As a 3rd grader can tell you, each number is represented by a single symbol and is followed by a single successor. A number is made bigger through multiplication and smaller with division.
As the Common Core State Standards push for earlier and deeper understanding of fractions, researchers and teachers are exploring ways to ensure students learn more than a sliver of the fractions pie.
“Developmental research shows even very young children have a fundamental grasp of fractions that can be built on through instruction,” said Nancy C. Jordan, a professor of education in the University of Delaware’s School of Education.
But, she added, “If children are taught math in a way that’s very rote, where they memorize procedures … it really doesn’t help you much.”
‘Whole New World’
The traditional approach to teaching fractions can make it more likely for students to show superficial progress without real understanding, some researchers and educators argue.
“We’ve had a tendency in our traditional scope and sequence of math that you teach all this whole number stuff… and then all of a sudden you get to fractions and it’s a whole new world of what to do—everything they learned in whole numbers has nothing to do with how you do fractions,” said Linda M. Gojak, the president of the National Council of Teachers of Mathematics, in Reston, Va. “It’s one of the hardest things for kids to get their heads around.”
Cynthia Hacker, the education director for Sylvan Learning of Irmo/Lexington in Columbia, S.C., sees that confusion a lot. For more than a dozen years, the center has run a week-long “Fraction Action” summer camp, at which students play games using shapes and number lines to compare fractions of different sizes and practice multiplying and dividing mixed and improper fractions.