### New study challenges consensus that math abilities are innate

##### November 1, 2016

A new theory on how the brain first learns basic math could alter approaches to identifying and teaching students with math-learning disabilities, according to Ben-Gurion University of the Negev (BGU) researchers.

The widely accepted “sense of numbers” theory suggests people are born with a “sense of numbers,” an innate ability to recognize different quantities, and that this ability improves with age. Early math curricula and tools for diagnosing math-specific learning disabilities such as dyscalculia, a brain disorder that makes it hard to make sense of numbers and math concepts, have been based on that consensus.

Other theories suggest that a “sense of magnitude” that enables people to discriminate between different “continuous magnitudes,” such as the density of two groups of apples or total surface area of two pizza trays, is even more basic and automatic than a sense of numbers.

**Not just numbers**

The new study, published in the *Behavioral and Brain Sciences* journal, combines these approaches. The researchers argue that understanding the relationship between size and number is what’s critical for the development of higher math abilities. By combining number and size (e.g., area, density, and perimeter), we can make faster and more efficient decisions.

For example: how do you choose the quickest checkout line at the grocery store? While most people intuitively get behind someone with a less filled-looking cart, a fuller-looking cart with fewer, larger items may actually be quicker. The way we make these kinds of decisions reveals that people use the natural correlation between number and continuous magnitudes to compare options — not just numbers.

Other factors, such as language and cognitive control, also play a role in acquiring numerical concepts, they note.

“This new approach will allow us to develop diagnostic tools that do not require any formal math knowledge, thus allowing diagnosis and treatment of dyscalculia before school age,” says Tali Leibovich, PhD, from University of Western Ontario, who led the study.

“If we are able to understand how the brain learns math, and how it understands numbers and more complex math concepts that shape the world we live in, we will be able to teach math in a more intuitive and enjoyable way,” says Leibovich.

The study was supported by the European Research Council under the European Union’s Seventh Framework Programme.

#### Abstract of *From ‘sense of number’ to ‘sense of magnitude’ – The role of continuous magnitudes in numerical cognition*

In this review, we are pitting two theories against each other: the more accepted theory—the ‘number sense’ theory—suggesting that a sense of number is innate and non-symbolic numerosity is being processed independently of continuous magnitudes (e.g., size, area, density); and the newly emerging theory suggesting that (1) both numerosities and continuous magnitudes are processed holistically when comparing numerosities, and (2) a sense of number might not be innate. In the first part of this review, we discuss the ‘number sense’ theory. Against this background, we demonstrate how the natural correlation between numerosities and continuous magnitudes makes it nearly impossible to study non-symbolic numerosity processing in isolation from continuous magnitudes, and therefore the results of behavioral and imaging studies with infants, adults and animals can be explained, at least in part, by relying on continuous magnitudes. In the second part, we explain the ‘sense of magnitude’ theory and review studies that directly demonstrate that continuous magnitudes are more automatic and basic than numerosities. Finally, we present outstanding questions. Our conclusion is that there is not enough convincing evidence to support the number sense theory anymore. Therefore, we encourage researchers not to assume that number sense is simply innate, but to put this hypothesis to the test, and to consider if such an assumption is even testable in light of the correlation of numerosity and continuous magnitudes.