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| Publications of Elizabeth M. Brannon :chronological alphabetical combined listing:
%% Journal Articles
@article{fds250856,
Author = {NK DeWind and GK Adams and ML Platt and EM Brannon},
Title = {Modeling the approximate number system to quantify the
contribution of visual stimulus features.},
Journal = {Cognition},
Volume = {142},
Pages = {247-265},
Year = {2015},
Month = {September},
ISSN = {0010-0277},
url = {http://dx.doi.org/10.1016/j.cognition.2015.05.016},
Abstract = {The approximate number system (ANS) subserves estimation of
the number of items in a set. Typically, ANS function is
assessed by requiring participants to compare the number of
dots in two arrays. Accuracy is determined by the numerical
ratio of the sets being compared, and each participant's
Weber fraction (w) provides a quantitative index of ANS
acuity. When making numerical comparisons, however,
performance is also influenced by non-numerical features of
the stimuli, such as the size and spacing of dots. Current
models of numerosity comparison do not account for these
effects and consequently lead to different estimates of w
depending on the methods used to control for non-numerical
features. Here we proffer a new model that teases apart the
effects of ANS acuity from the effects of non-numerical
stimulus features. The result is an estimate of w that is a
more theoretically valid representation of numerical acuity
and novel terms that denote the degree to which a
participant's perception of number is affected by
non-numerical features. We tested this model in a sample of
20 adults and found that, by correctly attributing errors
due to non-numerical stimulus features, the w obtained was
more reliable across different stimulus conditions. We found
that although non-numerical features biased numerosity
discriminations in all participants, number was the primary
feature driving discriminations in most of them. Our
findings support the idea that, while numerosity is a
distinct visual quantity, the internal representation of
number is tightly bound to the representation of other
magnitudes. This tool for identifying the different effects
of the numerical and non-numerical features of a stimulus
has important implications not only for the behavioral
investigation of the ANS, but also for the collection and
analyses of neural data sets associated with ANS
function.},
Doi = {10.1016/j.cognition.2015.05.016},
Key = {fds250856}
}
@article{fds250857,
Author = {J Holmes and S Butterfield and F Cormack and AV Loenhoud and L Ruggero and L Kashikar and S Gathercole},
Title = {Improving working memory in children with low language
abilities},
Journal = {Frontiers in Psychology},
Volume = {6},
Year = {2015},
Month = {April},
url = {http://dx.doi.org/10.3389/fpsyg.2015.00519},
Doi = {10.3389/fpsyg.2015.00519},
Key = {fds250857}
}
@article{fds250858,
Author = {J Park and EM Brannon},
Title = {Improving arithmetic performance with number sense training:
an investigation of underlying mechanism.},
Journal = {Cognition},
Volume = {133},
Number = {1},
Pages = {188-200},
Year = {2014},
Month = {October},
ISSN = {0010-0277},
url = {http://dx.doi.org/10.1016/j.cognition.2014.06.011},
Abstract = {A nonverbal primitive number sense allows approximate
estimation and mental manipulations on numerical quantities
without the use of numerical symbols. In a recent randomized
controlled intervention study in adults, we demonstrated
that repeated training on a non-symbolic approximate
arithmetic task resulted in improved exact symbolic
arithmetic performance, suggesting a causal relationship
between the primitive number sense and arithmetic
competence. Here, we investigate the potential mechanisms
underlying this causal relationship. We constructed multiple
training conditions designed to isolate distinct cognitive
components of the approximate arithmetic task. We then
assessed the effectiveness of these training conditions in
improving exact symbolic arithmetic in adults. We found that
training on approximate arithmetic, but not on numerical
comparison, numerical matching, or visuo-spatial short-term
memory, improves symbolic arithmetic performance. In
addition, a second experiment revealed that our approximate
arithmetic task does not require verbal encoding of number,
ruling out an alternative explanation that participants use
exact symbolic strategies during approximate arithmetic
training. Based on these results, we propose that nonverbal
numerical quantity manipulation is one key factor that
drives the link between the primitive number sense and
symbolic arithmetic competence. Future work should
investigate whether training young children on approximate
arithmetic tasks even before they solidify their symbolic
number understanding is fruitful for improving readiness for
math education.},
Doi = {10.1016/j.cognition.2014.06.011},
Key = {fds250858}
}
@article{fds250863,
Author = {M Pinhas and SE Donohue and MG Woldorff and EM
Brannon},
Title = {Electrophysiological evidence for the involvement of the
approximate number system in preschoolers' processing of
spoken number words.},
Journal = {Journal of cognitive neuroscience},
Volume = {26},
Number = {9},
Pages = {1891-1904},
Year = {2014},
Month = {September},
ISSN = {0898-929X},
url = {http://dx.doi.org/10.1162/jocn_a_00631},
Abstract = {Little is known about the neural underpinnings of number
word comprehension in young children. Here we investigated
the neural processing of these words during the crucial
developmental window in which children learn their meanings
and asked whether such processing relies on the Approximate
Number System. ERPs were recorded as 3- to 5-year-old
children heard the words one, two, three, or six while
looking at pictures of 1, 2, 3, or 6 objects. The auditory
number word was incongruent with the number of visual
objects on half the trials and congruent on the other half.
Children's number word comprehension predicted their ERP
incongruency effects. Specifically, children with the least
number word knowledge did not show any ERP incongruency
effects, whereas those with intermediate and high number
word knowledge showed an enhanced, negative polarity
incongruency response (N(inc)) over centroparietal sites
from 200 to 500 msec after the number word onset. This
negativity was followed by an enhanced, positive polarity
incongruency effect (P(inc)) that emerged bilaterally over
parietal sites at about 700 msec. Moreover, children with
the most number word knowledge showed ratio dependence in
the P(inc) (larger for greater compared with smaller
numerical mismatches), a hallmark of the Approximate Number
System. Importantly, a similar modulation of the P(inc) from
700 to 800 msec was found in children with intermediate
number word knowledge. These results provide the first
neural correlates of spoken number word comprehension in
preschoolers and are consistent with the view that children
map number words onto approximate number representations
before they fully master the verbal count
list.},
Doi = {10.1162/jocn_a_00631},
Key = {fds250863}
}
@article{fds250862,
Author = {CB Drucker and EM Brannon},
Title = {Rhesus monkeys (Macaca mulatta) map number onto
space.},
Journal = {Cognition},
Volume = {132},
Number = {1},
Pages = {57-67},
Year = {2014},
Month = {July},
ISSN = {0010-0277},
url = {http://dx.doi.org/10.1016/j.cognition.2014.03.011},
Abstract = {Humans map number onto space. However, the origins of this
association, and particularly the degree to which it depends
upon cultural experience, are not fully understood. Here we
provide the first demonstration of a number-space mapping in
a non-human primate. We trained four adult male rhesus
macaques (Macaca mulatta) to select the fourth position from
the bottom of a five-element vertical array. Monkeys
maintained a preference to choose the fourth position
through changes in the appearance, location, and spacing of
the vertical array. We next asked whether monkeys show a
spatially-oriented number mapping by testing their responses
to the same five-element stimulus array rotated ninety
degrees into a horizontal line. In these horizontal probe
trials, monkeys preferentially selected the fourth position
from the left, but not the fourth position from the right.
Our results indicate that rhesus macaques map number onto
space, suggesting that the association between number and
space in human cognition is not purely a result of cultural
experience and instead has deep evolutionary
roots.},
Doi = {10.1016/j.cognition.2014.03.011},
Key = {fds250862}
}
@article{fds250861,
Author = {EL MacLean and B Hare and CL Nunn and E Addessi and F Amici and RC
Anderson, F Aureli and JM Baker and AE Bania and AM Barnard and NJ
Boogert, EM Brannon and EE Bray and J Bray and LJ Brent and JM Burkart and J Call and JF Cantlon and LG Cheke and NS Clayton and MM Delgado and LJ
DiVincenti, K Fujita and E Herrmann and C Hiramatsu and LF Jacobs and KE
Jordan, JR Laude and KL Leimgruber and EJ Messer and AC Moura and L
Ostojić, A Picard and ML Platt and JM Plotnik and F Range and SM
Reader, RB Reddy and AA Sandel and LR Santos and K Schumann and AM Seed and KB Sewall and RC Shaw and KE Slocombe and Y Su and A Takimoto and J Tan and R
Tao, CP van Schaik and Z Virányi and E Visalberghi and JC Wade and A
Watanabe, J Widness and JK Young and TR Zentall and Y
Zhao},
Title = {The evolution of self-control.},
Journal = {Proceedings of the National Academy of Sciences of the
United States of America},
Volume = {111},
Number = {20},
Pages = {E2140-E2148},
Year = {2014},
Month = {May},
ISSN = {0027-8424},
url = {http://dx.doi.org/10.1073/pnas.1323533111},
Abstract = {Cognition presents evolutionary research with one of its
greatest challenges. Cognitive evolution has been explained
at the proximate level by shifts in absolute and relative
brain volume and at the ultimate level by differences in
social and dietary complexity. However, no study has
integrated the experimental and phylogenetic approach at the
scale required to rigorously test these explanations.
Instead, previous research has largely relied on various
measures of brain size as proxies for cognitive abilities.
We experimentally evaluated these major evolutionary
explanations by quantitatively comparing the cognitive
performance of 567 individuals representing 36 species on
two problem-solving tasks measuring self-control.
Phylogenetic analysis revealed that absolute brain volume
best predicted performance across species and accounted for
considerably more variance than brain volume controlling for
body mass. This result corroborates recent advances in
evolutionary neurobiology and illustrates the cognitive
consequences of cortical reorganization through increases in
brain volume. Within primates, dietary breadth but not
social group size was a strong predictor of species
differences in self-control. Our results implicate robust
evolutionary relationships between dietary breadth, absolute
brain volume, and self-control. These findings provide a
significant first step toward quantifying the primate
cognitive phenome and explaining the process of cognitive
evolution.},
Doi = {10.1073/pnas.1323533111},
Key = {fds250861}
}
@article{fds302514,
Author = {SM Jones and J Pearson and NK DeWind and D Paulsen and AM Tenekedjieva and EM Brannon},
Title = {Lemurs and macaques show similar numerical
sensitivity.},
Journal = {Anim Cogn},
Volume = {17},
Number = {3},
Pages = {503-515},
Year = {2014},
Month = {May},
url = {http://www.ncbi.nlm.nih.gov/pubmed/24068469},
Abstract = {We investigated the precision of the approximate number
system (ANS) in three lemur species (Lemur catta, Eulemur
mongoz, and Eulemur macaco flavifrons), one Old World monkey
species (Macaca mulatta) and humans (Homo sapiens). In
Experiment 1, four individuals of each nonhuman primate
species were trained to select the numerically larger of two
visual arrays on a touchscreen. We estimated numerical
acuity by modeling Weber fractions (w) and found
quantitatively equivalent performance among all four
nonhuman primate species. In Experiment 2, we tested adult
humans in a similar procedure, and they outperformed the
four nonhuman species but showed qualitatively similar
performance. These results indicate that the ANS is
conserved over the primate order.},
Doi = {10.1007/s10071-013-0682-3},
Key = {fds302514}
}
@article{fds250864,
Author = {J Park and R Li and EM Brannon},
Title = {Neural connectivity patterns underlying symbolic number
processing indicate mathematical achievement in
children},
Journal = {Developmental Science},
Volume = {17},
Number = {2},
Pages = {187-202},
Year = {2014},
Month = {March},
ISSN = {1363-755X},
url = {http://dx.doi.org/10.1111/desc.12114},
Abstract = {In early childhood, humans learn culturally specific symbols
for number that allow them entry into the world of complex
numerical thinking. Yet little is known about how the brain
supports the development of the uniquely human symbolic
number system. Here, we use functional magnetic resonance
imaging along with an effective connectivity analysis to
investigate the neural substrates for symbolic number
processing in young children. We hypothesized that, as
children solidify the mapping between symbols and underlying
magnitudes, important developmental changes occur in the
neural communication between the right parietal region,
important for the representation of non-symbolic numerical
magnitudes, and other brain regions known to be critical for
processing numerical symbols. To test this hypothesis, we
scanned children between 4 and 6 years of age while they
performed a magnitude comparison task with Arabic numerals
(numerical, symbolic), dot arrays (numerical, non-symbolic),
and lines (non-numerical). We then identified the right
parietal seed region that showed greater
blood-oxygen-level-dependent signal in the numerical versus
the non-numerical conditions. A psychophysiological
interaction method was used to find patterns of effective
connectivity arising from this parietal seed region specific
to symbolic compared to non-symbolic number processing. Two
brain regions, the left supramarginal gyrus and the right
precentral gyrus, showed significant effective connectivity
from the right parietal cortex. Moreover, the degree of this
effective connectivity to the left supramarginal gyrus was
correlated with age, and the degree of the connectivity to
the right precentral gyrus predicted performance on a
standardized symbolic math test. These findings suggest that
effective connectivity underlying symbolic number processing
may be critical as children master the associations between
numerical symbols and magnitudes, and that these
connectivity patterns may serve as an important indicator of
mathematical achievement. © 2013 John Wiley & Sons
Ltd.},
Doi = {10.1111/desc.12114},
Key = {fds250864}
}
@article{fds250866,
Author = {J Park and R Li and EM Brannon},
Title = {Neural connectivity patterns underlying symbolic number
processing indicate mathematical achievement in
children.},
Journal = {Dev Sci},
Volume = {17},
Number = {2},
Pages = {187-202},
Year = {2014},
Month = {March},
url = {http://www.ncbi.nlm.nih.gov/pubmed/24267664},
Abstract = {In early childhood, humans learn culturally specific symbols
for number that allow them entry into the world of complex
numerical thinking. Yet little is known about how the brain
supports the development of the uniquely human symbolic
number system. Here, we use functional magnetic resonance
imaging along with an effective connectivity analysis to
investigate the neural substrates for symbolic number
processing in young children. We hypothesized that, as
children solidify the mapping between symbols and underlying
magnitudes, important developmental changes occur in the
neural communication between the right parietal region,
important for the representation of non-symbolic numerical
magnitudes, and other brain regions known to be critical for
processing numerical symbols. To test this hypothesis, we
scanned children between 4 and 6 years of age while they
performed a magnitude comparison task with Arabic numerals
(numerical, symbolic), dot arrays (numerical, non-symbolic),
and lines (non-numerical). We then identified the right
parietal seed region that showed greater
blood-oxygen-level-dependent signal in the numerical versus
the non-numerical conditions. A psychophysiological
interaction method was used to find patterns of effective
connectivity arising from this parietal seed region specific
to symbolic compared to non-symbolic number processing. Two
brain regions, the left supramarginal gyrus and the right
precentral gyrus, showed significant effective connectivity
from the right parietal cortex. Moreover, the degree of this
effective connectivity to the left supramarginal gyrus was
correlated with age, and the degree of the connectivity to
the right precentral gyrus predicted performance on a
standardized symbolic math test. These findings suggest that
effective connectivity underlying symbolic number processing
may be critical as children master the associations between
numerical symbols and magnitudes, and that these
connectivity patterns may serve as an important indicator of
mathematical achievement.},
Doi = {10.1111/desc.12114},
Key = {fds250866}
}
@article{fds250865,
Author = {ME Libertus and A Starr and EM Brannon},
Title = {Number trumps area for 7-month-old infants.},
Journal = {Dev Psychol},
Volume = {50},
Number = {1},
Pages = {108-112},
Year = {2014},
Month = {January},
url = {http://www.ncbi.nlm.nih.gov/pubmed/23647413},
Abstract = {Over the past few decades, there has been extensive debate
as to whether humans represent number abstractly and, if so,
whether perceptual features of a set such as cumulative
surface area or contour length are extracted more readily
than number from the external world. Here we show that
7-month-old infants are sensitive to smaller ratio changes
in number than cumulative area when each variable is tested
separately and that infants prefer to look at number changes
compared with area changes when the 2 variables are pitted
directly against each other. Our results provide strong
evidence that number is a more salient dimension to young
infants than cumulative surface area and that infants'
ability to discriminate sets on the basis of number is more
finely tuned than their ability to discriminate sets on the
basis of cumulative surface area.},
Doi = {10.1037/a0032986},
Key = {fds250865}
}
@article{fds250869,
Author = {A Starr and ME Libertus and EM Brannon},
Title = {Number sense in infancy predicts mathematical abilities in
childhood.},
Journal = {Proc Natl Acad Sci U S A},
Volume = {110},
Number = {45},
Pages = {18116-18120},
Year = {2013},
Month = {November},
url = {http://www.ncbi.nlm.nih.gov/pubmed/24145427},
Abstract = {Human infants in the first year of life possess an intuitive
sense of number. This preverbal number sense may serve as a
developmental building block for the uniquely human capacity
for mathematics. In support of this idea, several studies
have demonstrated that nonverbal number sense is correlated
with mathematical abilities in children and adults. However,
there has been no direct evidence that infant numerical
abilities are related to mathematical abilities later in
childhood. Here, we provide evidence that preverbal number
sense in infancy predicts mathematical abilities in
preschool-aged children. Numerical preference scores at 6
months of age correlated with both standardized math test
scores and nonsymbolic number comparison scores at 3.5 years
of age, suggesting that preverbal number sense facilitates
the acquisition of numerical symbols and mathematical
abilities. This relationship held even after controlling for
general intelligence, indicating that preverbal number sense
imparts a unique contribution to mathematical ability. These
results validate the many prior studies purporting to show
number sense in infancy and support the hypothesis that
mathematics is built upon an intuitive sense of number that
predates language.},
Doi = {10.1073/pnas.1302751110},
Key = {fds250869}
}
@article{fds250903,
Author = {DJ Merritt and EM Brannon},
Title = {Nothing to it: precursors to a zero concept in
preschoolers.},
Journal = {Behav Processes},
Volume = {93},
Pages = {91-97},
Year = {2013},
Month = {February},
ISSN = {0376-6357},
url = {http://www.ncbi.nlm.nih.gov/pubmed/23219980},
Abstract = {Do young children understand the numerical value of empty
sets prior to developing a concept of symbolic zero? Are
empty sets represented as mental magnitudes? In order to
investigate these questions, we tested 4-year old children
and adults with a numerical ordering task in which the goal
was to select two stimuli in ascending numerical order with
occasional empty set stimuli. Both children and adults
showed distance effects for empty sets. Children who were
unable to order the symbol zero (e.g., 0<1), but who
successfully ordered countable integers (e.g., 2<4)
nevertheless showed distance effects with empty sets. These
results suggest that empty sets are represented on the same
numerical continuum as non-empty sets and that children
represent empty sets numerically prior to understanding
symbolic zero.},
Doi = {10.1016/j.beproc.2012.11.001},
Key = {fds250903}
}
@article{fds250867,
Author = {J Park and EM Brannon},
Title = {Training the Approximate Number System Improves Math
Proficiency},
Journal = {Psychological Science},
Volume = {24},
Number = {10},
Pages = {2013-2019},
Year = {2013},
Month = {January},
ISSN = {0956-7976},
url = {http://dx.doi.org/10.1177/0956797613482944},
Abstract = {Humans and nonhuman animals share an approximate number
system (ANS) that permits estimation and rough calculation
of quantities without symbols. Recent studies show a
correlation between the acuity of the ANS and performance in
symbolic math throughout development and into adulthood,
which suggests that the ANS may serve as a cognitive
foundation for the uniquely human capacity for symbolic
math. Such a proposition leads to the untested prediction
that training aimed at improving ANS performance will
transfer to improvement in symbolic-math ability. In the two
experiments reported here, we showed that ANS training on
approximate addition and subtraction of arrays of dots
selectively improved symbolic addition and subtraction. This
finding strongly supports the hypothesis that complex math
skills are fundamentally linked to rudimentary preverbal
quantitative abilities and provides the first direct
evidence that the ANS and symbolic math may be causally
related. It also raises the possibility that interventions
aimed at the ANS could benefit children and adults who
struggle with math. © The Author(s) 2013.},
Doi = {10.1177/0956797613482944},
Key = {fds250867}
}
@article{fds219915,
Author = {Park, J. and Li, R. and Brannon},
Title = {Effective connectivity underlying symbolic number processing
in children},
Journal = {Developmental Science},
Year = {2013},
url = {http://dx.doi.org/DOI: 10.1111/desc.12114},
Doi = {DOI: 10.1111/desc.12114},
Key = {fds219915}
}
@article{fds250868,
Author = {A Starr and ME Libertus and EM Brannon},
Title = {Infants show ratio-dependent number discrimination
regardless of set size},
Journal = {Infancy},
Volume = {18},
Number = {6},
Pages = {927-941},
Year = {2013},
ISSN = {1525-0008},
url = {http://dx.doi.org/10.1111/infa.12008},
Abstract = {Evidence for approximate number system (ANS) representations
in infancy is robust but has typically only been found when
infants are presented with arrays of four or more elements.
In addition, several studies have found that infants fail to
discriminate between small numbers when continuous variables
such as surface area and contour length are controlled.
These findings suggest that under some circumstances,
infants fail to recruit either the ANS or object file
representations for small sets. Here, we used a numerical
change detection paradigm to assess 6-month-old infants'
ability to represent small values. In Experiment 1, infants
were tested with 1 versus 3, 1 versus 2, and 2 versus 3
dots. Infants successfully discriminated 1 versus 3 and 1
versus 2, but failed with 2 versus 3. In Experiment 2, we
tested whether infants could compare small and large values
with a 2 versus 4 condition. Across both experiments,
infants' performance exhibited ratio dependence, the
hallmark of the ANS. Our results indicate that infants can
attend to the purely numerical attributes of small sets and
that the numerical change detection paradigm accesses ANS
representations in infancy regardless of set size. ©
International Society on Infant Studies (ISIS).},
Doi = {10.1111/infa.12008},
Key = {fds250868}
}
@article{fds250900,
Author = {SM Jones and EM Brannon},
Title = {Lemurs show ratio dependent number discrimination in a
spontaneous choice task},
Journal = {Frontiers in Comparative Psychology},
Year = {2013},
Key = {fds250900}
}
@article{fds250901,
Author = {AB Starr and ME Libertus and EM Brannon},
Title = {Infants Show Ratio-dependent Number Discrimination
Regardless of Set Size},
Journal = {Infancy},
Year = {2013},
ISSN = {1525-0008},
url = {http://dx.doi.org/10.1111/infa.12008},
Abstract = {Evidence for approximate number system (ANS) representations
in infancy is robust but has typically only been found when
infants are presented with arrays of four or more elements.
In addition, several studies have found that infants fail to
discriminate between small numbers when continuous variables
such as surface area and contour length are controlled.
These findings suggest that under some circumstances,
infants fail to recruit either the ANS or object file
representations for small sets. Here, we used a numerical
change detection paradigm to assess 6-month-old infants'
ability to represent small values. In Experiment 1, infants
were tested with 1 versus 3, 1 versus 2, and 2 versus 3
dots. Infants successfully discriminated 1 versus 3 and 1
versus 2, but failed with 2 versus 3. In Experiment 2, we
tested whether infants could compare small and large values
with a 2 versus 4 condition. Across both experiments,
infants' performance exhibited ratio dependence, the
hallmark of the ANS. Our results indicate that infants can
attend to the purely numerical attributes of small sets and
that the numerical change detection paradigm accesses ANS
representations in infancy regardless of set size. ©
International Society on Infant Studies (ISIS).},
Doi = {10.1111/infa.12008},
Key = {fds250901}
}
@article{fds311285,
Author = {NK DeWind and EM Brannon},
Title = {Malleability of the approximate number system: Effects of
feedback and training},
Journal = {Frontiers in Human Neuroscience},
Number = {APRIL 2012},
Year = {2012},
Month = {April},
Abstract = {Prior research demonstrates that animals and humans share an
approximate number system (ANS), characterized by ratio
dependence and that the precision of this system increases
substantially over human development. The goal of the
present research was to investigate the malleability of the
ANS (as measured by Weber fraction) in adult subjects in
response to feedback and to explore the relationship between
ANS acuity and acuity on another magnitude comparison task.
We tested each of 20 subjects over six 1-h sessions. The
main findings were that (a) Weber fractions rapidly
decreased when trial-by-trial feedback was introduced in the
second session and remained stable over continued training,
(b) Weber fractions remained steady when trial-by-trial
feedback was removed in session 6, (c)Weber fractions from
the number comparison task were positively correlated with
Weber fractions from a line length comparison task, (d)
improvement in Weber fractions in response to feedback for
the number task did not transfer to the line length task,
(e) finally, the precision of the ANS was positively
correlated with math, but not verbal, standardized aptitude
scores. Potential neural correlates of the perceptual
information and decision processes are considered, and
predictions regarding the neural correlates of ANS
malleability are discussed. © 2012 DeWind and
Brannon.},
Key = {fds311285}
}
@article{fds250897,
Author = {EL MacLean and LJ Matthews and BA Hare and CL Nunn and RC Anderson and F
Aureli, EM Brannon and J Call and CM Drea and NJ Emery and DBM Haun and E
Herrmann, LF Jacobs and ML Platt and AG Rosati and AA Sandel and KK
Schroepfer, AM Seed and J Tan and CP van Schaik and V
Wobber},
Title = {How does cognition evolve? Phylogenetic comparative
psychology},
Journal = {ANIMAL COGNITION},
Volume = {15},
Number = {2},
Pages = {223-238},
Year = {2012},
Month = {March},
ISSN = {1435-9448},
url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000300455900008&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
Abstract = {Now more than ever animal studies have the potential to test
hypotheses regarding how cognition evolves. Comparative
psychologists have developed new techniques to probe the
cognitive mechanisms underlying animal behavior, and they
have become increasingly skillful at adapting methodologies
to test multiple species. Meanwhile, evolutionary biologists
have generated quantitative approaches to investigate the
phylogenetic distribution and function of phenotypic traits,
including cognition. In particular, phylogenetic methods can
quantitatively (1) test whether specific cognitive abilities
are correlated with life history (e.g., lifespan),
morphology (e.g., brain size), or socio-ecological variables
(e.g., social system), (2) measure how strongly phylogenetic
relatedness predicts the distribution of cognitive skills
across species, and (3) estimate the ancestral state of a
given cognitive trait using measures of cognitive
performance from extant species. Phylogenetic methods can
also be used to guide the selection of species comparisons
that offer the strongest tests of a priori predictions of
cognitive evolutionary hypotheses (i.e., phylogenetic
targeting). Here, we explain how an integration of
comparative psychology and evolutionary biology will answer
a host of questions regarding the phylogenetic distribution
and history of cognitive traits, as well as the evolutionary
processes that drove their evolution.},
Doi = {10.1007/s10071-011-0448-8},
Key = {fds250897}
}
@article{fds250874,
Author = {SM Jones and EM Brannon},
Title = {Prosimian primates show ratio dependence in spontaneous
quantity discriminations.},
Journal = {Front Psychol},
Volume = {3},
Pages = {550},
Year = {2012},
url = {http://www.ncbi.nlm.nih.gov/pubmed/23420691},
Abstract = {We directly tested the predictions of the approximate number
system (ANS) and the object file system in the spontaneous
numerical judgments of prosimian primates. Prior work
indicates that when human infants and a few species of
non-human animals are given a single-trial choice between
two sequentially baited buckets they choose the bucket with
the greater amount of food but only when the quantities are
small. This pattern of results has been interpreted as
evidence that a limited capacity object file system is used
to track small numbers of objects and that the ANS is not
invoked under these circumstances. Here we tested prosimian
primates in food choice comparisons that were chosen to
contrast predictions of the ANS and object file systems. We
found that prosimian primates consistently chose the larger
of two sets when they differed by a 1:3 ratio regardless of
whether both values were small (≤3), both values were
large (>3), or there was one small and one large value.
Prosimians were not able to robustly discriminate quantities
that differed by a 1:2 ratio for the same three conditions,
nor did they show a preference for small quantities that
differed by a 2:3 ratio. These results implicate the ANS in
the spontaneous numerical discriminations of non-human
primates.},
Doi = {10.3389/fpsyg.2012.00550},
Key = {fds250874}
}
@article{fds250891,
Author = {DJ Paulsen and ML Platt and SA Huettel and EM Brannon},
Title = {From risk-seeking to risk-averse: the development of
economic risk preference from childhood to
adulthood.},
Journal = {Front Psychol},
Volume = {3},
Pages = {313},
Year = {2012},
url = {http://www.ncbi.nlm.nih.gov/pubmed/22973247},
Abstract = {Adolescence is often described as a period of heightened
risk-taking. Adolescents are notorious for impulsivity,
emotional volatility, and risky behaviors such as drinking
and driving under the influence of alcohol. By contrast, we
found that risk-taking declines linearly from childhood to
adulthood when individuals make choices over monetary
gambles. Further, with age we found increases in the
sensitivity to economic risk, defined as the degree to which
a preference for assured monetary gains over a risky payoff
depends upon the variability in the risky payoff. These
findings indicate that decisions about economic risk may
follow a different developmental trajectory than other kinds
of risk-taking, and that changes in sensitivity to risk may
be a major factor in the development of mature risk
aversion.},
Doi = {10.3389/fpsyg.2012.00313},
Key = {fds250891}
}
@article{fds250892,
Author = {JD Roitman and EM Brannon and ML Platt},
Title = {Representation of numerosity in posterior parietal
cortex},
Journal = {Frontiers in Integrative Neuroscience},
Number = {MAY 2012},
Pages = {1-9},
Year = {2012},
ISSN = {1662-5145},
url = {http://dx.doi.org/10.3389/fnint.2012.00025},
Abstract = {Humans and animals appear to share a similar representation
of number as an analog magnitude on an internal, subjective
scale. Neurological and neurophysiological data suggest that
posterior parietal cortex (PPC) is a critical component of
the circuits that form the basis of numerical abilities in
humans. Patients with parietal lesions are impaired in their
ability to access the deep meaning of numbers. Acalculiac
patients with inferior parietal damage often have difficulty
performing arithmetic (2 + 4?) or number bisection (what is
between 3 and 5?) tasks, but are able to recite
multiplication tables and read or write numerals. Functional
imaging studies of neurologically intact humans performing
subtraction, number comparison, and non-verbal magnitude
comparison tasks show activity in areas within the
intraparietal sulcus (IPS). Taken together, clinical cases
and imaging studies support a critical role for parietal
cortex in the mental manipulation of numerical quantities.
Further, responses of single PPC neurons in non-human
primates are sensitive to the numerosity of visual stimuli
independent of low-level stimulus qualities. When monkeys
are trained to make explicit judgments about the numerical
value of such stimuli, PPC neurons encode their cardinal
numerical value; without such training PPC neurons appear to
encode numerical magnitude in an analog fashion. Here we
suggest that the spatial and integrative properties of PPC
neurons contribute to their critical role in numerical
cognition. © 2012 Roitman, Brannon and Platt.},
Doi = {10.3389/fnint.2012.00025},
Key = {fds250892}
}
@article{fds250895,
Author = {J Roitman and EM Brannon and ML Platt},
Title = {Intraparietal Cortex: The Mental Number Line?”},
Journal = {Frontiers in Integrative Neuroscience},
Year = {2012},
Key = {fds250895}
}
@article{fds250899,
Author = {EL MacLean and TM Mandalaywala and EM Brannon},
Title = {Variance-sensitive choice in lemurs: constancy trumps
quantity},
Journal = {Animal Cognition},
Volume = {15},
Number = {2},
Pages = {15-25},
Year = {2012},
ISSN = {DOI: 10.1007/s10071-011-0425-2},
url = {http://www.ncbi.nlm.nih.gov/pubmed/21670948},
Abstract = {Numerous studies have demonstrated that animals' tolerance
for risk when foraging can be affected by changes in
metabolic state. Specifically, animals on a negative energy
budget increase their preferences for risk, while animals on
a positive energy budget are typically risk-averse. The
malleability of these preferences may be evolutionarily
advantageous, and important for maximizing chances of
survival during brief periods of energetic stress. However,
animals adapted to living in unpredictable conditions are
unlikely to benefit from risk-seeking strategies, and
instead are expected to reduce energetic demands while
maintaining risk-aversion. We measured risk preferences in
lemurs, a group of primates restricted to the island of
Madagascar. Lemurs have evolved diverse anatomical and
behavioral traits for survival in a harsh and unpredictable
ecology, and these traits have been explained as forms of
anatomical and behavioral risk reduction. We therefore
predicted that lemurs would also be risk-averse in a
behavioral task that offered subjects a choice between a
small certain reward, and an uncertain but potentially large
reward. In Experiment 1, the average rewards associated with
the constant and variable options were equal and lemurs
exhibited high levels of risk-aversion, replicating a
phenomenon that has been demonstrated in dozens of taxa. In
Experiment 2, we gradually increased the average value of
the variable option relative to the constant option. Lemurs'
preferences tracked these changes and subjects became more
risk-seeking as the risk premium increased. However, many
subjects maintained high levels of risk-aversion even when
the average payout of the variable option yielded double
that of the constant option. These results are consistent
with the notion that lemur cognition has evolved to minimize
risk in an unpredictable island environment.},
Doi = {10.1007/s10071-011-0425-2},
Key = {fds250899}
}
@article{fds250905,
Author = {NK Dewind and EM Brannon},
Title = {Malleability of the approximate number system: effects of
feedback and training.},
Journal = {Front Hum Neurosci},
Volume = {6},
Number = {MARCH 2012},
Pages = {68},
Year = {2012},
ISSN = {1662-5161},
url = {http://www.ncbi.nlm.nih.gov/pubmed/22529786},
Abstract = {Prior research demonstrates that animals and humans share an
approximate number system (ANS), characterized by ratio
dependence and that the precision of this system increases
substantially over human development. The goal of the
present research was to investigate the malleability of the
ANS (as measured by Weber fraction) in adult subjects in
response to feedback and to explore the relationship between
ANS acuity and acuity on another magnitude comparison task.
We tested each of 20 subjects over six 1-h sessions. The
main findings were that (a) Weber fractions rapidly
decreased when trial-by-trial feedback was introduced in the
second session and remained stable over continued training,
(b) Weber fractions remained steady when trial-by-trial
feedback was removed in session 6, (c)Weber fractions from
the number comparison task were positively correlated with
Weber fractions from a line length comparison task, (d)
improvement in Weber fractions in response to feedback for
the number task did not transfer to the line length task,
(e) finally, the precision of the ANS was positively
correlated with math, but not verbal, standardized aptitude
scores. Potential neural correlates of the perceptual
information and decision processes are considered, and
predictions regarding the neural correlates of ANS
malleability are discussed.},
Doi = {10.3389/fnhum.2012.00068},
Key = {fds250905}
}
@article{fds311320,
Author = {NK DeWind and EM Brannon},
Title = {Malleability of the approximate number system: Effects of
feedback and training},
Journal = {Frontiers in Human Neuroscience},
Number = {MARCH 2012},
Year = {2012},
url = {http://dx.doi.org/10.3389/fnhum.2012.00068},
Abstract = {Prior research demonstrates that animals and humans share an
approximate number system (ANS), characterized by ratio
dependence and that the precision of this system increases
substantially over human development. The goal of the
present research was to investigate the malleability of the
ANS (as measured by weber fraction) in adult subjects in
response to feedback and to explore the relationship between
ANS acuity and acuity on another magnitude comparison task.
We tested each of 20 subjects over six 1-hour sessions. The
main findings were that a) weber fractions rapidly decreased
when trial-by-trial feedback was introduced in the second
session and remained stable over continued training, b)
weber fractions remained steady when trial-by-trial feedback
was removed in session six, c) weber fractions from the
number comparison task were positively correlated with weber
fractions from a line length comparison task, d) improvement
in weber fractions in response to feedback for the number
task did not transfer to the line length task, e) finally,
the precision of the ANS was positively correlated with
math, but not verbal, standardized aptitude scores.
Potential neural correlates of the perceptual information
and decision processes are considered, and predictions
regarding the neural correlates of ANS malleability are
discussed. © 2012 Dewind and Brannon.},
Doi = {10.3389/fnhum.2012.00068},
Key = {fds311320}
}
@article{fds311286,
Author = {NK DeWind and EM Brannon},
Title = {Malleability of the approximate number system: Effects of
feedback and training},
Journal = {Frontiers in Human Neuroscience},
Number = {MARCH 2012},
Year = {2012},
ISSN = {1662-5161},
url = {http://dx.doi.org/10.3389/fnhum.2012.00068},
Abstract = {Prior research demonstrates that animals and humans share an
approximate number system (ANS), characterized by ratio
dependence and that the precision of this system increases
substantially over human development. The goal of the
present research was to investigate the malleability of the
ANS (as measured by weber fraction) in adult subjects in
response to feedback and to explore the relationship between
ANS acuity and acuity on another magnitude comparison task.
We tested each of 20 subjects over six 1-hour sessions. The
main findings were that a) weber fractions rapidly decreased
when trial-by-trial feedback was introduced in the second
session and remained stable over continued training, b)
weber fractions remained steady when trial-by-trial feedback
was removed in session six, c) weber fractions from the
number comparison task were positively correlated with weber
fractions from a line length comparison task, d) improvement
in weber fractions in response to feedback for the number
task did not transfer to the line length task, e) finally,
the precision of the ANS was positively correlated with
math, but not verbal, standardized aptitude scores.
Potential neural correlates of the perceptual information
and decision processes are considered, and predictions
regarding the neural correlates of ANS malleability are
discussed. © 2012 Dewind and Brannon.},
Doi = {10.3389/fnhum.2012.00068},
Key = {fds311286}
}
@article{fds200969,
Author = {Libertus, M.E. and Brannon, E.M. and Woldorff, M.},
Title = {Parallels in stimulus- driven oscillatory brain responses to
numerosity changes in 7-month-old infants and
adults},
Journal = {Developmental Neuropsychology},
Volume = {36},
Number = {6},
Pages = {651-667},
Year = {2011},
Key = {fds200969}
}
@article{fds250872,
Author = {S Dehaene and E Brannon},
Title = {Space, Time and Number in the Brain},
Journal = {Space, Time and Number in the Brain},
Year = {2011},
Abstract = {The study of mathematical cognition and the ways in which
the ideas of space, time and number are encoded in brain
circuitry has become a fundamental issue for neuroscience.
How such encoding differs across cultures and educational
level is of further interest in education and
neuropsychology. This rapidly expanding field of research is
overdue for an interdisciplinary volume such as this, which
deals with the neurological and psychological foundations of
human numeric capacity. A uniquely integrative work, this
volume provides a much needed compilation of primary source
material to researchers from basic neuroscience, psychology,
developmental science, neuroimaging, neuropsychology and
theoretical biology. * The first comprehensive and
authoritative volume dealing with neurological and
psychological foundations of mathematical cognition *
Uniquely integrative volume at the frontier of a rapidly
expanding interdisciplinary field * Features outstanding and
truly international scholarship, with chapters written by
leading experts in a variety of fields. © 2011 Elsevier
Inc. All rights reserved.},
Key = {fds250872}
}
@article{fds250896,
Author = {JF Cantlon and SW Davis and ME Libertus and J Kahane and EM Brannon and KA Pelphrey},
Title = {Inter-parietal white matter development predicts numerical
performance in young children},
Journal = {Learning and Individual Differences},
Volume = {21},
Number = {6},
Pages = {672-680},
Year = {2011},
ISSN = {1041-6080},
url = {http://dx.doi.org/10.1016/j.lindif.2011.09.003},
Abstract = {In an effort to understand the role of interhemispheric
transfer in numerical development, we investigated the
relationship between children's developing knowledge of
numbers and the integrity of their white matter connections
between the cerebral hemispheres (the corpus callosum). We
used diffusion tensor imaging (DTI) tractography analyses to
test the link between the development of the corpus callosum
and performance on symbolic and non-symbolic numerical
judgment tasks. We were especially interested in the
interhemispheric connections of parietal cortex in
6-year-old children, because regions of parietal cortex have
been implicated in the development of numerical skills by
several prior studies. Our results revealed significant
structural differences between children and adults in the
fibers of the corpus callosum connecting the left and right
parietal lobes. Importantly, these structural differences
were predictive of individual differences among children in
performance on numerical judgment tasks: children with poor
numerical performance relative to their peers exhibited
reduced white matter coherence in the fibers passing through
the isthmus of the corpus callosum, which connects the
parietal hemispheres. © 2011 Elsevier Inc.},
Doi = {10.1016/j.lindif.2011.09.003},
Key = {fds250896}
}
@article{fds250898,
Author = {DJ Paulsen and RM Carter and ML Platt and SA Huettel and EM
Brannon},
Title = {Neurocognitive development of risk aversion from early
childhood to adulthood.},
Journal = {Front Hum Neurosci},
Volume = {5},
Number = {72},
Pages = {178},
Year = {2011},
url = {http://www.ncbi.nlm.nih.gov/pubmed/22291627},
Abstract = {Human adults tend to avoid risk. In behavioral economic
studies, risk aversion is manifest as a preference for sure
gains over uncertain gains. However, children tend to be
less averse to risk than adults. Given that many of the
brain regions supporting decision-making under risk do not
reach maturity until late adolescence or beyond it is
possible that mature risk-averse behavior may emerge from
the development of decision-making circuitry. To explore
this hypothesis, we tested 5- to 8-year-old children, 14- to
16-year-old adolescents, and young adults in a
risky-decision task during functional magnetic resonance
imaging (fMRI) data acquisition. To our knowledge, this is
the youngest sample of children in an fMRI decision-making
task. We found a number of decision-related brain regions to
increase in activation with age during decision-making,
including areas associated with contextual memory retrieval
and the incorporation of prior outcomes into the current
decision-making strategy, e.g., insula, hippocampus, and
amygdala. Further, children who were more risk-averse showed
increased activation during decision-making in ventromedial
prefrontal cortex and ventral striatum. Our findings
indicate that the emergence of adult levels of risk aversion
co-occurs with the recruitment of regions supporting
decision-making under risk, including the integration of
prior outcomes into current decision-making behavior. This
pattern of results suggests that individual differences in
the development of risk aversion may reflect differences in
the maturation of these neural processes.},
Doi = {10.3389/fnhum.2011.00178},
Key = {fds250898}
}
@article{fds250902,
Author = {DJ Paulsen and ML Platt and SA Huettel and EM Brannon},
Title = {Decision-making under risk in children, adolescents, and
young adults.},
Journal = {Front Psychol},
Volume = {2},
Number = {72},
Pages = {72},
Year = {2011},
url = {http://www.ncbi.nlm.nih.gov/pubmed/21687443},
Abstract = {Adolescents often make risky and impulsive decisions. Such
behavior has led to the common assumption that a dysfunction
in risk-related decision-making peaks during this age.
Differences in how risk has been defined across studies,
however, make it difficult to draw conclusions about
developmental changes in risky decision-making. Here, we
developed a non-symbolic economic decision-making task that
can be used across a wide age span and that uses coefficient
of variation (CV) in reward as an index of risk. We found
that young children showed the strongest preference for
risky compared to sure bet options of equal expected value,
adolescents were intermediate in their risk preference, and
young adults showed the strongest risk aversion.
Furthermore, children's preference for the risky option
increased for larger CVs, while adolescents and young adults
showed the opposite pattern, favoring the sure bet more
often as CV increased. Finally, when faced with two gambles
in a risk-return tradeoff, all three age groups exhibited a
greater preference for the option with the lower risk and
return as the disparity in risk between the two options
increased. These findings demonstrate clear age-related
differences in economic risk preferences that vary with
choice set and risk. Importantly, adolescence appears to
represent an intermediate decision-making phenotype along
the transition from childhood to adulthood, rather than an
age of heightened preference for economic
risk.},
Doi = {10.3389/fpsyg.2011.00072},
Key = {fds250902}
}
@article{fds250904,
Author = {D Merritt and E MacLean and JC Crawford and EM
Brannon},
Title = {Numerical rule-learning in ring-tailed Lemurs (Lemur
catta)},
Journal = {Frontiers in Comparative Psychology},
Volume = {2},
Number = {23},
Pages = {1-9},
Year = {2011},
url = {http://www.ncbi.nlm.nih.gov/pubmed/21713071},
Abstract = {We investigated numerical discrimination and numerical
rule-learning in ring-tailed lemurs (Lemur catta). Two
ring-tailed lemurs were trained to respond to two visual
arrays, each of which contained between one and four
elements, in numerically ascending order. In Experiment 1,
lemurs were trained with 36 exemplars of each of the
numerosities 1-4 and then showed positive transfer to
trial-unique novel exemplars of the values 1-4. In
Experiments 2A and 2B, lemurs were tested on their ability
to transfer an ascending numerical rule from the values 1-4
to novel values 5-9. Both lemurs successfully ordered the
novel values with above chance accuracy. Accuracy was
modulated by the ratio between the two numerical values
suggesting that lemurs accessed the approximate number
system when performing the task.},
Doi = {10.3389/fpsyg.2011.00023},
Key = {fds250904}
}
@article{fds250906,
Author = {S Cordes and EM Brannon},
Title = {Attending to one of many: When infants are surprisingly poor
at discriminating an item’s size},
Journal = {Frontiers in Developmental Psychology},
Volume = {2},
Number = {72},
Address = {10.3389/fpsyg.2011.00072},
Year = {2011},
ISSN = {1664-1078},
url = {http://dx.doi.org/10.3389/fpsyg.2011.00065},
Abstract = {Despite a prevailing assumption in the developmental
literature that changes in continuous quantities (i.e.,
surface area, duration) are easier to detect than changes in
number, very little research has focused on the verity of
this assumption. The few studies that have directly examined
infants' discriminations of continuous extent have revealed
that infants discriminate the duration of a single event and
the area of a single item with similar levels of precision
(Brannon et al., 2006; vanMarle and Wynn, 2006). But what
about when items are presented in arrays? Infants appear to
be much worse at representing the cumulative surface area
compared to the numerosity of an array (Cordes and Brannon,
2008a), however this may be due to a noisy accumulation
process and not a general finding pertaining to
representations of the extent within an array. The current
study investigates how well infants detect changes in the
size of individual elements when they are presented within
an array. Our results indicate that infants are less
sensitive to continuous properties of items when they are
presented within a set than when presented in isolation.
Specifically we demonstrate that infants required a fourfold
change in item size to detect a change when items were
presented within a set of homogeneous elements. Rather than
providing redundant cues that aided discrimination,
presenting a set of identical elements appeared to hamper an
infant's ability to detect changes in a single element's
size. In addition to providing some of the first evidence to
suggest that the presence of multiple items may hinder
extent representations, these results provide converging
lines of evidence to support the claim that, contrary to
popular belief, infants are better at tracking number than
continuous properties of a set. © 2011 Cordes and
Brannon.},
Doi = {10.3389/fpsyg.2011.00065},
Key = {fds250906}
}
@article{fds250918,
Author = {ME Libertus and EM Brannon and MG Woldorff},
Title = {Parallels in stimulus-driven oscillatory brain responses to
numerosity changes in adults and seven-month-old
infants.},
Journal = {Dev Neuropsychol},
Volume = {36},
Number = {6},
Pages = {651-667},
Year = {2011},
url = {http://www.ncbi.nlm.nih.gov/pubmed/21761991},
Abstract = {Previous studies provide indirect evidence for an
ontogenetically continuous Approximate-Number System. We
employed a rapid steady-state visual-presentation paradigm
combined with electroencephalography to measure
stimulus-driven neural oscillatory responses to numerosities
in infants and adults. Steady-state repetition of the same
numerosity across a 2.4-sec time block yielded an increase
in the stimulus-locked neural entrainment in both groups.
Entrainment changes following a numerosity switch varied by
the ratio of the numerosities, consistent with Weber's Law.
These similarities thus provide direct evidence for an
ontogenetically continuous Approximate-Number System.
Moreover, the degree of neural entrainment significantly
predicted infants' number discrimination measured
behaviorally two months later.},
Doi = {10.1080/87565641.2010.549883},
Key = {fds250918}
}
@article{fds304648,
Author = {DJ Merritt and EL Maclean and JC Crawford and EM
Brannon},
Title = {Numerical rule-learning in ring-tailed lemurs (lemur
catta).},
Journal = {Front Psychol},
Volume = {2},
Pages = {23},
Year = {2011},
url = {http://www.ncbi.nlm.nih.gov/pubmed/21713071},
Abstract = {We investigated numerical discrimination and numerical
rule-learning in ring-tailed lemurs (Lemur catta). Two
ring-tailed lemurs were trained to respond to two visual
arrays, each of which contained between one and four
elements, in numerically ascending order. In Experiment 1,
lemurs were trained with 36 exemplars of each of the
numerosities 1-4 and then showed positive transfer to
trial-unique novel exemplars of the values 1-4. In
Experiments 2A and 2B, lemurs were tested on their ability
to transfer an ascending numerical rule from the values 1-4
to novel values 5-9. Both lemurs successfully ordered the
novel values with above chance accuracy. Accuracy was
modulated by the ratio between the two numerical values
suggesting that lemurs accessed the approximate number
system when performing the task.},
Doi = {10.3389/fpsyg.2011.00023},
Key = {fds304648}
}
@article{fds304649,
Author = {S Cordes and EM Brannon},
Title = {Attending to one of many: When infants are surprisingly poor
at discriminating an item's size},
Journal = {Frontiers in Psychology},
Volume = {2},
Number = {APR},
Year = {2011},
ISSN = {1664-1078},
url = {http://dx.doi.org/10.3389/fpsyg.2011.00065},
Abstract = {Despite a prevailing assumption in the developmental
literature that changes in continuous quantities (i.e.,
surface area, duration) are easier to detect than changes in
number, very little research has focused on the verity of
this assumption. The few studies that have directly examined
infants' discriminations of continuous extent have revealed
that infants discriminate the duration of a single event and
the area of a single item with similar levels of precision
(Brannon et al., 2006; vanMarle and Wynn, 2006). But what
about when items are presented in arrays? Infants appear to
be much worse at representing the cumulative surface area
compared to the numerosity of an array (Cordes and Brannon,
2008a), however this may be due to a noisy accumulation
process and not a general finding pertaining to
representations of the extent within an array. The current
study investigates how well infants detect changes in the
size of individual elements when they are presented within
an array. Our results indicate that infants are less
sensitive to continuous properties of items when they are
presented within a set than when presented in isolation.
Specifically we demonstrate that infants required a fourfold
change in item size to detect a change when items were
presented within a set of homogeneous elements. Rather than
providing redundant cues that aided discrimination,
presenting a set of identical elements appeared to hamper an
infant's ability to detect changes in a single element's
size. In addition to providing some of the first evidence to
suggest that the presence of multiple items may hinder
extent representations, these results provide converging
lines of evidence to support the claim that, contrary to
popular belief, infants are better at tracking number than
continuous properties of a set. © 2011 Cordes and
Brannon.},
Doi = {10.3389/fpsyg.2011.00065},
Key = {fds304649}
}
@article{fds250916,
Author = {DJ Paulsen and MG Woldorff and EM Brannon},
Title = {Individual differences in nonverbal number discrimination
correlate with event-related potentials and measures of
probabilistic reasoning.},
Journal = {Neuropsychologia},
Volume = {48},
Number = {13},
Pages = {3687-3695},
Year = {2010},
Month = {November},
url = {http://www.ncbi.nlm.nih.gov/pubmed/20817003},
Abstract = {The current study investigated the neural activity patterns
associated with numerical sensitivity in adults.
Event-related potentials (ERPs) were recorded while adults
observed sequentially presented display arrays (S1 and S2)
of non-symbolic numerical stimuli (dots) and made
same/different judgments of these stimuli by pressing a
button only when numerosities were the same (target trials).
The main goals were to contrast the effects of numerical
distance (close, medium, and far) and change direction
(increasing, decreasing) between S1 and S2, both in terms of
behavior and brain activity, and to examine the influence of
individual differences in numeracy on the effects of these
manipulations. Neural effects of distance were found to be
significant between 360 and 600 ms after the onset of S2
(greater negativity-wave activity for closer numerical
distances), while direction effects were found between 320
and 440 ms (greater negativity for decreasing direction).
ERP change direction effects did not interact with numerical
distance, suggesting that the two types of information are
processed independently. Importantly, subjects' behavioral
Weber fractions (w) for the same/different discrimination
task correlated with distance-related ERP-activity
amplitudes. Moreover, w also correlated with a separate
objective measure of mathematical ability. Results thus draw
a clear link between brain and behavior measures of number
discrimination, while also providing support for the
relationship between nonverbal magnitude discrimination and
symbolic numerical processing.},
Doi = {10.1016/j.neuropsychologia.2010.08.014},
Key = {fds250916}
}
@article{fds250917,
Author = {DJ Merritt and D Casasanto and EM Brannon},
Title = {Do monkeys think in metaphors? Representations of space and
time in monkeys and humans.},
Journal = {Cognition},
Volume = {117},
Number = {2},
Pages = {191-202},
Year = {2010},
Month = {November},
url = {http://www.ncbi.nlm.nih.gov/pubmed/20846645},
Abstract = {Research on the relationship between the representation of
space and time has produced two contrasting proposals. ATOM
posits that space and time are represented via a common
magnitude system, suggesting a symmetrical relationship
between space and time. According to metaphor theory,
however, representations of time depend on representations
of space asymmetrically. Previous findings in humans have
supported metaphor theory. Here, we investigate the
relationship between time and space in a nonverbal species,
by testing whether non-human primates show space-time
interactions consistent with metaphor theory or with ATOM.
We tested two rhesus monkeys and 16 adult humans in a
nonverbal task that assessed the influence of an irrelevant
dimension (time or space) on a relevant dimension (space or
time). In humans, spatial extent had a large effect on time
judgments whereas time had a small effect on spatial
judgments. In monkeys, both spatial and temporal
manipulations showed large bi-directional effects on
judgments. In contrast to humans, spatial manipulations in
monkeys did not produce a larger effect on temporal
judgments than the reverse. Thus, consistent with previous
findings, human adults showed asymmetrical space-time
interactions that were predicted by metaphor theory. In
contrast, monkeys showed patterns that were more consistent
with ATOM.},
Doi = {10.1016/j.cognition.2010.08.011},
Key = {fds250917}
}
@article{fds250922,
Author = {ME Libertus and EM Brannon},
Title = {Stable individual differences in number discrimination in
infancy.},
Journal = {Dev Sci},
Volume = {13},
Number = {6},
Pages = {900-906},
Year = {2010},
Month = {November},
url = {http://www.ncbi.nlm.nih.gov/pubmed/20977560},
Abstract = {Previous studies have shown that as a group 6-month-old
infants successfully discriminate numerical changes when the
values differ by at least a 1:2 ratio but fail at a 2:3
ratio (e.g. 8 vs. 16 but not 8 vs. 12). However, no studies
have yet examined individual differences in number
discrimination in infancy. Using a novel numerical change
detection paradigm, we present more direct evidence that
infants' numerical perception is ratio-dependent even within
the range of discriminable ratios and thus adheres to
Weber's Law. Furthermore, we show that infants' numerical
discrimination at 6 months reliably predicts their numerical
discrimination abilities but not visual short-term memory at
9 months. Thus, individual differences in numerical
discrimination acuity may be stable within the first year of
life and provide important avenues for future longitudinal
research exploring the relationship between infant numerical
discrimination and later developing math
achievement.},
Doi = {10.1111/j.1467-7687.2009.00948.x},
Key = {fds250922}
}
@article{fds303792,
Author = {SH Suanda and W Tompson and EM Brannon},
Title = {Changes in the Ability to Detect Ordinal Numerical
Relationships Between 9 and 11 Months of
Age.},
Journal = {Infancy},
Volume = {13},
Number = {4},
Pages = {308-337},
Year = {2010},
Month = {August},
ISSN = {1525-0008},
url = {http://www.ncbi.nlm.nih.gov/pubmed/20703362},
Abstract = {When are the precursors of ordinal numerical knowledge first
evident in infancy? Brannon (2002) argued that by 11 months
of age, infants possess the ability to appreciate the
greater than and less than relations between numerical
values but that this ability experiences a sudden onset
between 9 and 11 months of age. Here we present 5
experiments that explore the changes that take place between
9 and 11 months of age in infants' ability to detect
reversals in the ordinal direction of a sequence of arrays.
In Experiment 1, we replicate the finding that 11- but not
9-month-old infants detect a numerical ordinal reversal. In
Experiment 2 we rule out an alternative hypothesis that
11-month-old infants attended to changes in the absolute
numerosity of the first stimulus in the sequence rather than
a reversal in ordinal direction. In Experiment 3, we
demonstrate that 9-month-old infants are not aided by
additional exposure to each numerosity stimulus in a
sequence. In Experiment 4 we find that 11-month-old but not
9-month-old infants succeed at detecting the reversal in a
nonnumerical size or area-based rule, casting doubt on
Brannon's prior claim that what develops between 9 and 11
months of age is a specifically numerical ability. In
Experiment 5 we demonstrate that 9-month-old infants are
capable of detecting a reversal in ordinal direction but
only when there are multiple converging cues to ordinality.
Collectively these data indicate that at 11 months of age
infants can represent ordinal relations that are based on
number, size, or cumulative area, whereas at 9 months of age
infants are unable to use any of these dimensions in
isolation but instead require a confluence of
cues.},
Doi = {10.1080/15250000802188800},
Key = {fds303792}
}
@article{fds250912,
Author = {JF Cantlon and KE Safford and EM Brannon},
Title = {Spontaneous analog number representations in 3-year-old
children.},
Journal = {Dev Sci},
Volume = {13},
Number = {2},
Pages = {289-297},
Year = {2010},
Month = {March},
ISSN = {1467-7687},
url = {http://www.ncbi.nlm.nih.gov/pubmed/20136925},
Abstract = {When enumerating small sets of elements nonverbally, human
infants often show a set-size limitation whereby they are
unable to represent sets larger than three elements. This
finding has been interpreted as evidence that infants
spontaneously represent small numbers with an object-file
system instead of an analog magnitude system (Feigenson,
Dehaene & Spelke, 2004). In contrast, non-human animals and
adult humans have been shown to rely on analog magnitudes
for representing both small and large numbers (Brannon &
Terrace, 1998; Cantlon & Brannon, 2007; Cordes, Gelman,
Gallistel & Whalen, 2001). Here we demonstrate that, like
adults and non-human animals, children as young as 3 years
of age spontaneously employ analog magnitude representations
to enumerate both small and large sets. Moreover, we show
that children spontaneously attend to numerical value in
lieu of cumulative surface area. These findings provide
evidence of young children's greater sensitivity to number
relative to other quantities and demonstrate continuity in
the process they spontaneously recruit to judge small and
large values.},
Doi = {10.1111/j.1467-7687.2009.00887.x},
Key = {fds250912}
}
@article{fds250919,
Author = {SM Jones and JF Cantlon and DJ Merritt and EM Brannon},
Title = {Context affects the numerical semantic congruity effect in
rhesus monkeys (Macaca mulatta).},
Journal = {Behav Processes},
Volume = {83},
Number = {2},
Pages = {191-196},
Year = {2010},
Month = {February},
url = {http://www.ncbi.nlm.nih.gov/pubmed/20015467},
Abstract = {Do monkeys anchor their numerical judgments based on the
context in which their choices are presented? We addressed
this question by varying the numerical range across sessions
while macaque monkeys made ordinal judgments. Monkeys were
trained to make a conditional discrimination whereby they
were reinforced for ordering arrays of dots in ascending or
descending numerical order, dependent on a color cue.
Monkeys were tested using two ranges of numerosities that
converged on a single pair. Similar to the findings of
Cantlon and Brannon (2005), we found a semantic congruity
effect whereby decision time was systematically influenced
by the congruity between the cue (ascending or descending)
and the relative Numerical Magnitude of the stimuli within
each range. Furthermore, monkeys showed a context effect,
such that decision time for a given pair was dependent on
whether it was a relatively small or large set of values
compared to the other values presented in that session. This
finding suggests that, similar to humans, the semantic
congruity effect observed in monkeys is anchored by the
context. Thus our data provide further evidence for the
existence of a shared numerical comparison process in
monkeys and humans.},
Doi = {10.1016/j.beproc.2009.12.009},
Key = {fds250919}
}
@article{fds250888,
Author = {E Brannon},
Title = {Editorial},
Journal = {Behavioural Processes},
Volume = {83},
Number = {2},
Pages = {137-138},
Year = {2010},
ISSN = {0376-6357},
url = {http://dx.doi.org/10.1016/j.beproc.2009.12.015},
Doi = {10.1016/j.beproc.2009.12.015},
Key = {fds250888}
}
@article{fds250907,
Author = {S Dehaene and EM Brannon},
Title = {Space, time, and number: A Kantian research
program},
Journal = {Trends in Cognitive Sciences},
Volume = {14},
Number = {12},
Pages = {517-519},
Year = {2010},
ISSN = {1364-6613},
url = {http://dx.doi.org/10.1016/j.tics.2010.09.009},
Doi = {10.1016/j.tics.2010.09.009},
Key = {fds250907}
}
@article{fds250908,
Author = {S Dehaene and EM Brannon},
Title = {Special issue on space, time, and number},
Journal = {Trends in Cognitive Sciences},
Volume = {14},
Number = {12},
Pages = {517-569},
Year = {2010},
Key = {fds250908}
}
@article{fds250915,
Author = {J Pearson and JD Roitman and EM Brannon and ML Platt and S
Raghavachari},
Title = {A physiologically-inspired model of numerical classification
based on graded stimulus coding},
Journal = {FRONTIERS IN BEHAVIORAL NEUROSCIENCE},
Volume = {4},
Number = {1},
Pages = {1},
Year = {2010},
ISSN = {1662-5153},
url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000208454700001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
Abstract = {In most natural decision contexts, the process of selecting
among competing actions takes place in the presence of
informative, but potentially ambiguous, stimuli. Decisions
about magnitudes - quantities like time, length, and
brightness that are linearly ordered - constitute an
important subclass of such decisions. It has long been known
that perceptual judgments about such quantities obey Weber's
Law, wherein the just-noticeable difference in a magnitude
is proportional to the magnitude itself. Current
physiologically inspired models of numerical classification
assume discriminations are made via a labeled line code of
neurons selectively tuned for numerosity, a pattern observed
in the firing rates of neurons in the ventral intraparietal
area (VIP) of the macaque. By contrast, neurons in the
contiguous lateral intraparietal area (LIP) signal
numerosity in a graded fashion, suggesting the possibility
that numerical classification could be achieved in the
absence of neurons tuned for number. Here, we consider the
performance of a decision model based on this analog coding
scheme in a paradigmatic discrimination task - numerosity
bisection. We demonstrate that a basic two-neuron classifier
model, derived from experimentally measured monotonic
responses of LIP neurons, is sufficient to reproduce the
numerosity bisection behavior of monkeys, and that the
threshold of the classifier can be set by reward
maximization via a simple learning rule. In addition, our
model predicts deviations from Weber Law scaling of choice
behavior at high numerosity. Together, these results suggest
both a generic neuronal framework for magnitude-based
decisions and a role for reward contingency in the
classification of such stimuli.},
Doi = {10.3389/neuro.08.001.2010},
Key = {fds250915}
}
@article{fds250921,
Author = {EM Brannon},
Title = {Introduction to thought without language: A tibute to the
contributions of H.S. Terrace},
Journal = {Behavioral Processes},
Volume = {83},
Number = {2},
Pages = {137-138},
Year = {2010},
ISSN = {0376-6357},
Key = {fds250921}
}
@article{fds250913,
Author = {ME Libertus and EM Brannon},
Title = {Behavioral and Neural Basis of Number Sense in
Infancy.},
Journal = {Curr Dir Psychol Sci},
Volume = {18},
Number = {6},
Pages = {346-351},
Year = {2009},
Month = {December},
ISSN = {0963-7214},
url = {http://www.ncbi.nlm.nih.gov/pubmed/20419075},
Abstract = {Approximate number discrimination in adult human and
nonhuman animals is governed by Weber's Law: The ratio
between the values determines discriminability. Here, we
review recent evidence from behavioral and neuroimaging
studies that suggests that number sense in human infancy
shares the same hallmark feature of Weber's Law and may rely
on the same neural substrates as previously found in adults,
children, and nonhuman animals. These findings support the
notion of ontogenetic and phylogenetic continuity in number
sense. New methods described here may help uncover how
infants' early number sense supports the development of a
mature number sense. Moreover, they may aid in understanding
how children learn to map nonsymbolic number representations
onto symbols for number by providing dependent measures that
capture individual variability.},
Doi = {10.1111/j.1467-8721.2009.01665.x},
Key = {fds250913}
}
@article{fds250943,
Author = {ME Libertus and LB Pruitt and MG Woldorff and EM
Brannon},
Title = {Induced alpha-band oscillations reflect ratio-dependent
number discrimination in the infant brain.},
Journal = {J Cogn Neurosci},
Volume = {21},
Number = {12},
Pages = {2398-2406},
Year = {2009},
Month = {December},
ISSN = {0898-929X},
url = {http://www.ncbi.nlm.nih.gov/pubmed/19016603},
Abstract = {Behavioral studies show that infants are capable of
discriminating the number of objects or events in their
environment, while also suggesting that number
discrimination in infancy may be ratio-dependent. However,
due to limitations of the dependent measures used with
infant behavioral studies, the evidence for ratio dependence
falls short of the vast psychophysical datasets that have
established ratio dependence, and thus, adherence to Weber's
Law in adults and nonhuman animals. We addressed this issue
in two experiments that presented 7-month-old infants with
familiar and novel numerosities while electroencephalogram
measures of their brain activity were recorded. These data
provide convergent evidence that the brains of 7-month-old
infants detected numerical novelty. Alpha-band and
theta-band oscillations both differed for novel and familiar
numerical values. Most importantly, spectral power in the
alpha band over midline and right posterior scalp sites was
modulated by the ratio between the familiar and novel
numerosities. Our findings provide neural evidence that
numerical discrimination in infancy is ratio dependent and
follows Weber's Law, thus indicating continuity of these
cognitive processes over development. Results are also
consistent with the idea that networks in the frontal and
parietal cortices support ratio-dependent number
discrimination in the first year of human life, consistent
with what has been reported in neuroimaging studies in
adults and older children.},
Doi = {10.1162/jocn.2008.21162},
Key = {fds250943}
}
@article{fds250941,
Author = {JF Cantlon and ME Libertus and P Pinel and S Dehaene and EM Brannon and KA Pelphrey},
Title = {The neural development of an abstract concept of
number.},
Journal = {J Cogn Neurosci},
Volume = {21},
Number = {11},
Pages = {2217-2229},
Year = {2009},
Month = {November},
ISSN = {0898-929X},
url = {http://www.ncbi.nlm.nih.gov/pubmed/19016605},
Abstract = {As literate adults, we appreciate numerical values as
abstract entities that can be represented by a numeral, a
word, a number of lines on a scorecard, or a sequence of
chimes from a clock. This abstract, notation-independent
appreciation of numbers develops gradually over the first
several years of life. Here, using functional magnetic
resonance imaging, we examine the brain mechanisms that 6-
and 7-year-old children and adults recruit to solve
numerical comparisons across different notation systems. The
data reveal that when young children compare numerical
values in symbolic and nonsymbolic notations, they invoke
the same network of brain regions as adults including
occipito-temporal and parietal cortex. However, children
also recruit inferior frontal cortex during these numerical
tasks to a much greater degree than adults. Our data lend
additional support to an emerging consensus from adult
neuroimaging, nonhuman primate neurophysiology, and
computational modeling studies that a core neural system
integrates notation-independent numerical representations
throughout development but, early in development,
higher-order brain mechanisms mediate this
process.},
Doi = {10.1162/jocn.2008.21159},
Key = {fds250941}
}
@article{fds250945,
Author = {S Cordes and EM Brannon},
Title = {Crossing the divide: infants discriminate small from large
numerosities.},
Journal = {Dev Psychol},
Volume = {45},
Number = {6},
Pages = {1583-1594},
Year = {2009},
Month = {November},
url = {http://www.ncbi.nlm.nih.gov/pubmed/19899916},
Abstract = {Although young infants have repeatedly demonstrated
successful numerosity discrimination across large sets when
the number of items in the sets changes twofold (E. M.
Brannon, S. Abbott, & D. J. Lutz, 2004; J. N. Wood & E. S.
Spelke, 2005; F. Xu & E. S. Spelke, 2000), they consistently
fail to discriminate a twofold change in number when one set
is large and the other is small (<4 items; F. Feigenson, S.
Carey, & M. Hauser, 2002; F. Xu, 2003). It has been
theorized that this failure reflects an incompatibility in
representational systems for small and large sets. The
authors investigated the ability of 7-month-old infants to
compare small and large sets over a variety of conditions.
Results reveal that infants can successfully discriminate
small from large sets when given a fourfold change, but not
a twofold change, in number. The implications of these
results are discussed in light of current theories of number
representation.},
Doi = {10.1037/a0015666},
Key = {fds250945}
}
@article{fds250944,
Author = {DJ Merritt and R Rugani and EM Brannon},
Title = {Empty sets as part of the numerical continuum: conceptual
precursors to the zero concept in rhesus
monkeys.},
Journal = {J Exp Psychol Gen},
Volume = {138},
Number = {2},
Pages = {258-269},
Year = {2009},
Month = {May},
ISSN = {0096-3445},
url = {http://www.ncbi.nlm.nih.gov/pubmed/19397383},
Abstract = {The goal of the current research was to explore whether
monkeys possess conceptual precursors necessary for
understanding zero. We trained rhesus monkeys on a
nonsymbolic numerical matching-to-sample task, and on a
numerical ordering task. We then introduced
nondifferentially reinforced trials that contained empty
sets to determine whether monkeys would treat empty sets as
numerical values. All monkeys successfully matched and
ordered the empty sets without any training. Accuracy showed
distance effects, indicating that they treated empty sets as
values on a numerical continuum.},
Doi = {10.1037/a0015231},
Key = {fds250944}
}
@article{fds250942,
Author = {S Cordes and EM Brannon},
Title = {The relative salience of discrete and continuous quantity in
young infants.},
Journal = {Dev Sci},
Volume = {12},
Number = {3},
Pages = {453-463},
Year = {2009},
Month = {April},
url = {http://www.ncbi.nlm.nih.gov/pubmed/19371370},
Abstract = {Whether human infants spontaneously represent number remains
contentious. Clearfield & Mix (1999) and Feigenson, Carey &
Spelke (2002) put forth evidence that when presented with
small sets of 1-3 items infants may preferentially attend to
continuous properties of stimuli rather than to number, and
these results have been interpreted as evidence that infants
may not have numerical competence. Here we present three
experiments that test the hypothesis that infants prefer to
represent continuous variables over number. In Experiment 1,
we attempt to replicate the Clearfield & Mix study with a
larger sample of infants. Although we replicated their
finding that infants attend to changes in contour length,
infants in our study attended to number and perimeter/area
simultaneously. In Experiments 2 and 3, we pit number
against continuous extent for exclusively large sets
(Experiment 2) and for small and large sets combined
(Experiment 3). In all three experiments, infants noticed
the change in number, suggesting that representing discrete
quantity is not a last resort for human infants. These
results should temper the conclusion that infants find
continuous properties more salient than number and instead
suggest that number is spontaneously represented by young
infants, even when other cues are available.},
Doi = {10.1111/j.1467-7687.2008.00781.x},
Key = {fds250942}
}
@article{fds250910,
Author = {ME Libertus and EM Brannon and KA Pelphrey},
Title = {Developmental changes in category-specific brain responses
to numbers and letters in a working memory
task.},
Journal = {Neuroimage},
Volume = {44},
Number = {4},
Pages = {1404-1414},
Year = {2009},
Month = {February},
url = {http://www.ncbi.nlm.nih.gov/pubmed/19027079},
Abstract = {Neuroimaging studies have identified a common network of
brain regions involving the prefrontal and parietal cortices
across a variety of working memory (WM) tasks. However,
previous studies have also reported category-specific
dissociations of activation within this network. In this
study, we investigated the development of category-specific
activation in a WM task with digits, letters, and faces.
Eight-year-old children and adults performed a 2-back WM
task while their brain activity was measured using
functional magnetic resonance imaging (fMRI). Overall,
children were significantly slower and less accurate than
adults on all three WM conditions (digits, letters, and
faces); however, within each age group, behavioral
performance across the three conditions was very similar.
FMRI results revealed category-specific activation in adults
but not children in the intraparietal sulcus for the digit
condition. Likewise, during the letter condition,
category-specific activation was observed in adults but not
children in the left occipital-temporal cortex. In contrast,
children and adults showed highly similar brain-activity
patterns in the lateral fusiform gyri when solving the
2-back WM task with face stimuli. Our results suggest that
8-year-old children do not yet engage the typical brain
regions that have been associated with abstract or semantic
processing of numerical symbols and letters when these
processes are task-irrelevant and the primary task is
demanding. Nevertheless, brain activity in letter-responsive
areas predicted children's spelling performance underscoring
the relationship between abstract processing of letters and
linguistic abilities. Lastly, behavioral performance on the
WM task was predictive of math and language abilities
highlighting the connection between WM and other cognitive
abilities in development.},
Doi = {10.1016/j.neuroimage.2008.10.027},
Key = {fds250910}
}
@article{fds250940,
Author = {JF Cantlon and ML Platt and EM Brannon},
Title = {Beyond the number domain.},
Journal = {Trends Cogn Sci},
Volume = {13},
Number = {2},
Pages = {83-91},
Year = {2009},
Month = {February},
ISSN = {1364-6613},
url = {http://www.ncbi.nlm.nih.gov/pubmed/19131268},
Abstract = {In a world without numbers, we would be unable to build a
skyscraper, hold a national election, plan a wedding or pay
for a chicken at the market. The numerical symbols used in
all these behaviors build on the approximate number system
(ANS) which represents the number of discrete objects or
events as a continuous mental magnitude. Here, we first
discuss evidence that the ANS bears a set of behavioral and
brain signatures that are universally displayed across
animal species, human cultures and development. We then turn
to the question of whether the ANS constitutes a specialized
cognitive and neural domain - a question central to
understanding how this system works, the nature of its
evolutionary and developmental trajectory and its physical
instantiation in the brain.},
Doi = {10.1016/j.tics.2008.11.007},
Key = {fds250940}
}
@article{fds250923,
Author = {JF Cantlon and S Cordes and ME Libertus and EM
Brannon},
Title = {Comment on "Log or linear? Distinct intuitions of the number
scale in Western and Amazonian indigene cultures".},
Journal = {Science},
Volume = {323},
Number = {5910},
Pages = {38},
Year = {2009},
Month = {January},
url = {http://www.ncbi.nlm.nih.gov/pubmed/19119201},
Abstract = {Dehaene et al. (Reports, 30 May 2008, p. 1217) argued that
native speakers of Mundurucu, a language without a
linguistic numerical system, inherently represent numerical
values as a logarithmically spaced spatial continuum.
However, their data do not rule out the alternative
conclusion that Mundurucu speakers encode numbers linearly
with scalar variability and psychologically construct
space-number mappings by analogy.},
Doi = {10.1126/science.1164773},
Key = {fds250923}
}
@article{fds166828,
Author = {Dustin, M. Casasanto and D. and Brannon, E.M.},
Title = {Do monkeys think in metaphors? Representations of space and
time in monkeys},
Year = {2009},
Key = {fds166828}
}
@article{fds250914,
Author = {JF Cantlon and S Cordes and ME Libertus and EM
Brannon},
Title = {Numerical abstraction: It ain't broke (commentary)},
Journal = {Behavioral and Brain Sciences},
Volume = {32},
Number = {3-4},
Pages = {331-332},
Year = {2009},
ISSN = {0140-525X},
url = {http://dx.doi.org/10.1017/S0140525X09990513},
Abstract = {The dual-code proposal of number representation put forward
by Cohen Kadosh & Walsh (CK&W) accounts for only a
fraction of the many modes of numerical abstraction.
Contrary to their proposal, robust data from human infants
and nonhuman animals indicate that abstract numerical
representations are psychologically primitive. Additionally,
much of the behavioral and neural data cited to support
CK&W's proposal is, in fact, neutral on the issue of
numerical abstraction. © 2009 Cambridge University
Press.},
Doi = {10.1017/S0140525X09990513},
Key = {fds250914}
}
@article{fds250926,
Author = {M Libertus and EM Brannon},
Title = {Change detection paradigm for numerosity discrimination
thresholds},
Journal = {Developmental Science},
Year = {2009},
Key = {fds250926}
}
@article{fds250939,
Author = {EL MacLean, SR Prior and ML Platt and EM Brannon},
Title = {Primate location preference in a double-tier cage: the
effects of illumination and cage height.},
Journal = {J Appl Anim Welf Sci},
Volume = {12},
Number = {1},
Pages = {73-81},
Year = {2009},
url = {http://www.ncbi.nlm.nih.gov/pubmed/19107666},
Abstract = {Nonhuman primates are frequently housed in double-tier
arrangements with significant differences between the
environments of the upper and lower-row cages. Although
several studies have investigated whether this arrangement
alters monkeys' behavior, no studies have addressed the two
most notable differences, light and height, individually to
determine their relative importance. This experiment
examined how rhesus and long-tailed macaques allocated their
time between the upper and lower-row cages of a 1-over-1
apartment module under different lighting conditions. In
Condition A, monkeys' baseline degree of preference for the
upper- and lower-row was tested. In Condition B, the
lighting environment was reversed by limiting illumination
in the upper-row cage and increasing illumination in the
lower-row cage. In both conditions, monkeys spent more time
in the upper-row cage, thus indicating a strong preference
for elevation regardless of illumination. The amount of time
that monkeys spent in the lower-row cage increased by 7%
under reversed lighting, but this trend was not significant.
These results corroborate the importance of providing
captive primates with access to elevated
areas.},
Doi = {10.1080/10888700802536822},
Key = {fds250939}
}
@article{fds304647,
Author = {JF Cantlon and S Cordes and ME Libertus and EM
Brannon},
Title = {Numerical abstraction: It ain't broke},
Journal = {Behavioral and Brain Sciences},
Volume = {32},
Number = {3-4},
Pages = {331-332},
Year = {2009},
ISSN = {0140-525X},
url = {http://dx.doi.org/10.1017/S0140525X09990513},
Abstract = {The dual-code proposal of number representation put forward
by Cohen Kadosh & Walsh (CK&W) accounts for only a
fraction of the many modes of numerical abstraction.
Contrary to their proposal, robust data from human infants
and nonhuman animals indicate that abstract numerical
representations are psychologically primitive. Additionally,
much of the behavioral and neural data cited to support
CK&W's proposal is, in fact, neutral on the issue of
numerical abstraction. © 2009 Cambridge University
Press.},
Doi = {10.1017/S0140525X09990513},
Key = {fds304647}
}
@article{fds250948,
Author = {S Cordes and EM Brannon},
Title = {Quantitative competencies in infancy.},
Journal = {Dev Sci},
Volume = {11},
Number = {6},
Pages = {803-808},
Year = {2008},
Month = {November},
url = {http://www.ncbi.nlm.nih.gov/pubmed/19046148},
Abstract = {We review recently published papers that have contributed to
our understanding of how the preverbal infant represents
number, area and time. We review evidence that infants rely
on two distinct systems to represent number nonverbally and
highlight the similarities in the ratio-dependent
discrimination of number, time and area. Contrary to earlier
assertions that continuous dimensions are more salient (and
thus more discriminable) to the infant than numerosity, we
argue that the opposite conclusion is better supported by
the data. The preverbal infant may be better able to extract
numerosity than continuous variables from arrays of discrete
items.},
Doi = {10.1111/j.1467-7687.2008.00770.x},
Key = {fds250948}
}
@article{fds250946,
Author = {EL Maclean and DJ Merritt and EM Brannon},
Title = {Social Complexity Predicts Transitive Reasoning in Prosimian
Primates.},
Journal = {Anim Behav},
Volume = {76},
Number = {2},
Pages = {479-486},
Year = {2008},
Month = {August},
ISSN = {0003-3472},
url = {http://www.ncbi.nlm.nih.gov/pubmed/19649139},
Abstract = {Transitive Inference is a form of deductive reasoning that
has been suggested as one cognitive mechanism by which
animals could learn the many relationships within their
group's dominance hierarchy. This process thus bears
relevance to the social intelligence hypothesis which posits
evolutionary links between various forms of social and
nonsocial cognition. Recent evidence corroborates the link
between social complexity and transitive inference and
indicates that highly social animals may show superior
transitive reasoning even in nonsocial contexts. We examined
the relationship between social complexity and transitive
inference in two species of prosimians, a group of primates
that diverged from the common ancestor of monkeys, apes, and
humans over 50 million years ago. In Experiment 1, highly
social ring-tailed lemurs, Lemur catta, outperformed the
less social mongoose lemurs, Eulemur mongoz, in tests of
transitive inference and showed more robust representations
of the underlying ordinal relationships between the stimuli.
In Experiment 2, after training under a correction procedure
that emphasized the underlying linear dimension of the
series, both species showed similar transitive inference.
This finding suggests that the two lemur species differ not
in their fundamental ability to make transitive inferences,
but rather in their predisposition to mentally organize
information along a common underlying dimension. Together,
these results support the hypothesis that social complexity
is an important selective pressure for the evolution of
cognitive abilities relevant to transitive
reasoning.},
Doi = {10.1016/j.anbehav.2008.01.025},
Key = {fds250946}
}
@article{fds250947,
Author = {S Cordes and EM Brannon},
Title = {The difficulties of representing continuous extent in
infancy: using number is just easier.},
Journal = {Child Dev},
Volume = {79},
Number = {2},
Pages = {476-489},
Year = {2008},
Month = {March},
ISSN = {0009-3920},
url = {http://www.ncbi.nlm.nih.gov/pubmed/18366435},
Abstract = {This study investigates the ability of 6-month-old infants
to attend to the continuous properties of a set of discrete
entities. Infants were habituated to dot arrays that were
constant in cumulative surface area yet varied in number for
small (< 4) or large (> 3) sets. Results revealed that
infants detected a 4-fold (but not 3-fold) change in area,
regardless of set size. These results are in marked contrast
to demonstrations that infants of the same age successfully
discriminate a 2- or 3-fold change in number, providing
strong counterevidence to the claim that infants use solely
nonnumerical, continuous extent variables when
discriminating sets. These findings also shed light on the
processes involved in tracking continuous variables in
infants.},
Doi = {10.1111/j.1467-8624.2007.01137.x},
Key = {fds250947}
}
@article{fds250935,
Author = {EM Brannon and ME Libertus and WH Meck and MG Woldorff},
Title = {Electrophysiological measures of time processing in infant
and adult brains: Weber's Law holds.},
Journal = {J Cogn Neurosci},
Volume = {20},
Number = {2},
Pages = {193-203},
Year = {2008},
Month = {February},
ISSN = {0898-929X},
url = {http://www.ncbi.nlm.nih.gov/pubmed/18275328},
Abstract = {Behavioral studies have demonstrated that time perception in
adults, children, and nonhuman animals is subject to Weber's
Law. More specifically, as with discriminations of other
features, it has been found that it is the ratio between two
durations rather than their absolute difference that
controls the ability of an animal to discriminate them.
Here, we show that scalp-recorded event-related electrical
brain potentials (ERPs) in both adults and 10-month-old
human infants, in response to changes in interstimulus
interval (ISI), appear to obey the scalar property found in
time perception in adults, children, and nonhuman animals.
Using a timing-interval oddball paradigm, we tested adults
and infants in conditions where the ratio between the
standard and deviant interval in a train of homogeneous
auditory stimuli varied such that there was a 1:4 (only for
the infants), 1:3, 1:2, and 2:3 ratio between the standard
and deviant intervals. We found that the amplitude of the
deviant-triggered mismatch negativity ERP component
(deviant-ISI ERP minus standard-ISI ERP) varied as a
function of the ratio of the standard to deviant interval.
Moreover, when absolute values were varied and ratio was
held constant, the mismatch negativity did not
vary.},
Doi = {10.1162/jocn.2008.20016},
Key = {fds250935}
}
@article{fds250909,
Author = {KE Jordan and SH Suanda and EM Brannon},
Title = {Intersensory redundancy accelerates preverbal numerical
competence},
Journal = {Cognition},
Volume = {108},
Number = {1},
Pages = {210-221},
Year = {2008},
ISSN = {0010-0277},
url = {http://dx.doi.org/10.1016/j.cognition.2007.12.001},
Abstract = {Intersensory redundancy can facilitate animal and human
behavior in areas as diverse as rhythm discrimination,
signal detection, orienting responses, maternal call
learning, and associative learning. In the realm of
numerical development, infants show similar sensitivity to
numerical differences in both the visual and auditory
modalities. Using a habituation-dishabituation paradigm, we
ask here, whether providing redundant, multisensory
numerical information allows six-month-old infants to make
more precise numerical discriminations. Results indicate
that perceptually redundant information improved preverbal
numerical precision to a level of discrimination previously
thought attainable only after additional months of
development. Multimodal stimuli may thus boost abstract
cognitive abilities such as numerical competence. © 2007
Elsevier B.V. All rights reserved.},
Doi = {10.1016/j.cognition.2007.12.001},
Key = {fds250909}
}
@article{fds250933,
Author = {KE Jordan and EL MacLean and EM Brannon},
Title = {Monkeys match and tally quantities across
senses},
Journal = {Cognition},
Volume = {108},
Number = {3},
Pages = {617-625},
Year = {2008},
ISSN = {0010-0277},
url = {http://dx.doi.org/10.1016/j.cognition.2008.05.006},
Abstract = {We report here that monkeys can actively match the number of
sounds they hear to the number of shapes they see and
present the first evidence that monkeys sum over sounds and
sights. In Experiment 1, two monkeys were trained to choose
a simultaneous array of 1-9 squares that numerically matched
a sample sequence of shapes or sounds. Monkeys numerically
matched across (audio-visual) and within (visual-visual)
modalities with equal accuracy and transferred to novel
numerical values. In Experiment 2, monkeys presented with
sample sequences of randomly ordered shapes or tones were
able to choose an array of 2-9 squares that was the
numerical sum of the shapes and sounds in the sample
sequence. In both experiments, accuracy and reaction time
depended on the ratio between the correct numerical match
and incorrect choice. These findings suggest monkeys and
humans share an abstract numerical code that can be divorced
from the modality in which stimuli are first experienced. ©
2008 Elsevier B.V. All rights reserved.},
Doi = {10.1016/j.cognition.2008.05.006},
Key = {fds250933}
}
@article{fds250949,
Author = {JF Cantlon and EM Brannon},
Title = {Basic math in monkeys and college students.},
Journal = {PLoS Biol},
Volume = {5},
Number = {12},
Pages = {e328},
Year = {2007},
Month = {December},
ISSN = {1544-9173},
url = {http://www.ncbi.nlm.nih.gov/pubmed/18092890},
Abstract = {Adult humans possess a sophisticated repertoire of
mathematical faculties. Many of these capacities are rooted
in symbolic language and are therefore unlikely to be shared
with nonhuman animals. However, a subset of these skills is
shared with other animals, and this set is considered a
cognitive vestige of our common evolutionary history.
Current evidence indicates that humans and nonhuman animals
share a core set of abilities for representing and comparing
approximate numerosities nonverbally; however, it remains
unclear whether nonhuman animals can perform approximate
mental arithmetic. Here we show that monkeys can mentally
add the numerical values of two sets of objects and choose a
visual array that roughly corresponds to the arithmetic sum
of these two sets. Furthermore, monkeys' performance during
these calculations adheres to the same pattern as humans
tested on the same nonverbal addition task. Our data
demonstrate that nonverbal arithmetic is not unique to
humans but is instead part of an evolutionarily primitive
system for mathematical thinking shared by
monkeys.},
Doi = {10.1371/journal.pbio.0050328},
Key = {fds250949}
}
@article{fds250920,
Author = {D Merritt and EL Maclean and S Jaffe and EM Brannon},
Title = {A comparative analysis of serial ordering in ring-tailed
lemurs (Lemur catta).},
Journal = {J Comp Psychol},
Volume = {121},
Number = {4},
Pages = {363-371},
Year = {2007},
Month = {November},
ISSN = {0735-7036},
url = {http://www.ncbi.nlm.nih.gov/pubmed/18085919},
Abstract = {Research over the last 25 years has demonstrated that
animals are able to organize sequences in memory and
retrieve ordered sequences without language. Qualitative
differences have been found between the serial organization
of behavior in pigeons and monkeys. Here the authors test
serial ordering abilities in ring-tailed lemurs, a
strepsirrhine primate whose ancestral lineage diverged from
that of monkeys, apes, and humans approximately 63 million
years ago. Lemurs' accuracy and response times were similar
to monkeys, thus suggesting that they may share mechanisms
for serial organization that dates to a common primate
ancestor.},
Doi = {10.1037/0735-7036.121.4.363},
Key = {fds250920}
}
@article{fds250951,
Author = {EM Brannon and S Suanda and K Libertus},
Title = {Temporal discrimination increases in precision over
development and parallels the development of numerosity
discrimination.},
Journal = {Dev Sci},
Volume = {10},
Number = {6},
Pages = {770-777},
Year = {2007},
Month = {November},
ISSN = {1363-755X},
url = {http://www.ncbi.nlm.nih.gov/pubmed/17973794},
Abstract = {Time perception is important for many aspects of human
behavior, and a large literature documents that adults
represent intervals and that their ability to discriminate
temporal intervals is ratio dependent. Here we replicate a
recent study by vanMarle and Wynn (2006) that used the
visual habituation paradigm and demonstrated that temporal
discrimination in 6-month-old infants is also ratio
dependent. We further demonstrate that between 6 and 10
months of age temporal discrimination increases in precision
such that by 10 months of age infants succeed at
discriminating a 2:3 ratio, a ratio that 6-month-old infants
were unable to discriminate. We discuss the potential
implications of the fact that temporal discrimination
follows the same developmental progression that has been
previously observed for number discrimination in infancy
(Lipton & Spelke, 2003).},
Doi = {10.1111/j.1467-7687.2007.00635.x},
Key = {fds250951}
}
@article{fds250934,
Author = {JD Roitman and EM Brannon and ML Platt},
Title = {Monotonic coding of numerosity in macaque lateral
intraparietal area.},
Journal = {PLoS Biol},
Volume = {5},
Number = {8},
Pages = {e208},
Year = {2007},
Month = {August},
ISSN = {1544-9173},
url = {http://www.ncbi.nlm.nih.gov/pubmed/17676978},
Abstract = {As any child knows, the first step in counting is summing up
individual elements, yet the brain mechanisms responsible
for this process remain obscure. Here we show, for the first
time, that a population of neurons in the lateral
intraparietal area of monkeys encodes the total number of
elements within their classical receptive fields in a graded
fashion, across a wide range of numerical values (2-32).
Moreover, modulation of neuronal activity by visual quantity
developed rapidly, within 100 ms of stimulus onset, and was
independent of attention, reward expectations, or stimulus
attributes such as size, density, or color. The responses of
these neurons resemble the outputs of "accumulator neurons"
postulated in computational models of number processing.
Numerical accumulator neurons may provide inputs to neurons
encoding specific cardinal values, such as "4," that have
been described in previous work. Our findings may explain
the frequent association of visuospatial and numerical
deficits following damage to parietal cortex in
humans.},
Doi = {10.1371/journal.pbio.0050208},
Key = {fds250934}
}
@article{fds250884,
Author = {J Cantlon and R Fink and K Safford and EM Brannon},
Title = {Heterogeneity impairs numerical matching but not numerical
ordering in preschool children.},
Journal = {Dev Sci},
Volume = {10},
Number = {4},
Pages = {431-440},
Year = {2007},
Month = {July},
ISSN = {1363-755X},
url = {http://www.ncbi.nlm.nih.gov/pubmed/17552933},
Abstract = {Do preschool children appreciate numerical value as an
abstract property of a set of objects? We tested the
influence of stimulus features such as size, shape, and
color on preschool children's developing nonverbal numerical
abilities. Children between 3 and 5 years of age were tested
on their ability to estimate number when the sizes, shapes,
and colors of the elements in an array were varied
(heterogeneous condition) versus when they did not vary
(homogeneous condition). One group of children was tested on
an ordinal task in which the goal was to select the smaller
of two arrays while another group of children was tested on
a match-to-sample task in which the goal was to choose one
of two visual arrays that matched the sample in number.
Children performed above chance on both homogeneous and
heterogeneous stimuli in both tasks. However, while children
showed no impairment on heterogeneous relative to
homogeneous arrays in the ordering task, performance was
impaired by heterogeneity in the matching task. We suggest
that nonverbal numerical abstraction occurs early in
development, but specific task objectives may prevent
children from engaging in numerical abstraction.},
Doi = {10.1111/j.1467-7687.2007.00597.x},
Key = {fds250884}
}
@article{fds250883,
Author = {JD Roitman and EM Brannon, JR Andrews and ML
Platt},
Title = {Nonverbal representation of time and number in
adults.},
Journal = {Acta Psychol (Amst)},
Volume = {124},
Number = {3},
Pages = {296-318},
Year = {2007},
Month = {March},
ISSN = {0001-6918},
url = {http://www.ncbi.nlm.nih.gov/pubmed/16759623},
Abstract = {A wealth of human and animal research supports common neural
processing of numerical and temporal information. Here we
test whether adult humans spontaneously encode number and
time in a paradigm similar to those previously used to test
the mode-control model in animals. Subjects were trained to
classify visual stimuli that varied in both number and
duration as few/short or many/long. Subsequently subjects
were tested with novel stimuli that varied time and held
number constant (eight flashes in 0.8-3.2s) or varied number
and held time constant (4-16 flashes in 1.6s). Adult humans
classified novel stimuli as many/long as monotonic functions
of both number and duration, consistent with simultaneous,
nonverbal, analog encoding. Numerical sensitivity, however,
was finer than temporal sensitivity, suggesting differential
salience of time and number. These results support the
notion that adults simultaneously represent the number and
duration of stimuli but suggest a possible asymmetry in
their representations.},
Doi = {10.1016/j.actpsy.2006.03.008},
Key = {fds250883}
}
@article{fds250925,
Author = {JF Cantlon and EM Brannon},
Title = {Adding up the effects of cultural experience on the
brain.},
Journal = {Trends Cogn Sci},
Volume = {11},
Number = {1},
Pages = {1-4},
Year = {2007},
Month = {January},
ISSN = {1364-6613},
url = {http://www.ncbi.nlm.nih.gov/pubmed/17129750},
Abstract = {How does the brain represent number and perform mathematical
calculations? According to a recent and provocative study by
Tang and colleagues, it depends on which language you learn.
They found that the divergent linguistic and cultural
experiences of native Chinese and native English speakers
are associated with distinct patterns of brain activity
during mathematical processing. Their results raise
important questions about the cognitive and neural
specificity of cultural influences on mathematical processes
and the core nature of mathematical cognition.},
Doi = {10.1016/j.tics.2006.10.008},
Key = {fds250925}
}
@article{fds250937,
Author = {JF Cantlon and EM Brannon},
Title = {How much does number matter to a monkey (Macaca
mulatta)?},
Journal = {J Exp Psychol Anim Behav Process},
Volume = {33},
Number = {1},
Pages = {32-41},
Year = {2007},
Month = {January},
ISSN = {0097-7403},
url = {http://www.ncbi.nlm.nih.gov/pubmed/17227193},
Abstract = {Although many animal species can represent numerical values,
little is known about how salient number is relative to
other object properties for nonhuman animals. In one
hypothesis, researchers propose that animals represent
number only as a last resort, when no other properties
differentiate stimuli. An alternative hypothesis is that
animals automatically, spontaneously, and routinely
represent the numerical attributes of their environments.
The authors compared the influence of number versus that of
shape, color, and surface area on rhesus monkeys' (Macaca
mulatta) decisions by testing them on a matching task with
more than one correct answer: a numerical match and a
nonnumerical (color, surface area, or shape) match. The
authors also tested whether previous laboratory experience
with numerical discrimination influenced a monkey's
propensity to represent number. Contrary to the last-resort
hypothesis, all monkeys based their decisions on numerical
value when the numerical ratio was favorable.},
Doi = {10.1037/0097-7403.33.1.32},
Key = {fds250937}
}
@article{fds250950,
Author = {ME Libertus and MG Woldorff and EM Brannon},
Title = {Electrophysiological evidence for notation independence in
numerical processing.},
Journal = {Behav Brain Funct},
Volume = {3},
Number = {1},
Pages = {1},
Year = {2007},
url = {http://www.ncbi.nlm.nih.gov/pubmed/17214890},
Abstract = {BACKGROUND: A dominant view in numerical cognition is that
numerical comparisons operate on a notation independent
representation (Dehaene, 1992). Although previous human
neurophysiological studies using scalp-recorded
event-related potentials (ERPs) on the numerical distance
effect have been interpreted as supporting this idea,
differences in the electrophysiological correlates of the
numerical distance effect in symbolic notations (e.g. Arabic
numerals) and non-symbolic notations (e.g. a set of visually
presented dots of a certain number) are not entirely
consistent with this view. METHODS AND RESULTS: Two
experiments were conducted to resolve these discrepancies.
In Experiment 1, participants performed a symbolic and a
non-symbolic numerical comparison task ("smaller or larger
than 5?") with numerical values 1-4 and 6-9 while ERPs were
recorded. Consistent with a previous report (Temple &
Posner, 1998), in the symbolic condition the amplitude of
the P2p ERP component (210-250 ms post-stimulus) was larger
for values near to the standard than for values far from the
standard whereas this pattern was reversed in the
non-symbolic condition. However, closer analysis indicated
that the reversal in polarity was likely due to the presence
of a confounding stimulus effect on the early sensory ERP
components for small versus larger numerical values in the
non-symbolic condition. In Experiment 2 exclusively large
numerosities (8-30) were used, thereby rendering sensory
differences negligible, and with this control in place the
numerical distance effect in the non-symbolic condition
mirrored the symbolic condition of Experiment 1. CONCLUSION:
Collectively, the results support the claim of an abstract
semantic processing stage for numerical comparisons that is
independent of input notation.},
Doi = {10.1186/1744-9081-3-1},
Key = {fds250950}
}
@article{fds250936,
Author = {KE Jordan and EM Brannon},
Title = {A common representational system governed by Weber's law:
nonverbal numerical similarity judgments in 6-year-olds and
rhesus macaques.},
Journal = {J Exp Child Psychol},
Volume = {95},
Number = {3},
Pages = {215-229},
Year = {2006},
Month = {November},
ISSN = {0022-0965},
url = {http://www.ncbi.nlm.nih.gov/pubmed/16808924},
Abstract = {This study compared nonverbal numerical processing in
6-year-olds with that in nonhuman animals using a numerical
bisection task. In the study, 16 children were trained on a
delayed match-to-sample paradigm to match exemplars of two
anchor numerosities. Children were then required to indicate
whether a sample intermediate to the anchor values was
closer to the small anchor value or the large anchor value.
For two sets of anchor values with the same ratio, the
probability of choosing the larger anchor value increased
systematically with sample number, and the psychometric
functions superimposed when plotted on a logarithmic scale.
The psychometric functions produced by the children also
superimposed with the psychometric functions produced by
rhesus monkeys in an analogous previous experiment. These
examples of superimposition demonstrate that nonverbal
number representations, even in children who have acquired
the verbal counting system, are modulated by Weber's
law.},
Doi = {10.1016/j.jecp.2006.05.004},
Key = {fds250936}
}
@article{fds250938,
Author = {EM Brannon and D Lutz and S Cordes},
Title = {The development of area discrimination and its implications
for number representation in infancy.},
Journal = {Dev Sci},
Volume = {9},
Number = {6},
Pages = {F59-F64},
Year = {2006},
Month = {November},
ISSN = {1363-755X},
url = {http://www.ncbi.nlm.nih.gov/pubmed/17059447},
Abstract = {This paper investigates the ability of infants to attend to
continuous stimulus variables and how this capacity relates
to the representation of number. We examined the change in
area needed by 6-month-old infants to detect a difference in
the size of a single element (Elmo face). Infants
successfully discriminated a 1:4, 1:3 and 1:2 change in the
area of the Elmo face but failed to discriminate a 2:3
change. In addition, the novelty preference was linearly
related to the ratio difference between the novel and
familiar area. Results suggest that Weber's Law holds for
area discriminations in infancy and also reveal that at 6
months of age infants are equally sensitive to number, time
and area.},
Doi = {10.1111/j.1467-7687.2006.00530.x},
Key = {fds250938}
}
@article{fds250882,
Author = {KE Jordan and EM Brannon},
Title = {Weber's Law influences numerical representations in rhesus
macaques (Macaca mulatta).},
Journal = {Anim Cogn},
Volume = {9},
Number = {3},
Pages = {159-172},
Year = {2006},
Month = {July},
ISSN = {1435-9448},
url = {http://www.ncbi.nlm.nih.gov/pubmed/16575587},
Abstract = {We present the results of two experiments that probe the
ability of rhesus macaques to match visual arrays based on
number. Three monkeys were first trained on a delayed
match-to-sample paradigm (DMTS) to match stimuli on the
basis of number and ignore continuous dimensions such as
element size, cumulative surface area, and density. Monkeys
were then tested in a numerical bisection experiment that
required them to indicate whether a sample numerosity was
closer to a small or large anchor value. Results indicated
that, for two sets of anchor values with the same ratio, the
probability of choosing the larger anchor value
systematically increased with the sample number and the
psychometric functions superimposed. A second experiment
employed a numerical DMTS task in which the choice values
contained an exact numerical match to the sample and a
distracter that varied in number. Both accuracy and reaction
time were modulated by the ratio between the correct
numerical match and the distracter, as predicted by Weber's
Law.},
Doi = {10.1007/s10071-006-0017-8},
Key = {fds250882}
}
@article{fds250911,
Author = {JF Cantlon and EM Brannon and EJ Carter and KA
Pelphrey},
Title = {Functional imaging of numerical processing in adults and
4-y-old children.},
Journal = {PLoS Biol},
Volume = {4},
Number = {5},
Pages = {e125},
Year = {2006},
Month = {May},
ISSN = {1545-7885},
url = {http://www.ncbi.nlm.nih.gov/pubmed/16594732},
Abstract = {Adult humans, infants, pre-school children, and non-human
animals appear to share a system of approximate numerical
processing for non-symbolic stimuli such as arrays of dots
or sequences of tones. Behavioral studies of adult humans
implicate a link between these non-symbolic numerical
abilities and symbolic numerical processing (e.g., similar
distance effects in accuracy and reaction-time for arrays of
dots and Arabic numerals). However, neuroimaging studies
have remained inconclusive on the neural basis of this link.
The intraparietal sulcus (IPS) is known to respond
selectively to symbolic numerical stimuli such as Arabic
numerals. Recent studies, however, have arrived at
conflicting conclusions regarding the role of the IPS in
processing non-symbolic, numerosity arrays in adulthood, and
very little is known about the brain basis of numerical
processing early in development. Addressing the question of
whether there is an early-developing neural basis for
abstract numerical processing is essential for understanding
the cognitive origins of our uniquely human capacity for
math and science. Using functional magnetic resonance
imaging (fMRI) at 4-Tesla and an event-related fMRI
adaptation paradigm, we found that adults showed a greater
IPS response to visual arrays that deviated from standard
stimuli in their number of elements, than to stimuli that
deviated in local element shape. These results support
previous claims that there is a neurophysiological link
between non-symbolic and symbolic numerical processing in
adulthood. In parallel, we tested 4-y-old children with the
same fMRI adaptation paradigm as adults to determine whether
the neural locus of non-symbolic numerical activity in
adults shows continuity in function over development. We
found that the IPS responded to numerical deviants similarly
in 4-y-old children and adults. To our knowledge, this is
the first evidence that the neural locus of adult numerical
cognition takes form early in development, prior to
sophisticated symbolic numerical experience. More broadly,
this is also, to our knowledge, the first cognitive fMRI
study to test healthy children as young as 4 y, providing
new insights into the neurophysiology of human cognitive
development.},
Doi = {10.1371/journal.pbio.0040125},
Key = {fds250911}
}
@article{fds250955,
Author = {JF Cantlon and EM Brannon},
Title = {Shared system for ordering small and large numbers in
monkeys and humans.},
Journal = {Psychol Sci},
Volume = {17},
Number = {5},
Pages = {401-406},
Year = {2006},
Month = {May},
ISSN = {0956-7976},
url = {http://www.ncbi.nlm.nih.gov/pubmed/16683927},
Abstract = {There is increasing evidence that animals share with adult
humans and perhaps human infants a system for representing
objective number as psychological magnitudes that are an
analogue of the quantities they represent. Here we show that
rhesus monkeys can extend a numerical rule learned with the
values 1 through 9 to the values 10, 15, 20, and 30, which
suggests that there is no upper limit on a monkey's
numerical capacity. Instead, throughout the numerical range
tested, both accuracy and latency in ordering two numerical
values were systematically controlled by the ratio of the
values compared. In a second experiment, we directly
compared humans' and monkeys' performance in the same
ordinal comparison task. The qualitative and quantitative
similarity in their performance provides the strongest
evidence to date of a single nonverbal, evolutionarily
primitive mechanism for representing and comparing numerical
values.},
Doi = {10.1111/j.1467-9280.2006.01719.x},
Key = {fds250955}
}
@article{fds250931,
Author = {EM Brannon and JF Cantlon and HS Terrace},
Title = {The role of reference points in ordinal numerical
comparisons by rhesus macaques (Macaca mulatta).},
Journal = {J Exp Psychol Anim Behav Process},
Volume = {32},
Number = {2},
Pages = {120-134},
Year = {2006},
Month = {April},
ISSN = {0097-7403},
url = {http://www.ncbi.nlm.nih.gov/pubmed/16634655},
Abstract = {Two experiments examined ordinal numerical knowledge in
rhesus macaques (Macaca mulatta). Experiment 1 replicated
the finding (E. M. Brannon & H. S. Terrace, 2000) that
monkeys trained to respond in descending numerical order
(4-->3-->2-->1) did not generalize the descending rule to
the novel values 5-9 in contrast to monkeys trained to
respond in ascending order. Experiment 2 examined whether
the failure to generalize a descending rule was due to the
direction of the training sequence or to the specific values
used in the training sequence. Results implicated 3 factors
that characterize a monkey's numerical comparison process:
Weber's law, knowledge of ordinal direction, and a
comparison of each value in a test pair with the reference
point established by the first value of the training
sequence.},
Doi = {10.1037/0097-7403.32.2.120},
Key = {fds250931}
}
@article{fds250953,
Author = {EM Brannon},
Title = {The representation of numerical magnitude.},
Journal = {Curr Opin Neurobiol},
Volume = {16},
Number = {2},
Pages = {222-229},
Year = {2006},
Month = {April},
ISSN = {0959-4388},
url = {http://www.ncbi.nlm.nih.gov/pubmed/16546373},
Abstract = {The combined efforts of many fields are advancing our
understanding of how number is represented. Researchers
studying numerical reasoning in adult humans, developing
humans and non-human animals are using a suite of behavioral
and neurobiological methods to uncover similarities and
differences in how each population enumerates and compares
quantities to identify the neural substrates of numerical
cognition. An important picture emerging from this research
is that adult humans share with non-human animals a system
for representing number as language-independent mental
magnitudes and that this system emerges early in
development.},
Doi = {10.1016/j.conb.2006.03.002},
Key = {fds250953}
}
@article{fds250928,
Author = {KE Jordan and EM Brannon},
Title = {The multisensory representation of number in
infancy.},
Journal = {Proc Natl Acad Sci U S A},
Volume = {103},
Number = {9},
Pages = {3486-3489},
Year = {2006},
Month = {February},
ISSN = {0027-8424},
url = {http://www.ncbi.nlm.nih.gov/pubmed/16492785},
Abstract = {Human infants can discriminate visual and auditory stimuli
solely on the basis of number, suggesting a developmental
foundation for the nonverbal number representations of adult
humans. Recent studies suggest that these
language-independent number representations are multisensory
in both adult humans and nonhuman animals. Surprisingly,
however, previous studies have yielded mixed evidence
concerning whether nonverbal numerical representations
independent of sensory modality are present early in human
development. In this article, we use a paradigm that avoids
stimulus confounds present in previous studies of
cross-modal numerical mapping in infants. We show that
7-month-old infants preferentially attend to visual displays
of adult humans that numerically match the number of adult
humans they hear speaking. These data provide evidence that
by 7 months of age, infants connect numerical
representations across different sensory modalities when
presented with human faces and voices. Results support the
possibility of a shared system between preverbal infants and
nonverbal animals for representing number.},
Doi = {10.1073/pnas.0508107103},
Key = {fds250928}
}
@article{fds250929,
Author = {ML Corre and GVD Walle and EM Brannon and S Carey},
Title = {Re-visiting the competence/performance debate in the
acquisition of the counting principles},
Journal = {Cognitive Psychology},
Volume = {52},
Number = {2},
Pages = {130-169},
Year = {2006},
url = {http://dx.doi.org/10.1016/j.cogpsych.2005.07.002},
Abstract = {Advocates of the "continuity hypothesis" have argued that
innate non-verbal counting principles guide the acquisition
of the verbal count list (Gelman & Gallistel, 1978).
Some studies have supported this hypothesis, but others have
suggested that the counting principles must be constructed
anew by each child. Defenders of the continuity hypothesis
have argued that the studies that failed to support it
obscured children's understanding of counting by making
excessive demands on their fragile counting skills. We
evaluated this claim by testing two-, three-, and
four-year-olds both on "easy" tasks that have supported
continuity and "hard" tasks that have argued against it. A
few noteworthy exceptions notwithstanding, children who
failed to show that they understood counting on the hard
tasks also failed on the easy tasks. Therefore, our results
are consistent with a growing body of evidence that shows
that the count list as a representation of the positive
integers transcends pre-verbal representations of number. ©
2005 Elsevier Inc. All rights reserved.},
Doi = {10.1016/j.cogpsych.2005.07.002},
Key = {fds250929}
}
@article{fds250954,
Author = {JF Cantlon and EM Brannon},
Title = {The effect of heterogeneity on numerical ordering in rhesus
monkeys},
Journal = {Infancy},
Volume = {9},
Number = {2},
Pages = {173-189},
Year = {2006},
ISSN = {1525-0008},
url = {http://dx.doi.org/10.1207/s15327078in0902_5},
Abstract = {We investigated how within-stimulus heterogeneity affects
the ability of rhesus monkeys to order pairs of the
numerosities 1 through 9. Two rhesus monkeys were tested in
a touch screen task where the variability of elements within
each visual array was systematically varied by allowing
elements to vary in color, size, shape, or any combination
of these dimensions. We found no evidence of a cost (or
benefit) in accuracy or reaction time when monkeys were
tested with stimuli that were heterogeneous in color, size,
or shape. This was true even though both monkeys experienced
extended initial training with arrays that were homogeneous
in the color, shape, and size of elements. The implications
of this finding for the mechanisms that monkeys use to
represent and compare numerosities are discussed. Copyright
© 2006, Lawrence Erlbaum Associates, Inc.},
Doi = {10.1207/s15327078in0902_5},
Key = {fds250954}
}
@article{fds250927,
Author = {JF Cantlon and EM Brannon},
Title = {Semantic congruity affects numerical judgments similarly in
monkeys and humans.},
Journal = {Proc Natl Acad Sci U S A},
Volume = {102},
Number = {45},
Pages = {16507-16511},
Year = {2005},
Month = {November},
ISSN = {0027-8424},
url = {http://www.ncbi.nlm.nih.gov/pubmed/16260752},
Abstract = {Monkeys (Macaca mulatta) were trained to order visual arrays
based on their number of elements and to conditionally
choose the array with the larger or smaller number of
elements dependent on a color cue. When the screen
background was red, monkeys were reinforced for choosing the
smaller numerical value first. When the screen background
was blue, monkeys were reinforced for choosing the larger
numerical value first. Monkeys showed a semantic congruity
effect analogous to that reported for human comparison
judgments. Specifically, decision time was systematically
influenced by the semantic congruity between the cue
("choose smaller" or "choose larger") and the magnitude of
the choice stimuli (small or large numbers of dots). This
finding demonstrates a semantic congruity effect in a
nonlinguistic animal and provides strong evidence for an
evolutionarily primitive magnitude-comparison algorithm
common to humans and monkeys.},
Doi = {10.1073/pnas.0506463102},
Key = {fds250927}
}
@article{fds250932,
Author = {KE Jordan and EM Brannon and NK Logothetis and AA
Ghazanfar},
Title = {Monkeys match the number of voices they hear to the number
of faces they see.},
Journal = {Curr Biol},
Volume = {15},
Number = {11},
Pages = {1034-1038},
Year = {2005},
Month = {June},
ISSN = {0960-9822},
url = {http://www.ncbi.nlm.nih.gov/pubmed/15936274},
Abstract = {Convergent evidence demonstrates that adult humans possess
numerical representations that are independent of language
[1, 2, 3, 4, 5 and 6]. Human infants and nonhuman animals
can also make purely numerical discriminations, implicating
both developmental and evolutionary bases for adult humans'
language-independent representations of number [7 and 8].
Recent evidence suggests that the nonverbal representations
of number held by human adults are not constrained by the
sensory modality in which they were perceived [9]. Previous
studies, however, have yielded conflicting results
concerning whether the number representations held by
nonhuman animals and human infants are tied to the modality
in which they were established [10, 11, 12, 13, 14 and 15].
Here, we report that untrained monkeys preferentially looked
at a dynamic video display depicting the number of
conspecifics that matched the number of vocalizations they
heard. These findings suggest that number representations
held by monkeys, like those held by adult humans, are
unfettered by stimulus modality.},
Doi = {10.1016/j.cub.2005.04.056},
Key = {fds250932}
}
@article{fds250924,
Author = {EM Brannon},
Title = {The independence of language and mathematical
reasoning.},
Journal = {Proc Natl Acad Sci U S A},
Volume = {102},
Number = {9},
Pages = {3177-3178},
Year = {2005},
Month = {March},
ISSN = {0027-8424},
url = {http://www.ncbi.nlm.nih.gov/pubmed/15728346},
Doi = {10.1073/pnas.0500328102},
Key = {fds250924}
}
@article{fds250930,
Author = {KP Lewis and S Jaffe and EM Brannon},
Title = {Analog number representations in mongoose lemurs (Eulemur
mongoz): Evidence from a search task},
Journal = {Animal Cognition},
Volume = {8},
Number = {4},
Pages = {247-252},
Year = {2005},
ISSN = {1435-9448},
url = {http://dx.doi.org/10.1007/s10071-004-0251-x},
Abstract = {A wealth of data demonstrating that monkeys and apes
represent number have been interpreted as suggesting that
sensitivity to number emerged early in primate evolution, if
not before. Here we examine the numerical capacities of the
mongoose lemur (Eulemur mongoz), a member of the prosimian
suborder of primates that split from the common ancestor of
monkeys, apes and humans approximately 47-54 million years
ago. Subjects observed as an experimenter sequentially
placed grapes into an opaque bucket. On half of the trials
the experimenter placed a subset of the grapes into a false
bottom such that they were inaccessible to the lemur. The
critical question was whether lemurs would spend more time
searching the bucket when food should have remained in the
bucket, compared to when they had retrieved all of the food.
We found that the amount of time lemurs spent searching was
indicative of whether grapes should have remained in the
bucket, and furthermore that lemur search time reliably
differentiated numerosities that differed by a 1:2 ratio,
but not those that differed by a 2:3 or 3:4 ratio. Finally,
two control conditions determined that lemurs represented
the number of food items, and neither the odor of the
grapes, nor the amount of grape (e.g., area) in the bucket.
These results suggest that mongoose lemurs have numerical
representations that are modulated by Weber's Law. ©
Springer-Verlag 2005.},
Doi = {10.1007/s10071-004-0251-x},
Key = {fds250930}
}
@article{fds250956,
Author = {EM Brannon and LW Roussel and WH Meck and M Woldorff},
Title = {Timing in the baby brain.},
Journal = {Brain Res Cogn Brain Res},
Volume = {21},
Number = {2},
Pages = {227-233},
Year = {2004},
Month = {Spring},
ISSN = {0926-6410},
url = {http://www.ncbi.nlm.nih.gov/pubmed/15464354},
Abstract = {Ten-month-old infants and adults were tested in an auditory
oddball paradigm in which 50-ms tones were separated by 1500
ms (standard interval) and occasionally 500 ms (deviant
interval). Both infants and adults showed marked brain
responses to the tone that followed a deviant inter-stimulus
interval (ISI). Specifically, the timing-deviance
event-related-potential (ERP) difference waves (deviant-ISI
ERP minus standard-ISI ERP) yielded a significant,
fronto-centrally distributed, mismatch negativity (MMN) in
the latency range of 120-240 ms post-stimulus for infants
and 110-210 ms for adults. A robust, longer latency,
deviance-related positivity was also obtained for infants
(330-520 ms), with a much smaller and later deviance-related
positivity observed for adults (585-705 ms). These results
suggest that the 10-month-old infant brain has already
developed some of the same mechanisms as adults for
detecting deviations in the timing of stimulus
events.},
Doi = {10.1016/j.cogbrainres.2004.04.007},
Key = {fds250956}
}
@article{fds250952,
Author = {EM Brannon and S Abbott and DJ Lutz},
Title = {Number bias for the discrimination of large visual sets in
infancy.},
Journal = {Cognition},
Volume = {93},
Number = {2},
Pages = {B59-B68},
Year = {2004},
Month = {September},
ISSN = {0010-0277},
url = {http://www.ncbi.nlm.nih.gov/pubmed/15147939},
Abstract = {This brief report attempts to resolve the claim that infants
preferentially attend to continuous variables over number
[e.g. Psychol. Sci. 10 (1999) 408; Cognit. Psychol.44 (2002)
33] with the finding that when continuous variables are
controlled, infants as young as 6-months of age discriminate
large numerical values [e.g. Psychol. Sci. 14 (2003) 396;
Cognition 89 (2003) B15; Cognition 74 (2000) B1]. In two
parallel experiments, we compare 6-month-old infants'
ability to discriminate number and ignore continuous
variables with their ability to form a representation of a
cumulative surface area and ignore number. We find that
infants discriminate a 2-fold change in number but fail to
discriminate a 2-fold change in cumulative surface area. The
results point to a more complicated relationship between
discrete and continuous dimensions than implied by previous
literature.},
Doi = {10.1016/j.cognition.2004.01.004},
Key = {fds250952}
}
@article{fds250960,
Author = {EM Brannon and M Andrews and L Rosenblum},
Title = {The reward value of social video for socially housed Bonnet
Macaques},
Journal = {Perceptual and Motor Skills},
Volume = {98},
Number = {3 I},
Pages = {849-858},
Year = {2004},
ISSN = {0031-5125},
Abstract = {Two experiments were conducted to examine the effectiveness
of presenting brief video of conspecifics to socially housed
bonnet macaques as a reward for performing a joystick task.
Using a joystick, subjects tracked a moving target with the
cursor on a computer monitor. In Exp. 1, subjects completed
significantly more joystick trials for food reward than for
video reward or no reward. Subjects also preferred viewing
video of another group (Other Group Video) to receiving no
reward or to viewing video of their own group (Own Group
Video). In Exp. 2, subjects were given two reward
conditions, video of a familiar social group or video of a
new social group. Two monkeys contributed the vast majority
of trials, and both responded more frequently when the
reward was video of the new social group. Results of these
two experiments suggest that viewing video of conspecifics
may serve as an effective reward for at least some socially
housed primates and suggests that novelty of the individuals
depicted in the video is an important factor contributing to
the reward value of video.},
Key = {fds250960}
}
@article{fds304646,
Author = {EM Brannon and MW Andrews and LA Rosenblum},
Title = {Effectiveness of video of conspecifics as a reward for
socially housed bonnet macaques (macaca radiata)},
Journal = {Perceptual and Motor Skills},
Volume = {98},
Number = {3 I},
Pages = {849-858},
Year = {2004},
ISSN = {0031-5125},
Abstract = {Two experiments were conducted to examine the effectiveness
of presenting brief video of conspecifics to socially housed
bonnet macaques as a reward for performing a joystick task.
Using a joystick, subjects tracked a moving target with the
cursor on a computer monitor. In Exp. 1, subjects completed
significantly more joystick trials for food reward than for
video reward or no reward. Subjects also preferred viewing
video of another group (Other Group Video) to receiving no
reward or to viewing video of their own group (Own Group
Video). In Exp. 2, subjects were given two reward
conditions, video of a familiar social group or video of a
new social group. Two monkeys contributed the vast majority
of trials, and both responded more frequently when the
reward was video of the new social group. Results of these
two experiments suggest that viewing video of conspecifics
may serve as an effective reward for at least some socially
housed primates and suggests that novelty of the individuals
depicted in the video is an important factor contributing to
the reward value of video.},
Key = {fds304646}
}
@article{fds250961,
Author = {HS Terrace and LK Son and EM Brannon},
Title = {Serial expertise of rhesus macaques},
Journal = {Psychological Science},
Volume = {14},
Number = {1},
Pages = {66-73},
Year = {2003},
url = {http://dx.doi.org/10.1111/1467-9280.01420},
Abstract = {Here we describe the development of serial expertise in 4
experimentally naive rhesus monkeys that learned, by trial
and error, the correct order in which to respond to 3-, 4-,
and 7-item lists of arbitrarily selected photographs. The
probabilities of guessing the correct sequence on 3-, 4-,
and 7-item lists were, respectively, 1/6, 1/24, and 1/5,040.
Each monkey became progressively more efficient at
determining the correct order in which to respond on new
lists. During subsequent testing, the subjects were
presented with all possible pairs of the 28 items used to
construct the four 7-item lists (excluding pairs of items
that occupied the same ordinal position in different lists).
Subjects responded to pairs from different lists in the
correct order 91% of the time on the first trials on which
these pairs were presented. These features of subjects'
performance, which cannot be attributed to procedural
memory, satisfy two criteria of declarative memory: rapid
acquisition of new knowledge and flexible application of
existing knowledge to a new problem.},
Doi = {10.1111/1467-9280.01420},
Key = {fds250961}
}
@article{fds250957,
Author = {EM Brannon},
Title = {The development of ordinal numerical knowledge in
infancy.},
Journal = {Cognition},
Volume = {83},
Number = {3},
Pages = {223-240},
Year = {2002},
Month = {April},
ISSN = {0010-0277},
url = {http://www.ncbi.nlm.nih.gov/pubmed/11934402},
Abstract = {A critical question in cognitive science concerns how
numerical knowledge develops. One essential component of an
adult concept of number is ordinality: the greater than and
less than relationships between numbers. Here it is shown in
two experiments that 11-month-old infants successfully
discriminated, whereas 9-month-old infants failed to
discriminate, sequences of numerosities that descended in
numerical value from sequences that increased in numerical
value. These results suggest that by 11 months of age
infants possess the ability to appreciate the greater than
and less than relations between numerical values but that
this ability develops between 9 and 11 months of age. In an
additional experiment 9-month-old infants succeeded at
discriminating the ordinal direction of sequences that
varied in the size of a single square rather than in number,
suggesting that a capacity for non-numerical ordinal
judgments may develop before a capacity for ordinal
numerical judgments. These data raise many questions about
how infants represent number and what happens between 9 and
11 months to support ordinal numerical judgments.},
Key = {fds250957}
}
@article{fds250878,
Author = {EM Brannon and GAVD Walle},
Title = {Erratum: The development of ordinal numerical competence in
young children (Cognitive Psychology (2001) 43, 1 (53-81)
doi: 10.1006/cogp.2001.0756)},
Journal = {Cognitive Psychology},
Volume = {44},
Number = {2},
Pages = {191-192},
Year = {2002},
url = {http://dx.doi.org/10.1006/cogp.2001.0780},
Doi = {10.1006/cogp.2001.0780},
Key = {fds250878}
}
@article{fds304644,
Author = {EM Brannon and GA Van de Walle},
Title = {The development of ordinal numerical competence in young
children.},
Journal = {Cogn Psychol},
Volume = {43},
Number = {1},
Pages = {53-81},
Year = {2001},
Month = {August},
ISSN = {0010-0285},
url = {http://www.ncbi.nlm.nih.gov/pubmed/11487294},
Abstract = {Two experiments assessed ordinal numerical knowledge in 2-
and 3-year-old children and investigated the relationship
between ordinal and verbal numerical knowledge. Children
were trained on a 1 vs 2 comparison and then tested with
novel numerosities. Stimuli consisted of two trays, each
containing a different number of boxes. In Experiment 1, box
size was held constant. In Experiment 2, box size was varied
such that cumulative surface area was unrelated to number.
Results show children as young as 2 years of age make purely
numerical discriminations and represent ordinal relations
between numerosities as large as 6. Children who lacked any
verbal numerical knowledge could not make ordinal judgments.
However, once children possessed minimal verbal numerical
competence, further knowledge was entirely unrelated to
ordinal competence. Number may become a salient dimension as
children begin to learn to count. An analog magnitude
representation of number may underlie success on the ordinal
task.},
Doi = {10.1006/cogp.2001.0756},
Key = {fds304644}
}
@article{fds304645,
Author = {EM Brannon and CJ Wusthoff and CR Gallistel and J
Gibbon},
Title = {Numerical subtraction in the pigeon: evidence for a linear
subjective number scale.},
Journal = {Psychol Sci},
Volume = {12},
Number = {3},
Pages = {238-243},
Year = {2001},
Month = {May},
ISSN = {0956-7976},
url = {http://www.ncbi.nlm.nih.gov/pubmed/11437307},
Abstract = {When humans and animals compare two numbers, responding is
faster and more accurate with increasing numerical disparity
and decreasing numerical size. Researchers explaining these
distance and size effects often, assume that the subjective
number continuum is logarithmically compressed. An
alternative hypothesis is that the subjective number
continuum is linear, but positions farther along it are
proportionately fuzzier, that is, less precisely located.
These two hypotheses have been treated as functionally
equivalent because of their similar empirical predictions.
The current experiment sought to resolve this issue with a
paradigm originally developed to address the subjective
representation of time (time left). In our adaptation,
pigeons were required to compare a constant number with the
number remaining after a numerical subtraction. Our results
indicate that subjective number is linearly, not
logarithmically, related to objective number.},
Key = {fds304645}
}
@article{fds250963,
Author = {E Brannon and CJ Wusthoff and CR Gallistel and J
Gibbon},
Title = {Subtraction in the Pigeon: Evidence for a Linear Subjective
Number Scale},
Journal = {Psychological Science},
Volume = {12},
Number = {3},
Pages = {238-243},
Year = {2001},
ISSN = {0956-7976},
url = {http://www.ncbi.nlm.nih.gov/pubmed/11437307},
Abstract = {When humans and animals compare two numbers, responding is
faster and more accurate with increasing numerical disparity
and decreasing numerical size. Researchers explaining these
distance and size effects often, assume that the subjective
number continuum is logarithmically compressed. An
alternative hypothesis is that the subjective number
continuum is linear, but positions farther along it are
proportionately fuzzier, that is, less precisely located.
These two hypotheses have been treated as functionally
equivalent because of their similar empirical predictions.
The current experiment sought to resolve this issue with a
paradigm originally developed to address the subjective
representation of time (time left). In our adaptation,
pigeons were required to compare a constant number with the
number remaining after a numerical subtraction. Our results
indicate that subjective number is linearly, not
logarithmically, related to objective number.},
Key = {fds250963}
}
@article{fds250964,
Author = {E Brannon and G Van de Walle},
Title = {Ordinal Numerical Knowledge in Young Children},
Journal = {Cognitive Psychology},
Volume = {43},
Number = {1},
Pages = {53-81},
Year = {2001},
ISSN = {0010-0285},
url = {http://www.ncbi.nlm.nih.gov/pubmed/11487294},
Abstract = {Two experiments assessed ordinal numerical knowledge in 2-
and 3-year-old children and investigated the relationship
between ordinal and verbal numerical knowledge. Children
were trained on a 1 vs 2 comparison and then tested with
novel numerosities. Stimuli consisted of two trays, each
containing a different number of boxes. In Experiment 1, box
size was held constant. In Experiment 2, box size was varied
such that cumulative surface area was unrelated to number.
Results show children as young as 2 years of age make purely
numerical discriminations and represent ordinal relations
between numerosities as large as 6. Children who lacked any
verbal numerical knowledge could not make ordinal judgments.
However, once children possessed minimal verbal numerical
competence, further knowledge was entirely unrelated to
ordinal competence. Number may become a salient dimension as
children begin to learn to count. An analog magnitude
representation of number may underlie success on the ordinal
task.},
Doi = {10.1006/cogp.2001.0756},
Key = {fds250964}
}
@article{fds250965,
Author = {CR Gallistel and EM Brannon and J Gibbon and CJ
Wusthoff},
Title = {Response to Dehaene’s Commentary},
Journal = {Psychological Science},
Volume = {12},
Number = {3},
Pages = {247},
Year = {2001},
Key = {fds250965}
}
@article{fds250962,
Author = {EM Brannon and HS Terrace},
Title = {Representation of the numerosities 1-9 by rhesus macaques
(Macaca mulatta)},
Journal = {Journal of Experimental Psychology: Animal Behavior
Processes},
Volume = {26},
Number = {1},
Pages = {31-49},
Year = {2000},
ISSN = {0097-7403},
Abstract = {Three rhesus monkeys (Macaca mulatta) were trained to
respond to exemplars of 1,2,3, and 4 in an ascending,
descending, or a nonmonotonic numerical order
(1→2→3→4, 4→3→2→1, 3→1→4→2). The monkeys
were then tested on their ability to order pairs of the
novel numerosities 5-9. In Experiment 1, all 3 monkeys
ordered novel exemplars of the numerosities 1-4 in ascending
or descending order. The attempt to train a nonmonotonic
order (3→1→4→2) failed. In Experiment 2A, the 2
monkeys who learned the ascending numerical rule ordered
pairs of the novel numerosities 5-9 on unreinforced trials.
The monkey who learned the descending numerical rule failed
to extrapolate the descending rule to new numerosities. In
Experiment 2B all 3 monkeys ordered novel exemplars of pairs
of the numerosities 5-9. Accuracy and latency of responding
revealed distance and magnitude effects analogous to
previous findings with human participants (R. S. Moyer &
T. K. Landaeur, 1967). Collectively these studies show that
monkeys represent the numerosities 1-9 on at least an
ordinal scale. Copyright 2000 by the American Psychological
Association, Inc.},
Key = {fds250962}
}
@article{fds250875,
Author = {PL Stocklin and EM Brannon and HS Terrace},
Title = {Monkey numeration [4] (multiple letters)},
Journal = {Science},
Volume = {283},
Number = {5409},
Pages = {1851-1852},
Year = {1999},
ISSN = {0036-8075},
Key = {fds250875}
}
@article{fds250959,
Author = {EM Brannon and HS Terrace},
Title = {Ordering of the numerosities 1 to 9 by monkeys},
Journal = {Science},
Volume = {282},
Number = {5389},
Pages = {746-749},
Year = {1998},
ISSN = {0036-8075},
url = {http://dx.doi.org/10.1126/science.282.5389.746},
Abstract = {A fundamental question in cognitive science is whether
animals can represent numerosity (a property of a stimulus
that is defined by the number of discriminable elements it
contains) and use numerical representations computationally.
Here, it was shown that rhesus monkeys represent the
numerosity of visual stimuli and detect their ordinal
disparity. Two monkeys were first trained to respond to
exemplars of the numerosities 1 to 4 in an ascending
numerical order (1 → 2 → 3 → 4). As a control for
non-numerical cues, exemplars were varied with respect to
size, shape, and color. The monkeys were later tested,
without reward, on their ability to order stimulus pairs
composed of the novel numerosities 5 to 9. Both monkeys
responded in an ascending order to the novel numerosities.
These results show that rhesus monkeys represent the
numerosities 1 to 9 on an ordinal scale.},
Doi = {10.1126/science.282.5389.746},
Key = {fds250959}
}
@article{fds250958,
Author = {ML Platt and EM Brannon and TL Briese and JA French},
Title = {Differences in feeding ecology predict differences in
performance between golden lion tamarins (Leontopithecus
rosalia) and Wied's marmosets (Callithrix kuhli) on spatial
and visual memory tasks},
Journal = {Animal Learning & Behavior},
Volume = {24},
Number = {4},
Pages = {384-393},
Year = {1996},
ISSN = {0090-4996},
url = {http://dx.doi.org/10.3758/BF03199010},
Abstract = {Golden lion tamarins (Leontopithecus rosalia) and Wied's
marmosets (Callithrix kuhli) exhibited adaptive differences
in performance on several distinct memory tasks. On both an
open-field analogue of a radial arm maze and a spatial
delayed matching-to-sample task, the marmosets performed
better than the tamarins after short (5-min) retention
intervals, but only the tamarins continued to perform above
chance after long (24- or 48-h) retention intervals. The
marmosets also required less training than the tamarins did
to learn a color memory task, but again only the tamarins
performed above chance when the retention interval was
increased to 24 h. The results of these experiments are
consistent with predictions based on knowledge of the
feeding ecology of these species in the wild and raise the
possibility that they possess different visuospatial memory
abilities specialized for tracking the spatial and temporal
distribution of their principal foods. © 1996 Psychonomic
Society, Inc.},
Doi = {10.3758/BF03199010},
Key = {fds250958}
}
%% Books
@book{fds183751,
Author = {Dehaene, S. and Brannon, E.M.},
Title = {Space, time, and number in the brain: Searching for the
foundations of mathematical thought},
Publisher = {Elsevier},
Year = {2011},
Key = {fds183751}
}
@book{fds140017,
Author = {Purves, D. and Brannon, E. and Cabeza, R. and Huettel, S. and LaBar, K. and Platt, M. and Woldorff, M},
Title = {Principles of Cognitive Neuroscience},
Publisher = {Sunderland, Massachusetts: Sinauer Associates},
Year = {2008},
Key = {fds140017}
}
%% Chapters in Books
@misc{fds220649,
Author = {E.M. Brannon and Park, J.},
Title = {Navigator Chapter for: Phylogeny and Ontogeny of
Mathematical and Numerical understanding},
Booktitle = {Handbook on Mathematical Cognition},
Publisher = {Oxford Press},
Year = {2014},
Key = {fds220649}
}
@misc{fds212762,
Author = {Merritt, D. and DeWind, N. and Brannon, E.M.},
Title = {Comparative cognition of number representation},
Booktitle = {Handbook of Comparative Cognition},
Editor = {Thomas Zentall and Ed Wasserman},
Year = {2012},
Key = {fds212762}
}
@misc{fds183744,
Author = {Merritt, D. and DeWind, N. and Brannon, E.M.},
Title = {Comparative cognition of number representation},
Booktitle = {Handbook of comparative cognition},
Editor = {T. Zentall and E. Wasserman},
Year = {2011},
Key = {fds183744}
}
@misc{fds250870,
Author = {EM Brannon and DJ Merritt},
Title = {Evolutionary Foundations of the Approximate Number
System},
Journal = {Space, Time and Number in the Brain},
Pages = {207-224},
Booktitle = {Space, Time, and Number in the Brain: searching for the
foundations of mathematical thought},
Publisher = {Elsevier},
Editor = {Dehaene, S. and Brannon, E.M.},
Year = {2011},
url = {http://dx.doi.org/10.1016/B978-0-12-385948-8.00014-1},
Abstract = {This chapter reviews the behavioral evidence for numerical
capacities in animals. When adult humans are tested in tasks
that avoid verbal counting, they too show ratio-dependent
number discrimination. In fact, animals and humans tested in
parallel tasks often show remarkably similar patterns of
performance. While ratio dependence is a behavioral
signature of the approximate number system (ANS), the
semantic congruity effect appears to be a universal hallmark
of the wider class of all ordinal judgments. Zero is a
special number in symbolic number systems for many reasons.
First it serves as the additive identity for natural numbers
such that when added to any element x in a set, the result
remains x. For both ascending and descending trials, the
monkeys were able to spontaneously place the empty set in
the proper order with above chance accuracy. Further, as
with the matching task, the monkeys showed distance effects
that were comparable to those observed with the other
numerical values. © 2011 Elsevier Inc. All rights
reserved.},
Doi = {10.1016/B978-0-12-385948-8.00014-1},
Key = {fds250870}
}
@misc{fds183746,
Author = {Brannon, E.M. and Jordan, K.E. and Jones, S.},
Title = {Behavioral signatures of numerical discrimination},
Booktitle = {Primate Neuroethology},
Publisher = {Oxford Press},
Editor = {M.L. Platt and A. Ghazanfar},
Year = {2010},
Key = {fds183746}
}
@misc{fds166473,
Author = {Cantlon, J.F. and Brannon, E.M.},
Title = {Animal Arithmetic},
Booktitle = {Encyclopedia of Animal Behavior},
Publisher = {Oxford: Elsevier Press},
Year = {2010},
Key = {fds166473}
}
@misc{fds153284,
Author = {Brannon E.M. and Cantlon, J.F.},
Title = {A comparative perspective on the origin of numerical
thinking.},
Booktitle = {Cognitive biology: Evolutionary and developmental
perspectives on mind, brain, and behavior},
Publisher = {Cambridge: MIT Press},
Editor = {L. Tomasi and M.A. Peterson and L. Nadel},
Year = {2009},
Key = {fds153284}
}
@misc{fds153283,
Author = {Jordan, K.E. and Brannon, E.M.},
Title = {A comparative approach to understanding human numerical
cognition},
Booktitle = {The origins of object knowledge},
Publisher = {Oxford University Press},
Address = {Oxford},
Editor = {B. Hood and L. Santos},
Year = {2009},
Key = {fds153283}
}
@misc{fds27805,
Author = {E. Brannon},
Title = {What Animals Know About Numbers},
Pages = {85-107},
Booktitle = {Handbook of Mathematical Cognition},
Publisher = {Psychology Press},
Editor = {Jamie Campbell (Ed.).},
Year = {2005},
Key = {fds27805}
}
@misc{fds26119,
Author = {E. M. Brannon},
Title = {Quantitative thinking: From monkey to human and human infant
to human adult},
Booktitle = {Handbook of Mathematical Cognition},
Editor = {Stanislas Dehaene},
Year = {2004},
Key = {fds26119}
}
@misc{fds26120,
Author = {E. M. Brannon and Roitman, J.},
Title = {Nonverbal Representations of Time and Number in Non-Human
Animals and Human Infants},
Pages = {143-182},
Booktitle = {Functional and Neural Mechanisms of Interval
Timing},
Publisher = {New York, NY: CRC Press},
Editor = {Warren Meck},
Year = {2003},
Key = {fds26120}
}
@misc{fds26123,
Author = {E. Brannon and Terrace, H.S.},
Title = {The Evolution and Ontogeny of Ordinal Numerical
Ability},
Pages = {197-204},
Booktitle = {The Cognitive Animal},
Publisher = {Cambridge, MA: The MIT Press},
Editor = {Beckoff, M. and Allen, C. and Burghardt, G.M.},
Year = {2002},
Key = {fds26123}
}
@misc{fds250871,
Author = {RL Maddox and D Leclerc},
Title = {Foreword.},
Journal = {manual},
Pages = {ix-xii},
Booktitle = {Singleness of Heart: Gender, Sin, and Holiness in Historical
Perspective},
Publisher = {Scarecrow Press},
Year = {2001},
url = {http://hdl.handle.net/10161/7964 Duke open
access},
Key = {fds250871}
}
%% Commentaries/Book Reviews
@article{fds250879,
Author = {EM Brannon},
Title = {Number knows no bounds.},
Journal = {Trends Cogn Sci},
Volume = {7},
Number = {7},
Pages = {279-281},
Year = {2003},
Month = {July},
url = {http://www.ncbi.nlm.nih.gov/pubmed/12860181},
Abstract = {Is the approximate representation of large numbers in adult
humans bound to a sensory modality or other aspects of the
stimulus presentation, or are these non-verbal numerical
representations abstract? A recent paper by Barth, Kanwisher
and Spelke provides compelling evidence that non-verbal
mental magnitudes are modality-independent.},
Key = {fds250879}
}
@article{fds26917,
Author = {E. M. and Brannon and Terrace, H.S.},
Title = {Letter to the Editor},
Journal = {Science},
Volume = {283},
Pages = {1852},
Year = {1999},
Key = {fds26917}
}
%% Other
@misc{fds51975,
Author = {Santos, L R.},
Title = {Primate Cognition: Putting Two and Two Together},
Journal = {Current Biology},
Volume = {15},
Number = {1},
Pages = {R545-R547},
Year = {2005},
Key = {fds51975}
}
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