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Why frequencies are natural

Published online by Cambridge University Press:  29 October 2007

Brian Butterworth
Affiliation:
Institute of Cognitive Neuroscience, University College London, London WC1N 3AR, United Kingdom. b.butterworth@ucl.ac.uk

Abstract

Research in mathematical cognition has shown that rates, and other interpretations of x/y, are hard to learn and understand. On the other hand, there is extensive evidence that the brain is endowed with a specialized mechanism for representing and manipulating the numerosities of sets – that is, frequencies. Hence, base-rates are neglected precisely because they are rates, whereas frequencies are indeed natural.

Type
Open Peer Commentary
Copyright
Copyright © Cambridge University Press 2007

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References

Antell, S. E. & Keating, D. P. (1983) Perception of numerical invariance in neonates. Child Development 54:695701.Google Scholar
Bonato, M., Fabbri, S., Umiltà, C. & Zorzi, M. (in press) The mental representation of numerical fractions: Real or integer? Journal of Experimental Psychology: Human Perception and Performance.Google Scholar
Brannon, E. M. & Terrace, H. S. (1998) Ordering of the numerosities 1 to 9 by monkeys. Science 282:746–49.CrossRefGoogle ScholarPubMed
Brannon, E. M. & Terrace, H. S. (2000) Representation of the numerosities 1–9 by rhesus macaques (Macaca mulatta). Journal of Experimental Psychology: Animal Behavior Processes 26(1):3149.Google ScholarPubMed
Bright, G. W., Behr, M. J., Post, T. R. & Wachsmuth, I. (1988) Identifying fractions on number lines. Journal for Research in Mathematics Education 19(3):215–32.Google Scholar
Butterworth, B. (1999) The mathematical brain. Macmillan.Google Scholar
Butterworth, B. (2001) What seems natural? Science 292:853–54.CrossRefGoogle ScholarPubMed
Cantlon, J. F., Brannon, E. M., Carter, E. J. & Pelphrey, K. A. (2006) Functional imaging of numerical processing in adults and 4-year-old children. Public Library of Science Biology 4(5):844–54.Google Scholar
Castelli, F., Glaser, D. E. & Butterworth, B. (2006) Discrete and analogue quantity processing in the parietal lobe: A functional MRI study. Proceedings of the National Academy of Science 103(12):4693–98.CrossRefGoogle ScholarPubMed
Cosmides, L. & Tooby, J. (1996) Are humans good intuitive statisticians after all? Rethinking some conclusions from the literature on judgment under uncertainty. Cognition 58:173.CrossRefGoogle Scholar
Dehaene, S., Spelke, E., Pinel, P., Stanescu, R. & Tsivkin, S. (1999) Sources of mathematical thinking: Behavioral and brain-imaging evidence. Science 284(5416):970–74.CrossRefGoogle ScholarPubMed
Fabbri, S., Tang, J., Butterworth, B. & Zorzi, M. (submitted) The mental representation of fractions: Interaction between numerosity and proportion processing with non-symbolic stimuli.Google Scholar
Fodor, J. A. (1983) Modularity of mind. MIT Press.CrossRefGoogle Scholar
Gigerenzer, G. & Hoffrage, U. (1995) How to improve Bayesian reasoning without instruction: Frequency formats. Psychological Review 102:684704.CrossRefGoogle Scholar
Hartnett, P. & Gelman, R. (1998) Early understandings of numbers: Paths or barriers to the construction of new understandings? Learning and Instruction 8(4):341–74.CrossRefGoogle Scholar
Hauser, M., MacNeilage, P. & Ware, M. (1996) Numerical representations in primates. Proceedings of the National Academy of Sciences USA 93:1514–17.Google Scholar
Lemer, C., Dehaene, S., Spelke, E. & Cohen, L. (2003) Approximate quantities and exact number words: dissociable systems. Neuropsychologia 41(14):1942–58.Google Scholar
Mack, N. (1995) Confounding whole-number and fraction concepts when building on informal knowledge. Journal for Research Mathematics Education 26:422–41.Google Scholar
Matsuzawa, T. (1985) Use of numbers by a chimpanzee. Nature 315:5759.Google Scholar
Ni, Y. & Zhou, Y. (2005) Teaching and learning fraction and rational numbers: The origins and implications of whole number bias. Educational Psychologist 40:2752.CrossRefGoogle Scholar
Nieder, A. (2005) Counting on neurons: The neurobiology of numerical competence. Nature Reviews Neuroscience 6(3):114.CrossRefGoogle ScholarPubMed
Piazza, M., Izard, V., Pinel, P., Le Bihan, D. & Dehaene, S. (2004) Tuning curves for approximate numerosity in the human intraparietal sulcus. Neuron 44:547–55.Google Scholar
Piazza, M., Mechelli, A., Butterworth, B. & Price, C. (2002) Are subitizing and counting: implemented as separate or functionally overlapping processes? NeuroImage 15(2):435–46.CrossRefGoogle ScholarPubMed
Piazza, M., Mechelli, A., Price, C. J. & Butterworth, B. (2006) Exact and approximate judgements of visual and auditory numerosity: An fMRI study. Brain Research 1106:177–88.Google Scholar
Piazza, M., Pinel, P., Le Bihan, D., & Dehaene, S. (2007) A magnitude code common to numerosities and number symbols in human intraparietal cortex. Neuron 53(2):293305.CrossRefGoogle ScholarPubMed
Smith, C. L., Solomon, G. E. A. & Carey, S. (2005) Never getting to zero: Elementary school students' understanding of the infinite divisibility of number and matter. Cognitive Psychology 51:101–40.CrossRefGoogle ScholarPubMed
Stafylidou, S. & Vosniadou, S. (2004) The development of student's understanding of the numerical value of fractions. Learning and Instruction 14:508–18.CrossRefGoogle Scholar
Starkey, P. & Cooper, R. G. Jr. (1980) Perception of numbers by human infants. Science 210:1033–35.Google Scholar
Tversky, A. & Kahneman, D. (1974) Judgment under uncertainty: Heuristics and biases. Science 185:1124–31.Google Scholar
Wynn, K., Bloom, P. & Chiang, W. C. (2002) Enumeration of collective entities by 5-month-old infants. Cognition 83(3):B55B62.Google Scholar