Most Popular
1500 questions
19
votes
15 answers
What is fairly new theorem one can teach (and prove) to an undergraduate student?
Many students complain about how old the things in mathematics are. When students finish their undergraduate studies, there are usually not able to state results and prove them which were found after the 1950s (or even older). Of course, the…
Markus Klein
- 9,438
- 3
- 41
- 96
19
votes
3 answers
What should I do if I have a student 'hiding' their working out?
I recall in one of my classes earlier this year that I had a student who always 'hid' their working out from me when I walked around to see how well they're going with the question. The usual practice is for me to do a few worked examples, and then…
Trogdor
- 1,106
- 7
- 14
19
votes
5 answers
How to award points for sense-making at the end of a problem?
Here is a statistics question I asked on a recent exam:
How high should the doorway be to allow 97% of men to fit through it?
I got a very large number of answers like "3 inches" or "0.0001 feet". This makes me sad. I'd like to know if these…
Chris Cunningham
- 21,474
- 6
- 63
- 148
19
votes
5 answers
Learning Mathematics with the aid of spaced repetition systems
I am currently self-studying, so I learn using a textbook which I work through in a linear fashion. As I am introduced to new concepts I ask myself questions and I attempt to answer these questions and if all else fails I ask Maths SE. Only after…
seeker
- 915
- 1
- 7
- 21
19
votes
6 answers
Motivating the study of matrices
In Brazil's curriculum students are taught matrices in high school. Here, however, there is no linear algebra or pre-calculus, therefore matrices end up being just tables with lots of "arbitrary" definitions.
Is there a way to motivate the…
Lucas Virgili
- 919
- 5
- 16
19
votes
5 answers
Presenting a solution with a stroke of genius
When presenting the $3$-dimensional proof of the Desargues' theorem an average student might have, speaking informally, a "WTF moment".
It is an extreme case, but a similar situation could happen in an ordinary setting: what is interesting for…
dtldarek
- 8,947
- 2
- 28
- 60
19
votes
2 answers
Should I correct only one mistake at a time?
I am working as a teaching assistant in a course that first year mathematics students take. Some students who have maths as a minor also take it.
I run what is called a supervising session in the official translation - guidance session would be more…
Tommi
- 7,018
- 2
- 25
- 54
19
votes
3 answers
"Proof" meaning in maths and society
When we ask students to prove a particular result in a math class, students often reply with examples. For example, if I state: if a number is even its square will be even, and ask the students to prove it, they will reply with an example (such as,…
Madhu
19
votes
4 answers
Teaching limits of sequences before limits of functions in Calculus?
Most Calculus courses/textbooks I have seen teach the different topics in that order: limits of functions, continuity, differentiability, integration. Then, depending on the teacher/textbook's preference, sequences, series, power series,…
Taladris
- 1,433
- 7
- 18
19
votes
4 answers
Applications of Vector Calculus to Economics/Finance
I will be teaching a course focusing on multivariable integration soon, for the millionth time. The most difficult topic in such a course is certainly Vector Calculus, by which I mean line and surface integrals of vector fields. It is essential to…
Santiago Canez
- 1,293
- 2
- 10
- 11
19
votes
9 answers
Was there an SMSG (New Math) "Algebra 2" text?
This question has been kicking around in the back of my head for a couple of years, but the impetus to post it now came from reading the related question at When did the American school system's progression of math classes take its current form?.
I…
mweiss
- 17,341
- 1
- 41
- 89
19
votes
7 answers
"Correct the following mistake"-style questions?
Does anyone have any experience giving students incorrectly "solved" math problems and asking them to identify this error? Being self-critical is one of the skills that I would like my students to take away from a remedial/intro college-level math…
David Steinberg
- 3,890
- 18
- 36
19
votes
4 answers
Whether to tell students how difficult (you think) a problem is
Background: Most textbooks end a section with a set of questions ranked either by topic or by difficulty. A distinction is often made between "exercises", which are for directly practicing a known skill, and "problems", which are generally some kind…
Nick C
- 9,436
- 25
- 59
19
votes
4 answers
Why do we teach linear algebra in precalculus classes?
When I took precalculus, we learned about polynomials and how to factor them, we learned about trigonometry and lots of great and useful identities there, and we learned about matrices. They didn't call it linear algebra, they just called it…
Joel Croteau
- 404
- 1
- 8
19
votes
18 answers
Concrete vectors spaces without an obvious basis or many "obvious" bases?
I am teaching a class on linear algebra to sophomore and junior science majors, and am having some trouble illustrating the difference between $\mathbb{R}^n$ and an n-dimensional vector space. The main example the textbook uses is the set of…
David Steinberg
- 3,890
- 18
- 36