The Relation of Mathematics and Language Ability (original) (raw)
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Abstract representations of numbers in the animal and human brain
Trends in Neurosciences, 1998
). The number domain is a prime example where strong evidence points to an evolutionary endowment of abstract domain-specific knowledge in the brain because there are parallels between number processing in animals and humans.The numerical distance effect, which refers to the finding that the ability to discriminate between two numbers improves as the numerical distance between them increases, has been demonstrated in humans and animals, as has the number size effect, which refers to the finding that for equal numerical distance,discrimination of two numbers worsens as their numerical size increases.
Brain and Language, 2000
Most nonhuman species are able to work through numerical quantities at various levels, such as memorizing, comparing or adding, although at an approximate level. On the other hand, their ability to manipulate symbolic numerical labels is, at best, primitive (for a review see Dehaene, 1997; Butterworth, 1999). Similarly, while nonhuman species use elaborate communication systems, language, a formal grammatical system, is a species-specific innate ability (for a review see Pinker, 1994). From the above considerations the following questions arise: are number processing abilities and language underpinned by specific cognitive systems, provided with dedicated neural substrates, or do they share, partially or totally, the same functional and anatomical substrates? A substantial contribution, although not exhaustive, in trying to disentangle such problems has been offered by neuropsychology. Since Déjerine's (1892) pioneering observations of a selective sparing of numerical processing in pure alexia and the report of a relative preservation of number comprehension in comparison to other semantic category in a group of aphasic patients (Goodglass, Klein, Carey, & Jones, 1966), the independence of number and language processing seemed to be firmly established. Similarly, the report of pure acalculia following left parietal lesion highlighted the autonomy, both from an anatomical and functional point of view of calculation from language system.
Links Between the Intuitive Sense of Number and Formal Mathematics Ability
Child Development Perspectives, 2013
Humans share with other animals a system for thinking about numbers in an imprecise and intuitive way. The approximate number system (ANS) that underlies this thinking is present throughout the lifespan, is entirely nonverbal, and supports basic numerical computations like comparing, adding, and subtracting quantities. Humans, unlike other animals, also have a system for representing exact numbers. This linguistically mediated system is slowly mastered over the course of many years and provides the basis for most of our formal mathematical thought. A growing body of evidence suggests that the nonverbal ANS and the culturally invented system of exact numbers are fundamentally linked. In this article, we review evidence for this relation, describing how group and individual differences in the ANS correlate with and even predict formal math ability. In this way, we illustrate how a system of ancient core knowledge may serve as a foundation for more complex mathematical thought.
Number sense in infancy predicts mathematical abilities in childhood
Proceedings of the National Academy of Sciences, 2013
Significance The uniquely human mathematical mind sets us apart from all other animals. How does this powerful capacity emerge over development? It is uncontroversial that education and environment shape mathematical ability, yet an untested assumption is that number sense in infants is a conceptual precursor that seeds human mathematical development. Our results provide the first support for this hypothesis. We found that preverbal number sense in 6-month-old infants predicted standardized math scores in the same children 3 years later. This discovery shows that number sense in infancy is a building block for later mathematical ability and invites educational interventions to improve number sense even before children learn to count.
Representation of Number in the Brain
Annual Review of Neuroscience, 2009
Number symbols have allowed humans to develop superior mathematical skills that are a hallmark of technologically advanced cultures. Findings in animal cognition, developmental psychology, and anthropology indicate that these numerical skills are rooted in nonlinguistic biological primitives. Recent studies in human and nonhuman primates using a broad range of methodologies provide evidence that numerical information is represented and processed by regions of the prefrontal and posterior parietal lobes, with the intraparietal sulcus as a key node for the representation of the semantic aspect of numerical quantity.
The evolution of numerical cognition: from number neurons to linguistic quantifiers
The Journal of …, 2008
It is well established that children, adults, and nonhuman animals share a basic ability to perceive and compare nonsymbolic quantities of items, commonly referred to as "numerosity." Symbolic numerical representations build on these basic abilities to enable human children and adults to use precise number words, symbols, and linguistic quantifiers. In the past five years, results from single-unit physiology, behavioral studies of human and monkey performance on numerosity tasks, computational modeling, and functional neuroimaging have provided profound insights into the neural mechanisms that underlie these symbolic numerical abilities, and suggest how higher-order human numerical capacities may have arisen from these evolutionarily conserved more basic mechanisms. These studies converge on two regions, the intraparietal sulcus (IPS) and the prefrontal cortex (PFC), as being critical for representing numerosity and for the acquisition of higher-order numerical abilities.
The cognitive basis of arithmetic
Arithmetic is the theory of the natural numbers and one of the oldest areas of mathematics. Since almost all other mathematical theories make use of numbers in some way or other, arithmetic is also one of the most fundamental theories of mathematics. But numbers are not just abstract entities that are subject to mathematical ruminations—they are represented, used, embodied, and manipulated in order to achieve many different goals, e.g., to count or denote the size of a collection of ob jects, to trade goods, to balance bank accounts, or to play the lottery. Consequently, numbers are both abstract and intimately connected to language and to our interactions with the world. In the present paper we provide an overview of research that has addressed the question of how animals and humans learn, represent, and process numbers.