All Questions
Tagged with mathematical-pedagogy calculus
38
questions
33
votes
14
answers
2k
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Revisiting topics from previous courses [closed]
I teach calculus to students who have almost all taken calculus before. (Primarily first-year college students who took calculus in high school but didn't perform well enough to skip the course.)
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- 11.6k
28
votes
4
answers
1k
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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
27
votes
6
answers
795
views
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 ...
- 1,218
27
votes
3
answers
1k
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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. ...
- 1,446
26
votes
7
answers
4k
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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
23
votes
2
answers
1k
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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
21
votes
6
answers
6k
views
How rigorous should high school calculus be?
In the UK, calculus taught in secondary school focuses mainly on computation of derivatives and integrals and solving simple differential equations. There is a small amount of discussion about limits ...
- 1,725
20
votes
4
answers
1k
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Evaluating the reception of (epsilon, delta) definitions
Both education researchers and mathematicians discuss the challenge of (epsilon, delta) type definitions in real analysis and the student reception of them. My impression has been that mathematicians ...
- 2,238
20
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3
answers
2k
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What to do when a majority of students have insufficient mastery of the prerequisite material?
I'm currently teaching a second-semester calculus course in which a significant percentage of my students (over half) either tested into the course just out of high school, took a much easier first ...
- 1,723
18
votes
5
answers
2k
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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
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
15
votes
15
answers
7k
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Students can't seem to grasp the intent of tangent lines and getting general trends of derivatives from graphs
Background
I'm informally helping a few students with college Calc 1. This isn't the first time I've aided people with calculus, and so they've sought me for help, though I don't consider myself to ...
- 291
15
votes
6
answers
3k
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Is there any difference between teaching calculus for math and engineering students?
In our university both math and engineering students attend in the same calculus classes. There are arguments in our department about the possible influences of this approach on students. It seems ...
user230
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
13
votes
7
answers
2k
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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, ...
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