Abstract not found

Dehaene (this volume) articulates a naturalistic approach to the cognitive foundations of mathematics. Further, he argues that the `number line' (analog magnitude) system of representation is the evolutionary and ontogenetic foundation of numerical concepts. Here I endorse Dehaene's naturalistic stance and also his characterization of analog magnitude number representations. Although analog magnitude representations are part of the evolutionary foundations of numerical concepts, I argue that they are unlikely to be part of the ontogenetic foundations of the capacity to represent natural number. Rather, the developmental source of explicit integer list representations of number are more likely to be systems such as the object--file representations that articulate mid--level object based attention, systems that build parallel representations of small sets of individuals.

Previous research has shown that children go through a stage in which they know that the number words each refer to a distinct numerosity, yet do not know which numerosity each number word picks out (Wynn, 1992). How do children attain this level of knowledge? We explore the possibility that particular properties of how number words are used within sentences inform children of the semantic class to which they belong. An analysis of transcripts of the spontaneous speech of three one- and two-year-old children and their parents (from the CHILDES database; MacWhinney & Snow, 1990) suggests that the relevant cues are available as input in parents ’ speech to children, and that children generally honour these properties of number words in their own speech. Implications of this proposal for word learning more generally are discussed.

We present data from a preferential looking method to investigate when infants have mapped singular and plural markers in English onto the semantic distinction between singleton sets and sets with more than 1 individual. Twenty- to 36-month-old children heard sentences that marked number in 1 of 2 ways: (a) redundantly with verb morphology, lexical quantifiers, and noun morphology (“Look, there ARE SOME blicketS”/“Look, there IS A blicket”) or (b) only with noun morphology (“Look at the blicketS”/“Look at the blicket”). Twenty-four-month-old infants, but not 20-month-old infants, looked at the screen that matched the carrier sentence with respect to singular–plural distinction when number was expressed on the verb, on the noun, and with quantifiers. Detailed looking-time analyses suggest that the arrays begin to be differentiated on the child’s hearing are or is. Twenty-four-month-olds failed when number was marked on the noun alone, whereas 36-month-olds suc-Correspondence should be addressed to Sid Kouider, Laboratoire de Sciences Cognitives et

What are the origins of abstract concepts such as “seven, ” and what role does language play in their development? These experiments probed the natural number words and concepts of 3-year-old children who can recite number words to ten but who can comprehend only one or two. Children correctly judged that a set labeled eight retains this label if it is unchanged, that it is not also four, and that eight is more than two. In contrast, children failed to judge that a set of 8 objects is better labeled by eight than by four, that eight is more than four, that eight continues to apply to a set whose members are rearranged, or that eight ceases to apply if the set is increased by 1, doubled, or halved. The latter errors contrast with children’s correct application of words for the smallest numbers. These findings suggest that children interpret number words by relating them to 2 distinct preverbal systems that capture only limited numerical information. Children construct the system of abstract, natural number concepts from these foundations.

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 a symbolic game, like tic-tac-toe. Its rules are more complicated, but not a great deal more complicated. Mathematics is the study of the properties of this game and of the systems that may be constructed on the foundation that it provides. Why should this symbolic game be so powerful and resourceful when it comes to building models of the physical world? And on what psychological foundations does the human mastery of this game rest? The first question is metaphysical—why is the world the way it is? We do not treat it, because it lies beyond the realm of experimental behavioral science. We review the answers to the second question that experimental research on human and non-human animal cognition suggests.

for assistance, and Nora Newcombe and Elliott Blass for advice and comments on the manuscript. Above all, I am grateful to Ariel Grace and Kristin Shutts for their unending support and after-hours labor on this project. Draft, 4/20/05. This paper has not yet been peer reviewed. Please do not copy or cite without author's permission. This report considers three prominent claims that boys and men have greater natural aptitude for high-level careers in mathematics and science. According to the first claim, males are more focused on objects and mechanical systems from the beginning of life. According to the second claim, males have a profile of spatial and numerical abilities that predisposes them to greater aptitude in mathematics. According to the third claim, males show greater variability in mathematical aptitude, yielding a preponderance of males at the upper end of the distribution of mathematical talent. Research on cognitive development in human infants and preschool children, and research on cognitive performance by students at all levels, provides evidence against these claims. Mathematical and scientific reasoning develop from a set of biologically based capacities that males and females share. From these capacities, men and women appear to develop equal talent for mathematics and science.

I observe that in an earlystage of child Catalan and Spanish, no overt subjects are used. At this same age and MEAN LENGTH OF UTTERANCE (MLU), child speakers of overt subject languages such as French, German, Dutch, and English use at least some overt subjects optionally. I explain this crosslinguistic variation bysuggesting that the adult target grammars varywith respect to the position in which overt subjects are realized. In the overt subject languages, subjects are realized in the canonical specifier-of-IP position, whereas in the null subject languages (such as Catalan and Spanish), subjects are located in a topic/focus position, which becomes accessible onlylater in development. As evidence for this, I show that overt subjects, fronted objects, and WH-questions begin to be used at the same point in development in child Catalan and Spanish. I also argue that subject agreement constitutes an incorporated pronominal subject in Catalan and Spanish and that children converge on this parametric option veryearly. The inabilityof child Spanish- and Catalan-speakers to use discourse-pragmatic information is explained as a delayin the development of the interface between grammar and discourse-pragmatics.* 1. INTRODUCTION. It

Young children experience difficulties establishing conceptual representations of color compared with everyday objects. We argue that comparing the development of color cognition to that of familiar objects is inappropriate since color is a perceptual attribute that can be abstracted from an object and by itself lacks functional significance. Instead, we compared the recognition, perceptual saliency, and naming of color to that of three other perceptual object attributes (motion, form, and size) in 47 children aged 2 to 5 years as a function of language age. Results revealed that, although color was perceptually salient relative to the other visual attributes, no selective impairment to color cognition (recognition and naming) was found relative to the three other visual attributes tested. Thus, when the appropriate comparisons are made, we find no special delay in the development of color conceptualization. Furthermore, the striking disparity between perceptual saliency and cognition of color in our youngest age groups suggests that perceptual saliency has little influence on the conceptual development of color. © 2001 Academic Press Key words: color cognition; visual development; perceptual saliency. It has long been believed that young children have difficulty establishing conceptual representations of color, based on the striking discrepancy in their ability to learn the names for everyday objects and the tardy, erratic nature by which they

Mathematicians frequently evoke their “intuition” when they are able to quickly and automatically solve a problem, with little introspection into their insight. Cognitive neuroscience research shows that mathematical intuition is a valid concept that can be studied in the laboratory in reduced paradigms, and that relates to the availability of “core knowledge” associated with evolutionarily ancient and specialized cerebral subsystems. As an illustration, I discuss the case of elementary arithmetic. Intuitions of numbers and their elementary transformations by addition and subtraction are present in all human cultures. They relate to a brain system, located in the intraparietal sulcus of both hemispheres, which extracts numerosity of sets and, in educated adults, maps back and forth between numerical symbols and the corresponding quantities. This system is available to animal species and to preverbal human infants. Its neuronal organization is increasingly being uncovered, leading to a precise mathematical theory of how we perform tasks of number comparison or number naming. The next challenge will be to understand how education changes our core intuitions of number.