We all know people who, it seems, just can’t get mathematics. I was once in a store, buying a $10.00 item that was on sale at 15% off. The salesperson got into a bit of a dither looking for a calculator to perform this abstruse computation, and was amazed when I said the price should be $8.50. As she rang up the sale, she told me, “I was good at math, but I never could do fractions.”
According to some new research, described in a press release from the University of Waterloo, this story is more representative than it might at first appear. Traditionally, the view of educators has been that “math anxiety” hindered students in intermediate to advanced courses (from algebra onwards), but didn’t affect their ability to do simple arithmetic tasks But, according to this research (abstract), even very basic tasks, like counting, are affected. The study compared matched groups of students that had high and low scores on a math anxiety test, and evaluated their performance in a simple test that involved counting the number of black squares displayed on a computer screen.
In two experiments, 28 undergraduate students – 14 with low math anxiety and 14 with high math anxiety – were shown a set of black squares on a computer screen. The squares ranged in number from one to nine and participants were simply asked to identify the number of squares.
An interesting pattern was observed in the results. When the number of black squares was in the range 1 to 4, both groups of students did equally well on the test. However, when the number of squares was 5 or more, the high math anxiety group performed significantly worse.
The differences in the number of squares correspond to two apparently different mental processes that people use to answer the question “How many?”. When the number is small (1-4), the person typically just “gets” the number, without consciously counting, a process called “subitizing” (cf. Latin subitus, “sudden”). When the number is greater, the person consciously counts, and the process takes noticeably longer. (It’s interesting, and perhaps related, that all human languages, even in very primitive societies, have words for small integers, such as “one”, “two”, “three”. Once the number gets bigger than 5-7, most primitive languages just have a word for “many”.)
It appears that, once conscious effort is involved, math anxiety kicks in with visible effects. The researchers go on to suggest, in the paper’s conclusions, that math anxiety somehow compromises the capacity for working memory. In any case, gaining a better understanding of the sources and effects of math anxiety is a worthwhile goal for educators. You can’t always count on finding your calculator.