Mathematics Educators Stack Exchange
Mathematics Educators Stack Exchange

Most Popular

more tags
1500 questions
17
votes
5 answers

How can we focus students on the various data types in multivariable calculus?

To try to find out if students knew what the gradient was, after the computational questions, I asked the following question on an exam: Let $f(x, y) = 5 - x - y$. Why doesn't it make sense to find $\nabla(\nabla f)$? My students almost…
Chris Cunningham
  • 21,474
  • 6
  • 63
  • 148
17
votes
1 answer

Addressing fundamental math errors

I am looking for ways I can correct fundamental math mistakes. I am currently tutoring someone taking a course which is a cross between first year calculus and grade 12 functions. In high school he learned math by memorizing a bunch of rules and…
Gareth Shepherd
  • 271
  • 1
  • 3
17
votes
4 answers

Mindless use of "antisimplifications" such as $1/x+1/y=(x+y)/xy$ and $1/\sqrt{2}=\sqrt{2}/2$

I recently gave an exam problem that roughly 2/3 of the class made much more difficult by using the identity $1/x+1/y=(x+y)/xy$. Their work would have been much simpler if they hadn't done this. It seems like a symptom of the type of intellectual…
user507
17
votes
2 answers

What are some strategies to remedy and accommodate dysgraphia?

I have a few students that have difficulties writing. To generalize, these students have nearly illegible handwriting, they take a very long time to write, they become anxious or fatigued when writing large amounts or writing in a timed task, and…
Andrew
  • 1,776
  • 10
  • 22
17
votes
11 answers

topics for an undergraduate Math seminar

What are some good topics for an undergraduate Math seminar? I am looking for topics which are: Approachable for at least second or third year students and beyond (The students have taken all of the introductory Math courses, Logic, Real Analysis,…
Tom
  • 279
  • 1
  • 2
  • 5
17
votes
3 answers

How to invite humanities students to study mathematics?

This question comes from the perspective of an undergraduate math major who feels that much (although not all) of the mathematical discipline is a liberal art, rather than a science, and should be presented as such. I regularly interact with bright,…
Reuben Stern
  • 273
  • 1
  • 5
17
votes
5 answers

Frequent calculus error: replacing interior part of an expression with its limit

For example $$\lim\limits_{n\to\infty}\left(1+\frac{1}{2n+1}\right)^{n} =\lim\limits_{n\to\infty}{1}^{n}=1\,.$$ Here the student has replaced the sub-part $\frac{1}{2n+1}$ with its limit $0$, but he left the other $n$ at the exponent. I always tell…
amarius8312
  • 757
  • 5
  • 12
17
votes
6 answers

What is the ideal course sequence for an advanced student of mathematics?

Suppose that you meet a student who: has a firm grasp of algebra and trigonometry and is at least moderately intelligent has read a book such as Love and Math by Edward Frenkel so has some appreciation of math as a discipline including its scope…
James S. Cook
  • 10,840
  • 1
  • 33
  • 65
17
votes
9 answers

Evaluating integrals geometrically, without using the fundamental theorem of calculus

I'm designing a lesson for an Introduction to Integral Calculus class, and I want to encourage students to evaluate integrals without just going straight for the antiderivative and using the fundamental theorem of calculus. I want them to think…
Mike Pierce
  • 4,845
  • 1
  • 20
  • 56
17
votes
4 answers

How to explain what is wrong in this "proof" that $\sqrt N$ must be irrational?

Here is the problem that I asked undergraduate students of an introductory number theory course to prove: Prove that if $N$ is a nonsquare natural number, then $\sqrt N $ is irrational. Many of them proceeded as follows: Suppose we can write…
Amir Asghari
  • 4,428
  • 17
  • 40
17
votes
12 answers

Geometric intuition for $D(e^x) = e^x$

I'm teaching a preparatory course on mathematics at a university. The content is mostly calculus, manipulating expressions and solving equations and inequalities. I show a couple of simple derivations/proofs and ask the students to occasionally…
Tommi
  • 7,018
  • 2
  • 25
  • 54
17
votes
3 answers

Efficient ways to grade proof-based math courses

My school employs undergradates graders for most of the undergraduate math courses, and this year I have been tasked with grading an intro to proof-based linear algebra course. This is students' second exposure to proofs after the…
user369210
  • 271
  • 1
  • 2
17
votes
3 answers

Does the "how old is the shepherd" phenomenon occur for more relatable word problems?

A friend of mine just showed me this article about the "how old is the shepherd" problem: Link Of course, I'm shocked by the finding that 75 percent of kids give an answer other than "there isn't enough information." But I wonder whether the…
Tim kinsella
  • 491
  • 2
  • 13
17
votes
6 answers

What is a better way to explain these claims about limit are not true in general?

As a TA who led calculus* 1 and 2 discussion section and holds office hour** in the previous year, I heard the following (wrong) arguments several times. $\displaystyle \lim_{x\to \infty} \sqrt{x+1}-\sqrt{x}=0$ because…
user2139
17
votes
4 answers

Do students confuse $\log_ab$ and $\log a^b$?

I recently observed a group of students being introduced to logarithms for the first time. Some of them had trouble writing $\log_ab$ properly, and it looked more like $\log a^b$. All logarithms have a base, so $\log a^b$ doesn't even mean anything…
Joonas Ilmavirta
  • 3,750
  • 1
  • 18
  • 51
1 2 3
…
99 100