Salah satu mitos dalam belajar matematika, tentang berpikir lambat
This is true for all levels of math. It is extremely beneficial to struggle and to make mistakes on math problems as that will create synapse firing and brain growth. The most successful students are not those who don’t mess up, they are the ones who mess up and learn from it and continue on.
Something else that is really important to know about math is that being good at math does not mean being fast at math. In fact the opposite may be true.
Mathematicians, who we could think of as the world’s top math people are some of the slowest math thinkers I have met. I don’t say that to disrespect mathematicians, I work with many mathematicians, but they are not usually fast math thinkers. They are deep mathematical thinkers.
This is Laurent Schwartz. He won the Fields Medal which is the top math prize. It’s like winning an Oscar in math. He struggled in school because his school valued speed, and he was one of the slowest math thinkers in his class. After he became very successful he wrote an auto-biography, and this is how he describes his school days.
“I was always deeply uncertain about my own intellectual capacity. I thought I was unintelligent. And it is true that I was, and still am, rather slow. I need time to seize things because I always need to understand them fully. Towards the end of the eleventh grade, I secretly thought of myself as stupid. I worried about this for a long time. I’m still just as slow. At the end of the eleventh grade, I took the measure of the situation, and came to the conclusion that rapidity doesn’t have a precise relation to intelligence. What is important is to deeply understand things and their relations to each other. This is where intelligence lies. The fact of being quick or slow isn’t really relevant.”
Many strong mathematical thinkers, like Laurent Schwartz, think deeply and slowly and like to understand things fully. If you are one of those people do not be put off by people who may be faster, that isn’t important. What is important, to repeat Laurent Schwartz, is to deeply understand things and the way they relate to each other.
It is fine — good even — to think slowly about math and it is really good to think deeply and ask questions that will allow more depth Questions like why does this work? How is this method connected to other methods? What would a drawing of this situation look like? And its important if you are a slower thinker never to think it means you cannot be a math person. It is great to think deeply and carefully, to fully understand, to ask questions, we need those thinkers in math.
Doing well at math is not about being quick or slow. It is about thinking about connections, thinking deeply Laurent Schwartz talks about deeply understanding things. But how do you do that?
In the next and last 3 sessions of the course we are going to give you learning strategies, which will help you learn deeply and well.