Most Popular
1500 questions
37
votes
10 answers
Combative students in proofs classes
When teaching my first discrete math class recently, I found a subset of about 5 out of 35 of my primarily computer science students who I struggled to reach. If these students simply struggled with the material this would be one thing, but they…
Opal E
- 3,986
- 18
- 45
37
votes
10 answers
Interesting things you learned while grading?
What are some interesting mathematical things you have learned while grading student work (or marking, if you prefer)?
It is final exams time here, so if anyone can help cast a more positive light on the grading experience, it would be most…
Zach Teitler
- 539
- 4
- 8
37
votes
4 answers
Taxonomy of bad proofs
I am interested in finding examples of poorly written proofs that exemplify the types of mistakes made by undergraduate students in their first year or two of writing proofs. I am interested both in examples of poor writing that introduce logical…
Patrick Lutz
- 521
- 5
- 10
37
votes
7 answers
A Lexicon of Math Mistakes
Neil Postman wrote an interesting (and freely available) article called "The Educationist as Painkiller." I highly recommend you read the article for your own enjoyment and as a background to this question, especially pp. 4-6. Here is one of his…
David Ebert
- 3,895
- 2
- 22
- 36
37
votes
4 answers
How to convey the meaning of "mathematical maturity"?
Some university-level courses have no specific prerequisites, yet are mathematically involved to the extent that someone with little to no experience in math will probably find themselves in over their heads. Such courses are often cross-listed and…
Adam Bjorndahl
- 2,071
- 13
- 19
37
votes
13 answers
Examples why university education is important for future high school teachers
At my university, the students in math are mixed up (1/3-1/2 are bachelor/master students, the rest are future high school teachers). A problem arising very often is the discussion dramatically summarized by "I don't need this in high school/I…
Markus Klein
- 9,438
- 3
- 41
- 96
37
votes
7 answers
A calculus book that uses differentials?
All introductory calculus books that I have seen spend most of their chapters on differential calculus talking about derivatives, with at most a short section defining differentials as $dy = f'(x) \, dx$. However, differentials are useful for…
Mike Shulman
- 6,560
- 21
- 53
37
votes
5 answers
What fraction of the population is incapable of learning algebra?
In the comment thread of this academia.SE question, the following generated some strong reactions:
My very different (community-college) perspective is that the math discipline will end up as a filter no matter how much the institution desires…
user507
36
votes
17 answers
Dividing by zero
I was having a discussion with a friend and fellow mathematics teacher the other day when the topic of dividing by zero came up. She is the department head and had this in a questionnaire she gave to prospective teachers at her school. She was…
Andrew Sanfratello
- 3,681
- 2
- 18
- 38
36
votes
9 answers
How can we help students learn to write about their mathematics?
As a guiding example, imagine an undergraduate Calculus II course where students have to complete a guided "research project" and write a "paper" about their work. This can be a shockingly new experience for them, even if the creativity component is…
Brendan W. Sullivan
- 10,779
- 1
- 38
- 82
36
votes
6 answers
How can teachers warn students about common mistakes without causing the student to make the mistake?
For example, if you're teaching integration of $\int \frac{dx}{1+x^2}$, would you mention the common wrong answer of $\ln\left(1+x^2\right)+C$?
--
For myself, I very rarely mention common mistakes since I'd feel I'm possibly causing the very problem…
user13544
36
votes
15 answers
Should I change my take-home exam policy because of one suspected cheater?
This is just the third semester I've been teaching, but I've been tutoring for many years. At the moment I'm teaching to community college students a "Business Calculus" course whose curriculum is attempting to cram an entire semester of calculus…
bloomers
- 617
- 1
- 5
- 10
36
votes
3 answers
How to cure students from the idea that root and squaring are identity operators?
I tutor high school algebra and I’ve noticed that a lot of my students don’t seem to understand what they’re doing when they “convert” between different ways of writing numbers involving perfect squares. For instance, I have seen students simplify…
Swiftheart
- 471
- 4
- 5
36
votes
24 answers
Imbuing a six year old with a sense of mathematical wonder
My six year old started school a few months back and he's loving it. This first year is more about social skills than anything academic and I like that approach. But we're spending some time at home with letters and numbers. In the numbers…
Mathdad
- 580
- 5
- 8
35
votes
15 answers
Justifications for: Why learn mathematics?
I wonder how you teachers walk the line between justifying mathematics because of
its many—and sometimes surprising—applications, and justifying it as the study
of one of the great intellectual and creative achievements of humankind?
I have quoted…
Joseph O'Rourke
- 29,827
- 6
- 61
- 140