Those of you who can explain mathematical concepts, please reply.
I know who you are; you posted, rather eloquently, on Venus' thread regarding a teacher making a mistake in mathematics.
My brain is not wired to explain concepts that come to you naturally. Certainly, it is a combination of both your innate ability as well as training in a field in which you excel. My question centers on those of us who did well in mathematics but cannot explain what we are doing. I used to teach algebra and I had one student, who, like me in my school years, always found the correct answer. Always. Even in those trying word problems.
I can explain matters relative to the arts, in which I am trained, but I cannot explain how I once arrived at correct answers in math. Why, I even showed my work!
Any thoughts you offer will be appreciated. Why my walk in the rain, meant to clear my head, came up with this, I dunno. Your collective reasoning on mathematics in the above-mentioned thread did make an impression . . .
CoCo: My brain is not wired to explain concepts that come to you naturally.
In my experience, I've found that it is easier to teach ideas and concepts which only came to me with difficulty in contrast to those which came quickly and easily to me.
The reason is probably obvious: by having to work harder to understand a concept, I had to clearly think through the process of "getting it," and had to explicitly recall any and all linking ideas and how they are all related to each other. This makes it easier to explain it to someone else.
Here is an article you might enjoy which explores the philosophical question of whether or not math is a science:
In my experience, I've found that it is easier to teach ideas and concepts which only came to me with difficulty in comparison to those which came easily to me. -- jp1692
In your succinct paragraph, you have given me a basis for an answer to what has long puzzled me. Perhaps, then, I will learn how to explain my work in math!
Thanks, too, for the science checklist info.
In working through a problem, you often walk through, re-invent the steps of the original developer. If you have to talk about it in a conversation, searching for words often helps you to really understand things yourself. thank you for the Math link!
I'm going to generalize, when I taught something like differential equations, matrix analysis or complex numbers, the issues with explaining and transmitting knowledge in a way that flows is hindered (at times) when the students lack or barely understand the foundation for whatever concept you are teaching.
Math concepts are progressive and incremental, meaning that lacking a basic skill or concept harms understanding the next. Many times it's not what/how you are explaining, is making the assumption that the foundation to understand a given concept is there when sometimes it's not.
In Engineering school I had a lot of professors who were great Engineers but horrible teachers. The number one issue that I had with them was them not knowing how to review or introduce a given concept.
When you teach art, many times you have to introduce some context to understand a concept. The same applies to math, only that the context is something that is supposed to have been learned and practiced; it's more implicit.
They way I used to explain math when I taught it was showing some practical application when I could find it (There were many things that were more applicable to developing the analytical skills, not directly applicable knowledge per se). As I explain a concept, I give an example, show step by step how to arrive to the solution, explaining in each step what is needed to know from previous math material. And then repeat, repeat, repeat. I give a few classroom practice exercises and discuss them, them leave them on their own and hope I gave a good class.
If you have to talk about it in a conversation, searching for words often helps you to really understand things yourself. -- waton
I haven't taught math in years, but I do teach creative writing classes, my students varying in age from 11 to 76 years old. Your practical method, as shown above, works for me in so many ways, both as a teacher and as an everyday sort of bloke who wants to understand as well as to explain things.
As I explain a concept, I give an example, show step by step how to arrive to the solution, explaining in each step what is needed to know from previous math material. And then repeat, repeat, repeat. I give a few classroom practice exercises and discuss them, them leave them on their own and hope I gave a good class. -- scratchme1010
Well, scratchme1010, you certainly gave a good class here! Your laying a basis first, then proceeding step by step to further levels is key. You have just given this old teacher a master class!
Thanks, jp, waton, and scratchme!
I appreciate these comments and would be grateful for more. There are more mathematicians out there, yes?
CoCo, have you heard? There are three kinds of people in the world: those that are good at math and those that aren't!
I knew I could "count" on you, jp!