Pedagogy Matters: The Fractions Edition

Most education ‘reform’ plans focus on labor management issues, which means little insignificant things like teaching are ignored by our political betters. Myself, I’ve never understood this attitude in academia, where people spend lots of time figuring out what they’re going to teach (curriculum) and how they’re going to teach it (pedagogy). But I digress.

Anyway, one of the big stumbling blocks in K-12 mathematics is fractions:

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.” New federal standards known as the Common Core, 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, a Los Angeles-based franchiser with 385 U.S. tutoring centers.

It appears that how one teaches fractions matters (boldface mine):

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, an education professor at the University of Delaware, Newark’s Center for Improving Learning of Fractions. The effect continues at least through fifth grade, based on recent research, Dr. Jordan says.

I can’t help but think that if a state were to adopt this method, it would see NAEP fourth grade math scores increase by five or ten points (a very rough rule of thumb is that ten points equals one year of schooling), especially in poorly performing states*. It certainly seems that way according to the NAEP Long-Term Trends Report (p.33/31 of the pdf).

Might be worth implementing. Or we could just continue to shriek about Obamacore.

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2 Responses to Pedagogy Matters: The Fractions Edition

  1. Lindsay says:

    Good to know!

  2. edivimo says:

    “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.”

    This quote remind me about the warning against usage of pie charts that I recently learned. It applies with children too.

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