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This semester is my first time to teach Calculus II in a classroom which contains around 25 students. (In fact, this is a discussion class.) I didn't have much experience about teaching. For instance, I thought I explained something quite clearly in the class, but the students still did not do very well in the weekly quiz.

Do you have any useful suggestions for how to start with teaching and being a good teacher?

(By the way, I am not a native English speaker. My accent might confuse them, however, I wrote down most of what I said on the blackboard.)

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    $\begingroup$ This is an excellent question, but this site is the wrong place for it. Your question is too broad and too opinion-based for the goals of this site. Try this at Quora.com or another broader site. Or you could edit your question to be much more specific. $\endgroup$ – Rory Daulton Sep 11 '17 at 0:03
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    $\begingroup$ I think there are two questions valid here: 1. Non-native speaker teaching mathematics in English. What issues are there? 2. I'm about to teach mathematics for the first time and I don't even know what questions to ask. What should I do? $\endgroup$ – Tommi Brander Sep 11 '17 at 5:31
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    $\begingroup$ The biggest problem with non-native English speakers teaching math, is that they mispronounce key math words. It is a big problem in English, because it isn't phonetic. Suggest you find someone to go over pronunciation of the math vocabulary that you are using. You might also alert students that you are trying to learn to pronounce words correctly and ask them to let you know if you mispronounce words; this will ensure that someone corrects you if you mispronounce a word so that the whole class isn't lost. $\endgroup$ – Amy B Sep 11 '17 at 9:51
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    $\begingroup$ Sometimes students don't do well on a quiz, because they didn't study or do the work. It isn't always a reflection on the teacher. $\endgroup$ – Amy B Sep 11 '17 at 9:52
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    $\begingroup$ If you are a grad student perhaps you can get advice from your advisor or some of the other professors in the department. Your department or university might already have some resources for grad students who are learning to teach. $\endgroup$ – John Coleman Sep 11 '17 at 10:53
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I highly suggest reading the book How to Teach Mathematics by Steven G. Krantz, published by the American Mathematical Society (AMS).

https://www.amazon.com/How-Teach-Mathematics-Steven-Krantz/dp/1470425521

https://www.maa.org/press/maa-reviews/how-to-teach-mathematics

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    $\begingroup$ A good, though tendentious, selection :) $\endgroup$ – kcrisman Sep 11 '17 at 11:09
  • $\begingroup$ What is tendentious about it? $\endgroup$ – Sue VanHattum Sep 15 '17 at 15:17
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I'll give you the answer I got from several professors when I started teaching:

"talk slow and pause" and "write what you say and say what you write"

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Two things you need to realise: if you say things completely wrong, then nobody will have understood it, so if there are questions not one student answers during a quiz it most probably means that you did not explain/pronounce it correctly.

As far as "Which questions should I ask?", I can only advise you to go to another math teacher in your school, and ask him/her about "Are the questions too easy/too difficult/ ..."? In case you don't do that, you risk ending up in my situation: I had a very bad student who came to me after the exams and told me "Thank you, sir! I never had such good grades for mathematics!!!", and this gave him the impression that even not paying attention during my class, he could still pass the exams, so he became completely unmanageable. Apparently my questions were far too easy.

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I would do more drill, recitation, games, etc. IOW practice. Students have limited time and work ethic. If you use the time to practice rather than sage on the stage ing, than they will actually get some traction with the problems.

I would say this in general, but even more so for someone who is a first time instructor and with a foreign accent. Lecture can be torture. You can probably much quicker move to a practice model than to being a fluent enjoyable lecturer. And even with the most fluent and entertaining lectures, I still learn more from practice than from listening and watching.

Watch the movie Stand and Deliver.

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    $\begingroup$ Then, after watching "Stand and Deliver," read the web sites that explain the differences between the movie and reality. The movie was pretty accurate, 90% according to the movie's subject Escalante, but that 10% can lead a math teacher astray. Even Escalante could not take kids who didn't know algebra and take them through an AP Calculus class in just two years (as the movie shows). $\endgroup$ – Rory Daulton Sep 13 '17 at 0:22

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