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"There is no royal road to mathematics", Euclid is thought to have said to Alexander the Great. Well, I don't think there's a royal road to teaching mathematic

"There is no royal road to mathematics", Euclid is thought to have said to Alexander the Great. Well, I don't think there's a royal road to teaching mathematics. First ingredient if you want to be a good mathematics teacher: preparation. When you go to class, just make sure you went through all the examples, all the exercises and problems, and you know them in and out. Be prepared. When they train you how to teach, they never tell you that. It is just assumed. They tell you about the attention curve (which supposedly looks like a bathtub: high at the beginning and at the end, low in the middle), about body position, voice volume, and other stuff. But for some reason they forget to tell you that first and foremost you need to prepare. Second ingredient: feedback. Ask a colleague to come and observe you, and, if possible, go with the same colleague and observe another teacher whom you want to learn from. They (the colleague) can point at what you did differently from that teacher, what you did well, what you should work on next. If that colleague is good, they will give you a list of 20 things to work on, but also tell you to focus on the first one or two. Are you stopping to look at the kids and see if they understood? Are you making eye contact with a single kid, rather than cycle through all the classroom? Is your voice loud enough (pro tip: it never is, speak louder). Did you leave the kids enough time to think on their own? Did you give them too many hints? Are you biased in always letting only the best kids in class answer out loud? Are you pointing with your finger when you want to emphasize something (it's natural, but don't do it, it intimidates the kids). But all these things are second order things. First thing: prepare for the math you are going to teach. It's much more important to not make any mistakes, such as a sign mistake in the middle of a calculation, than to make eye contact. Mistakes erode the kids' trust in you. Avoid them. Prepare. Once you got to a point where you consistently deliver a flawless lecture, then you can think of becoming the next 3Blue1Brown. But you need to walk before you run.

catbird 6y ago
Thanks for your comment. It sounds like you have learned these lessons through a lot of experience - do you have any suggestions on a book to read to get the very basics of teaching? > When they train you to teach... I started a job as a professor this year and never got any of that basic training. Before this I was a postdoc reading papers and writing code all day. In job interviews my lack of teaching experience wasn't seen as an issue. The faculty would say, "oh teaching isn't so hard, you'll figure it out quick enough." So far I have been muddling along ok, but I have this anxious feeling that there are a lot of aspects to this that I don't know that I don't know, and don't know where to get started on finding out about them.
- credit_guy 6y ago
  I did receive a bit of training, but as I said, I didn't find it to be too valuable. I was extraordinarily fortunate to have just such a colleague as I mentioned. I consider her to be a genius when it comes to pedagogy. We went together and observed a great Professor teaching. She pointed to me lots of things, but one stuck to my mind: "Did you notice that he was wearing a tie? He doesn't wear a tie when he's in his office, or on the hallways of the Department, but he wears a tie when he teaches". That's respect for your students and for the action of teaching. My Dad was a teacher. One day a former student of his told me this: "I remember the day he came and taught us X"(where X was a great poet - my Dad was teaching literature, not math). "He was wearing a black suite and white shirt and tie. That's how much he cared about teaching about X." I was impressed. I realized that kids care. And they notice. They notice if you put the effort, and they appreciate it. Good luck in your career. I don't know of any book. I'm not a teacher or a Professor anymore. I work in the industry, but I do take interns every year, and in a sense that's a teaching (and research) experience. I enjoy it a lot, my next intern will join exactly one month from today. And just like I was preparing for my kids in the past, I'm preparing a lot for this intern. I hope he'll enjoy the experience.
- jonsen 6y ago
  The basics of good teaching is a mindset. “You’ve got to love your students. It’s as simple as that”, a colleague of mine once said. You could look into some of Kieran Egan’s writings: https://en.m.wikipedia.org/wiki/Kieran_Egan_(philosopher) https://en.m.wikipedia.org/wiki/Kieran_Egan_(philosopher) Personally I found the book To Know as We are Known very inspirational: https://www.amazon.com/Know-Are-Known-Education-Spiritual/dp/0060664517 https://www.amazon.com/Know-Are-Known-Education-Spiritual/dp...
ultramundane828 6y ago
Preparation definitely helps me as a student. > Mistakes erode the kids' trust in you. In addition to this, I often find myself trying to digest concepts broadly because my mind is lackluster with the mechanical side of calculations. When a professor makes a mistake, I occasionally have to revert an already imperfect record (with or without notes) and adjust my conceptual framework. Just an anecdote about why I personally suffer from poor teacher preparedness as a student.
analog31 6y ago
>>>> ... It's much more important to not make any mistakes, such as a sign mistake in the middle of a calculation, than to make eye contact. Mistakes erode the kids' trust in you. Avoid them. Prepare. I wonder if that's really the best way to teach, like a classical music performance where you can't play a single wrong note. This almost conveys that the teacher has some special intuition that the students will never get. It's also far removed from how anybody actually uses math. We try things, go down blind alleys, look stuff up, check our work to see that it's believable, etc. Now I do believe you need to be solid on the concepts, so that when you do make a mistake, you can say: "See, this is a mistake because it violated X."
- teachingassist 6y ago
  I find it useful to say: "I don't know, let's figure out how to look it up", or occasionally "Whoops I made a mistake", but not too often. If you make mistakes regularly on curriculum content, on content that students are expected to perform in a test without mistake, students will quickly lose confidence that you can teach them anything. What is a mistake and what is new material often looks the same, to a student: strange processes that they haven't seen before. They will have to overcome your mistakes in order to figure out what they are supposed to be learning.

catbird 6y ago

Thanks for your comment. It sounds like you have learned these lessons through a lot of experience - do you have any suggestions on a book to read to get the very basics of teaching? > When they train you to teach... I started a job as a professor this year and never got any of that basic training. Before this I was a postdoc reading papers and writing code all day. In job interviews my lack of teaching experience wasn't seen as an issue. The faculty would say, "oh teaching isn't so hard, you'll figure it out quick enough." So far I have been muddling along ok, but I have this anxious feeling that there are a lot of aspects to this that I don't know that I don't know, and don't know where to get started on finding out about them.

credit_guy 6y ago
I did receive a bit of training, but as I said, I didn't find it to be too valuable. I was extraordinarily fortunate to have just such a colleague as I mentioned. I consider her to be a genius when it comes to pedagogy. We went together and observed a great Professor teaching. She pointed to me lots of things, but one stuck to my mind: "Did you notice that he was wearing a tie? He doesn't wear a tie when he's in his office, or on the hallways of the Department, but he wears a tie when he teaches". That's respect for your students and for the action of teaching. My Dad was a teacher. One day a former student of his told me this: "I remember the day he came and taught us X"(where X was a great poet - my Dad was teaching literature, not math). "He was wearing a black suite and white shirt and tie. That's how much he cared about teaching about X." I was impressed. I realized that kids care. And they notice. They notice if you put the effort, and they appreciate it. Good luck in your career. I don't know of any book. I'm not a teacher or a Professor anymore. I work in the industry, but I do take interns every year, and in a sense that's a teaching (and research) experience. I enjoy it a lot, my next intern will join exactly one month from today. And just like I was preparing for my kids in the past, I'm preparing a lot for this intern. I hope he'll enjoy the experience.
jonsen 6y ago
The basics of good teaching is a mindset. “You’ve got to love your students. It’s as simple as that”, a colleague of mine once said. You could look into some of Kieran Egan’s writings: https://en.m.wikipedia.org/wiki/Kieran_Egan_(philosopher) https://en.m.wikipedia.org/wiki/Kieran_Egan_(philosopher) Personally I found the book To Know as We are Known very inspirational: https://www.amazon.com/Know-Are-Known-Education-Spiritual/dp/0060664517 https://www.amazon.com/Know-Are-Known-Education-Spiritual/dp...

ultramundane828 6y ago

Preparation definitely helps me as a student. > Mistakes erode the kids' trust in you. In addition to this, I often find myself trying to digest concepts broadly because my mind is lackluster with the mechanical side of calculations. When a professor makes a mistake, I occasionally have to revert an already imperfect record (with or without notes) and adjust my conceptual framework. Just an anecdote about why I personally suffer from poor teacher preparedness as a student.

analog31 6y ago

>>>> ... It's much more important to not make any mistakes, such as a sign mistake in the middle of a calculation, than to make eye contact. Mistakes erode the kids' trust in you. Avoid them. Prepare. I wonder if that's really the best way to teach, like a classical music performance where you can't play a single wrong note. This almost conveys that the teacher has some special intuition that the students will never get. It's also far removed from how anybody actually uses math. We try things, go down blind alleys, look stuff up, check our work to see that it's believable, etc. Now I do believe you need to be solid on the concepts, so that when you do make a mistake, you can say: "See, this is a mistake because it violated X."

teachingassist 6y ago
I find it useful to say: "I don't know, let's figure out how to look it up", or occasionally "Whoops I made a mistake", but not too often. If you make mistakes regularly on curriculum content, on content that students are expected to perform in a test without mistake, students will quickly lose confidence that you can teach them anything. What is a mistake and what is new material often looks the same, to a student: strange processes that they haven't seen before. They will have to overcome your mistakes in order to figure out what they are supposed to be learning.