American math teachers frequently complain about the mastery level of their incoming students. College professors are frustrated because they find themselves having to teach high school level material. High school teachers are frustrated because they have to teach middle school material. Middle school teachers are frustrated because they have to teach elementary school material.
Evidence backs up their collective lament. According to multiple international assessments, American high school students rank in the bottom half of industrialized countries when it comes to math achievement. Numerous East Asian countries boast much better test scores and content retention even though countries like China, Japan, and South Korea spend less per student and often have larger class sizes.
So what are teachers in East Asia doing that helps students retain what they learn? Turns out, there is a key difference in pedagogy that Western teachers can emulate.
Lesson Structure in the U.S.
In the United States, a typical math lesson looks something like this:
 Teacher introduces and explains a new concept
 Teacher demonstrates several sample uses
 Teacher gives students related problems to solve in class
 Students complete homework and eventually take a quiz, both of which contain similar problems to the ones in class
A lesson on exponents, for example, would begin with the teacher writing 2^3 on the board, telling everyone that it signifies 2 × 2 × 2, and then giving more examples. The second half of the lesson would be arithmetic problems where students compute 3^3, 5^3, and so on and so forth.
A general rule of communication is that what you end with is what you emphasize. Therefore, in the lesson structure described above, the emphasis is on problem solving, not on the actual mathematical concept. The implicit and often explicit lesson to students is:
“Don’t worry about understanding the math: just try to get the questions right.”
It turns out that this method may be less than optimal, both for learning math and also for acing standardized tests.
Lesson Structure in Japan
Japanese classrooms, by contrast, use the exact opposite structure. A typical math lesson in Japan looks something like this:
 Teacher presents a problem
 Students attempt to solve this problem using their existing understanding.
 The teacher works with the class, using the process to help students deduce a new concept.
For example, in Japan, instead of just explaining the rules for exponents and then spending forty minutes on practice problems, the teacher will start by showing students 2^3 = 8 and 3^2 = 9 and focus on getting students to see the pattern and deduce what operation leads to these results.
By “proving” the mathematical concepts and making them the focus of the lesson, East Asian teachers can significantly improve longterm retention of content.
Takeaway
The goal in all teaching is to leave students with the feeling “I have this new skill / understanding that I did not have at the start of class!” instead of “Great, now I may do a little better on my standardized tests.” The latter sentiment motivates only the highachievers and sends the message that what you are teaching lacks intrinsic value.
Though this lesson structure is particularly applicable to math, it can be applied to almost any subject. Making an effort to ensure students understand the concepts involved rather than just demanding rote memorization will pay off in the end.
If you’re a teacher looking for new ways to engage your students, try it out!
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