### 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.

## Comments (14)

November 14, 2016by JT

Try a half adder (exclusive OR gate and an And gate) and for fun you can look at the transistors that are used to make the logic gates – it’s all electrical engineering — not programming!

November 13, 2016by deavman

Would it not more accurate to specify that BGU (in the Negev) is located in Israel.

November 5, 2016by Mikeg123

I thought some people learn visually and some others have to read it or be shown how to do it? I have too “See” math in my head. I was never good a rote learning at least if I dint understand it.

November 4, 2016by GatorALLin

I remember hearing about a study discussing why asian students were often found to be better at math than other students. I think it came down to how much longer you were trained to work on a problem vs. give up. I think a small difference of working on a math problem for a few extra minutes proved a huge difference, especially if a student were to get stuck at any early point in their schooling, as most math builds on itself so that future math required you were penalized greatly if any of the key building blocks were missed. We are all being affected by the digital world and thus our attention spans seem to shorten and thus our willingness to suffer just 2 minutes longer on a Math/word problem may be the “kiss of death” for students used to being distracted within seconds, or just not building up a self expectation to struggle, regardless if you are sure you can succeed. Maybe the recent USA concept of “everyone gets a trophy” could play into the psychology that if I don’t like something or if that subject (math) does not come easily to me, I only want to do things where I win could play a role IMHO.

I think Math is more about your teacher and introduction and perceived need than your innate ability. We likely would all benefit from learning how to best solve difficult problems vs. just memorizing equations and learning theorems. No Pain, No Gain may hold true for Math in theory.

November 7, 2016by Terryinasia

Asian students study more (homework) in the course of one week than an average North American student would study in a month, and that’s a pretty conservative estimate. This is probably the reason that they would score higher in any type of study in mathematics skills.

School can start as early as 7 a.m. in the morning and finished by 4: to 5 p.m. with an additional 4 plus hours of homework studies in the evening. Saturdays are usually just half day, yes Saturdays are not off limits and there’s lots of homework to be done and the evening as well.

One would think that if someone had an innate ability this grueling schedule would certainly hone those skills

November 2, 2016by DSM

Math abilities are innate, in all primates, and damage to a single gene can retard the ability significantly.

Selection pressures on a human population that reward the more numerate, with more offspring, will drive the evolution of enhanced mathematical abilities in that population.

http://web.mit.edu/fustflum/documents/papers/AshkenaziIQ.jbiosocsci.pdf

November 2, 2016by eldras3

Nurture/Nature. But a man has more innate abilities than a tadpole, so something’s inherited.

November 2, 2016by DavidMills

It seems to me that the title (given by your editor) goes somewhat beyond the actual paper’s title and abstract: The authors seem to call only for an re-evaluation of the hypothesis, they do not seem to feel that they have “debunked” it. That is, they are showing that the continuous hypothesis may account for most of the variance, that the integer counting may not be needed. I think there is still much evidence elsewhere in studies of certain kinds of dyscalculia that there are dysfunctions in the basic counting that are the root causes of the problem. I have worked with such students, and know that something basic is clearly wrong, though I admit that I cannot be sure what it was on the wiring level. It certainly could be ‘continuous’, as these authors suggest. It still seems to me, though, that there is evidence from other research that there can be dysfunctions in the basic integer counting system that also can result in dysfunction.

November 2, 2016by Editor

Agreed. Title changed.

November 2, 2016by Skydog

1+1= 2 there’s a difference between math and programming

November 2, 2016by JohnLobell

Yea, Srinivasa Ramanujan never happened. And those math whizzes —-

November 2, 2016by arrowrod

1 + 1 = 10. With that knowledge you are now a programmer.

November 2, 2016by DevilDocNowCiv

arrow,

If we just worried about coding life would be much simpler. The thing I usually read about math teaching is either a given State teaches math to most students well, or poorly per some standard. I find this article interesting because it goes into details about innate math ability I had never heard of. Most of what I’ve read about math learning over the recent past concerns Grad and High School. Over the last few years I’d say math issues have been related to Common Core a lot as well. For grade and high school I’d just break it down to one of two philosophies. (Neither simply focuses on coding).

Viewpoint 1) we’re all mathletes, almost, if only we taught it right. If we just stopped teaching this part that so many fail, etc.

Viewpoint 2) The second case is…Holy Shnikeys, there really is a bell curve / normal distribution!

And it hits math ability! But…but..what about that town on NPR where “all kids are above average?” And didn’t Arkansas rule at one time that Pi equals three? Yes! So lets not get our knickers in a twist if some kids keep sliding through everything except math, and let’s stop minimizing what kids need to have to try to minimize our “bad math school stats.”

Try this very basic math idea, and divert kids from it as it goes. Teach a very stripped down version of basic statistics only: three dif kinds of “ave,” continuous vs discrete stats, with examples of common misuse of continuous data being misrepresented as a discrete issue (applying to a given person). Focus a while on ratio’s and percentage, but keep it basic and drum it in.

Basic algebra only for algebra.

Leave pre-calc to kids who seem interested, forget all beyond the most basic counting, multiplying and dividing of whole numbers. Leave the rest of the mountain of number rule data out. If little Jimmie and Janey can’t count, reroute immediately to remedial math.

The diversion I noted earlier would have three math tracks. The simple middle I just described is one, and it would be the one most stay with. The next would be remedial (local communities do what they feel they must). The third would be the proto – mathletes. With this group we strive for the stars. Bring in Johns Hopkins, Cal Tech, MIT. Inspire! Bring in volunteer mentors using mountains of donated mathlete money. With the money actually going to real math oriented kids, it will indeed pour in.

You’re welcome.

November 2, 2016by DSM

LOL

1+1=10, in BINARY NOTATION! Which BTW is as old as the “I Ching”.

And the 1+1 joke would have to be at least half a century old too, however the correct presentation (which is less misleading) is:

01 + 01 = 10