South Korea has some of the highest math scores in the world. On the 2012 PISA math test, the mean score for a South Korean student was 70 points higher than for an American student. Lots of theories have been floated about why South Korean students do so much better than their American peers: longer school days, higher parental involvement, greater cultural investment in the value of education. One factor that does not seem to be driving the gap, though, is better textbooks. A study published in the February issue of Educational Studies in Mathematics compared American and South Korean high-school math textbooks and found the American ones to be more challenging overall.
Dae S. Hong and Kyong Mi Choi analyzed the South Korean textbooks Mathematics 9A and 10A alongside the American Core-Plus Mathematics Project books, a standards-aligned series used by more than 500 high schools. They discovered that while the South Korean books introduce some topics earlier, the American books had more problems on average per lesson. More important, the problems in the American books were on a higher cognitive level. Hong and Choi write:
Korean textbooks provide fewer opportunities for students to solve, explain, and reason about mathematics problems using multiple representations than CPMP students and CPMP students have more opportunities to solve problems with higher level cognitive demand. Our findings indicate that CPMP students are involved in more meaningful and desirable material to learn mathematics.
The authors acknowledge that relatively high complexity of the problems in American textbooks "seems to conflict with American students' struggling in international comparative studies." So why are American students behind in math when their textbooks are better? One answer is that the Americans who take the international assessments might not be using the CPMP textbooks. In South Korea, there's a national curriculum; as a result, according to the authors, "the content in all textbooks is almost identical." In America, on the other hand, curriculum decisions are left up to the states, and there are wide variations among textbooks. The CPMP is a popular series, but it is not representative of all the country's math textbooks in the way that the South Korean books in the study are.
Another answer the authors point to is quality of instruction: "the missing link between what textbooks potentially offer to students and what students actually learn is the significance of teacher's role," they write. A textbook is only as good as the teacher who uses it. It's the teacher who helps explain the concepts in the textbook; it's the teacher who tells her students which problems to complete. If she can't explain those concepts clearly, or assigns only the easy problems, a great textbook loses a lot of its value. Conversely, a great teacher can do a lot with a mediocre textbook. She can fill in the areas where the book is confusing or cursory in its descriptions; she can write her own, more challenging problems.
South Korean students spend a tremendous amount of time each day receiving academic instruction. After a full school day, they report to "hagwons" for additional drilling and tutoring. Some of the hagwon teachers are in such high demand that they make six or seven figures a year. These are the sort of instructors who don't need a good textbook to be effective.
This is a lesson worth remembering as the United States continues to roll out the Common Core, new math and language arts standards intended to improve American students' academic performance. No matter how high these standards are, the push to implement them will fail if teachers don't know how to teach them.