Most Popular
1500 questions
21
votes
3 answers
At what point is it a disservice to pass someone on to the next math class?
Background information
I'm currently teaching common core geometry, which assumes that a student has algebraic knowledge coming in. Clearly, we shouldn't expect students to retain everything from their algebra class before they take geometry. I've…
Opal E
- 3,986
- 18
- 45
21
votes
4 answers
Applications and motivation of abstract linear algebra topics for engineers
This semester I'm teaching introductory linear algebra for engineering students, and I don't think I'm doing a good job explaining why these topics are important; specifically, everything having to do with linear transformations. I'm a physicist…
Javier
- 675
- 3
- 8
21
votes
2 answers
Impossibility of trisecting the angle, doubling the cube and alike, what are reasons for or against discussing them in a course on algebra?
When I taught courses on algebra giving a first exposition to Galois theory I usually included some discussion of classical results showing the impossibility of constructing certain points with ruler and compass, such a the cube root of $2$ (Delian…
quid
- 7,692
- 2
- 32
- 63
21
votes
5 answers
What is a method you use to handle the students who thinks they "know it all"?
This is a typical problem in my undergraduate Calculus I class. Many of these freshmen come in having made an A in their High-School Calculus class, and believe they know everything they need to about Calculus. They love to try to challenge my…
Todd Thomas
- 1,208
- 9
- 15
21
votes
2 answers
Math Blogging - what is a decent set up?
I hope this question is not deemed off-topic, but I cannot think of a more appropriate place to ask it (few tech sites care about support for MathJax and $\LaTeX$), and I think that blogging about mathematical topics is certainly part of…
Gordon Royle
- 703
- 3
- 11
21
votes
3 answers
Should we tell students to never replace parts of an expression by their limits when taking a limit?
Let me explain. Suppose we want to calculate $\lim\limits_{n\to\infty} n^2-n$. Since this limit is indeterminate, one way to do it is to write it as $\lim\limits_{n\to\infty} n^2(1-1/n)$. Since $n^2$ goes to infinity and $1-1/n$ goes to $1$, the…
Javier
- 675
- 3
- 8
21
votes
2 answers
DIY/Hack Instructional Implements
As a secondary teacher in an underfunded district, I get paid very little money for the time and energy I put in to my teaching. I am totally cool with this, I never got into teaching for money, I enjoy a minimalist life style. However, there are…
celeriko
- 5,070
- 2
- 18
- 56
21
votes
4 answers
Multiple Solutions Methods vs. Encouraging a Particular Approach
It happens frequently in math that problems have multiple possible solutions. This might become troublesome, e.g. when students use some other approach, hence, not learning the current topic.
One could say that it is the task that is wrong, but in…
dtldarek
- 8,947
- 2
- 28
- 60
21
votes
9 answers
Why do students have problems with showing that something is well-defined? How can this be improved?
I see a lot of students struggling when they have to show that something is well-defined. I have the feeling that this is often not understood.
Two examples:
When defining a sequence $x_n= g(x_{n-1})$ (for some function $g$) and asking to show…
Markus Klein
- 9,438
- 3
- 41
- 96
21
votes
7 answers
Should students be told they're wrong
I base this question off where I got my motivation for math and science. Throughout several attempts in my junior years, I was able to design a perpetual motion machine, design a free energy device, prove Einstein $E=mc^2$ wrong. Obviously I was…
user1244
21
votes
13 answers
How can I familiarize elementary school students with infinities larger than $\aleph_0$?
Cantor's discovery of the existence of more than one infinity was a revolutionary change in human knowledge. He defined the notion of counting by bijections and showed that one can use infinities as numbers for counting mathematical objects.
I am…
user230
21
votes
12 answers
How to explain that we live in a three-dimensional world?
How does one explain, clearly and simply, that we live in a three-dimensional world?
The explanation has to be understandable for a twelve year old child.
Ortomala Lokni
- 355
- 1
- 2
- 10
21
votes
2 answers
Benefits of Having the Same Professor Teach the Entire Calculus Sequence
Is there any research supporting the idea that a single professor should teach the entire calculus sequence as opposed to splitting the duty amongst multiple professors? What are the pros and cons of having the same professor teach all the calculus…
James Rohal
- 461
- 3
- 7
21
votes
5 answers
Good way to explain why an absolute value in an equation does not automatically mean to make the other side +/-
I was helping out in a learning support class today and we were working through some absolute value problems when something like $|x + 4| - 5 = 10$ came up and both students I was working with split the problem up into
$|x + 4| - 5 = 10$ and
$|x +…
celeriko
- 5,070
- 2
- 18
- 56
21
votes
4 answers
How do you handle a wide ability range when delivering a 50 min tutorial with lots of material to get through?
So far I've tried building my presentation from elements, each of which is differently paced.
A lot of tutorials are given just by rapidly writing fully worked solutions on the board, thereby leaving little room for actual discussion of concepts. I…
Geoff Pointer
- 313
- 2
- 10