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Précis of "The number sense"
"... Number sense " is a shorthand for our ability to quickly understand, approximate, and manipulate numerical quantities. My hypothesis is that number sense rests on cerebral circuits that have evolved specifically for the purpose of representing basic arithmetic knowledge. Four lines of evidence sugg ..."
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Cited by 151 (21 self)
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Number sense " is a shorthand for our ability to quickly understand, approximate, and manipulate numerical quantities. My hypothesis is that number sense rests on cerebral circuits that have evolved specifically for the purpose of representing basic arithmetic knowledge. Four lines of evidence suggesting that number sense constitutes a domainspecific, biologicallydetermined ability are reviewed: the presence of evolutionary precursors of arithmetic in animals; the early emergence of arithmetic competence in infants independently of other abilities, including language; the existence of a homology between the animal, infant, and human adult abilities for number processing ; and the existence of a dedicated cerebral substrate. In adults of all cultures, lesions to the inferior parietal region can specifically impair number sense while leaving the knowledge of other cognitive domains intact. Furthermore, this region is demonstrably activated during number processing. I postulate that higherlevel cultural developments in arithmetic emerge through the establishment of linkages between this core analogical representation (the " number line ") and other verbal and visual representations of number notations. The neural and cognitive organization of those representations can explain why some mathematical concepts are intuitive, while others are so difficult to grasp. Thus, the ultimate foundations of mathematics rests on core representations that have been internalized in our brains through evolution.
The psychology of science: review and integration of a nascent discipline. Review of general psychology
 Review of General Psychology
, 1998
"... Disciplines that study science are relatively well established in philosophy, history, and sociology. Psychology of science, by comparison, is a late bloomer but has recently shown signs of codification. The authors further this codification by integrating and reviewing the growing literature in the ..."
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Cited by 8 (0 self)
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Disciplines that study science are relatively well established in philosophy, history, and sociology. Psychology of science, by comparison, is a late bloomer but has recently shown signs of codification. The authors further this codification by integrating and reviewing the growing literature in the developmental, cognitive, personality, and social psychology of science. Only by integrating the findings from each of these perspectives can the basic questions in the study of scientific behavior be answered: Who becomes a scientist and what role do biology, family, school, and gender play? Are productivity, scientific reasoning, and theory acceptance influenced by age? What thought processes and heuristics lead to successful discovery? What personality characteristics distinguish scientists from nonscientists and eminent from less eminent scientists? Finally, how do intergroup relations and social forces influence scientific behavior? A model that integrates the consensual empirical findings from the psychology of science is proposed. Without the addition of a psychological dimension, I believe, it is impossible to appreciate fully the essence
What Can Cognitive Psychology and Sensory Evaluation Learn From Each Other?
, 2002
"... Two questions are addressed in this paper: What can cognitive psychology bring to sensory evaluation? And what can cognitive psychology learn from sensory evaluation? In the first part, I will argue that one important contribution from psychology to sensory evaluation is to interpret flavor as a ..."
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Cited by 1 (1 self)
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Two questions are addressed in this paper: What can cognitive psychology bring to sensory evaluation? And what can cognitive psychology learn from sensory evaluation? In the first part, I will argue that one important contribution from psychology to sensory evaluation is to interpret flavor as a cognitively unified system made of three anatomically separated systems (smell, taste, and the trigeminal system). In the second part, I will argue that the applied field of sensory evaluation stresses the importance of using ecologically valid, naturalistic stimuli. Sensory evaluation also provides results that challenge accepted interpretations in psychology, especially in the field of evaluation of expertise.
A Course in Multicultural Mathematics
"... The course described in this paper, Multicultural Mathematics, aims to strengthen and expand students’ understanding of fundamental mathematics—number systems, arithmetic, geometry, elementary number theory, and mathematical reasoning—through study of the mathematics of world cultures. In addition, ..."
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The course described in this paper, Multicultural Mathematics, aims to strengthen and expand students’ understanding of fundamental mathematics—number systems, arithmetic, geometry, elementary number theory, and mathematical reasoning—through study of the mathematics of world cultures. In addition, the course is designed to explore the connections between mathematics and the arts, to engage students’ imagination and creativity, and to increase the diversity of offerings in the mathematics classroom. This article details a course in multicultural mathematics for liberal arts and education majors I have been teaching for several years. The first three sections describe the rationale, structure, and main topics of the course. Sample projects and questions for class work and discussion are provided in the final two sections. An extensive source list is included.
The sexual politics of genius
"... The modern West believes in genius, but definitions vary widely when they can be come by at all. I think this ..."
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The modern West believes in genius, but definitions vary widely when they can be come by at all. I think this
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"... www.elsevier.com/locate/foodqual What can cognitive psychology and sensory evaluation learn from each other? ..."
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www.elsevier.com/locate/foodqual What can cognitive psychology and sensory evaluation learn from each other?
Who Can Name the Bigger Number?
, 1999
"... In an old joke, two noblemen vie to name the bigger number. The first, after ruminating for hours, triumphantly announces ”Eightythree! ” The second, mightily impressed, replies ”You win.” A biggest number contest is clearly pointless when the contestants take turns. But what if the contestants wri ..."
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In an old joke, two noblemen vie to name the bigger number. The first, after ruminating for hours, triumphantly announces ”Eightythree! ” The second, mightily impressed, replies ”You win.” A biggest number contest is clearly pointless when the contestants take turns. But what if the contestants write down their numbers simultaneously, neither aware of the other’s? To introduce a talk on ”Big Numbers, ” I invite two audience volunteers to try exactly this. I tell them the rules: You have fifteen seconds. Using standard math notation, English words, or both, name a single whole number–not an infinity–on a blank index card. Be precise enough for any reasonable modern mathematician to determine exactly what number you’ve named, by consulting only your card and, if necessary, the published literature. So contestants can’t say ”the number of sand grains in the Sahara, ” because sand drifts in and out of the Sahara regularly. Nor can they say ”my opponent’s number plus one, ” or ”the biggest number anyone’s ever thought of plus one”–again, these are illdefined, given what our reasonable mathematician has available. Within the rules, the contestant who names the bigger number wins. Are you ready? Get set. Go. The contest’s results are never quite what I’d hope. Once, a seventhgrade boy filled his card with a string of successive 9’s. Like many other bignumber tyros, he sought to maximize his number by stuffing a 9 into every place value. Had he chosen easytowrite 1’s rather than curvaceous 9’s, his number could have been millions of times bigger. He still would been decimated, though, by the girl he was up against, who wrote a string of 9’s followed by the superscript 999. Aha! An exponential: a number multiplied by itself 999 times. Noticing this innovation, I declared the girl’s victory without bothering to count the 9’s on the cards. And yet the girl’s number could have been much bigger still, had she stacked the mighty exponential more than once. Take 999, for example. This behemoth, equal to 9387,420,489, has 369,693,100 digits. By comparison, the number of elementary particles in the observable universe has a meager 85 digits, give or take. Three 9’s, when stacked exponentially, already lift us incomprehensibly ∗ Revised by Florian Mayer 1 beyond all the matter we can observe–by a factor of about 10369,693,015. And we’ve said nothing of 9 999