## Knowledge of fractions is critical to success in higher-level math

A child’s knowledge of fractions in fifth grade predicts performance in high-school math classes, even after controlling for IQ, reading achievement, working memory, family income and education, and knowledge of whole numbers, according to a 2012 study led by Bob Siegler, a professor of cognitive psychology at Carnegie Mellon University.

The critical role of fractions in higher-level math makes this news particularly unsettling:

National tests show nearly half of eighth-graders aren’t able to put three fractions in order by size.

This is not a new problem, and was highlighted by the 2008 National Mathematics Advisory Panel report.

A major goal for K–8 mathematics education should be proficiency with fractions (including decimals, percent, and negative fractions), for such proficiency is foundational for algebra and, at the present time, seems to be severely underdeveloped.

It is hoped that more government-funded research will help.

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.

I am suspicious of recommendations that conceptual understanding should always preface procedural knowledge.  This line of thinking has proven to be a trap for students who spend hours on pie charts and brightly colored manipulatives, but then reach high school without knowing how to manipulate fractions.  They seem to get stuck by the tendency among educators to overemphasize the conceptual at the expense of the procedural.  However, it is promising to see the renewed focus on using number lines, a core feature of Singapore Math and other similarly successful programs.

The 2008 National Mathematics Advisory Panel reached a conclusion that seems like a reasonable approach.

As with learning whole numbers, conceptual and procedural knowledge of fractions reinforce one another and influence such varied tasks as estimation, computation, and the solution of word problems. One key mechanism linking conceptual and procedural knowledge is the ability to represent fractions on a number line.