Can teaching methods change the way children understand numerical representation?

According to John Opfer and Robert Siegler in their research on the “Development of Quantitative Thinking”, young children have a difficult time visualizing numbers on a number line, which changes over time. Nonsymbolic numbers, ones where the numerical properties are implicit, such as there being 4 or 10 of something, develops in infancy. However, the symbolic numbers, the word five or the heard number 8, don’t develop their exactness until later in childhood.

In Elizabeth Green’s article “Why Do Americans Stink At Math?” she discusses the possibilities with why children are not confident in their mathematical abilities, beginning at a very young age. She introduces a Japanese elementary school teacher who taught his classes according to American studies on more efficient teaching methods for math. Though, when he had the opportunity to come to America and observe grade school classes none of the teachers had switched from the classic teaching methods to the new efficient ways.

Could our classical American teaching methods be slowing down the rate of development in number representation? According to Green, students are not encouraged to learn methods to understanding basic arithmetic or the relationship between numbers, but they are merely taught to practice a system to add or subtract, without having that basic understanding that is necessary to build a mathematical foundation.

If Opfer and Siegler’s research was taken to Japan, where most students are taught the importance of understand the relationship between numbers and inventing and really thinking about the equations, would the outcome be different? If children are taught from an early age to visualize numbers so they can manipulate them easier to solve equations, then will the age at which symbolic numbers are recognized and correctly understood on a number line become lower?

Whether or not numerical representation changes because of a different teaching technique, it should be important for Americans to change the way that math is taught in schools to better prepare students for higher level thinking. Technique is important, but basic understanding of relationships between numbers is a much more essential tool for learning mathematics, and, who knows? Children might even begin to enjoy their math classes!

           

Opfer, J. E., Siegler, R. S., (2012). Development of Quantitative Thinking. The Oxford Handbook of Thinking and Reasoning, 585-605.

Green, E., (2014). Why do Americans Stink at Math?. The New York Times, MM22. Retrieved from http://www.nytimes.com/2014/07/27/magazine/why-do-americans-stink-at-math.html