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Approximate Number Sense: Preschoolers can do Algebra without learning How to

Apparently, some preschoolers who are able to do Algebra before entering secondary schools may not necessarily be genius after all. At least, this is what this study found out.

Researchers from Johns Hopkins University’s Krieger School of Arts and Sciences found that most preschoolers and kindergarteners, or children between 4 and 6, can do basic algebra naturally. What was more surprising was that these children were either learning to count or had only just started to attend school. They used a system called ‘Approximate Number System:’ their gut-level, inborn sense of quantity and number.

What is Approximate Number System?

Also known as ‘number sense’, it describes humans’ and animals’ ability to quickly size up the quantity of objects in their everyday environments. Some preschoolers with naturally better number sense will tend to go on to have better math achievements and this number sense will peak at 35 years of age.


 

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How the Study was Conducted

In the study, children sat down individually with an examiner who introduced them to two furry stuffed animals – Gator and Cheetah and each of whom had a cup filled with an unknown quantity of items. The items were buttons, plastic doll shoes and pennies. Children were told that each character’s cup would “magically” add more items to a pile of objects already sitting on a table.

However, the 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 interesting to note was boys and girls answered questions correctly in equal proportions during the experiments. In short, the myth that boys were better at maths did not hold water.


 

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Then Why is Algebra so Difficult for Teens?

With preschoolers able to handle algebra naturally, one reason that researchers guess why algebra is difficult for teenagers is due to the memorized rules and symbols for the various algebra formulas.  One way to tackle this problem, researchers suggest, is to encouraging students to harness ANS before introducing and mastering symbols to trip them up.

Another thing to note is that 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.

Source
Melissa M. Kibbe, Lisa Feigenson. Young children ‘solve forx’ using the Approximate Number System. Developmental Science, 2014

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