Funded Grants

The origins and organization of numerical information in the mind and brain

Thirty-thousand years ago, humans kept track of numerical quantities by carving slashes on fragments of bone. It took approximately twenty-five thousand years 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 six years (between ages 2 and 8). What cognitive abilities enabled our ancestors to record tallies in the first place? And, what cognitive abilities allow children to rapidly acquire the formal mathematics knowledge that took our ancestors many millennia to invent? Our 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.

This essay traces the origins of numerical processing from "primitive" numerical abilities to math IQ. Pre-verbal children and non-human animals possess the 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, akin to the way in which a machine represents intensities in currents or voltages (1). We have shown that humans and non-human primates share cognitive algorithms for encoding numerical values as analogs, comparing numerical values, and arithmetic. Further, my colleagues and I have shown that the brain regions recruited to perform these tasks are also shared by adult humans, non-human primates, and 4-year-old children who cannot yet count to 30. Recently, we have found that neural regions involved in analog numerical processing are important for the development of math IQ (and not verbal IQ). Taken together, the data implicate a degree of continuity in numerical abilities ranging from primitive approximation to complex and sophisticated math.

Although there is general agreement that nonsymbolic, analog numerical estimation is a cognitive antecedent of formal (symbolic) mathematical knowledge, there is considerable debate over how numerical information is organized in the mind. The debate can be distilled down to three main issues. The first issue concerns the role of general-purpose mechanisms in numerical processing. Some researchers hypothesize that domain-general aspects of cognition, such as working memory, provide the critical mechanism that influences the time-course of mathematics learning. Other researchers argue that early-developing, domain-specific properties of numerical processing, such as analog number encoding, permanently impact mathematical understanding throughout development. Second, a recent debate has emerged over the degree to which numerical representations draw on mechanisms from other functionally specialized domains, such as spatial cognition: Does 'space' ground numerical and quantitative concepts or do 'space' and 'number' develop independently? Finally, the degree to which language and formal culture (i.e., schooling) play a unique role in the organization of numerical information in the human brain continues to be unresolved: Which aspects of numerical processing are altered qualitatively by language and human cultural practices?

Our current studies aim to address these questions and others using a combination of developmental, neuroimaging, and non-human primate research -- both to understand numerical cognition in its own right and to provide crucial input for educational practices in mathematics.