Confronted with a simple mathematical problem, most children ages 4 to 6 can use algebraic concepts intuitively to solve for a hidden variable, say researchers.

“These very young children, some of whom are just learning to count, and few of whom have even gone to school yet, are doing basic algebra and with little effort,” says Melissa Kibbe, a post-doctoral fellow at Johns Hopkins University. “They do it by using what we call their ‘Approximate Number System:’ their gut-level, inborn sense of quantity and number.”

Kibbe, lead author of a report in the journal *Developmental Science*, says the “Approximate Number System,” or “number sense,” is the ability to quickly estimate the quantity of objects in their everyday environments. Humans and a host of other animals are born with this ability, probably an evolutionary adaptation to help them survive in the wild, scientists say.

Previous research has revealed that adolescents with better math abilities also had superior number sense when they were preschoolers, and that number sense peaks around age 35.

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### ‘Magic cups’

Kibbe, working in the Johns Hopkins lab of Lisa Feigenson, associate professor of psychological and brain sciences, wondered if preschool children could harness that intuitive mathematical ability to do something akin to basic algebra. The answer was “yes,” at least when the algebra problem was acted out by two furry stuffed animals—Gator and Cheetah—using “magic cups” filled with objects like buttons, plastic doll shoes, and pennies.

Children sat down individually with a researcher who introduced them to the two characters, each of whom had a cup filled with an unknown quantity of items. Children were told that each character’s cup would “magically” add more items to a pile of objects already sitting on a table. But children were not allowed to see the number of objects in either cup: they only saw the pile before it was added to, and after, so they had to infer approximately how many objects Gator’s cup or Cheetah’s cup contained.

At the end, the examiner pretended that she had mixed up the cups, and asked the children—after showing them what was in one of the cups—to help her figure out whose cup it was. The majority of the children knew the correct answer, revealing for the researchers that the pint-sized participants had been solving for a missing quantity, the essence of basic algebra.

“What was in the cup was the x and y variable, and children nailed it,” says Feigenson, director of the Laboratory for Child Development. “Gator’s cup was the x variable and Cheetah’s cup was the y variable. We found out that young children are very, very good at this. It appears that they are harnessing their gut level number sense to solve this task.”

### Why’s it so hard?

If this kind of basic algebraic reasoning is so simple and natural for 4-, 5-, and 6-year-olds, the question remains why formal, more complex algebra problems can be so difficult for teens and others.

“One possibility is that formal algebra relies on memorized rules and symbols that seem to trip many people up,” Feigenson says. She and her team want to explore if encouraging teachers to foster children’s gut-level ability—which they can use long before mastering symbols—can help.

“Teachers may be able to help children master these kind of computations earlier, and more easily, giving them a wedge into the system,” Feigenson says.

The researchers also found that ANS aptitude does not split across gender lines. Boys and girls answered questions correctly in equal proportions during the experiments, the researchers say.

Although other research shows that even young children can be influenced by gender stereotypes about girls’ versus boys’ math prowess, “we see no evidence for gender differences in our work on basic number sense,” Feigenson says.

The National Science Foundation and the National Institute of Child Health and Human Development supported the research.

*Source: Johns Hopkins University*