Most Popular
1500 questions
27
votes
9 answers
How can I teach my students that other disciplines are important too?
I'm sorry if this is the wrong place to ask this but I don't know any other place to ask.
I'm a research professor, but I enjoy teaching and put a lot of time into my classes. I mainly teach introductory calculus and physics to mainly engineering…
AJS
- 271
- 3
- 4
27
votes
5 answers
"Opinionated" textbooks
It's been said that no one explains anything so well as when they are trying to persuade you of something.
One of my favourite textbooks is E.T. Jayne's "Probability Theory: The Logic of Science". The entire book is designed to convince the reader…
Oscar Cunningham
- 387
- 2
- 6
27
votes
9 answers
Teaching students to find and correct their own errors
Many students have a fairly good grasp of the topics they are learning but fall down because they miss fatal errors in their work. Some don't check for errors at all, while many simply can't find them. Indeed, many of them get very frustrated when…
DavidButlerUofA
- 9,083
- 33
- 67
27
votes
3 answers
What do you do when you realize mid-lecture that your lesson plan is not working?
I had this happen today, and several times before. I had had difficulty preparing the material, because I knew my students strengths and it didn't seem suited to them. However, it seemed the right material at the time I was preparing.
As I gave the…
Brian Rushton
- 11,680
- 14
- 67
- 137
27
votes
4 answers
How should LaTeX be taught to university students?
There are several groups of people that would benefit from learning LaTeX in college. Future teachers can use it to write exams, scientists and mathematicians can write papers, and everyone can write theses with it.
There are three ways to introduce…
Brian Rushton
- 11,680
- 14
- 67
- 137
27
votes
6 answers
Would taking 5 minutes to explain the history behind a mathematical idea help stimulate learning the idea?
I read a paper in my "Research Issues in Mathematical Education" class that I have applied to the Undergraduate Calculus I and Calculus II class that I teach. I take five minutes to explain the history behind the material we learn each day. So…
Todd Thomas
- 1,208
- 9
- 15
27
votes
7 answers
Why not think of derivatives as fractions?
Back in high school—back in the 1900s, as my sons say—when our calculus teacher was introducing the chain rule...
$\frac{dy}{dx} = \frac{dy}{dt} \cdot \frac{dt}{dx}$
...he made a special point of saying that we shouldn't think of the $dt$ as…
adam.baker
- 401
- 1
- 2
- 7
27
votes
6 answers
Students confusing "object types" in introductory proofs class
In my intro to proofs (and discrete mathematics) class, I see a common mistake where students make nonsensical statements because, for lack of a better term, they confuse the types of the mathematical objects they work with. Some examples:
In a…
Daniel
- 381
- 3
- 5
27
votes
10 answers
Should LaTeX be taught in high school?
This semester, I was forced to learn LaTeX for my Real Analysis class. The professor wanted all homework assignments to be typed in LaTeX in order to produce "high-quality" work. At first I was annoyed because I had no choice but to learn a new…
FoiledIt24
- 1,283
- 10
- 31
27
votes
6 answers
Should we stop differentiating between ln and log?
In many U.S. middle schools and high schools, $\ln$ and $\log$ are treated differently, with the intent that $\log$ is equivalent to $\log_{10}$. However, in undergraduate courses and in the academic world, $\log$ always means $\log_{e}$, and $\ln$…
Nahmid
- 403
- 1
- 4
- 5
27
votes
2 answers
Students who know high-level math before going to college
There is a high school in the city I live in which has some high-level math courses in their curriculum. It's a special math class mentored by some university lecturers, and the children basically do the first year of university math courses…
dtldarek
- 8,947
- 2
- 28
- 60
27
votes
7 answers
What arguments can I give a high school student why mathematics is important?
In almost all countries all over the world, mathematics is a main subject in school. Maybe the subject bringing trouble to families with kids.
It is clear that scientist, engineers, etc. need mathematics as a part of their higher education at…
Markus Klein
- 9,438
- 3
- 41
- 96
27
votes
16 answers
How to motivate equivalence classes
Equivalence classs are very useful in mathematics, but many of the applications require further background, like quotient spaces in topology or quotient groups in algebra. One good example is residue classes (I.e. $\mathbb{Z}/n\mathbb{Z}$).
What is…
Brian Rushton
- 11,680
- 14
- 67
- 137
27
votes
16 answers
Grading a limit problem
In an exam we have
Question (5points)
find $\lim_{x\to\infty}(x-\sqrt{x})$.
A student answered: $\lim_{x\to\infty}(x-\sqrt{x}) =\lim \sqrt{x}(\sqrt{x}-1)=\infty \cdot\infty=\infty$.
My question is: how many point you will give the student? A…
Muath Karaki
- 661
- 1
- 6
- 8
27
votes
3 answers
Counterexamples in first year calculus
Many believe (I think rightly so) that the presentation of counterexamples should play an important role in the teaching upper level mathematics courses such as real analysis and topology. Counterexamples show why the hypotheses of various theorems…
Gamma Function
- 1,446
- 12
- 26