Rochel Gelman

Rutgers, The State University of New Jersey | Rutgers · Rutgers Center for Cognitive Science; Department of Psychology (New Brunswick )

A striking characteristic of human thought is that we form representations about abstract kinds (Giraffes have purple tongues), despite experiencing only particular individuals (This giraffe has a purple tongue). These generic generalizations have been hypothesized to be a cognitive default, that is, more basic and automatic than other forms of gen...

A great many students at a major research university make basic conceptual mistakes in responding to simple questions about two successive percentage changes. The mistakes they make follow a pattern already familiar from research on the difficulties that elementary school students have in coming to terms with fractions and decimals. The intuitive c...

Many famous paintings illustrate variations in what we here dub "referential depth." For example, paintings often include not only portrayals of uniquely referenced items, but also reflections of those items in mirrors or other polished surfaces. If a painting includes both a dancer and that dancer's reflection in a mirror, are there one or two dan...

Significance We provide an experimental demonstration that young infants possess abstract biological expectations about animals. Our findings represent a major breakthrough in the study of the foundations of human knowledge. In four experiments, 8-mo-old infants expected novel objects they categorized as animals to have filled insides. Thus, infant...

The approximate number system (ANS) allows people to quickly but inaccurately enumerate large sets without counting. One popular account of the ANS is known as the accumulator model. This model posits that the ANS acts analogously to a graduated cylinder to which one "cup" is added for each item in the set, with set numerosity read from the "height...

We expand upon a previous proposal by Bloom and Wynn (1997) that young children learn about the meaning of number words by tracking their occurrence in particular syntactic environments, in combination with the discourse context in which they are used. An analysis of the Childes database (MacWhinney, 2000) reveals that the environments studied by B...

Research Findings: This paper reports on children's use of science materials in preschool classrooms during their free choice time. Baseline observations showed that children and teachers rarely spend time in the designated science area. An intervention was designed to “market” the science center by introducing children to 1 science tool, the balan...

This article defends a continuity position. Infants can abstract numerosity and young preschool children do respond appropriately to tasks that tap their ability to use a count and cardinal value and/or arithmetic principles. Active use of a nonverbal domain of arithmetic serves to enable the child to find relevant data to build knowledge about the...

When making judgments, people often favor information received from a few individual sources over large-sample statistical data. Individual information is usually acquired piece by piece, whereas statistical information combines many observations into a single summary. We examined whether this difference in the frequency of encounters affects how d...

This chapter focuses on domain-specific approaches to learning. It discusses the notion of a domain, core and noncore domains, structure mapping, and the domains of animate and inanimate causality. The chapter also identifies the primary features of noncore domains and concludes by contrasting core and noncore domains.

The meaning and function of counting are subservient to the arithmetic principles of ordering, addition, and subtraction for positive cardinal values. Beginning language learners can take advantage of their nonverbal knowledge of counting and arithmetic principles to acquire sufficient knowledge of their initial verbal instantiations and move onto...

To ensure they're meeting state early learning guidelines for science, preschool educators need fun, age-appropriate, and research-based ways to teach young children about scientific concepts. The basis for the PBS KIDS show "Sid the Science Kid," this teaching resource helps children ages 3-5 investigate their everyday world and develop the basics...

Number concepts must support arithmetic inference. Using this principle, it can be argued that the integer concept of exactly ONE is a necessary part of the psychological foundations of number, as is the notion of the exact equality - that is, perfect substitutability. The inability to support reasoning involving exact equality is a shortcoming in...

This chapter examines the innate basis of our concepts of the positive integers. In practice, real valued variables are never exactly equal; nor is it easy to specify an algorithm for establishing exact equality between two random Gaussian variables. Furthermore, because number concepts must support arithmetic inference, a necessary part of the psy...

Normatively, a statistical pairwise comparison is a function of the mean, standard deviation (SD), and sample size of the data. In our experiment, 203 undergraduates compared product pairs and judged their confidence thatone product was better than the other. We experimentally manipulated (within subjects) theaverage productratings, the number of r...

Animal and human data suggest the existence of a cross-species system of analog number representation (e.g., Cordes, Gelman, Gallistel, & Whalen, 2001; Meeck & Church, 1983), which may mediate the computation of statistical regularities in the environment (Gallistel, Gelman, & Cordes, 2006). However, evidence of arithmetic manipulation of these non...

Using an interference paradigm, we show across three experiments that adults' order judgments of numbers, sizes, or combined area of dots in pairs of arrays occur spontaneously and automatically, but at different speeds and levels of accuracy. Experiment 1 used circles whose sizes varied between but not within arrays. Variation in circle size inter...

When preschoolers count to check their arithmetic predictions, their counts are better than when they simply count a set of items on count-only tasks. This is so even for 2 1/2- and 3-year-olds dealing with small values. Such results lend support to the view that learning about verbal counting benefits from a nonverbal count-arithmetic system and c...

Number terms and quantifiers share a range of linguistic (syntactic, semantic, and pragmatic) properties. On the basis of these similarities, one might expect these 2 classes of linguistic expression to pose similar problems to children acquiring language. We report here the results of an experiment that explicitly compared the acquisition of numer...

Biological and cultural processes have evolved together, in a symbiotic spiral; they are now indissolubly linked, with human survival unlikely without such culturally produced aids as clothing, cooked food, and tools. The twelve original essays collected in this volume take an evolutionary perspective on human culture, examining the emergence of cu...

Does the ability to develop numerical concepts depend on our ability to use language? We consider the role of the vocabulary of counting words in developing numerical concepts. We challenge the 'bootstrapping' theory which claims that children move from using something like an object-file - an attentional process for responding to small numerositie...

Mathematics is a system for representing and reasoning about quantities, with arithmetic as its foundation. Its deep interest for our understanding of the psychological foundations of scientific thought comes from what Eugene Wigner called the unreasonable efficacy of mathematics in the natural sciences. From a formalist perspective, arithmetic is...

Cordes and Gelman present research and arguments that development of counting skills is based on a domain-specific, nonverbal counting, and arithmetic structure. These nonverbal mechanisms provide young learners with a basis for understanding the cardinal counting principle, and the framework to acquire a verbal count routine. (PsycINFO Database Re...

Mathematics educators frequently recommend that students use strategies for measurement estimation, such as the reference point or benchmark strategy; however, little is known about the effects of using this strategy on estimation accuracy or representations of standard measurement units. One reason for the paucity of research in this area is that...

Reports of research with the Pirahã and Mundurukú Amazonian Indians of Brazil lend themselves to discussions of the role of language in the origin of numerical concepts. The research findings indicate that, whether or not humans have an extensive counting list, they share with nonverbal animals a language-independent representation of number, with...

Preschool Pathways to Science (PrePS©) is a science and math program for pre-K children that has been developed by a team of developmental psychologists in full collaboration with preschool directors, teachers and other staff. The PrePS© approach is rooted in domain-specific theories of development, theories that assume that different areas of know...

We argue that to test preschoolers' understanding of counting, one has to use tasks that relate counting to the goal of doing arithmetic, as counting and arithmetic principles are mutually constrained. A naturalistic study in the preschool classroom led to the development of an "arithmetic-counting" task, where counting was being related to the goa...

This chapter examines second-language sentence production both as a skill and as an on-line process by measuring relationships among linguistic and content characteristics of language samples both between and within participants. Written language samples were obtained from high school students enrolled in an intermediate-level English as a Second L...

In non-verbal counting tasks derived from the animal literature, adult human subjects repeatedly attempted to produce target numbers of key presses at rates that made vocal or subvocal counting difficult or impossible. In a second task, they estimated the number of flashes in a rapid, randomly timed sequence. Congruent with the animal data, mean es...

In this chapter, we review the distinction between development and learning, showing why what is innate and what is learned cannot be treated as mutually exclusive categories. The learning that is essential to cognitive development is driven by domain‐specific skeletal structures, which seek relevant inputs and organize and structure what is reveal...

This chapter interleaves a review of theories of cognitive development with accounts of the nature of concepts. Of central concern is how young children come to share concepts with members of the community they join. Different classes of cognitive development make contact with different theories about the nature of concepts. Learning theories (e.g....

ous (uncountable) quantities is the system of real numbers. It includes the irrational numbers, like 2, and the transcendental numbers, like p. It is used by modern humans to represent many distinct systems of continuous quantity--duration, length, area, volume, density, rate, intensity, and so on. Because the system of real numbers is isomorphic t...

nthesis of these findings, the tension between the discrete and the continuous, which has been central to the historical development of mathematical thought, is rooted in the non-verbal foundations of numerical thinking, which, it is argued, are common to humans and non-verbal animals. In this view, the non-verbal representatives of number are ment...

Microdevelopment is the process of change in abilities, knowledge and understanding during short time-spans. This book presents a new process-orientated view of development and learning based on recent innovations in psychology research. Instead of characterising abilities at different ages, researchers investigate processes of development and lear...

Interdisciplinary essays on central issues in cognitive science. In the early 1960s, the bold project of the emerging field of cognition was to put the human mind under the scrutiny of rational inquiry, through the conjoined efforts of philosophy, linguistics, computer science, psychology, and neuroscience. Forty years later, cognitive science is a...

Humans appear to share with animals a nonverbal counting process. In a nonverbal counting condition, subjects pressed a key a numeral-specified number of times, while saying “the” at every press. The mean number of presses increased as a power function of the target number, with a constant coefficient of variation (c.v.), both within and beyond the...

Kay (1955) presented a text passage to participants on a weekly basis and found that most errors and omissions in recall persisted despite repeated re-presentation of the text. Experiment 1 replicated and extended Kay s original research, demonstrating that after a first recall attempt there was very little evidence of further learning, whether mea...

There are core-specific and noncore-specific domains of knowledge, but only the core-specific domains benefit from innate skeletal structures. Core skeletal domains are universally shared, even though their particular foci may vary; individuals vary extensively in terms of the noncore domains they acquire.

The proclivity of young children to engage relevant environments actively helps explain how 3-year-old children in cultures that offer a variety of mathematical examples develop coherent understandings about natural numbers. A similar line of reasoning accounts for the development of other kinds of early cognitive accomplishments, such as understan...

Data on numerical processing by verbal (human) and non-verbal (animal and human) subjects are integrated by the hypothesis that a non-verbal counting process represents discrete (countable) quantities by means of magnitudes with scalar variability. These appear to be identical to the magnitudes that represent continuous (uncountable) quantities suc...

In three studies, we examined the roles of ontological and syntactic information in children's learning of words for physical entities, such as objects and substances. In Experiment 1, 3-year-olds and 4- to 5-year-olds, and adults first saw either an Object or Substance Standard labelled with either a mass or a count noun. Transfer items varied in...

In a nonverbal counting task derived from the animal literature, adult human subjects repeatedly attempted to produce target numbers of key presses at rates that made vocal or subvocal counting difficult or impossible. In a second task, they estimated the number of flashes in a rapid, randomly timed sequence. Congruent with the animal data, mean es...

Measurement estimation has been identified as a critical area for mathematical development, yet little is known about how estimators make their judgments and how competency in measurement estimation can be supported through instruction. We present a framework in which skilled estimators move fluently back and forth between written or verbal linear...

We propose that concept development is facilitated when existing conceptual structures overlaps with the structure of the to-be-learned data. When the new inputs do not map readily or are inconsistent with available mental structures, the risk is high that the data will be misinterpreted as examples of what is known. Results of two kinds of studies...

All theories of cognitive development make assumptions about constraints on learning, even those which commonly are seen as nonconstraint theories. We do not ask whether a constraint theory or a nonconstraint theory is better. Instead, we ask what kind of theory best accommodates key facts about cognitive development and concept learning. Our answe...

Evidence from a hearing-impaired woman after 13 years of language instruction & exposure (delayed until after her early 30s) supports the argument that grammar & number are distinct mental faculties, in contrast to James Hurford's analysis (1978, 1987), & that number cannot be bootstrapped from language as per Paul Bloom & Michael C. Corballis (199...

The goal of this project was the development of a program of science and mathematics activities that is suitable for use in preschool and daycare settings, for children before they enter kindergarten. More and more members of the business, government, education and military communities are calling for a notable upgrading of the scientific and techn...

Forty-eight children (mean age= 64.4 months, range = 52–75 months), unschooled in writing, were asked to draw a picture of and write the name for common objects depicted in line drawings. Analyses of the children's videotaped action sequences while drawing and writing revealed reliable, systematic differences. For example, drawings were often made...

What is the nature of human thought? A long dominant view holds that the mind is a general problem-solving device that approaches all questions in much the same way. Chomsky's theory of language, which revolutionised linguistics, challenged this claim, contending that children are primed to acquire some skills, like language, in a manner largely in...

We describe the preverbal system of counting and arithmetic reasoning revealed by experiments on numerical representations in animals. In this system, numerosities are represented by magnitudes, which are rapidly but inaccurately generated by the Meck and Church (1983) preverbal counting mechanism. We suggest the following. (1) The preverbal counti...

take up the question of individual contributions to the construction of shared conceptions . . . stressing not information availability but individuals' predispositions to attend to certain kinds of information examined the nature of learning in a children's museum, an environment structured to encourage parent-child interactions / observing chil...

many account for the capacity of infants, young children, and animals to discriminate small numerosities by an appeal to subitizing [a process used by adults to give rapid numerosity judgments for small arrays of simultaneously presented dots] our hypothesis is that preverbal representatives of numerosity (preverbal numerons) are magnitudes gener...

given that children do not possess the adult model for a given domain of understanding and that the model-building principles that enable them to acquire that model do not focus on the aspects of the domain that are rendered salient by the to-be-acquired adult model, the kinds of inputs necessary to foster their acquisition of the adult model may d...

Contents: Preface. Part I: Biological Contributions to Cognition. C.R. Gallistel, A.L. Brown, S. Carey, R. Gelman, F.C. Keil, Lessons From Animal Learning for the Study of Cognitive Development. P. Marler, The Instinct to Learn. A. Diamond, Neuropsychological Insights into the Meaning of Object Concept Development. E.L. Newport, Contrasting Concept...

Across several experiments, 6- to 8-month-old human infants were found to detect numerical correspondences between sets of entities presented in different sensory modalities and bearing no natural relation to one another. At the basis of this ability, we argue, is a sensitivity to numerosity, an abstract property of collections of objects and event...

Jean Mandler set the stage for the preparation of this isssue when she invited me to organize a symposium on constraints on cognitive development for the 1986 meeting of the Psychonomic Society. In responding to Jim Greeno's suggestion that we prepare manuscripts based on those talks, we tended to focus on a particular question: How is it that our...

Early cognitive development benefits from nonllngulstlc representations of skeletal sets of domain-specific principles and complementary domain-relevant data abstraction processes. The principles outline the domain, identify relevant Inputs, and structure coherently what Is learned. Knowledge acquisition within the domain is a joint function of suc...

We compare 3-year-old children's superordinate level classification under two experimental conditions. In the Complementary condition, children were instructed to sort a set of pictures three times, each time extracting a different "target" class (e.g., Animals) from the remaining items (e.g., Clothing and Food). In the Contrastive condition, they...

This book covers recent research with neurobiological and cognitive features of Down syndrome. This book covers recent research with neurobiological and cognitive features of Down syndrome. There has been notable progress in understanding the psychobiological concomitants of Down syndrome. New data have pinpointed selective neurological defects, an...

Does the preschooler's use of the animate–inanimate distinction reflect knowledge about which category types engage in self-initiated movements? Three- and 4-year-olds viewed photographs of unfamiliar objects, including mammalian animals, nonmammalian animals, statues with animal-like forms and parts, wheeled vehicles, and multipart rigid objects,...

The present study is an investigation of the interplay between social and developmental processes in children's numerical understandings in working- and middle-class home settings. Methods included interviews with 78 middle- and working-class 2½- and 4½-year-olds to assess their numerical understandings, interviews with the mothers about their chil...

2 experiments on the development of the understanding of random phenomena are reported. Of interest was whether children understand the characteristic uncertainty in the physical nature of random phenomena as well as the unpredictability of outcomes. Children were asked, for both a random and a determined phenomenon, whether they knew what its next...

Preschoolers' difficulty in accessing superordinate relations in classification contrasts sharply with their facility in accessing superordinate relations in language use. We consider two hypotheses regarding this discrepancy. First, certain aspects of classification tasks may obscure superordinate relations. In free classification tasks, the open-...

In their analysis of numerical competence, Creeno, Riley, and Gelman 1984 distinguish between conceptual, procedural, and utilization competence. Principled knowledge about a domain, for example, counting, serves as the basis of conceptual competence. Conceptual competence does not provide recipes for procedures but does set constraints on the clas...

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Presents a framework for characterizing competence for cognitive tasks and a hypothesis about competence for counting by typical 5-yr-old children. It is proposed that competence has 3 main components: conceptual, procedural, and utilizational. Conceptual competence is the implicit understanding of general principles of the domain. Procedural compe...

Infants prefer to look at an array of objects that corresponds in number to a sequence of sounds. In doing so, infants disregard the modality (visual or auditory) and type (object or event) of items presented. This finding indicates that infants possess a mechanism that enables them to obtain information about number.

Three- to 5-year-old children participated in one of 4 counting experiments. On the assumption that performance demands can mask the young child's implicit knowledge of the counting principles, 3 separate experiments assessed a child's ability to detect errors in a puppet's application of the one-one, stable-order and cardinal count principles. In...

This chapter is followed by comments by Clyde A. Crego. (PsycINFO Database Record (c) 2012 APA, all rights reserved)

None to add. From a book.