Children struggle with multiplication tables containing 4, 7 or 8: study


Jul 23, 2008
Children can easily recite multiplication tables when it comes to one figure multiplied by the same figure, while it takes longer for them to say tables containing the figures 4, 7, or 8, a Japanese researcher has found.

So Goto, professor at Hokkai-Gakuen University in Hokkaido, discovered the tendency in a study of the multiplication tables, or "kuku" in Japanese.

"I hope this discovery will provide teachers with clues about how to better teach children who perform poorly in arithmetic and help them understand lessons," Goto said.

Children who stumble in early arithmetic education are likely to exhibit poor academic performance in the subject in the long run. Fukuda has devoted himself to studying "kuku" since around 1990 and has announced his research results at several academic societies, including the Japan Society for Educational Technology.

The survey was conducted at a public elementary school in Tokyo, covering 26 third-graders who had just learned the multiplication tables and 26 fourth-graders who had already acquired the times tables as part of their skills set. Fukuda measured the time it took for children to answer after the "kuku" questions were displayed on PCs in front of them. The results were then analyzed by each multiplier and multiplicand.

As a result, children were found to be quicker to reel off answers to questions in which one figure is multiplied by the same figure, such as "3 x 3," as well as to questions containing the figures 2 or 5. Among third-graders, children were slowest in responding to questions that contained the figures 4, 7 or 8. Among fourth-graders, the larger the figures in the questions were, the longer it took them to answer. Children in both grades took longest to give the answer to "4 x 7" -- with third-graders taking an average 2.886 seconds and fourth-graders an average 1.832 seconds. Meanwhile, the questions answered fastest were "5 x 2" among third-graders at an average 1.43 seconds and an average "2 x 5" among fourth-graders.

Professor Goto surmises that children are quicker to answer questions containing the same figures and those containing the number 5 because "those questions are obviously distinctive and more easily retrieved from their memories."

Regarding the weak responses among third-graders to questions containing the figures 4, 7 or 8, Goto said, "Because people memorize the times tables by reciting them aloud, it is likely hard for them to say similar-sounding numbers (in Japanese) such as 4 (shi), 7 (shichi) or 8 (hachi) one after another, resulting in slow responses."