The mental representations of fractions: Adults' same-different judgments

Frontiers in Psychology

Volumn 4, Issue JUL, 2013, Pages

  Gabriel, Florence ^a   Szucs, Denes ^a   Content, Alain ^a  

^a University of Cambridge   (United Kingdom)

Author keywords

Fractions; Magnitude processing; Numerical cognition; Same different task; Symbolic distance effect

Indexed keywords

EID: 84885344137     PISSN: None     EISSN: 16641078     Source Type: Journal    
DOI: 10.3389/fpsyg.2013.00385     Document Type: Article

References (24)

1. Baayen, R. H., Davidson, D. J., and Bates, D. (2008). Mixed-effects modeling with crossed random effects for subjects and items. J. Mem. Lang. 59, 390-412. doi: 10.1016/j.jml.2007.12.005
2. Bonato, M., Fabbri, S., Umiltà, C., and Zorzi, M. (2007). The mental representation of numerical fractions: realor integer. J. Exp. Psychol. Hum. Percept. Perform. 33, 1410-1419.
3. Cohen, D. (2009). Integers do not automatically activate their quantity representation. Psychon. Bull. Rev. 16, 332-336. doi: 10.3758/PBR.16.2.332
4. Dehaene, S. (1997). The Number Sense. New York, NY: Oxford University Press. Dehaene, S., and Akhavein, R. (1995). Attention, automaticity and levels of representation in number processing. J. Exp. Psychol. Learn. Mem. Cogn. 21, 314-326. doi: 10.1037/0278-7393.21.2.314
5. Dehaene, S., and Akhavein, R. (1995). Attention, automaticity and levels of representation in number processing. J. Exp. Psychol. Learn. Mem. Cogn. 21, 314-326. doi: 10.1037/0278-7393.21.2.314
6. Faulkenberry, T. J., and Pierce, B. H. (2011). Mental representations in fraction comparison. Exp. Psychol. 58, 480-489. doi: 10.1027/1618-3169/a000116
7. Gallistel, C. R., Gelman, R., and Cordes, S. (2005). "The cultural and evolutionary history of the real numbers," in Culture and Evolution: A Fyssen Foundation Symposium, eds P. Jaisson and S. C. Levinson (Cambridge, MA: MITPress), 247-274.
8. Henik, A., and Tzelgov, J. (1982). Is three greater than five: The relation between physical and semantic size in comparison tasks. Mem. Cognit. 10, 389-395. doi: 10.3758/BF03202431
9. Ischebeck, A., Schocke, M., and Delazer, M. (2009). The processing and representation of fractions within the brain. An fMRI investigation. Neuroimage 47, 403-413. doi: 10.1016/j.neuroimage.2009.03.041
10. Jacob, S., and Nieder, A. (2009). Notation-independent representation of fractions in the human parietal cortex. J. Neurosci. 29, 4652-4657. doi: 10.1523/JNEUROSCI.0651-09.2009
11. Kallai, A., and Tzelgov, J. (2009). A generalized fraction: an entity smaller than one on the mental number line. J. Exp. Psychol. Hum. Percept. Perform. 35, 1845-1864.
12. Mack, N. (1993). "Learning rational numbers with understanding: the case of informal knowledge," in Rational Numbers: An Integration of Research, eds T. P. Carpenter, E. Fennema, and T. A. Romberg (Hillsdale, NJ: Lawrence Erlbaum Associates), 85-105.
13. McCrink, K., and Wynn, K. (2007). Ratio abstraction by 6-month-old infants. Psychol. Sci. 18, 740-745. doi: 10.1111/j.1467-9280.2007.01969.x
14. Meert, G., Grégoire, J., and Noël, M.-P. (2009). Rational numbers: componential versus holistic representation of fractions in a magnitude comparison task. Q. J. Exp. Psychol. 62, 1598-1616. doi: 10.1080/17470210802511162
15. Meert, G., Grégoire, J., and Noël, M. P. (2010). Comparing 5/7 and 2/9: adults can do it by accessing the magnitude of the whole fractions. Acta Psychol. 135, 284-292. doi: 10.1016/j.actpsy.2010.07.014
16. Moyer, R. S., and Landauer, T. K. (1967). Time required for judgements of numerical inequality. Nature 215, 1519-1520. doi: 10.1038/2151519a0
17. Quené, H., and Van den Bergh, H. (2008). Examples of mixed-effects modeling with crossed random effects and withbinomial data. J. Mem. Lang. 59, 413-425. doi: 10.1016/j.jml.2008.02.002
18. Schneider, M., and Siegler, R. S. (2010). Representations of the magnitudes of fractions. J. Exp. Psychol. Hum. Percept. Perform. 36, 1227-1238. doi: 10.1037/a0018170
19. Szucs, D., Soltész, F., Jármi, É., and Csépe, V. (2007). The speed of magnitude processing and executive functions in controlled and automatic number comparison in children: an electro-encephalography study. Behav. Brain Funct. 3:23. doi: 10.1186/1744-9081-3-23
20. Tzelgov, J., and Ganor-Stern, D. (2004). "Automaticity in processing ordinal information," in Handbook of Mathematical Cognition, ed J. I. D. Campbell (New York, NY: Psychology Press), 55-67.
21. Tzelgov, J., and Henik, A. (1991). Suppression situations in psychological research: definitions, implications, and applications. Psychol. Bull. 109, 524-536. doi: 10.1037/0033-2909.109.3.524
22. Vallentin, D., and Nieder, A. (2008). Behavioral and prefrontal representation of spatial proportions in the monkey. Curr. Biol. 18, 1420-1425. doi: 10.1016/j.cub.2008.08.042
23. Van Opstal, F., and Verguts, T. (2011). The origins of the numerical distance effect: the same different task. J. Cogn. Psychol. 23, 112-120. doi: 10.1080/20445911.2011.466796
24. 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. doi: 10.1016/j.cognition.2007.06.003