33 votes
Accepted

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 \...
Dan Fox's user avatar
  • 5,719
32 votes
Accepted

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,...
mweiss's user avatar
  • 17.2k
29 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 ...
Daniel R. Collins's user avatar
27 votes
Accepted

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 ...
Daniel R. Collins's user avatar
25 votes
Accepted

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 ...
vonbrand's user avatar
  • 12.2k
22 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 ...
Amy B's user avatar
  • 7,929
20 votes
Accepted

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 ...
Steve's user avatar
  • 1,374
17 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 ...
Daniel R. Collins's user avatar
16 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}...
Daniel R. Collins's user avatar
16 votes
Accepted

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 ...
Andrew's user avatar
  • 1,746
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 ...
DavidButlerUofA's user avatar
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 ...
tbrookside's user avatar
15 votes
Accepted

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 ...
Daniel R. Collins's user avatar
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 ...
Matthew Daly's user avatar
  • 5,589
14 votes

Teaching a student who refuses to learn

This is not an answer, but an assertion that what you are experiencing is not something new. Here are some quotes from a 1993 article of an Estonian math prof, who moved to the U.S. in the early 1990s,...
Rusty Core's user avatar
  • 1,299
13 votes

Teaching a student who refuses to learn

If you are a private tutor, hired by an undergrad or adult student, or hired by the parents of a student in 6-12 (middle school/high-school), then I'd suggest that when you meet with a "client" as a ...
amWhy's user avatar
  • 2,075
12 votes
Accepted

Is There Such Thing as Learning Disability in Math?

The inabilities described in the question don't strike me as either particularly unusual nor as clear signs of a neurological learning disability. They strike me as more likely the passivity and ...
Dan Fox's user avatar
  • 5,719
11 votes

How to Teach Adults Elementary Concepts

Any advice for teaching simple concepts and rules to adults, specifically working with negatives or proper application of PEMDAS? This will be an adjunct to mweiss' answer, which I fully agree with ...
Daniel R. Collins's user avatar
11 votes

When should students stop receiving tutoring for mathematics?

At University of Jyväskylä there is Ratkomo twice a week for some hours. It means at least one faculty member and typically some PhD students wander a corridor with tables and chairs and help everyone ...
Tommi's user avatar
  • 6,109
11 votes

Teaching a student who refuses to learn

This is how most students perceive math tests. Whether it's fair or not, this is the perception and it is the normal response to a broken math education system. Imagine you are a teenager and your ...
WeCanLearnAnything's user avatar
11 votes

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

Regarding "How do I recruit students:" You should start here -- you have started with this cool thing you want to do, and are wondering how to do it. But you should instead try to find some ...
Chris Cunningham's user avatar
10 votes
Accepted

How to teach a weak student?

Weaker students need drill and rote. Make flashcards and drill the heck out of him. That will help him more than any kind of detailed explanations or motivation talks. Just treat it like a sports ...
guest's user avatar
  • 284
10 votes

How to teach a student algebra who misses too much previous knowledge?

My guess is that he depends on "following the rules", and there are now too many rules for him, because none of the 'rules' makes any sense to him. I believe he needs to see things differently to ...
Sue VanHattum's user avatar
  • 19.4k
10 votes

Teaching a student who refuses to learn

Well, there is a recent and excellent book about this question: Why Students Resist Learning: A Practical Model for Understanding and Helping Students by Anton O. Tolman, Janine Kremling and Anton O. ...
Humberto José Bortolossi's user avatar
10 votes
Accepted

How can I help/tutor a friend who is taking the same course as me?

I had two goals the whole time: do the homework as quickly as I could do it well, and teach him the concepts. If you really want to help, the first goal should be scrapped entirely, IMHO. The best ...
fedja's user avatar
  • 3,439
9 votes
Accepted

Material on tutoring university level math classes

I am very fond of the book by Steven G. Krantz, How to Teach Mathematics, published by the American Mathematical Society (AMS), now in its 3rd edition. The book is mostly aimed at professors and ...
Daniel R. Collins's user avatar
9 votes

Students understand during course but can't solve exam

I always make homework (from the textbook and online in WeBWorK) and written assignments MORE difficult than exam questions. I tell my students this, with the reason being “if you can run 10 miles in ...
BobaFret's user avatar
  • 806
9 votes
Accepted

More intermediate steps or check well-understanding

Part 1: Do they really understand? My first thought is that you are running into the limits of working memory. As students try hard to understand step 5, they are pushing previous thoughts about step ...
WeCanLearnAnything's user avatar
9 votes
Accepted

Is playing and teaching chess appropriate in private lessons?

It's a bad idea. (1) It's not that special. He can get a game from chess very easily from anyone. An individual session with you is not high value, not best use of time. (2) It will raise hackles. ...
guest's user avatar
  • 116

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