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Results tagged with undergraduate-education
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user 1550
For questions about teaching students at the undergraduate (university) level.
2
votes
How long would it take to teach proper limit calculations?
In the spirit of paw88789's answer, first show:
$\color{red}{ 1 = \lim_{x\to\infty} 1 = \lim_{x\to\infty} \dfrac{x}{\sqrt{x}\sqrt{x}} \overset{???}{=} \dfrac{\infty}{\infty\infty} \overset{???}{=} …
- 2,794
8
votes
Getting students to actually read definitions
You asked:
Students trying to learn all kinds of facts [...] by heart rather than recognizing that these are just consequences of the general definitions. [...] Are there any better techniques to get …
- 2,794
0
votes
Teaching students how to check the validity of their proofs
On request from the asker, I will give my answer based on my decades of experience in teaching mathematics.
Frankly, anyone who is unable to check the validity of his/her own proof (excluding careless …
- 2,794
0
votes
Is it natural for self-learners to forget most proofs of the theorems they learn?
I also wonder, What should math student do with proofs? [...] just keeping the idea of the proof and reconstruct the details herself when needed?
Yes, and not just a mathematics student. In my op …
- 2,794
14
votes
Learn university maths or train for high school competitions: which is better?
Short answer: The skewed content is not a good reason for avoiding IMO-style contest training, because if the training is done right then the students will be led to explore mathematics and would neve …
- 2,794
15
votes
Why are induction proofs so challenging for students?
Logic foundation
In my opinion, the only way for anyone to really understand induction is to really understand the logical structure behind it. So a prerequisite is a complete grasp of working in firs …
- 2,794
25
votes
Why are induction proofs so challenging for students?
For CS students specifically, there is another approach that would work better than the usual way induction is taught, namely by teaching structural induction, which goes like this:
If you want to pr …
- 2,794
4
votes
What to do if there is a disagreement on fundamentals, e.g. axioms or inference rules?
You could ask the student to come up with his own rules and axioms from which he can prove whatever theorems he thinks are valid. Usually when they really get down to doing that systematically and for …
- 2,794
20
votes
Accepted
Can we avoid confusion over using "let" as a quantifier?
Many logicians that I have spoken to have concurred with my assessment that this is an issue of the misleading use of "let". Many teachers use this word in two very different and incompatible ways. Th …
- 2,794
3
votes
How to teach pure mathematics to a well-educated adult who did badly in maths at school
"How to Prove It" is a good book for beginners in proofs in mathematics. But there is also "Nets, Puzzles, and Postmen" that is an excellent introduction to graph theory for lay people that even has i …
- 2,794
6
votes
Can students tell the difference between the "definition if" and the "theorem if"?
iff and if
In my experience, students who have a solid grasp of first-order logic have absolutely no problem with the inconsistent use of "if" in definitions. The problem is that most students don't, …
- 2,794