Guess the Number of Gumballs, Then Do a Differential Equation

By Eliza Strickland | September 8, 2008 2:12 pm

equation blackboardA new study argues that people have an intuitive understanding of numbers that closely correlates with their aptitude for complex math, and that some people are simply better at it. The research team found that 14-year-olds who were better at estimating quantities were more likely to have gotten high grades in math. Says lead researcher Justin Halberda: “We discovered that a child’s ability to quickly estimate how many things are in a group significantly predicts their performance in school mathematics all the way back to kindergarten” [Washington Post].

Researchers expressed surprise that the basic “number sense” that has been observed in some animals is linked to the ability to solve complicated equations. “Maximising your search for food, finding a seat on the bus, recognizing the difference between a mating call and an alarm call in a particular species of bird by the number of warbles — all of these require [number sense]…. What is surprising is that the formal mathematics we work so hard to learn in school … is related in any way to what a rat is doing when it is out looking for scraps of food, or what you and I are doing when we look for a seat on a bus,” said Halberda [AFP].

In the study, published in the journal Nature [subscription required], researchers quickly flashed displays containing many yellow and blue dots in front of the students, then asked them to estimate how many dots of each color they had just seen. Teenagers with the highest … scores also tended to have the best scores in maths tests all the way back to the age of 5, even after measurements of IQ and visual-spatial reasoning skills were taken into account. “There are vast individual differences in the acuity of this number sense in 14-year-olds,” says Halberda [New Scientist].

The researchers did not go so far as to say that mathematic ability is purely genetic, or that a good number sense is the best predictor of grades in math class. “It remains to be seen if one can improve a student’s innate number sense by practice and training, and whether such training will lead to improvements in school math performance,” Halberda said [AFP].

Image: flickr/meneldur

Related Post: Humans May Be Born With the Ability to Do Math

MORE ABOUT: math, numbers
  • Hank Campbell

    Not to rain on the correlation/causation parade but sentences like “individual differences in achievement in school mathematics are related to individual differences in the acuity of an evolutionarily ancient, unlearned approximate number sense” in that study are almost meaningless.

    This study could also mean that kids who are better at math just guess better about the number of objects. A good mechanic also has a better chance of guessing at the problem in my car by the sound than a bad one. That does not make it an ‘ancient’ biological ability.

  • DAW

    That’s a crazy comment, Hank Campbell. The writers of the articles were very careful to say that “an intuitive understanding of numbers that closely correlates with their aptitude for complex math”, and the phrase, “are related to” includes correlational relationships.

    There initial premise before starting the study was that the correlation coefficient between the two things was zero – in other words, that they are uncorrelated. But next, they were found to be correlated, and that is a very important step. The next steps in such studies involve looking for stronger connections. Perhaps a causal connection will be found someday – or a term you’ve probably never heard of, one of them could be “mean-square predictable” from the other, which is a much stronger relationship than merely correlated.

    So, now is not the time to make gripes and complaints. These things progress in a step-by-step matter – just like putting men in orbit is a step towards putting men on the Moon.


  • Everett Williams


    There is nothing new about this type of research. In the early work with children who had hemispherectomies, it was thought that they would need special intervention to be able to perform normally. This turned out not to be the case, but some of the techniques used to train these children produced interesting results. As part of their curriculum, flash cards were used with various numbers of randomly placed symbols. Over time, it was discovered that these children could glance at a group of people or a field full of animals and tell you how many, with great accuracy. Since hemispherectomies are seldom done in this day in time, there is no longer a cohort to test, but it would be interesting to examine the adults to see what their overall mathematical abilities test out to.


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