Apr 20, 2010 by Bill Jenkins, Ph.D.

math skills Let’s talk about the Approximate Number System, or just "the ANS." The ANS is the instinctive ability to nonverbally represent numbers. We constantly use this capability in every day decision making, such as choosing the shorter checkout line at the store or wanting to try a meal at a crowded restaurant. In these situations, our gut decisions are mathematically based. Evidence shows that many different species not only share this capacity, but use it to guide everyday behaviors such as foraging and judging time and distance.

So how does the ANS work in non-humans? Let’s do a little study of my two labs, Bella and Buddy. Both love to chase tennis balls, love to swim, and are highly competitive in the ball-chasing department. Buddy clearly exercises his ANS judgment routinely when I throw the ball into the water. If he and Bella approach the water’s edge at about the same time, they both jump in. On the other hand, if Bella beats him to the water by a significant distance, he recognizes instinctively that he can’t beat her to the ball in the water, so he’ll stop and wait until she brings it nearly to the shore. At that point, he jumps in and goes for the steal.

Why is the ANS important for math skills? It is believed that human mathematical competence comes from two representational systems. One is the "symbolic representations" that must be explicitly taught and are the basis for calculus and geometry. The other–the same one that Buddy uses above–is the older approximate number system. The evidence suggests that very young babies can use this ANS to make approximate number judgments, differentiating one item from two, two items from three and three items from greater than three. Further, a growing body of evidence indicates that individual differences in math achievement are related to variations in the acuity of an evolutionarily ancient, unlearned approximate number sense. Interestingly, evidence also suggests that this ANS may be subject to influence by early learning.

If you’d like to dig deeper into understanding the science of the ANS, I recommend reading Halberda and Feigernson’s 2008 study, "Developmental Change in the Acuity of the ’Number Sense’: The Approximate Number System in 3-, 4-, 5-, and 6-Year-Olds and Adults." For an overview, The New York Times published a write up on the articleand even included a link to an interactive, online activitythat demonstrates the ANS in action.