Math, monkeys, and the developing brain

Abstract

Thirty thousand years ago, humans kept track of numerical quantities by carving slashes on fragments of bone. It took approximately 25,000 y for the first iconic written numerals to emerge among human cultures (e.g., Sumerian cuneiform). Now, children acquire the meanings of verbal counting words, Arabic numerals, written number words, and the procedures of basic arithmetic operations, such as addition and subtraction, in just 6 y (between ages 2 and 8). What cognitive abilities enabled our ancestors to record tallies in the first place? Additionally, what cognitive abilities allow children to rapidly acquire the formal mathematics knowledge that took our ancestors many millennia to invent? Current research aims to discover the origins and organization of numerical information in humans using clues from child development, the organization of the human brain, and animal cognition.analog magnitude | functional MRI | mathematics education | numerical cognition | numerosity T his review traces the origins of numerical processing from "primitive" quantitative abilities to math intelligence quotient (IQ). "Primitive" quantitative abilities are those that many animals use to estimate the value of an object or event, for instance its distance, length, duration, number, amplitude, saturation, or luminance (among others). The constraints on how human and animal minds process these different quantities are similar (1). For example, all of these quantities show cognitive processing limitations that can be predicted by Weber's law. Weber's law states that quantity discrimination is determined by the objective ratio between their values. This ratio-based psychological and neural signature of quantity processing indicates that many quantities are represented in an analog format, akin to the way in which a machine represents intensities in currents or voltages (1). I discuss the types of constraints that influence quantity discrimination, using "number" as the initial example, and then consider the psychological and neural relationship between "number" and other quantitative dimensions. Similar constraints on processing across different quantities have been interpreted as evidence that they have a common evolutionary and/or developmental origin and a common foundation in the mind and brain (2-11). The resolution of these issues is important for understanding the inherent organization of our most basic conceptual faculties. The issue is also important for understanding how our formal mathematical abilities originated.Primitive quantitative abilities play a role in how modern humans learn culture-specific, formal mathematical concepts (1). Preverbal children and nonhuman animals possess a primitive ability to appreciate quantities, such as the approximate number of objects in a set, without counting them verbally. Instead of counting, children and animals can mentally represent quantities approximately, in an analog format. Studies from our group and others have shown that human adults, children, and nonhuman primates share cogni...

The amodal brain and the offloading hypothesis

“…The most striking behavioral findings supporting the existence of amodal concepts come from the research on the number sense (Cantlon, 2012;Dehaene, 2011;see Dove, 2009 andMachery, 2007 for further discussion). Visual estimation of the number of objects in a set of objects and auditory estimation of the number of sounds in an auditory sequence obey Weber's law: The standard deviation of participants' estimations linearly increases with the mean number of objects and sounds (Dehaene, Dehaene-Lambertz, & Cohen, 1998).…”

How do symbolic and non-symbolic numerical magnitude processing skills relate to individual differences in children's mathematical skills? A review of evidence from brain and behavior

“…While non-symbolic representations of numerical magnitudes are thought be shared across species and can already be measured in early infancy (Cantlon, 2012), symbolic representations are uniquely human and relatively recent cultural inventions to provide abstract representations of numerical magnitude. Thus, by investigating the relationship between, on the one hand symbolic and non-symbolic numerical magnitude processing and, on the other, children's mathematical achievement, larger questions concerning the role of evolutionary ancient skills for the acquisition of uniquely human number skills and representations can also be constrained.…”

Cross-Modal Correspondences in Non-human Mammal Communication

“…In both humans and other animals, magnitude-related, or 'prothetic', dimensions (e.g., numerosity, area, spatial length, duration, luminance and intensity) are represented using an analogue format, where representations of larger values become increasingly noisy (Cantlon, 2012;Srinivasan and Carey, 2010). Indeed, in most of the species in which quantitative discriminations have been studied, their estimations of 'more' or 'less' appear to obey…”