A Global Look at Math Instruction

In this article by Ji-Won Son, the author shares a glimpse of how the concept of fractions is taught in Korea. Korean students consistently outrank American students in mathematics according to many international studies, hence the authors curiosity as to their methods. When comparing the Korean curriculum to that of the USA, Korean students are exposed to fraction concepts sooner and are advanced more quickly than what is recommended by the NCTM in their Curriculum Focal Points. Of the five possible meanings of fractions (part-whole, measure, quotient, ratio, and operator), three are introduced in third grade (part-whole,  operator, and measure). The Korean textbooks begin using similar initial representations of fractions as those used in the USA, such as the sharing a single piece of food or paper among a group of people. In addition, they use discrete models, such as sharing multiple pieces of candies or buns. Only after these contexts have become familiar, do the Korean texts introduce measurement. It is suggested that this use of multiple models my improve students understanding and conceptual flexibility. In addition, the Korean books display a fractional part separately from the divided, yet unshaded, whole. The author postulates that students better appreciate the value of the denominator in a fraction by this alternate representation. Finally, the Korean texts employ many leading questions that act as verbal cues, guiding students through the necessary logic to complete the problem correctly.  While the author does not wish to announce the Korean method as superior, it is clear there is much to be learned from these techniques.

There is no end to what I am going to learn in this class. Before this article I had never heard of a nonunit fraction. (It would appear that spell-check hasn't either.) From my own life experience I was well aware that different countries taught math differently. I moved from the Canada to the US in second grade. I returned to Canada in 8th grade. In the process I missed half a year of geometry and algebra. This article has convinced me to be open to new ideas, not only from my local colleagues, but from around the world. It is amazing to me that a simple change in how a concept is presented or how a question is asked can make such a big difference. I particularly liked how they present the shaded fraction as separate from the divided whole. I will most definitely borrow that technique. I found myself wishing I was more familiar with how American texts present fractions. I will be eyeing my daughter's math homework in the coming weeks. I will also be sure to use both discrete and area representations. I can appreciate how measurement might pose a challenge to many students, but the Korean style of questioning makes the relationship between area models and measurement rather apparent.  Asking the right questions the right way: the secret to teaching fractions.

Son, Ji-Won. (2011). A global look at math instruction. Teaching Children Mathematics 17(6), 360-370.