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Why are Fractions Key To Future Math Success?
by Sue Shellenbarger
Many students cruise along just fine in math until fourth grade or so. Then, they hit a wall—fractions.
The wall is about to get taller. With mastery of the topic seen as a crucial stepping stone to progressing in math, federal standards are stepping up emphasis on fractions starting in third grade. National tests show nearly half of eighth-graders aren't able to put three fractions in order by size.
The government is funding new research on more effective ways to teach the often dreaded subject. The new methods preface early rote learning of complicated fraction rules with more work on building a conceptual understanding of fractions. And instead of traditional pie charts, they rely more on tools like number lines, paper models and games putting fractions in context.
Teachers typically introduce fractions in third grade, explaining denominators—the bottom half of the fraction—as equal parts of a whole. Students study drawings of pizzas cut into wedges and label the fractional parts as fourths or sixths. Lessons then move into memorizing step-by-step rules for adding, subtracting, multiplying and dividing fractions. Some children have trouble grasping what fractions measure. When two pizzas sit side by-side, slices of one divided into sixths may not look that different from slices of another divided into fifths.
Fractions are especially confusing because they break rules third-graders have already learned. Whole numbers increase when multiplied, but fractions get smaller, for example."Those are hard concepts" for children, says Lynn Fuchs, a professor of special education at Vanderbilt University. Teachers using the new method wait to introduce problem-solving until after students understand what denominators and numerators mean, and how fractions compare to each other. Fraction bars and number lines are considered easier than circles for children to draw and divide into parts. They also let students line up fractions in a row and see the difference in size, something they can't do when dividing up a pie in the traditional approach.
Knowing how to place fractions on a number line in third grade is a better predictor of kids' fourth-grade fraction skills than calculation ability, working memory or the ability to pay attention, according to a recent study of 357 children headed by Nancy Jordan. The effect continues at least through fifth grade, based on recent research, Dr. Jordan says.
Another recent study, led by Dr. Fuchs, shows working with number lines made a difference for struggling fourth-graders in 13 Nashville public schools. Using paper and kids' own drawings is a way of making it easy for them to practice many approaches to problem-solving. A child's knowledge of fractions in fifth grade predicts performance in high-school math classes according to a 2012 study led by Bob Siegler, a professor of cognitive psychology at Carnegie Mellon University.
The finding is based on long-term studies of a total of 4,276 students in the U.S. and Britain comparing their scores on math tests at ages 10 to 12, and again at ages 16 to 17. Researchers believe the reason may be that to master advanced math, students must broaden their understanding of how different kinds of numbers relate to each other, and how they must apply different rules as needed when working with different kinds of numbers.
"If you don't understand fractions, it's literally impossible for you to understand algebra, geometry, physics, statistics, chemistry," Dr. Siegler says. "It closes a lot of doors for children." Common Core Standards, which are being implemented in most states, require students to be multiplying and dividing fractions by fifth grade.
Trouble with fractions is the most common reason parents seek math help for their fourth and fifth-graders, says Larry Martinek, chief instructional officer of Mathnasium Learning Centers. Many students are confused by the terms often used to describe fractions, such as "common denominator." Denominators, for example, are "the name of the fraction," rather than simply "the bottom number," Mr. Martinek says. This helps kids understand why they can't add 1/2 and 1/3 and get 2/5, he says. "One apple plus one apple is two apples. One banana plus one banana is two bananas. But one apple plus one banana isn't two banapples."
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