude. Manuscript submitted for publication.
34. Zorzi M., Stoianov I., and Umiltà C. Computational modeling of numerical cognition. In: Campbell J. (Ed). Handbook of mathematical cognition (2005), Psychology Press, New York 67-84