Kim Man-gon's Education Column The Truth About Studying, as Told by a Top-Tier Math Instructor

The virtue of 'effort,' long recognized as a paragon of moral teachings, has become the subject of satirical parody among young people. When we sarcastically cry out "Ef~fort!" in the face of difficult tasks, the days we have lived by such maxims somehow feel embarrassing.

A renowned math instructor said so on a popular talk show. Elementary students become 'math-dropouts' at fractions, middle school students at square roots, and high school students at functions and calculus. While those born with genes for academic success certainly have an advantage, he said it is an excuse to blame not receiving a top score on the College Entrance Exam on lacking such genes.

Why? Because Korea's College Entrance Exam math problems test whether one understands the concepts themselves. It is studying that requires understanding and practice rather than memorization, and anyone can succeed with it.

He also made an important point: calling the answer to a math problem a 'model answer' is undesirable; it should be called 'such-and-such teacher's opinion.' The host laughed it off, but that is a very important perspective that would be good for our primary and secondary schools to adopt as a guideline. Even in elementary schools, some teachers cut off the sprouting of students' thoughts when answers are reached through methods different from the textbook, saying 'when did you start doing things that way?' or insisting the textbook method is faster and more efficient. In the more rigorous learning environment of middle and high schools, students would not even attempt to solve problems using methods different from textbooks or reference books.

He also shared an experience of confronting a student who was inattentive in class, asking why he sat in the lecture room while suffering like that. The point was that being good at math is not an absolute good. Math educators claim that those good at math can also excel at philosophy, music, and other studies, and they point to one or two individuals who have demonstrated such talent. However, they do not mention that there are many people who are not so talented.

There was a problem that he failed to address, which was unfortunate. If Korea's math education is (realistically) aimed at preparing for the College Entrance Exam and one can achieve a top score through effort alone, why aren't students taught to solve problems that few can solve? If students spend 12 years in primary and secondary school or 6 years in middle and high school that way (by which time most students would have already reached a stage of being thoroughly fed up), when should students who wish to pursue mathematics wait? This seems like a question that math education scholars need to answer. After all, achieving a top score on the College Entrance Exam is not the purpose of mathematics education.

An anecdote from that instructor was impressive. Academy instructors only talk about the number of students during company dinners, but during a gathering with school teachers, he heard one teacher worry about how a student would feel if hurt after paying for a school trip out of pocket. He realized there was a world he did not know, and came to think of school as the place where teachers are, as that different world. He then told his students that they should never call him 'teacher' from that point on.

If math education scholars and administrators in charge of math education policy think it is more convenient to maintain and uphold the current College Entrance Exam-oriented policy and see no reason to create unnecessary problems, then the only entity we can reasonably expect to take action is school teachers.

Andrew John Wiles, who solved 'Fermat's Last Theorem,' did not receive the Fields Medal until age 42. How many mathematicians in Korea have missed the Fields Medal after turning 40? There may be many scholars who love mathematics and have devoted themselves to mathematical research. However, if by the time they have become so engrossed in mathematics they are already too old, then the Fields Medal, which is only awarded to mathematicians with sufficient time remaining to conduct research, would be beyond their reach. Some might quip that they are not researching to win an award, but...

There are students who understand more quickly than memorizing, who understand more broadly, more engagingly, and can explore for longer periods. It would be good if there were policies that permit and encourage such students to move ahead. That would be fair education. This is not to say we need something like Korea's 'gifted education' program!

This is not only true of mathematics. It is commonly true across all areas called studying.