Think Right to Do Right in Geometry

November 19, 2008

A combination of verbal and spatial strategies, rather than shape-based imagery strategies, is the best approach to finding solutions in geometry, says a new study published in the journal Mind, Brain, and Education.

Researchers investigated whether middle school students solved geometry problems more successfully that their peers when they received clues consistent with their own style of thinking. They focused on three styles of thinking: verbal deductive, spatial imagery, and object imagery. Participating students took a geometry test in which each problem could be solved on the basis of verbal reasoning clues, mental rotation clues, or shape memory clues.

For geometry problems having either mental rotation or shape memory clues, students with a combination of both verbal and spatial cognitive styles tended to do best. For problems with verbal reasoning clues, students with either a verbal or a spatial cognitive style did well, with each cognitive style contributing to mathematical success. Thus, both spatial imagery and verbal deductive cognitive styles turned out to be important for solving geometry problems, whereas object imagery was not.

For girls, a spatial imagery cognitive style was advantageous for geometry problem solving, regardless of the type of clues provided.

"Our research may have an impact on the teaching of geometry, and perhaps mathematics in general," the researchers state. "Specifically, teaching students how to think spatially and manipulate and hold in mind images may improve their performance in geometry class."

"Thus," they concluded, "it is important for students to consider other thinking styles than approaches usually taught in most introductory geometry classes in the U.S."

The results appear in the article titled "Performance on Middle School Geometry Problems With Geometry Clues Matched to Three Different Cognitive Styles," by Karen L. Anderson (Stonehill College); M. Beth Casey (Boston College); William L. Thompson (Harvard University); Marie S. Burrage (Harvard University); Elizabeth Pezaris (Northeastern University); and Stephen M. Kosslyn (Harvard University).

Source: Mind, Brain, and Education, Nov. 12, 2008