It occurred to me that I never really understood mathematics, even while I was studying it in University. As a student, perhaps I believed it was the job of my teachers to give me understanding. More likely is that I did not desire understanding at all. Instead, I was working only to get good grades because that is often the misguided goal in schools throughout history.
As a student, you end up memorizing a bunch of facts, placing them in your short-term memory, soon to be forgotten. Real learning happens when you direct your own mind toward understanding, which places concepts in your long-term memory. It seems to me that I started to really understand math, almost at the same time I began teaching, rather than studying math. It is helpful to think about the reasons for this and it is my desire that this exploration will help you too.
In my opinion, I developed a strong desire to understand, because I wanted to be confident in the classroom. Without understanding, how could I ever hope to have my students understand math? I discovered my own mind, when I realized I could sit down and think, and solve problems on my own. It turned out I did not need someone else to teach me everything, and I learned way more when I discovered things for myself. I believe this has a lot to do with the fact that I was not being marked, so I was free to explore and enjoy the learning process for its own sake.
In terms of the previous blog post, preparing to teach made me listen to myself more, as well as doing research when needed, to learn from others. For any topic I was going to teach that I did not fully understand, I first made the effort to think carefully about it, on my own. Next, I looked up videos on the topic until I found one that explained it well, so I could fill in any missing details. [A side note here is that I highly recommend Khan Academy, which is a wonderful resource for learning math. I often watch their videos to improve my understanding.]
All this effort meant that I was well-prepared for each class, and able to deliver the material based on real understanding. Of course, I learn a lot from my students in the classroom, as I continue to discover what works for them and what does not. So, the preparation really helps me to understand the math, as well as thinking about teaching strategies. I also learn a lot about success in planning to teach as I read and continue to read as many books about success as I can find.
In what ways can you prepare yourself for class as if you are going in to teach rather than to be taught? How would working for real understanding, rather than for marks, change the way you work? Thanks for reading!