SALT LAKE CITY — Over the last 30 years, U.S. high school students have been falling behind their counterparts in China, Japan, Finland, the Netherlands and Canada in mathematics achievement.

The source of the achievement gap, according to a new study: inadequate understanding of fractions and long division. Among grade five students, a team of researchers at Carnegie Mellon University led by Robert Siegler found a strong positive correlation between students' understanding of fractions and long division and their ability to learn more complex mathematics.

The results of the study, according to Siegler, provide important cues about how to improve mathematics performance. “We need to improve instruction in long division and fractions, which will require helping teachers to gain a deeper understanding of the concepts that underlie these mathematical operations,” he said.

Spatial skills are also predictive of success in mathematics, according to a new study. Researchers at the University of Chicago "found that young children who understand how shapes fit together are better able to use a number line and to solve computation problems," reports MindShift. Moreover, students with strong spatial skills at an early age also scored highest on measures of mathematical ability at age 8.

Parents can help their children develop spatial skills, according to Temple University psychology professor Nora Newcombe. She found that parents and children who play with blocks were more likely to use spatial terms like “over,” “around” and “through” than participants who play with pre-assembled toys. Hearing and voicing such words together improves children's spatial awareness, according to Newcombe.

Similarly, researchers at the University of Chicago report that the number of spatial terms (like “circle,” “curvy” and “edge”) parents used while interacting with their toddlers predicted how many of these kinds of words children themselves produced, and how well they performed on spatial problem-solving tasks at a later age.

Fractions are key for sucess in mathematics

Robert Siegler discusses the importance of learning fractions.