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 \...
- 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,...
- 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 ...
- 23.6k
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 ...
- 23.6k
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 ...
- 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 ...
- 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 ...
- 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 ...
- 23.6k
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}...
- 23.6k
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 ...
- 1,746
16
votes
Accepted
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 ...
- 8,953
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 ...
- 261
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 ...
- 23.6k
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 ...
- 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,...
- 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 ...
- 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 ...
- 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 ...
- 23.6k
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 ...
- 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 ...
- 2,775
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 ...
- 20.8k
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 ...
- 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 ...
- 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. ...
- 1,802
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 ...
- 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 ...
- 23.6k
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 ...
- 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 ...
- 2,775
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.
...
- 116
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