Okay class, solve this problem: 1+2+3=1+ ___. Pencils down. When you were 9 years old chances are you ignored the equal sign and added up all the numbers, arriving at the wrong answer of 7, or you added only the numbers to the left of the equal sign, incorrectly giving you 6, says Notre Dame cognitive psychologist Nicole McNeil. The equal sign would have been a mystery.
In a study of elementary school children ages 7 to 11, the assistant professor of psychology found that 9-year-olds were the least likely to correctly solve equivalence problems. Ironically, she suspects the reason may be that they have learned their arithmetic too well.
Younger children, even preschoolers, appear to have a grasp of equivalence, but as they learn arithmetic many lose that understanding, bottoming out around age 9. Most eventually regain an understanding as they grow older, McNeil says. “When you ask them what the equal sign means, they will tell you it means ‘total’ or ‘put your answer.’ And those answers predict later problems understanding algebra.”
Children pick up on the operational patterns of their math instruction, the ND researcher observes. “If you think about it, when we teach arithmetic, we almost always have the mathematical operations on the left side of the equal sign, never the right,” she says. “Children internalize that structure, so when they see a math problem they think it must have operations only on the left.” They also tend to treat all numbers the same, McNeil adds. Therefore, if a problem calls for addition and they don’t understand the equal sign, they may ignore it, merely adding up every number.
Interestingly, Asian children are not as confused by the equal sign as American children, and McNeil believes it may be significant that early on in their math training the Asians are exposed to operations on both sides of the equation. Her current research is focused on identifying specific practices in American math instruction that contribute to students’ later confusion.