All Questions
Tagged with mathematical-pedagogy calculus
38
questions
6
votes
3
answers
493
views
What is the ULTIMATE Calculus syllabus
After such amazing answers I got here for a related question (link at the end if someone still wants to share with me their views)...
Here is the concept:
If you were to create the ULTIMATE Calculus ...
- 625
2
votes
0
answers
99
views
what is the standard subdivision or classification of calculus related rates problems?
I am working on a project where I have to group/classify calculus problems. Now with most the calculus topics, it's usually obvious how it's divided in various textbooks, but when it comes to related ...
- 81
8
votes
1
answer
193
views
How can I deal with the time pressure of teaching a short course?
I am an undergraduate applied math student. In about a month, I will be teaching two nine-hour math courses (one precalculus, one calculus) to a small group of motivated high school students. My broad ...
- 81
7
votes
2
answers
261
views
How to catch students from different subjects' interest to math?
I have just started to teach Calculus to freshmans and sophomores who study non-mathematical subjects, e.g., international relations, psychology. They have to take few mathematics classes -including ...
- 311
28
votes
4
answers
1k
views
The Undergraduate Responsibility Gradient
We tell undergraduate students that they should study two to three hours for every hour they spend in class. We know that many students don't follow through with this nearly to the degree that they ...
- 6,173
14
votes
4
answers
744
views
Is there research for or against such an approach in teaching calculus?
Copying from Calculus Made Easy by Silvanus Thompson (2nd ed., 1914):
CHAPTER I:TO DELIVER YOU FROM THE PRELIMINARY TERRORS
The preliminary terror, which chokes off most fifth-form boys from ...
- 1,552
4
votes
4
answers
2k
views
How are the basic trigonometric functions introduced to students?
The fundamental trigonometric functions $\sin(x)$ and $\cos(x)$ are used throughout the sciences, but I believe students are often introduced to a very limited initial understanding where it is ...
- 1,137
23
votes
2
answers
1k
views
Is Knuth's suggestion on teaching calculus a good idea?
Note: I myself am not a math educator, though I plan to be one someday.
In this letter, Donald Knuth suggests an alternate way of teaching calculus, based on big-O (introduced via a related big-A ...
- 331
16
votes
2
answers
530
views
Nontraditional calculus recitations
I'm a math grad student, and next semester I start TAing a calculus class for the first time. We all know about the standard recitations: instructor gives short lecture on some more difficult topic ...
- 300
18
votes
5
answers
2k
views
How to convince students of the integral identity $\int_0^af(x)dx=\int_0^af(a-x)dx$?
A common identity in integration is $\int_0^af(x)dx=\int_0^af(a-x)dx$.
The steps to prove it (algebraically, ignoring the geometric method) are as follows.
Let $u=a-x$ so $dx=-du$.
$\int_0^af(a-x)...
- 1,106
11
votes
6
answers
1k
views
How can I convince students that Fourier series are useful?
Main question: Calculating the coefficients of a Fourier series can be difficult and time-consuming. How might a student be motivated/convinced to go through these (potentially tedious) details? Are ...
- 1,243
10
votes
1
answer
701
views
Language to Distinguish Between Variables and Arbitrary Constants
Today in second semester calculus, I found myself stumbling a bit to provide a natural-sounding explanation for all the letters involved in the expression
$$
\lim_{t \rightarrow \infty} \int_1^t \frac{...
- 596
13
votes
7
answers
2k
views
When should we get into limits in introductory calculus courses?
All of the calculus textbooks I've used (teaching at community colleges) start with the first chapter covering limits. (Perhaps after a review chapter.) I think this order is wrong.
Historically, ...
- 21.1k
26
votes
7
answers
4k
views
Why are we so careful in saying that dy/dx is not a fraction?
Calculus instructors are mostly very careful to explain that $\frac{\mathrm{d}y}{\mathrm{d}x}$ is not a fraction, and multiplying both sides of an equation by $\mathrm{d}x$ is nonsense, wrong, or evil....
- 21.7k
3
votes
5
answers
396
views
Average Rate of Change isn't/is Statistics
I have the common misconception in my business calculus classes that the Average Rate of Change, say from $x=1$ to $x=5$, is the statistical average of the rates on the four unit intervals $1$ to $2$, ...
- 8,039