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Kids can learn algebra from age four to six, say scientists

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Most preschoolers and kindergarteners, or children between four and six, can do basic algebra naturally using their Approximate Number System, say scientists in a new study. Why struggle through 'brutal' algebra courses that you may attribute to not being good at math, when you can learn algebra in kindergarten?

Can learning algebra as a preschooler help kids from developing math anxiety later on in middle school? Can it open doors to more occupations that require advanced math, such as college-level science, medical, or technical courses later on when some students choose their major based on whether or not they can pass math classes required to take other courses?

You can check out the abstract of the new study, "Young children ‘solve for x’ using the Approximate Number System," published March 3, 2014 in the journal Developmental Science. Or see, "Early View (Online Version of Record published before inclusion in an issue)."

Millions of high school and college algebra students are united in a shared agony over solving for x and y, and for those to whom the answers don’t come easily, it gets worse: Most preschoolers and kindergarteners can do some algebra before even entering a math class. You can check out the YouTube video, "Are You Smarter Than a 5-Year Old? Preschoolers Can Do Algebra, Psychologists Find."

In a recently published study in the journal Developmental Science, lead author and post-doctoral fellow Melissa Kibbe and Lisa Feigenson, associate professor of psychological and brain sciences at Johns Hopkins University's Krieger School of Arts and Sciences, find that most preschoolers and kindergarteners, or children between 4 and 6, can do basic algebra naturally.

“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,” Kibbe says, according to a March 6, 2014 news release, Are you smarter than a 5-year-old? Preschoolers can do algebra. “They do it by using what we call their ‘Approximate Number System:’ their gut-level, inborn sense of quantity and number.”

Number sense lets preschoolers quickly size up the quantity of objects

The “Approximate Number System,” or ANS, is also called “number sense,” and describes humans’ and animals’ ability to quickly size up the quantity of objects in their everyday environments. Humans and a host of other animals are born with this ability and it’s probably an evolutionary adaptation to help human and animal ancestors survive in the wild, scientists say.

Previous research has revealed some interesting facts about number sense, including that adolescents with better math abilities also had superior number sense when they were preschoolers, and that number sense peaks at age 35. Kibbe, working in Feigenson’s lab, wondered whether preschool-age children could harness that intuitive mathematical ability to solve for a hidden variable, or in other words, to do something akin to basic algebra before they ever received formal classroom mathematics instruction.

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

In the study, children sat down individually with an examiner 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 and 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 whose cup it was, a finding that revealed for the researchers that the pint-sized participants had been solving for a missing quantity, which is the essence of doing basic algebra.

“What was in the cup was the x and y variable, and children nailed it,” says Feigenson, according to the news release. Feigenson is the director of Johns Hopkins 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.”

If this kind of basic algebraic reasoning is so simple and natural for 4, 5 and 6-year-olds, the question remains why it is 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 in the news release. “So one of the exciting future directions for this research is to ask whether telling teachers that children have this gut level ability – long before they master the symbols – might help in encouraging students to harness these skills. Teachers may be able to help children master these kind of computations earlier, and more easily, giving them a wedge into the system.” While the ANS helps children in solving basic algebra, more sophisticated concepts and reasoning are needed to master the complex algebra problems that are taught later in the school age years.

Another finding from the research was that an ANS aptitude does not follow gender lines. Boys and girls answered questions correctly in equal proportions during the experiments, the researchers says, according to the news release. 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 explains in the news release.

Parents with numerically challenged kids shouldn’t worry that not showing a strong aptitude with numbers is a sign that Bobby or Becky will be bad at math

The psychologists say it’s more important to nurture and support young children’s use of the ANS in solving problems that will later be introduced more formally in school. “We find links at all ages between the precision of people’s Approximate Number System and their formal math ability,” Feigenson says in the news release. “But this does not necessarily mean that children with poorer precision grow up to be bad at math. For example, children with poorer number sense may need to rely on other strategies, besides their gut sense of number, to solve math problems. But this is an area where much future research is needed.” This research was supported by the National Science Foundation (NSF Living Lab 1113648) and the National Institute of Child Health and Human Development (NIH R01 HD057258).

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