56
votes
What skills do algebra teachers wish their students had mastered before taking algebra?
Automaticity on basic arithmetic.
That is, the ability to carry out basic arithmetic effortlessly without conscious thought.
Automaticity goes beyond capability, proficiency, and even fluency. Simply ...
- 12.9k
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 \...
- 5,879
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 ...
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29
votes
Students can't seem to grasp the intent of tangent lines and getting general trends of derivatives from graphs
Sadly, these students seem to think of math as a bunch of rules. You have done great work, and probably gotten them a little closer. But they are resisting the reasoning that can't easily be put into ...
- 21.5k
28
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 ...
- 26.9k
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 ...
- 12.4k
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 ...
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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 ...
- 1,594
20
votes
Students can't seem to grasp the intent of tangent lines and getting general trends of derivatives from graphs
When a concept just won't stick, no matter how many ways you explain it, that is usually a sign of a gap in the student's background knowledge. So I'd recommend searching for the gap.
Of course, you'...
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18
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 ...
- 26.9k
17
votes
What skills do algebra teachers wish their students had mastered before taking algebra?
For me, the top items are automaticity with:
Times tables
Negative numbers
Order of operations
I have a timed drill site on these skills at Automatic-Algebra.org.
For my incoming remedial algebra ...
- 26.9k
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 ...
- 1,796
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 ...
- 9,113
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
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 ...
- 8,093
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 ...
- 5,667
15
votes
Students can't seem to grasp the intent of tangent lines and getting general trends of derivatives from graphs
I taught physics for 25 years at a community college, and the situation you're describing is one that I'm very familiar with. (I also got the oportunity to teach first-semester calculus a couple of ...
- 151
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,...
- 1,327
14
votes
Accepted
Fixing wrong ideas about coefficients (e.g. subtract 3 from 3x to isolate x)
From very limited experience: have you tried writing $$3 \times x$$ (or using one of the various stars, dots, etc.)?
It might be that it’s not obvious that there is a multiplication here: you say that ...
- 266
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 ...
- 2,096
12
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 ...
- 21.5k
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 ...
- 5,879
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 ...
- 2,801
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 ...
- 22.1k
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
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 ...
- 846
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. ...
- 2,408
10
votes
What to do when uncertain about a question while tutoring
I think, especially in such a blatantly transactional interaction, you should be forthright with them, and allow them to make a decision.
I would say "I don't know how to do this. Do you want to ...
- 26k
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 ...
- 4,549
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