Summary: A new study challenges the longstanding “sense of numbers” theory that early numerical ability is innate.

New Research Proposes a ‘Sense of Magnitude’ Instead of an Innate Number Sense

Source: Ben-Gurion University

A team of researchers from Ben-Gurion University of the Negev and collaborators argues that basic numerical cognition may rely less on an innate “number sense” and more on a broader, earlier-developing “sense of magnitude.” Published in the journal Behavioral and Brain Sciences, the review reframes how we think about the emergence of everyday math skills and has implications for diagnosing and teaching students with math learning disabilities such as dyscalculia.

The dominant view in numerical cognition holds that humans are born with a “sense of numbers”—an inborn ability to perceive and compare quantities without using symbols. This idea has guided early math curricula and shaped screening methods for math-specific learning disabilities, including dyscalculia, which affects the ability to understand numbers and mathematical concepts.

Researchers Naama Katzin, Maayan Harel and Prof. Avishai Henik of the BGU Department of Psychology and the Zlotowski Center for Neuroscience collaborated with Dr. Tali Leibovich of the Numerical Cognition Laboratory at the University of Western Ontario. Together they review evidence suggesting that what underlies early numerical judgments may instead be a sensitivity to continuous magnitudes—attributes such as area, density, size and perimeter—that naturally correlate with number in the environment.

“If we can understand how the brain first learns about quantities and combines size and number, we can design teaching methods that are more intuitive and enjoyable,” says Dr. Leibovich. “This review is a first step toward that goal.”

The review explains that when people make quick quantity judgments—like choosing which checkout line will be faster—they rarely rely on number alone. Instead, they use a combination of cues such as how full a cart appears, item size, density and surface area. A fuller-looking cart may contain many small items, while another cart with fewer but much larger items may lead to a faster checkout. These everyday decisions demonstrate how number and continuous magnitude are processed together and how their natural correlation can guide behavior.

The authors contrast two theoretical positions. The traditional “number sense” theory proposes that non-symbolic numerosity (the ability to perceive discrete counts without symbols) is processed independently of continuous physical attributes. The alternative “sense of magnitude” perspective holds that continuous magnitudes are processed at least as automatically and perhaps more fundamentally than discrete number. According to this view, number-related judgments often reflect a holistic integration of multiple continuous cues rather than an isolated, innate numerosity system.

One consequence of this shift in perspective is a reconsideration of how dyscalculia is identified. Currently, reliable diagnosis typically does not occur until school age, at which point affected children may already be behind peers. The researchers suggest that recognizing the role of continuous magnitudes could enable development of diagnostic tools that do not rely on formal math skills, allowing earlier detection and intervention for children at risk of dyscalculia.

The review also encourages the field to examine how language, cognitive control and environmental learning interact with magnitude processing as children develop numerical concepts. The authors acknowledge that their proposal raises further questions and call for empirical work designed to separate the contributions of number and continuous magnitudes in infancy, childhood and across species.

Funding: The study, “From ‘sense of number’ to ‘sense of magnitude’ – The role of continuous magnitudes in numerical cognition,” was supported by the European Research Council (ERC) under the European Union’s Seventh Framework Programme (FP7/2007-2013), ERC Grant Agreement 295644 to A.H.

Source: Andrew Lavin – Ben-Gurion University

Image credit: Tali Leibovich

Original research: Tali Leibovich, Naama Katzin, Maayan Harel and Avishai Henik, “From ‘sense of number’ to ‘sense of magnitude’ – The role of continuous magnitudes in numerical cognition,” Behavioral and Brain Sciences, published online August 17, 2016. DOI: 10.1017/S0140525X16000960.

The review evaluates evidence for two models: the traditional “number sense” model that treats numerosity as an innate, discrete skill processed independently of continuous properties, and a “sense of magnitude” model that argues numerosities and continuous magnitudes are processed together and that a pure, innate number sense has not been convincingly demonstrated. The authors review behavioral and imaging studies across infants, children, adults and animals, and highlight how the natural correlation between number and continuous magnitudes complicates attempts to isolate numerosity processing. They conclude that current evidence does not definitively support the innate number sense hypothesis and call for research that explicitly addresses the role of continuous magnitudes in early numerical cognition.

The authors encourage researchers, educators and clinicians to test the assumptions of the number sense model and to explore diagnostic and instructional approaches that account for the joint influence of number and continuous magnitudes on mathematical development.