Results 1  10
of
23
Do humans have two systems to track beliefs and belief‐like states
 Psychological Review
, 2009
"... The lack of consensus on how to characterize humans ’ capacity for belief reasoning has been brought into ..."
Abstract

Cited by 16 (2 self)
 Add to MetaCart
The lack of consensus on how to characterize humans ’ capacity for belief reasoning has been brought into
Sex differences in intrinsic aptitude for mathematics and science? A critical review
 American Psychologist
, 2005
"... for assistance, and Nora Newcombe and Elliott Blass for advice and comments on the manuscript. Above all, I am grateful to Ariel Grace and Kristin Shutts for their unending support and afterhours labor on this project. Draft, 4/20/05. This paper has not yet been peer reviewed. Please do not copy or ..."
Abstract

Cited by 11 (2 self)
 Add to MetaCart
for assistance, and Nora Newcombe and Elliott Blass for advice and comments on the manuscript. Above all, I am grateful to Ariel Grace and Kristin Shutts for their unending support and afterhours labor on this project. Draft, 4/20/05. This paper has not yet been peer reviewed. Please do not copy or cite without author's permission. This report considers three prominent claims that boys and men have greater natural aptitude for highlevel careers in mathematics and science. According to the first claim, males are more focused on objects and mechanical systems from the beginning of life. According to the second claim, males have a profile of spatial and numerical abilities that predisposes them to greater aptitude in mathematics. According to the third claim, males show greater variability in mathematical aptitude, yielding a preponderance of males at the upper end of the distribution of mathematical talent. Research on cognitive development in human infants and preschool children, and research on cognitive performance by students at all levels, provides evidence against these claims. Mathematical and scientific reasoning develop from a set of biologically based capacities that males and females share. From these capacities, men and women appear to develop equal talent for mathematics and science.
Moving along the number line: Operational momentum in nonsymbolic arithmetic. manuscript submitted for publication
, 2006
"... Can human adults perform arithmetic operations with large approximate numbers, and what effect, if any, does an internal spatial–numerical representation of numerical magnitude have on their responses? We conducted a psychophysical study in which subjects viewed several hundred short videos of sets ..."
Abstract

Cited by 6 (4 self)
 Add to MetaCart
Can human adults perform arithmetic operations with large approximate numbers, and what effect, if any, does an internal spatial–numerical representation of numerical magnitude have on their responses? We conducted a psychophysical study in which subjects viewed several hundred short videos of sets of objects being added or subtracted from one another and judged whether the final numerosity was correct or incorrect. Over a wide range of possible outcomes, the subjects ’ responses peaked at the approximate location of the true numerical outcome and gradually tapered off as a function of the ratio of the true and proposed outcomes (Weber’s law). Furthermore, an operational momentum effect was observed, whereby addition problems were overestimated and subtraction problems were underestimated. The results show that approximate arithmetic operates according to precise quantitative rules, perhaps analogous to those characterizing movement on an internal continuum. Human adults possess an ability to estimate and manipulate approximate numerical magnitudes, which has been termed number sense (Dehaene, 1997). This ability appears to be largely independent of language and other symbol systems, since it is present in both infants (Xu & Spelke, 2000) and other animal species (Brannon & Roitman, 2003;
All Numbers Are Not Equal: An Electrophysiological Investigation of Small and Large Number Representations
"... & Behavioral and brain imaging research indicates that human infants, humans adults, and many nonhuman animals represent large nonsymbolic numbers approximately, discriminating between sets with a ratio limit on accuracy. Some behavioral evidence, especially with human infants, suggests that these r ..."
Abstract

Cited by 5 (3 self)
 Add to MetaCart
& Behavioral and brain imaging research indicates that human infants, humans adults, and many nonhuman animals represent large nonsymbolic numbers approximately, discriminating between sets with a ratio limit on accuracy. Some behavioral evidence, especially with human infants, suggests that these representations differ from representations of small numbers of objects. To investigate neural signatures of this distinction, eventrelated potentials were recorded as adult humans passively viewed the sequential presentation of dot arrays in an adaptation paradigm. In two studies, subjects viewed successive arrays of a single number of dots interspersed with test arrays presenting the same or a different number; numerical range (small numerical quantities 1–3 vs. large numerical quantities 8–24) and ratio difference varied across blocks as continuous variables were controlled. An earlyevoked component (N1), observed over widespread posterior scalp locations, was modulated by absolute number with small, but not large, number arrays. In contrast, a later component (P2p), observed over the same scalp locations, was modulated by the ratio difference between arrays for large, but not small, numbers. Despite many years of experience with symbolic systems that apply equally to all numbers, adults spontaneously process small and large numbers differently. They appear to treat smallnumber arrays as individual objects to be tracked through space and time, and largenumber arrays as cardinal values to be compared and manipulated. &
Origins of Mathematical Intuitions  The Case of Arithmetic
 THE YEAR IN COGNITIVE NEUROSCIENCE
, 2009
"... Mathematicians frequently evoke their “intuition” when they are able to quickly and automatically solve a problem, with little introspection into their insight. Cognitive neuroscience research shows that mathematical intuition is a valid concept that can be studied in the laboratory in reduced parad ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
Mathematicians frequently evoke their “intuition” when they are able to quickly and automatically solve a problem, with little introspection into their insight. Cognitive neuroscience research shows that mathematical intuition is a valid concept that can be studied in the laboratory in reduced paradigms, and that relates to the availability of “core knowledge” associated with evolutionarily ancient and specialized cerebral subsystems. As an illustration, I discuss the case of elementary arithmetic. Intuitions of numbers and their elementary transformations by addition and subtraction are present in all human cultures. They relate to a brain system, located in the intraparietal sulcus of both hemispheres, which extracts numerosity of sets and, in educated adults, maps back and forth between numerical symbols and the corresponding quantities. This system is available to animal species and to preverbal human infants. Its neuronal organization is increasingly being uncovered, leading to a precise mathematical theory of how we perform tasks of number comparison or number naming. The next challenge will be to understand how education changes our core intuitions of number.
Natural Number and Natural Geometry
"... How does the human brain support abstract concepts such as seven or square? Studies of nonhuman animals, of human infants, and of children and adults in diverse cultures suggest these concepts arise from a set of cognitive systems that are phylogenetically ancient, innate, and universal across human ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
How does the human brain support abstract concepts such as seven or square? Studies of nonhuman animals, of human infants, and of children and adults in diverse cultures suggest these concepts arise from a set of cognitive systems that are phylogenetically ancient, innate, and universal across humans: systems of core knowledge. Two of these systems—for tracking small numbers of objects and for assessing, comparing and combining the approximate cardinal values of sets—capture the primary information in the system of positive integers. Two other systems—for representing the shapes of smallscale forms and the distances and directions of surfaces in the largescale navigable layout—capture the primary information in the system of Euclidean plane geometry. As children learn language and other symbol systems, they begin to combine their core numerical and geometrical representations productively, in uniquely human ways. These combinations may give rise to the first truly abstract concepts at the foundations of mathematics. For millenia, philosophers and scientists have pondered the existence, nature and origins of abstract numerical and geometrical concepts, because these concepts have striking features. First, the integers, and the figures of the Euclidean plane, are so intuitive to human adults that the systems underlying them are called “natural number ” and, by some, “natural geometry”
Chapter for "The Cognitive Neuroscience, 3
"... INTRODUCTION Consider a lioness in her pride in the Serengeti National park, Tanzania. One night she is all alone and hears a roar from an intruder lioness. Should she try to drive the intruder off? That would be an even match, thus ending in a possibly fatal fight. She decides not to act. The foll ..."
Abstract
 Add to MetaCart
INTRODUCTION Consider a lioness in her pride in the Serengeti National park, Tanzania. One night she is all alone and hears a roar from an intruder lioness. Should she try to drive the intruder off? That would be an even match, thus ending in a possibly fatal fight. She decides not to act. The following night she is with four sisters, when they hear the roars of three intruder lionesses. This time it is three versus five. The lionesses peer into each others eyes and then launch the attack. But by the time they reach the expected location, they find no intruder, and that is because the sounds were actually coming from loudspeakers set up by a researcher investigating the numerical capacity of animals. This research shows that generally, animals decide to attack back only when the number of defenders is superior to the number of intruders (McComb, Packer, & Pusey, 1994). The process of "decision making" of these animals seems to be based on a multimodal comparison between the number of
degree of MSc in Logic at the Universiteit van Amsterdam.
, 2009
"... under the supervision of Prof Dr Michiel van Lambalgen, and submitted ..."