2008 — 2009 
Cantlon, Jessica F 
F32Activity Code Description: To provide postdoctoral research training to individuals to broaden their scientific background and extend their potential for research in specified healthrelated areas. 
The Organization of Mathematical Knowledge in Early Childhood and Adulthood
DESCRIPTION (provided by applicant): The proposed research aims to identify patterns of brain activity related to mathematics performance in children and adults. Severe developmental impairments in mathematics affect approximately 6% of people in the United States and many more people experience some degree of difficulty performing basic math. By examining brain activity related to mathematics in children and adults, the studies described in this proposal will help identify the cognitive and neural sources of learning impairments in mathematics. A potential application of this research is the use of neuroimaging techniques to identify abnormalities in the brain functions of children and adults.

0.97 
2010 — 2014 
Cantlon, Jessica F 
R01Activity Code Description: To support a discrete, specified, circumscribed project to be performed by the named investigator(s) in an area representing his or her specific interest and competencies. 
The Neural Organization of Quantitative Concepts in Early Childhood @ University of Rochester
DESCRIPTION (provided by applicant): Extraordinarily little is known about the organization of quantitative concepts in the young child's brain. In just six years'time (between the ages of 2 and 8 years), children traverse a complex series of learning "stages" to acquire the meanings of verbal counting words, Arabic numerals, written number words, and the procedures of basic arithmetic operations such as addition and subtraction. Researchers in the fields of psychology and education have determined that these early mathematical milestones influence children's abilities to learn mathematics for the remainder of their formal education. However, there is considerable debate over which aspects of early numerical and mathematical learning influence children's subsequent understanding of mathematics. Some researchers hypothesize that domaingeneral aspects of cognition provide the critical link between early and late mathematics learning whereas other researchers argue that earlydeveloping domainspecific properties of numerical understanding such as number encoding and comparison permanently impact mathematical understanding throughout development. Neuroimaging methods offer a means for bringing new data to bear on this debate, by providing a tool with which to examine associations and dissociations among the underlying processes of numerical cognition. Such data will offer a window into the organization of mathematical information in the young child's brain and will provide novel insights into the sources, functions, and specificity of mathematical processes in the developing brain. The current proposal aims to test children (4 to 8yearolds) and adults in functional magnetic resonance imaging (fMRI) and behavioral studies that examine the mechanisms of symbolic and nonsymbolic numerical representation and comparison, as well as the relationship between those mechanisms and performance on standardized tests. The study paradigms are designed to examine associations and dissociations among 1) symbolic and nonsymbolic numerical representation, 2) numerical encoding, comparison, and response selection, and 3) numerical quantities and nonnumerical quantities such as size and space. Moreover, the proposed studies aim to test the relationships between numberspecific brain responses versus domaingeneral brain responses and children's performance on standardized mathematics, IQ, and working memory tests. The results of these studies will reveal which numberrelated abilities are bound over development, how those abilities are organized in the brain during early childhood, and how number related and domaingeneral brain responses are related to children's performance on different types of standardized tests. More broadly, these studies will build on the vast amount of behavioral data from children's early mathematical performance by providing new (biological) insights into the early markers of numerical and mathematical learning and will illuminate the potential bases of disorders in mathematical performance. PUBLIC HEALTH RELEVANCE: The mathematics abilities that children possess at a young age (even in preschool) affect their ability to learn math for the rest of their life. Brain imaging studies of math in young children are important for understanding what causes math abilities to develop normally and what causes them to be impaired. The results of these studies will be important for understanding poor math performance in school as well as developmental disorders that cause severe mathematical impairments.

1 
2011 — 2015 
Pouget, Alexandre [⬀] Cantlon, Jessica Bavelier, Daphne (coPI) [⬀] 
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information 
Empirical Research  Collaborative Research  a Bayesian Approach to Number Reasoning @ University of Rochester
The ultimate goal of this project is to provide a novel model of the cognitive and neural basis of numerical cognition, and to use this knowledge to guide the development of new training methods that could improve mathematical abilities in children. The project is a collaboration among investigators at the University of Rochester, Johns Hopkins University, and Cold Spring Harbor Laboratories. Recent research suggests that acuity of numerosity judgments is predictive of success in formal mathematics education, and that similar cognitive processes can be trained by specific kinds of domaingeneral experience. The core idea is that the firing of neurons encodes a probability distribution, thereby representing simultaneously the most probable sample from the distribution and the variance (i.e., confidence) of the estimate.
This project will develop and test a formal Bayesian model that has the unique feature of naturally accounting for a number of metacognitive factors, a critical but undertested factor in the acquisition of expertise. The primary advantages of this Bayesian approach are its ability to provide a natural description of: 1) how the confidence of a learner relates to the precision of their number knowledge; 2) how a learner can combine information from multiple sources of information about number; 3) how intuitive preferences (also known as prior belief) predict learners' errors; and 4) how improvements in probabilistic inference may benefit the precision of the number sense.

0.915 
2015 — 2020 
Cantlon, Jessica 
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information 
The Origins of Numerical Concepts From Nonverbal Perception @ University of Rochester
Modern human mathematical cognition is shaped by evolutionary, developmental, and environmental influences. Researchers seek to understand how those influence affect the development of numerical concepts in human children at the cognitive and neural levels. This research program at the University of Rochester tests the hypothesis that children's early numerical concepts originate from a primitive cognitive and neural system for spatial reasoning.
The proposed research takes an interdisciplinary approach by combining animal cognition, cognitive development, neuroimaging, and mathematics education measures into an integrative analysis of the origins and basic structure of numerical concepts in human children. This interdisciplinary approach is powerful because it allows researchers to test a single hypothesis in a systematic fashion, using a consistent set of methods and across different levels of analysis. The experiments test: 1) the degree to which numerical and spatial perception overlap in the developing brain using functional magnetic resonance imaging (fMRI) with 4 to 6yearold children; 2) the degree to which numerical and spatial perception become distinct as children receive cultural input from counting education; and 3) the degree to which human children exhibit similar levels of perceptual integration to nonhuman animals in their representation of numerical and spatial properties. These experiments speak to whether spatial perception gives rise to mathematical cognition in the developing human brain and so reveals the evolutionary and cultural influences on the developmental trajectory of human numerical concepts.
The research program contributes widely to cognitive science, neuroscience, and mathematics education. The cognitive and neuroimaging data from human children advance our knowledge of the developing human brain and provide critical input for early childhood education practices and assumptions about individual differences and gender differences. The comparative data from human children and nonhuman animals allow researchers to identify fundamental principles that give rise to human mathematical concepts and intrinsic perceptual biases that young children bring to numerical concept learning as they enter school. Together, these data are critical for understanding how humans successfully develop mathematical concepts.

0.915 
2016 — 2020 
Cantlon, Jessica F Piantadosi, Steven Thomas (coPI) [⬀] 
R01Activity Code Description: To support a discrete, specified, circumscribed project to be performed by the named investigator(s) in an area representing his or her specific interest and competencies. 
Origins and Logic of Counting Algorithms @ University of Rochester
? DESCRIPTION (provided by applicant): Cognitive impairments in mathematics, which affect a substantial percentage of children, could be addressed earlier in development if we had an empiricallygrounded theory of the fundamental algorithms that children need to become numerate. For instance, an understanding of the cognitive system supporting early numeracy could be used to focus interventions specifically to each child's representational or processlevel problems. Previous research from our group and others suggests that some of the cognitive mechanisms underlying human verbal counting are derived from developmentally and evolutionarily more primitive processes. However, a formal theory of the logical principles that relate human counting to these earlier capacities is currently lacking. By using computational modeling and behavioral analyses in human children and nonhuman primates, we will assess the logical principles that serve as cognitive precursors to human counting. Our behavioral experiments will provide a new empirical basis for accounts of human counting acquisition and our computational approach will formalize the logical principles underlying this capacity. We ground our formal theories in behavioral data using a novel Bayesian data analysis method that permits us to statistically evaluate a wide range of alternative hypotheses. The proposed experimental aims are innovative in that they test a new frontier of unexplored relations between children's counting and evolutionarily primitive logical reasoning. The approach is innovative in the field of child development in its application of stateoftheart computational methods to data from human children and nonhuman animals. The proposed research thus stands to break substantial new ground in the methods that are used to study child development. Insights about the logical architecture underlying counting acquisition will have broad implications for our understanding of learning and development, and will provide a a new empirical basis to describe the neurology behind learning impairments in children.

1 
2017 — 2020 
Cantlon, Jessica F 
R01Activity Code Description: To support a discrete, specified, circumscribed project to be performed by the named investigator(s) in an area representing his or her specific interest and competencies. 
The Development of Number Words in the Human Brain @ CarnegieMellon University
Project Summary Our research program aims to define the systems that support number symbol learning during early childhood ? a foundational issue in the fields of cognitive development and cognitive neuroscience. The question of how number word acquisition unfolds in the developing brain is an untested phenomenon. By using fMRI in longitudinal studies of 3 to 7yearold children, we will assess, for the first time, how neural representations of numerical concepts change as children develop capacity with spoken number words and numerals and how patterns of cortical activation relate to children?s mathematical competence in school. Current evidence from adults and older children suggests that number words are not processed by the brain as typical words, in semantic regions of temporal cortex, but are instead grounded in the perceptual mechanisms of parietal cortex that represent spatial and quantitative dimensions. Based on previous research and our preliminary data, we hypothesize that the intraparietal sulcus (IPS) grounds the development of symbolic number representations in perceptual representations of quantity. We will test the degree to which perceptual representations of quantity in parietal cortex exhibit functional overlap with symbolic number representations during early childhood. Our research brings new theoretical distinctions, innovative methods, and new types of data to a longstanding behavioral research tradition on the development of number words. The hypotheses, experiments, and analyses that we propose are all well founded in prior research but also offer novel insights with broad significance for mathematical cognition, education, and language development. These basic research advances will provide foundational knoweldge for research on learning impairments.

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