Linked Questions

25
votes
9answers
1k views

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 ...
20
votes
4answers
7k views

How does one create “good” math problems?

As lifelong students of mathematics, we find problem-solving to be absolutely essential to enhance our understanding of the subject. Teaching others what we know serves to reinforce our existing ...
14
votes
4answers
1k views

When should I say “nothing is as it seems”?

"Intuition" is the best friend and worse enemy of mathematicians! Sometimes using intuitive arguments could be very helpful to understand the nature of a phenomenon. Many of the deepest true ...
10
votes
4answers
525 views

Creativity in mathematics

I have recently been engaging more and more with my creative side by drawing, writing, and (trying to) playing piano. I have come to see mathematics as much more of a creative field of study than I ...
7
votes
1answer
1k views

Jason Padgett's “Struck by Genius”

Can anyone comment knowledgeably on this intriguingly titled book? I have received publisher's promotional materials (as no doubt have many of you), but I know nothing about it. Jason Padgett. ...
13
votes
3answers
585 views

The interplay of memory and mathematical performance

As mathematicians and mathematics educators we very often see the Dunning-Kruger effect in action. Our calculus students are certain that they are masters of Calculus because they took the AP exam. To ...
18
votes
1answer
983 views

How much time to spend on a single question?

When I was self-studying as an undergraduate, I would spend up to two weeks working on a single problem or trying to understand a proof in Rudin's Principles of Mathematical Analysis. I realize now ...
4
votes
1answer
340 views

Learning vs. Development in Practice as a Math Educator

As a math educator, do you distinguish between the concepts of "learning" and "development?" If so, what is the distinction for you? What would you say the consequences of this distinction are to ...
3
votes
0answers
240 views

Learning a topic deeply [closed]

I am currently a "self-studier", so the manner in which I learn is I have a textbook and I work through it in a relatively linear fashion. As I am introduced to new concepts I ask questions (...
0
votes
0answers
142 views

Does this problem enhance mathematical creativity?

There are an equal number of red, yellow, green, and blue cards. Take one of them and put it in the box. Suppose that red cards was most selected, followed by yellow, green, and blue when we selected ...