Elizabeth M. Brannon - US grants

DESCRIPTION (adapted from applicant's abstract): The numerical competence of rhesus monkeys will be investigated to provide an animal model of the non-linguistic representation of number. The proposed research will focus on the ability of monkeys to determine the ordinal and cardinal values of novel exemplars of familiar and unfamiliar numerosities. Ordinal competence will be assessed in experiments in which monkeys are first trained on the numerosities 1-4 in a list learning paradigm. They will subsequently be tested on pair-wise judgements of exemplar of the trained numerosities 1-4 and of the untrained numerosities 5-9. No reinforcement will be provided during tests with the novel numerosities 5-9. That will provide a basis for determining if monkeys have an ordinal representation of numerosity. Cardinal competence will be studied in a second series of experiments with a variation of the widely used matching-to-sample paradigm. Subjects will be required to match the sample by selecting a physically distinct choice stimulus that contains the same number of elements as the sample, i.e., to match solely on the basis of cardinal number. Reaction time data will be analyzed to model how monkeys represent ordinal and cardinal numerosities, and to evaluate the hitherto unsubstantiated claim that subitizing accounts for all non-human numerical discriminations.

The goal of the proposed research is to investigate the development of numerical thinking in infancy. Number, like time, and space, appears to be one of the fundamental building blocks of adult cognition. Recent data suggests that infants too are sensitive to numerical properties of their environments (see Wynn, 1998 for a review). It is possible that the numerical abilities of infants are homologous to the analog numerical representations hypothesized for adult humans and non-human animals (see Dehaene, et al., 1998). To determine whether the numerical abilities of infants really are the precursors of adult numerical abilities it is important to understand the properties of numerical representations in infancy. Currently, little is known about the format of numerical representations in infancy or of the types of mathematical operations that can be performed on these representations. This proposal seeks evidence for two types of mathematical operations in infants: numerical ordering and ratio comparisons of numerosities. Two sets of experiments are proposed. In the first set of experiments, knowledge of numerical order will be tested in infants. A new paradigm is developed where a sequence of numerosities will be presented in descending or ascending order until the infant habituates to the sequences. Infants will then be tested with sequences of new numerosities in ascending and descending order. If infants represent ordinal relationships between numerosities then they should look longer at the numerical sequences presented in the new ordinal direction. Results will be compared to those obtained from an analogous experiment with stimuli that vary in size rather than number. In a second set of experiments, infants will be habituated to pairs of numerosities that differ by a specific numerical ratio (e.g., 1:2). They will then be tested with new numerosities that differ by the same ratio or a new ratio. If infants appreciate ratio relations between numbers then they should look longer at pairs that have a new ratio. The results of these experiments will provide a better understanding of the similarities and differences between the way infants, adults, and non-human animals process the numerical aspects of their environments. Moreover, understanding how infants process number without language may have important implications for teaching children linguistically-mediated arithmetic computations.

DESCRIPTION (provided by applicant): The goal of the proposed research is to investigate the neural about representation of number in infancy. Adult humans -possess sophisticated numerical reasoning abilities, however, it has recently been proposed that non-human animals and human infants may also have a primitive numerical sense. New research suggests that monkeys are capable of comparing numbers, and that chimpanzees can pair abstract symbols with numerosities. Furthermore, human infants spontaneously discriminate between novel and familiar numerical values, even when other stimulus attributes, such as surface area, are held constant. These recent findings have led some researchers to suggest the hypothesis that a primitive numerical processing system evolved in the ancient ancestors of humans and other vertebrates and that system is in place early in human development. The current proposal explores the ontogeny of numerical representations in human infants by testing two predictions of this hypothesis. First, numerical discrimination in infants is characterized by numerical distance and size effects consistent with Weber's Law, Just as it is in adults and nonhuman animals. Second, the same neural architecture supports numerical representations in infants and adults. These hypotheses will be tested by recording Event-Related-Potentials (ERPs) in both adults and infants during passive viewing of numerical stimuli. In the proposed experiments, subjects will first be familiarized with a standard numerical value and then will be shown new values that vary in numerical disparity from the standard. ERPs will be recorded during stimulus presentation and later analyzed as a function of the numerical distance between the numerical standard and test stimuli. Statistical modeling will also be used to make inferences about the sources of electrical activity in both adults and infants. While purely behavioral research has demonstrated that infants can discriminate stimuli based solely on number, the proposed non-invasive neurobiological research will provide new insights into both the format and the neural correlates of numerical representations in infants. Such insights will contribute to a fuller understanding of the development of mathematical thinking in adults, and may also have important implications for teaching elementary mathematics to children.

The broad goal of this proposal is to gain a deeper understanding of the adult human mathematical mind by studying its development in infancy. A major goal is to test the hypothesis that infants rely on analog magnitude representations of number similar to those used by adults, young children, and non-human animals. Previous studies suggest that infants may rely on two distinct systems for representing number; an object-file system for representing small values and an analog magnitude mechanism for representing large numerical values. This hypothesis will be tested by studying the psychophysics of number discrimination over a wide range of numerical values, testing whether infants are sensitive to ordinal relations between numerosities, and taking the first step to determine whether the enumeration process(es) that infants use involves serial or parallel processing. The proposed experiments will use the time that infants look at various displays and the location of infants. eye movements as dependent measures. The results of the proposed studies should provide a strong foundation for the development of a coherent model of the development of non-verbal numerical representations and will contribute to the principal investigator.s long-term goal of studying both the evolution and the development of numerical cognition.

DESCRIPTION (provided by applicant): The broad goal of the proposed studies is to contribute to a growing understanding of the precursors of mathematical knowledge in the first year of life. What is the cognitive foundation upon which complex culturally dependent and symbolic mathematics is built? Research with human adults, children, human infants and non- human animals suggests that there is a phylogenetically and developmentally primitive non-verbal system for representing number. The goal of this competitive renewal is to test the hypothesis that nonverbal numerosity representations serve as a foundation for later developing number skills. To this end we investigate variability in normative development in numerical cognition using behavioral and neurobiological methods and longitudinal designs to assess whether numerical sensitivity in infancy is predictive of variability in numerical cognition in early childhood. Aim 1 examines individual variation in numerical discrimination and the relationship between numerical discrimination and numerical rule learning using new paradigms never before applied to the study of numerical cognition in infancy. Aim 1 also studies infants longitudinally from 6-18 months to assess stability in numerical acuity over development. Aim 2 uses a longitudinal design to explore whether measures of numerical cognition in infancy predict later numerosity discrimination and numerosity-symbol mapping in early childhood. Aim 3 explores the relationship between brain and behavioral measures of number representation in infancy and early childhood and the specificity of neural markers to numerical discrimination in infancy. Beyond studying normal development of numerical acuity in infancy and the relationship between numerical abilities visible in the first year of life and later developing numerical abilities, this research sets the stage for studies of abnormal development by developing early assays that could identify children at risk for developmental dyscalculia (DD). DD affects approximately 6% of the global population (e.g., Badian, 1983;Gross-Tsur, Manor, &Shalev, 1996). A positive correlation between numerical acuity in infancy and early childhood or between numerical acuity in infancy and acquisition of the verbal counting system in childhood could lead to earlier identification of children with DD. PUBLIC HEALTH RELEVANCE: The broad goal of the proposal is to understand the development of non-verbal numerical thinking in infancy using behavioral and neurobiological assays. The studies are designed to assess individual variation and links between numerosity discrimination in the first year of life and later numerical abilities in an effort to set the stage for new assays to identify children at risk for developmental dyscalculia, a disorder that affects approximately 6% of the general public.

Adult humans quantify, label, and categorize almost every aspect of the world with numbers. The ability to use numbers is one of the most complex cognitive abilities that humans possess and is often held up as a defining feature of the human mind. Are there developmental precursors to adult mathematical cognition in human infants? Are there evolutionary precursors to the human computational mind in non-human primates? Is number a salient dimension for human infants or non-human primates (in this case, rhesus monkeys) or do other perceptual variables such as color and shape always trump number? Can human infants and monkeys add or subtract? Can they represent the number of objects in a heterogeneous array of objects? Are there nonlinguistic ways of representing number that are common to non-human primates and human infants? With support from a National Science Foundation CAREER award, Dr. Brannon will investigate these questions using both behavioral looking time methods and touch screen tasks that measure accuracy and reaction time in human infants, young children, and rhesus monkeys.

The intellectual merit of this project is that it will provide unique new insights into the building blocks of adult human mathematical abilities and shed light on the nature of thought without language. The broader impact of the research includes educating students at the undergraduate, graduate, and post-doctoral levels. The research is also the bases of a Duke University methods course on nonverbal cognition and a published reader that will pair empirical papers on animal and human developmental cognition, which will allow broad dissemination of the comparative developmental approach to studying cognition.

DESCRIPTION (provided by applicant): Mathematical abilities in adult humans exceed the numerical capacities of any non-human animal. Although neither rat nor monkey is likely to balance a checkbook or prove Pythagorous' theorem there is considerable evidence that non-human animals are capable of impressive mathematical feats in their own right. Animal genera as diverse as rats, pigeons, ferrets, raccoons, monkeys, and apes have been shown to make numerical judgments with stimuli that include light flashes, tones, abstract visual elements, house-hold objects, food morsels, and their own responses (for reviews see Boysen & Capaldi, 1992; Brannon & Roitman 2003; Gallistel & Gelman, 1992; Dehaene, 1997). The PI's previous research has contributed to this literature by demonstrating that rhesus monkeys represent abstract ordinal relations between numerosities and that pigeons represent number on a linear rather than a logarithmic scale. Furthermore, a growing body of data suggests that the nonverbal numerical system, held by animals, is shared by humans and appears early in development (e.g., Brannon, 2002; Brannon & Terrace, 2002; Whalen et al., 1999; Spelke, 2000). Studying the evolutionary basis of human numerical capacities will provide important insight into the nature of this system. Three main gaps remain in our knowledge of non-verbal numerical cognition in animals, 1) whether numerical representations are abstract or concrete, 2) the role of learning in the expression of particular numerical abilities, and 3) which aspects of human numerical cognition are phylogenetically conservative and which aspects are shared by some or all primates. The results of the proposed experiments will provide a more complete understanding of non-verbal numerical cognition and provide a springboard for understanding the evolutionary bases of human numerical cognition. Furthermore the proposed research seeks to provide a monkey model that will provide insight into normal numerical development in children and a basis for understanding atypical development. As such this research will contribute to the PIs broad goal of understanding the relationship between mathematical thinking in animals and human infants in an effort to shed light on thought without language and the building blocks of adult human cognition.

Number is important for almost everything we do as adult humans. Where does our quantitative mind originate? Previous research by Dr. Brannon and others has shown that very young infants can discriminate sets of items based on number alone. Despite the abundance of evidence that now demonstrates that infants have rudimentary abilities to perceive numerical differences, we do not yet understand whether or how these capacities relate to later mathematical cognition. The focus of this project is to ask whether nonverbal numerical abilities that emerge early in human development serve as a foundation for learning mathematics. To answer these questions Dr. Brannon and her research team have developed a new procedure that quantifies an individual infant's ability to see numerical differences. The procedure involves presenting babies with two streams of numerical images. One of the streams features a constant number of dots in each image; however, the images vary in the location and size of the dots. The other image features two different numerical values that alternate. Infants prefer to look at the changing numerical stream and the magnitude of their preference for the changing stream depends on the ratio between the two values in that stream. The project will use a longitudinal design to look at the relationship between numerical discrimination abilities in 6-month-old babies and later numerical discrimination and math concepts in the same children at 3.5 and 4.5 years of age. A large sample of 6-month-old infants will first be tested in the new numerical change detection task. The same infants will be tested in a variety of nonverbal numerical discrimination tasks at 9 and 18 months and then in both verbal and nonverbal numerical tasks at 3.5 and 4.5 years of age.

This project will provide a foundation for understanding the relationship between numerical abilities in infancy and later childhood. Establishing a link between rudimentary numerical abilities in infancy and later developing mathematical abilities could provide an important avenue for identifying early mathematics difficulties and developing interventions to address these difficulties.

DESCRIPTION (provided by applicant): This proposal is for funding to contribute towards an Attention and Performance meeting titled, "Space, Time and Number: The Cerebral Basis of Mathematical Intuitions. The meeting, organized by Dr.s Stanislas Dehaene and Elizabeth Brannon, will take place outside Paris in July of 2010. The objective of the meeting is to bring together researchers from around the world interested in the brain's architecture and how neuroscience can shed light on the representation of space, time and number. The meeting will foster a synthesis of cutting edge research in this area and culminate in a published volume (Oxford Press) and peer reviewed special edition of a journal (Trends in Cognitive Sciences or Cognition). The meeting is also likely to facilitate new collaborations and opportunities for junior researchers. The representations of number, time, and space are critical for most organisms'survival. Indeed, according to Immanuel Kant they represent "pure intuitions" that must precede and structure the experience of all objects. Considerable research with animals and human infants is now available to support this point of view. Collectively such research suggests that the cognitive algorithms for representing number, time, and space may have common developmental and evolutionary origins, involve a common set of basic computational algorithms for simple operations (such as addition), and perhaps even share brain circuitry. An important goal of this meeting will be to attempt to isolate the fundamental connections and divergences between the representation of number, space, and time. The study of number, space, and time is almost unparalleled in its multi-disciplinarity. It involves studying human cognitive development, adult cognition, nonhuman animals, behavioral and brain-based approaches and computational modeling. As such participants from diverse fields such as ethology, neurobiology, neuropsychology, developmental psychology, and computational modeling are invited to speak and discuss. Approximately 25 of the attendees will be invited speakers and 25 will be postdoctoral research associates and graduate students discussants. All participants will be chosen to balance gender and country of origin. Finally, 10 of the participants will be students chosen from open applications after widespread advertising. Students will be selected to increase ethnic, racial, and geographic diversity. PUBLIC HEALTH RELEVANCE: The proposed meeting on "Space, Time and Number: The Cerebral Basis of Mathematical Intuitions," will attempt to identify the developmental and evolutionary building blocks of quantitative cognition and focus on both behavioral and neurobiological evidence. Special attention will also be paid to discussing dysfunctions in quantitative cognition from a mental health perspective. The presentations will be published in an edited volume and special issue of a journal.

Getting around the world in space, keeping track of time, and quantifying the world around us is an essential part of being human. But how do we accomplish these feats? What are the neural mechanisms that allow us to navigate from home to work, to estimate when a traffic light should turn green, or to compare the number of people in two grocery checkout lines? The conference titled "Space, Time and Number: The Cerebral Basis of Mathematical Intuitions" will explore the state of the art in research on how these quantitative aspects of the world around us are represented and how they might relate to one another. An exciting aspect of this meeting is that the study of number, space, and time is almost unparalleled in its multidisciplinary nature. The topic requires studying human cognitive development, adult cognition, nonhuman animals, behavioral and brain-based approaches and computational modeling and thus brings together researchers from many different departments and fields of expertise. While the meeting will include senior scientists from around the globe, this NSF award will fund American junior scientists (graduate students, postdoctoral training associates, and assistant professors) who would otherwise be unable to attend.

The July 2010 meeting, organized by Dr. Stanislas Dehaene and Dr. Elizabeth Brannon (the Principal Investigator), will be the first international meeting of its kind to focus on the neural bases of the representation of time, space, and number. The conference will lead to a series of papers to be published for more widespread dissemination among scientists. Most importantly, by providing a means for junior scholars to attend, this award will support the formation of new research collaborations among this diverse, interdisciplinary group of researchers.

DESCRIPTION (provided by applicant): Mathematical ability is essential for almost every aspect of human existence and yet there is large variability in math competency in adults and extremely poor math ability is linked with long-term health problems and higher criminality (Parsons and Bynner, 2005). Math skills at school-entry predict later math achievement and are a better predictor of later overall academic achievement than literacy skills (Jordan, et al., 2009 Duncan et al., 2007). Therefore improving early math skills in very young children could have global effects on academic success and perhaps life outcomes. The goal of this proposal is to build upon a recent finding from our research group demonstrating that training with approximate nonsymbolic arithmetic (ApprA) using dot arrays leads to positive transfer in exact symbolic arithmetic (SymA) performance (Park and Brannon, In press). In Aim 1 we ask why ApprA training improves SymA. We decompose the cognitive ingredients of ApprA training to assess which aspects are critical for improving symbolic arithmetic. In Aim 2 we test specific predictions about how overlap in the brain regions that support approximate nonsymbolic arithmetic and exact symbolic arithmetic give rise to this transfer effect. For example, we ask whether ApprA training changes the neural tuning curves in the intraparietal sulcus, which are known to embody the mental representation of quantity. Such a finding would provide strong evidence that ApprA improves SymA by changing the primitive number sense. Finally Aim 3 proposes an iPad intervention study in a diverse public school district to test the efficacy of ApprA training to improve SymA in young children. Pilot data is presented for all three aims. Understanding the relationship between ApprA and SymA could have broad implications for understanding the roots of human mathematics. While ApprA training is unlikely to be practically useful as an avenue for improving math competency in adults or older children who have mastered the symbolic number system it could be critically important for improving math ability in very young children who have yet to master the symbolic number system.