조용히 무너지는 자리Where Students Quietly Give Way

The student types and example dialogue in this essay combine observations of several students. They are not records of an identifiable student or reconstructions of an actual conversation.

Too fast, even for the highest class

Even the highest class in the medical-track division said my lessons were too fast. This was in 2024, when I first taught at Gangnam Daesung Boarding Academy’s medical-track division. I taught at my own pace. The class’s high ranking did not justify that speed.

On teaching days, I got up before dawn and took the shuttle from Gangnam Daesung to the boarding academy in Icheon. I taught a class working through Daesung’s materials, in front of students who had moved into a boarding academy to prepare for medical school. I could solve and explain the problems. Whether the students could follow was a separate matter.

A lesson being too fast need not simply mean that the teacher speaks too quickly. While the teacher explains one line, a student may still be thinking about the reason for the previous one. Before moving on, the teacher needs to check what the student knows. What mattered to me was that even a high-scoring student might understand less than I expected.

I learnt that from students who came to ask questions. Assuming they knew something because their marks were high could leave a gap unnoticed. Knowing a student’s grade and knowing whether they understood the concept I was explaining were separate checks. My own mathematical ability could not do that checking for me.

After the student says yes

So I open a lesson with a simple question about the knowledge it requires. If students say they know it, I ask again to find out whether they really do. For a lesson on exponential functions, this could be illustrated as follows. “Do you know the laws of indices?” “Yes.” “What is two to the power of zero?” “One.” “Why one?” This is an example of what I want to check, not a transcript of an actual student conversation.

A student who remembers that the answer is one may stop when asked to explain why. Simply repeating the correct answer is not all the teacher needs to do. I need to know which rule the student knows and which connection they have missed before choosing the next explanation. There also needs to be room for the student to answer in their own words.

Some students will not write their working even when asked. I do not force them. Sometimes they have to make a mistake before they understand. I, too, developed the habit after getting things wrong by working only in my head. I just hope the exam in which they learn that lesson is not an important one.

As a teacher, you often have to repeat something you already know. A student may still be working towards accepting it. Remembering that I only began writing things down after making mistakes, I cannot expect a habit to change because I have said something once.

Working hard and getting nowhere

There was more than one way for students to drift away from their studies. The types below are composites. One student says, “I’m going to retake the year anyway.” There is still time left, but their mind has already moved on to next year and this year’s work is being put off. Giving that student more problems is not enough.

Their surroundings matter too. Some spend their time gaming with friends who do not study; others change as they spend more time with friends who work hard. Talking only about willpower can obscure whom a student spends each day with and what they actually do.

Then there is the student who works through several problem books, keeps an error notebook and watches online lectures, yet stays in the same place. It is difficult simply to tell that student to work harder. I need to see whether they check only the answer and move on, and whether they can use a supposedly understood concept alone. That kind of studying is what I tried to examine at length in the study book.

I hear related concerns in conversations with parents. “My child is bright, but…” Calling a child bright does not get the studying done. “They would do well if only they studied…” They need something that helps them start and continue. “They get things they know wrong.” Being able to use what you know correctly in an exam is part of your ability. I wrote the practical responses to these three questions separately in Don’t Solve Math in Your Head.

I look for changes in behaviour before marks: whether a student who only read solutions now writes their working, or whether someone who checked only wrong answers now examines why a correct one is right. A change in behaviour cannot promise an immediate improvement in marks. It does, however, let me see more precisely what studying is taking place.

I also taught students retaking their entrance exams at Daesung’s repeat-year programme. Some thought they knew material because they had studied it before, but gaps appeared when they tried to solve problems. Among grade-10 and grade-11 students, I saw children acknowledge what they did not know and approach learning eagerly. That was one reason I wanted to teach that age group. I do not mean it as a rule dividing all repeat-year students from all younger ones. These are people I met in class.

What the camera cannot show me

In Daesung MyMac’s live courses, Daeinra and Gangdae K Final, I taught practice-exam lessons in the latter half of the year. In a classroom, I can see a hand stop moving or a student’s eyes leave the problem. In front of a camera, I cannot. Not being able to check immediately how far students have followed was difficult.

At the boarding academy, I could hear that I was going too fast and reconsider the pace I needed to match. In an online lecture, my explanation keeps going even if a student on the other side of the screen stops. I therefore had to think about both recording a good explanation and finding out whether a student had followed it.

I have developed several ways to address that problem and intend to explain the details separately. I do not want to claim their effects in advance here. Having been told that I was too fast even for the highest class, I cannot assume that no one beyond the camera will struggle.