When I was in high school, classmates often came to me with math questions. Some of them were students I was competing with academically. They understood things quickly. I did not have to explain everything from the beginning. If I pointed out the part they had missed, or the key step where the problem changed direction, they usually picked it up right away. Good students really were quick.
But they were not the only ones who came to me. Sometimes a student who was somewhere in the middle, or even struggling, would come over hesitantly and ask about a problem. With those friends, I had to explain differently. I had to figure out where they had first gotten lost, which concept they had missed, and why a certain formula had to be used in the first place.
At first, I thought I was simply sharing what I knew. If someone asked, I explained as much as I could. If the person asking happened to be a competitor, I did not hide the answer or make the explanation vague. But I did not think of myself as especially generous either. It just felt natural to explain something when someone asked.
Then, little by little, I began to notice something. In order to explain something well, I had to understand it first. A problem I had solved only by instinct would quickly expose me once I tried to explain it out loud. Why this formula? Why this step? Why this condition first? To put those things into words, I had to organize the problem clearly in my own mind.
In the end, explaining math to my friends became a form of studying for me. When I solved a problem alone, it was easy to think I understood it and move on. But when I had to explain it to someone else, my understanding was tested one more time. After explaining it, the memory became clearer. The logic became firmer. A problem I had once spoken through in my own words no longer shook easily. That was why I did not panic much when a test question was slightly changed. I had not merely memorized a formula. I understood why the problem had to be solved that way. By teaching it to someone else, the problem had become truly mine.
I learned something else as well. I learned how to speak from the other person’s point of view. For a strong student, it was enough to point out the key step. For someone who was not yet comfortable with the subject, I had to lower the explanation to their level. The same problem had to be explained differently depending on who was listening. It was not about saying everything I wanted to say. It was about first seeing where the other person was stuck.
That habit stayed with me later in life. Even in ordinary conversations, I tended to listen more than I talked. I tried to sense what the other person was really trying to say, where they were hesitating, and what they still wanted to get off their chest. When you understand people’s words and respond at the right rhythm, without overdoing it, they often begin to speak more comfortably.
Looking back, perhaps that habit began in those high school days, when I was explaining math problems to my friends. I thought I was teaching them how to solve problems. In truth, I may have been learning more from them.
I learned math. I learned how to explain. And I learned how to see things from another person’s level.
There is a saying that the person who teaches learns the most. To me, that is not just a nice phrase. It is something I have confirmed many times in my own life.