Do you agree with the idea that students should memorize or be familiar with a “canon” of great proofs? Why or why not? What benefits can students derive from having seen these proofs presented clearly?
Why does Andrew call Euclid’s proof of the infinitude of primes “beautiful”? How can you communicate such appreciation for mathematical concepts to your students?
What is it about the proof of the Pythagorean theorem that Andrew presents that makes it so appealing? Would strictly visual proofs—ancient or otherwise—be more helpful or less helpful for your students? What are some pros and cons for a pictures-only format for proofs?
Andrew suggests we should make certain that before students use something, they understand where it came from. Looking back on your own math education, did you understand (for example) the fundamental theorem of calculus before you ever made use of it? How did that knowledge—or lack of it—affect how you learned its principles? How can you translate your own experience into a beneficial one for your math students?
Analytical cookies are used to understand how visitors interact with the website. These cookies help provide information on metrics the number of visitors, bounce rate, traffic source, etc.
This cookie is installed by Google Analytics. The cookie is used to calculate visitor, session, campaign data and keep track of site usage for the site's analytics report. The cookies store information anonymously and assign a randomly generated number to identify unique visitors.
This cookie is installed by Google Analytics. The cookie is used to store information of how visitors use a website and helps in creating an analytics report of how the website is doing. The data collected including the number visitors, the source where they have come from, and the pages visted in an anonymous form.
This domain of this cookie is owned by Vimeo. This cookie is used by vimeo to collect tracking information. It sets a unique ID to embed videos to the website.