January 13th, 2019, 04:40 PM  #91 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,681 Thanks: 2659 Math Focus: Mainly analysis and algebra 
One wouldn't have thought that Australia had much depth in eroticism. Their reputation is rather more neanderthal than that in such matters.

January 13th, 2019, 06:13 PM  #92  
Senior Member Joined: Aug 2012 Posts: 2,385 Thanks: 745  Quote:
On the other hand when it comes to the way we teach math, we create a lot of confusion in the minds of students. We tell them in high school that a real number is an "infinite decimal expression," whatever that's supposed to mean at that level. We tell them there's this number $\pi$, which is a special one of these "infinite decimals" that has something to do with circles. Remember, these are all students who have never seen a nonnumeric symbol used to represent a constant before. In algebra they learned to find "x" and most of them eventually accept that. But now this $\pi$ is Greek letter, another thing they've never seen before. But it's not a variable, it's some particular number that's special because it's "infinite," an impression a lot of people come away with. No wonder people are so confused and most of them hate math. By the way I believe that the poor teaching of the real numbers in high school is one of the main sources of confusion over Cantor's diagonal argument. People in general have a very shaky grasp of the real numbers and infinite decimals in the first place. The whole enterprise seems bogus to them. And it's not their fault. When I'm in charge, the math educators are in big trouble. Last edited by Maschke; January 13th, 2019 at 06:27 PM.  
January 14th, 2019, 12:09 AM  #93  
Senior Member Joined: Oct 2009 Posts: 863 Thanks: 328  Quote:
The knowledge of the students entering my university is extremely bad. The students are still very bright and smart, but have been taught very badly. I don't blame the students, I don't blame the teachers (their job is very difficult as it is), but I blame the curriculum and the socalled educators. They have succeeded in taking everything mathematical out of math. Math has been reduced to a series of plug and chug exercises and "rules to memorize". No critical thinking involved. No proofs or demonstrations involved (except in geometry, where the level of the "proofs" just is.... horrible).  
January 14th, 2019, 08:20 AM  #94 
Senior Member Joined: Oct 2009 Posts: 863 Thanks: 328 
Now we are on the subject, the following is a must read for anybody interested in education https://www.maa.org/external_archive...lin_03_08.html The points he brings up are extremely important. Sadly, he doesn't really give many good and viable solutions. 

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