Comments on: Math Learning Tip: Experience Ideas Directly

By: GEORGE JOHN

GEORGE JOHN — Thu, 22 Jun 2017 23:12:00 +0000

Superb insights about learning and teaching and well written. My perspective (not necessarily the correct one) is that short term memory involves electrical circuits in our brain (its rapid) and long term learning (insightful, felt concepts) needs to be embedded in our proteins. Some people can easily form the electrical circuits and regurgitate facts. Others need "deep, meaningful" learning to remember. The way much of educational evaluations are now structured, based on MCQs, test only the "superficial" component. I am a medical doctor who has been teaching for many years. I could see this in the students who score high on MCQs but are lost when faced with real life situations- there are others who love to dive into the experience and are very good at practical management but are lost when trying to convey it to admiring peers! I guess we need both...one for ourselves and the other to store and transmit experiences and insights for future generations.

By: Vlada

Vlada — Mon, 29 May 2017 16:48:29 +0000

Hi Kalid ,how do you find "the pieces"???

By: Alex K Chen

Alex K Chen — Thu, 25 May 2017 08:14:10 +0000

In reply to kalid.

I replied a comment mentioning two math stackexchange questions I have asked (intrigued by Tripti Paul's original question) from an account with the same name (you can google the question names to get the link) "Painless introduction to polynomials" (This refers to this article) and "Why are polynomials interesting", but the comment got deleted :(

Awaiting for the article on polynomials.

By: Alex K Chen

Alex K Chen — Thu, 25 May 2017 08:10:54 +0000

In reply to kalid.

Yeah, that insight is good. Things are simple and have good connection with number theory when you have polynomials with coefficients from the positive integers [0,1,...,n-1], so you can basically interpret them as numbers in base n or higher.

Things get completely out of intuition when coefficient go from positive integers to negative, then REALS, (rationals are same as integers, just multiply with lcm of denominators), then COMPLEX, and I have not idea then. I have also no idea what's the application of factorizing polynomials with non-integer coefficients or finding zeroes.

Inspired by Tripti Paul's above comment, I have asked this question: (https://math.stackexchange.com/questions/2295088/painless-introduction-to-polynomials) (you may see the comment section is pretty demotivating there) or this (https://math.stackexchange.com/questions/2286075/why-are-polynomials-interesting question).

Awaiting for a betterexplained article on polynomials soon. !