Mathematics is a skill. Some people are better at it than others, so an individual person's math ability can range anywhere from being able to do simple arithmetic to calculus and abstract set theory. 

But there is some math ability we all share, according to psychologists: a simple ability to estimate and compare quantities without overtly counting, like when choosing a checkout line at the grocery store - guesstimating, though not quite as lazy as it sounds.

Previous studies have suggested there's a connection between how well a person does at the approximate number system and how skilled they become at the symbolic math they learn in school. Duke University psychologists wanted to know if this ability could be enhanced by giving people more practice at approximate number math. 

It can, according to a new paper by Duke psychologist Elizabeth Brannon and post-doctoral researcher Joonkoo Park. 

To test the idea, they enrolled 26 adult volunteers and tested their symbolic math ability before and after 10 training sessions that were designed to hone their approximate number skills. On each of these training sessions, the participants practiced adding and subtracting large quantities of dots without counting.

They were briefly shown two arrays of nine to 36 dots on a computer screen and then asked whether a third set of dots was larger or smaller than the sum of the first two sets, or whether it matched the sum.

"It's not about counting, it's about rough estimates," Park said.

As participants improved at the game the automated sessions became more difficult by making the quantities they had to judge closer to each other.

Before the first training session and after the last one, their symbolic math ability was tested with a set of two- and three-digit addition and subtraction problems, sort of like a third-grader's homework. They solved as many of these problems as they could in 10 minutes. Another group of control participants took the math tests without the approximate number training.

Those who had received the 10 training sessions on approximate arithmetic showed more improvement in their math test scores compared to the control group.

In a second set of experiments, participants were divided into three groups to isolate whether there had been some sort of placebo effect on the first experiment that made the approximate arithmetic group perform better. One group added and subtracted quantities as before, a second performed a repetitive and fast-paced rank-ordering with Arabic digits, and the third answered multiple choice questions that tapped their general knowledge (e.g., "which city is the capital of France?")

Again, the people who were given the approximate arithmetic training showed significantly more improvement in the math test compared to either control group.

"We are conducting additional studies to try and figure out what's driving the effect, and we are particularly excited about the possibility that games designed to hone approximate number sense in preschoolers might facilitate math learning," Park said.

Park and Brannon can't yet isolate the mechanism behind their effect, but the research does suggest that there is an important causal link between approximate number sense and symbolic math ability.

"We think this might be the seeds -- the building blocks -- of mathematical thinking," Brannon said.

Citation: Joonkoo Park, Elizabeth M. Brannon, 'Training the Approximate Number System Improves Math Proficiency', Psychological Science August 6, 2013 doi: 10.1177/0956797613482944