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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 ...
Justin Skycak's user avatar
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
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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
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 ...
Sue VanHattum's user avatar
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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 ...
Daniel R. Collins's user avatar
25 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 ...
vonbrand's user avatar
  • 12.3k
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
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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 ...
Steve's user avatar
  • 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'...
user22788's user avatar
  • 854
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 ...
Daniel R. Collins's user avatar
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 ...
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
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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

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
  • 5,629
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 ...
user23001's user avatar
  • 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,...
Rusty Core's user avatar
  • 1,317
14 votes
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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 ...
D. Ben Knoble's user avatar
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
  • 2,095
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 ...
Sue VanHattum's user avatar
  • 21k
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
  • 5,869
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
  • 7,358
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

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

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 ...
Steven Gubkin'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
  • 3,939
10 votes

Fixing wrong ideas about coefficients (e.g. subtract 3 from 3x to isolate x)

If it were me, I'd try building on what you mentioned here: Use word problems. Even when she's just written down an equation where she knows that, e.g., $3x$ represents $3$ chocolates of unknown cost,...
Justin Skycak's user avatar

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