60 votes
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How to cure students from the idea that root and squaring are identity operators?

I suspect that there are several different and interacting things going on here. It's likely that these students don't understand the "equals" sign in the same way that you do. An ...
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38 votes
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How do I motivate my students to go to office hours?

When I'm the instructor for the course, I remind them of the time and location of my office hours by writing it on the board at the beginning of every lecture (if you're not the instructor, you can ...
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32 votes
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How important is knowledge of trig identities for use in Calculus

The specific identity \begin{equation}\tag{A} \tfrac{1}{1 - \sin{x}} + \tfrac{1}{1 + \sin{x}} = 2\sec^{2}{x} \end{equation} as such is probably not often encountered, but simplifications akin to \...
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  • 4,958
31 votes
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How to Teach Adults Elementary Concepts

But, when teaching adults, I've found that I can't just tell them "this is the way it's done, get used to it." Good! Students (at any age) should never be satisfied with "This is the way it's done,...
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28 votes

Tutoring a recalcitrant/awkward/exasperating student---special needs?

How do I reach [this] kid? Let me be blunt: You probably don't. This is a person who is so intransigent that you effectively need to black-tag them. A hard lesson is that you can't save everyone. At ...
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27 votes
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Students understand during course but can't solve exam

Do NOT give exam questions that are intentionally more challenging than homework or in-class problems. I would recommend precisely the opposite. The point of the exam is really a spot-check that ...
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26 votes
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What to do when you get "the empty stare"?

It's perhaps worth noting that there are (at least) two distinct reasons why your students might offer no reply when you ask them if they understand what you've just explained: They might not ...
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23 votes
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A smart student that struggles in exams

There are several possible explanations. Without much more information, it is impossible to give a clear-cut answer. Perhaps your student is able to "read" your unconcisious reactions very ...
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  • 12k
21 votes

Tutoring a recalcitrant/awkward/exasperating student---special needs?

This is a student who doesn't understand social cues. He only knows that if he is rude you keep trying. If acts disruptive, he will get the answer without working for it. As long as you reward him ...
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  • 6,735
20 votes

How to cure students from the idea that root and squaring are identity operators?

First: I do not think this is really an issue with a lack of understanding of the square root function. When someone writes $\sqrt9 = \sqrt3$ it means they are not thinking about what the equals sign ...
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  • 19.1k
20 votes
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Dealing with disagreeable students and not compromising

It sounds like your students are not getting what they wanted from your tutelage; since they are not getting a formal credential from their work with you, their likeliest motivation is that they think ...
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  • 520
19 votes

What to do when you get "the empty stare"?

It's hard to admit you don't understand if you think you're the only one in the class that's lost (rarely actually the case, but individuals get self-conscious). I employed a system where if I wanted ...
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18 votes
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How to tactfully discourage casual, implicit disparagement of mathematics

The tutors need training. Any volunteer job has job requirements, and one of the requirements of this job [for it to be done well] is being able to tutor anything that comes along. The training can ...
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  • 17k
17 votes
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Is it good to have solutions of homework published?

I think a great reason to post homework solutions is so that students have a way of reviewing their homework before exams (it would be nice if they were to review homeworks whenever they get their ...
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  • 806
17 votes

How to cure students from the idea that root and squaring are identity operators?

Late answer, but since it comes up every semester I have a stock response that I'd like to share. The most common mistake in this vein is for a student to write $\sqrt{16} = \sqrt{4} = 2$ or $\sqrt{81}...
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17 votes

How do I motivate my students to go to office hours?

When I teach courses, I usually see the majority of my students in office hours at least once a week. Here are some strategies for promoting office hours: Get a room. My office isn't nearly large ...
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  • 7,930
16 votes

How do I motivate my students to go to office hours?

As a TA, attend one of the class sessions and personally advertise your office hours. If the students see you in person, they may be more willing to come to you with questions. Also making yourself ...
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  • 558
16 votes

How to help motivate math when tutoring low level algebra (High school)

I was always honest: You won't use this. If you don't like math by now, it's probably not going to be useful to you in your career or life, or ever again once you graduate. If you're like most ...
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16 votes

What to do when you get "the empty stare"?

When I think of the what caused my students (or myself, back when I sat in lectures) to get to the point of an empty stare, it's that they were so confused that they didn't even know what to ask. They ...
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  • 860
16 votes
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Software to create video tutorial of mathematics topics

I've created roughly 40 videos for an online course and a flipped course in biology, so I've got some experience making videos. I researched the maker of your videos, and he deliberately does NOT ...
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  • 1,494
16 votes
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Helping a student exasperated by abstract concepts in linear algebra

Definitions and other facts One thing I find particularly helpful with Linear Algebra is to help the student deal with the definitions in multiple ways. In Linear Algebra there are definitions, and ...
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16 votes

Advice on teaching abstract algebra and logic to high-school students

Here's my advice. I have no teaching experience. Remedy that first before you lay out plans for a 6-month course of study. Find some way where you can teach just for a single day in some way at the ...
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16 votes

Dealing with disagreeable students and not compromising

I think the real issue here is that you thought you were essentially doing undergraduate tutoring, and you weren't. You were doing adult education, and that is not the same thing. When someone is in ...
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15 votes
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How to help motivate math when tutoring low level algebra (High school)

I think at this level, and for a tutor (not a teacher), the main carrot (really more of a stick) is getting good grades, getting into a good college, etc. Most people really will never use this later, ...
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15 votes
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Tutoring elementary student who reverses left and right

I think I need a simple graphic mnemonic he can use to remind himself which side the ones column goes on, and which direction we go in order to get bigger numbers. Suggestion: Start making ...
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15 votes
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Best way to find out what math topics a person struggles with when tutoring

Since you didn't mention what level your student is, I'll try to make my answer as general as possible, leaning more toward secondary math students. In my experience tutoring and teaching secondary ...
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  • 1,726
15 votes

How important is knowledge of trig identities for use in Calculus

Due to low enrollment, my AP Calc class was filled with the students who otherwise would have taken Pre-Calc this year. So you can imagine that "How much do you really need to know to see the bigger ...
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  • 5,539
13 votes

How to nurture a good student?

I don't see my thoughts expressed by anyone here so perhaps I can chip in! I'm currently a graduate student but I was once that kind of bright bored student you are talking about. I had my fair share ...
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13 votes
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How to balance higher order thinking and drill/practice

One of the benefits of practice is a deeper understanding. I don't care how fast you get the answer, but I hope you are not adding by columns when you add 101+99. And that's why thinking of practice ...
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