When it comes to math, people mis-characterize themselves quite often. About 20 percent of the people who say they are bad at math score in the top half of tests while about 33 percent of people who say they are good at math score in the bottom half.

What explains it? People have differing ideas about math. People who think they're good at math have a numeric competency that may be helpful in some real-life situations, so they think they are good at math even if they do poorly when actually tested.  

"Some people mis-categorize themselves. They really don't know how good they are when faced with a traditional math test," said Ellen Peters, co-author of the study and professor of psychology at The Ohio State University. "They just stop giving responses. We don't know why. It could be a lack of confidence with numbers, or they are just not motivated. This has important implications for everyday life. People who are low in subjective numeracy may not do their taxes on time or they may not make thoughtful choices on their health insurance because they just give up when faced with a lot of numbers."

Peters conducted the study with Par Bjalkebring, a visiting scholar from the University of Gothenburg, which was published in the Journal of Personality and Social Psychology.

Peters said this new study is an attempt to look at numeracy as a skill that has more than one dimension.

"There are different ways you can be good and bad with numbers. And these fundamental differences in how people approach numbers seem to matter to how they judge and decide," she said.

The study involved 130 people recruited at a university to take part in a four-day study. The study examined three different types of numeric competency.

One is objective numeracy, which is what most people think of when they think of "being good at math." This is the ability to work with numbers and score well on traditional math tests. This was measured with a test that asked questions like "If the chance of getting a disease is 10 percent, how many people would be expected to get the disease out of 1000?"

The second was subjective numeracy, which is people's self-reports on their ability and preference to work with numbers. This was measured by asking people to answer questions like "How good are you at working with percentages?" and "How often do you find numerical information to be useful?"

The third is symbolic-number mapping, which is the ability of some people to estimate numeric magnitudes quickly in their head and map them to a number line. This was measured by giving participants a line drawn on a piece of paper that they were told began at zero and ended at 1,000. They were asked to indicate where on the line various numbers (4, 6, 18, 71, 230 and 780) would be located. Peters said this may be what would allow a carpenter, for example, to quickly estimate how much wood he would need to put in a hardwood floor in a complex room with intricate corners.

The researchers had participants do a variety of judgment and decision-related tasks related to numbers. For example, they were asked to rate the attractiveness of various simple and risky bets and to recall numbers paired with objects in a memory test.

The results showed that people approached each problem through their combined strengths and weaknesses on each of the three types of numeric competency studied.

For example, those who scored higher in objective numeracy were more likely than others to do actual number comparisons and calculations to determine whether a bet would be attractive or not. Those high in subjective numeracy were more likely to find all the bets attractive, regardless of the expected value of the return.

Those who scored high in symbolic-number mapping produced valuations of the risky bets that were close to, but not equal to, the gamble's expected value. That suggests that these people didn't use an actual calculation - like those high in objective numeracy - but were making rough estimates that were close to correct.

Those who scored high in symbolic-number mapping were also more likely than others to remember the numbers in the memory test, but they didn't do any better remembering the non-numeric objects. Interestingly, those who scored high on subjective numeracy were more likely than those who scored lower to respond to all the questions on the memory test - even if they were wrong.

"Presumably, if you're high in subjective numeracy you feel more confident or comfortable in guessing," Peter said.

Overall, Peters said the results suggest that there may be more than one way for people to be successful at math and at using numbers important to their everyday decisions.

For example, people who are good at objective numeracy probably have no problems keeping track of their credit card spending because they may find it easy to keep a running list of purchase amounts. Those who are better at symbolic-number mapping may not keep detailed records, but they may be good at roughly estimating their credit card purchases so they don't spend too much.

"Some of the ways we can be good at numbers can compensate for other ways that we're bad at numbers," Peters said. "That may not work for everyone in every situation, but there is more than one way to be good at math."