Most Popular
1500 questions
27
votes
3 answers
Breaking students from the habit of relying on examples
One of the most frustrating things about my experiences teaching math (at the university level, if that matters) is that students seem very reluctant to actually learn the material. Instead, they seem to want to be presented with a series of…
anomaly
- 535
- 5
- 11
27
votes
15 answers
What books are like Knuth's Surreal Numbers?
I'm looking to find more examples of books which bridge the gap between "story" and "mathematics" using narrative and all those other wonderful features we might find in Harry Potter or some other well known children's book.
So far, Knuth's Surreal…
John
- 1,127
- 8
- 15
27
votes
2 answers
What methods successfully identify and eliminate severe math anxiety?
What methods are effective in identifying and eliminating severe math anxiety, this most terrible and unfortunate part of modern mathematics education? This question is not about ordinary math anxiety but about a severe version of the condition that…
John
- 1,127
- 8
- 15
27
votes
8 answers
When should we first teach variables in school math? And how?
From a pedagogical point of view, when is the "right" moment to introduce letters and variables to school children?
Let's say we taught arithmetic, the four operations, did computation exercises, or even "disguised" equations, when in place of a…
amarius8312
- 757
- 5
- 12
27
votes
2 answers
Can students tell the difference between the "definition if" and the "theorem if"?
The word "if" is used in two meanings in mathematics:
Definition. A topological space is compact if every open cover has a finite subcover.
Theorem. A topological space is compact if it is finite.
Remark. There are infinite compact topological…
Joonas Ilmavirta
- 3,750
- 1
- 18
- 51
26
votes
4 answers
How is teaching calculus in high school different from teaching calculus in college?
I've taught calculus in college for five years, and it's always interesting to see students coming in who already had calculus in high school. Many of them do very well, and don't even seem like they needed the course. Others struggle.
I took…
Brian Rushton
- 11,680
- 14
- 67
- 137
26
votes
6 answers
Too much motivation?
This is something that I felt like was difficult for me in some classes, especially lower division differential equations and linear algebra classes. I know professors want to motivate certain topics but I feel like offering motivation honestly…
user5108
26
votes
8 answers
How can I convince someone to use a calculator and not worry about the mechanics too much?
I'm trying to help someone pass their final exam (analysis of functions) so they can graduate high school and move on to college. (Not a teacher, just another student, currently in high level math)
They are currently struggling with many concepts,…
Bassinator
- 363
- 3
- 7
26
votes
9 answers
How can mathematics educators encourage innovation and creativity?
Almost by definition, innovation requires that things be done differently than established custom has it, and comes from the young more often than from the old.
In a field as old and established as mathematics, it can be difficult to find something…
Confutus
- 1,765
- 13
- 23
26
votes
7 answers
A Non-Unique Factorization of Integers!
I'm going to introduce my students to the fundamental theorem of arithmetic (uniqueness of integer factorization to prime factors), and I don't want them to take the uniqueness for granted! To make my students understand that the uniqueness is not…
Behzad
- 2,363
- 1
- 19
- 25
26
votes
8 answers
How to write like a mathematician?
I learned to do math proofs in college. But recently I have begun studying more advanced math books and I've noticed some mathematicians frequently make assumptions that I don't. When I write proofs, I tend to state every detail possible. But…
Stan Shunpike
- 1,076
- 1
- 9
- 20
26
votes
13 answers
What is a good motivation/showcase for a student for the study of eigenvalues?
Courses about linear algebra make great demands on looking for eigenvalues and transforming matrices to diagonal matrices (or, at least, to Jordan normal form). This is somehow a technical, recipe-like part where many students don't see a deeper…
Markus Klein
- 9,438
- 3
- 41
- 96
26
votes
7 answers
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.
However, I really want to be able to say that…
Chris Cunningham
- 21,474
- 6
- 63
- 148
26
votes
14 answers
How to teach pure mathematics to a well-educated adult who did badly in maths at school
My partner is a PhD student in philosophy and has recently developed a keen interest in learning pure mathematics. I am doing my best to teach her (I'm a pure maths PhD student myself) and it is turning out to be a rewarding experience for the both…
user829347
- 361
- 2
- 4
26
votes
4 answers
Common Core, threat or menace? Or maybe ok after all?
I have a background in math but no contact with secondary education or kids. I hear all sorts of stories ... horror stories mostly ... about the Common Core math curriculum in the USA. Then I hear that it will lead to more mathematical thinking so…
user4894
- 361
- 3
- 5