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Of Culture, Calculators, Math Anxiety And How We Learn

Two studies that suggest how everything from culture and instruction to anxiety can support or inhibit success in math appear in the June 2001 issue of the Journal of Experimental Psychology: General, published by the American Psychological Association (APA).

Psychologists Jamie Campbell, Ph.D., and Qilin Xue, Ph.D., of the University of Saskatchewan, Saskatoon, report in "Cognitive Arithmetic Across Cultures" on a straightforward study that compared the math performance and strategies of three groups of students who either were educated in different places or grew up in somewhat different cultures, resulting in interesting findings about their differing math performance, especially for complex math.

Specifically, Campbell and Xue asked Canadian college students in each group -- Chinese educated in the People's Republic of China, Chinese educated in Canada, and non-Chinese educated in Canada -- to solve simple and complex arithmetic problems and to report how they solved them.

Both Chinese groups were better at simple math no matter where they had gone to school, but only the China-educated Chinese were better (far better, at that) at complex math.

Campbell and Xue assess the possible reasons why: "Better performance on the complex arithmetic was associated with lower reported calculator use in elementary and secondary school," says Campbell. "This does not imply that those who used a calculator more performed very poorly or that only differences in calculator use explain the performance differences."

Complex arithmetic places special demands on short-term memory skills that simple arithmetic usually does not, because complex arithmetic involves operations such as carrying, borrowing and place-keeping.

"This is demanding mental juggling for most people's short-term working memory processes," says Campbell. "Using a calculator might restrict the level of expertise achieved with respect to short-term memory skills for complex arithmetic."

Should students throw away their calculators? Educators may require more research before making a recommendation. For now, this study suggests only that calculator use correlates with lower performance at complex math. For math overall, the superior simple-math performance of both groups of Chinese students suggests that outside cultural factors also matter.

Campbell and Xue discuss previous research that implicates social and educational influences on math performance, such as (at least among the Chinese) family support and stress on achievement, extracurricular instruction and more.

"Performance differences apparently involve multiple factors, such as differences in formal and informal pedagogy, culture-specific attitudes, culture-specific differences in tool usage such as the abacus and calculator, different linguistic influences, etc.," says Campbell. "These factors may interact in rather complex ways."

In a different study, approaching math competence from the vantage point of problems, Mark Ashcraft and Elizabeth Kirk, both then at Cleveland State University (Kirk is now with Florida State University) examined "The Relationships Among Working Memory, Math Anxiety, and Performance."

By finding that people with high math anxiety had smaller spans of "working memory" (temporary, not long-term, storage) when doing math (in particular computation), the authors started to "tease out" the underlying cognitive mechanisms at work in this vexing problem.

Shorter working memory was associated with slower, more error-ridden performance, suggesting that anxiety constricts working memory, which, in turn, hurts math performance.

Until recently, say Ashcraft and Kirk, studies of math anxiety did not probe what actually goes on mentally when math-anxious people do math. It has long been speculated that anxiety disrupts working memory by presenting afflicted individuals with distracting worrisome thoughts.

The authors propose that math anxiety worsens performance in two ways: First, it leads to avoidance, which leads to lower competence; second, it temporarily inhibits working memory capacity, possibly by failure to inhibit attention to intrusive thoughts.

The authors also propose a timeline showing how math anxiety can, by harming working memory, significantly interfere with learning and mastery during early middle school, when students originally learn difficult arithmetic and math.

The findings might explain why, says Ashcraft, "the most effective interventions for math anxiety are the cognitive-behavioral ones," -- in other words, help with managing the anxiety itself.

"Our results," he continues, "certainly suggest that spending 'mental time' worrying about your anxiety is exactly what disrupts working memory and performance. The anxiety reaction is causing the problem, not some deep-seated deficiency at math. Math anxiety is learned, so it can be unlearned and overcome."

(Article: "Cognitive Arithmetic Across Cultures," Jamie I.D. Campbell and Qilin Xue, University of Saskatchewan, Saskatoon, Saskatchewan, Canada; Journal of Experimental Psychology: General, 2001, Vol. 130, No. 2.)

Full text of this article will be available after June 3 at this URL.

(Article: "The Relationships Among Working Memory, Math Anxiety, and Performance," Mark H. Ashcraft and Elizabeth P. Kirk, Cleveland State University; Journal of Experimental Psychology: General, Vol. 130, No. 2.)

Full text of this article will also be available after June 3 at the same URL.

[Contact: Jamie Campbell, Mark Ashcraft]






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