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What is mathematical thinking? (2012)

devlinsangle.blogspot.com

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Re: What is mathematical thinking? (2012)

#11

Post by new_guy »

devnonymous wrote: post #9
rvba wrote: post #4

If someone claims to be a "mathematical thinker" then probably they should be able to convey their thoughts in a precise and concise manner. For example by starting with a definition and then expanding/explaining it. Blogspam written by someone who sounds like a teenager with ADHD should be posted in the "iamverysmart" subreddit, not on HN.

Ehe ...you do realise you're speaking about this guy here right? http://profkeithdevlin.com/

Does it magically stop being blogspam if we know who that is supposed to be?

Re: What is mathematical thinking? (2012)

#12

Post by devnonymous »

new_guy wrote: post #11
devnonymous wrote: post #9

Earlier quoted context omitted.

Ehe ...you do realise you're speaking about this guy here right? http://profkeithdevlin.com/

Does it magically stop being blogspam if we know who that is supposed to be?

Yes, A blog post from someone authoritative about the content certainly warrants higher consideration before being dismissed as blogspam by a random passing comment by someone who isn't, imho.

Re: What is mathematical thinking? (2012)

#13

Post by Jensson »

rvba wrote: post #4

If someone claims to be a "mathematical thinker" then probably they should be able to convey their thoughts in a precise and concise manner. For example by starting with a definition and then expanding/explaining it. Blogspam written by someone who sounds like a teenager with ADHD should be posted in the "iamverysmart" subreddit, not on HN.

> they should be able to convey their thoughts in a precise and concise manner.

But that is exactly the thing, most people aren't able to convey their thoughts in a precise manner, it requires a lot of words. Programmers knows this as well, it is hard to describe things precisely, human written language is very imprecise. The difference is that mathematicians has to explain things precisely to other humans, while programmers just has to explain things precisely to a computer, never to other humans, it is fine if the other humans just gets a cursory understanding.

So when it comes to explaining things precisely to other humans mathematicians are the experts, not programmers, programmers still thinks that imprecise explanations are good enough for human consumption.

Re: What is mathematical thinking? (2012)

#14

Post by Oron7 »

Mathematical thinking is logical, relational, recursive, quantitative and analytical thinking. All these types of thinking are expressed through various mathematical techniques. A good book on the subject is "Essentials of Discrete Mathematics" by David Hunter.

Re: What is mathematical thinking? (2012)

#15

Post by hans1729 »

devnonymous wrote: post #10
hans1729 wrote: post #3

So, so much hubris. - "My analogies are brilliant, but you need to already understand the field for them to be brilliant, which I learned after tons of people told me that the analogy is actually not brilliant. But they are brilliant!" - "You need to identify as an X to be good at X" -- No. Polar opposite. The best people in any area don't identify as anything. If anything, the opposite is the case - once you think y…

I'm not sure you either read the entire post or if you did, you grasped the point of the post. Prof. Delvin [1], the author, has been pushing to make math literacy and mathematical thinking more accessible for a long time now. This post is a guide to what that means. [1] http://profkeithdevlin.com/ ..so much for the irony of calling out hubris and stating 'the author is not even close to being competent'

>..so much for the irony of calling out hubris and stating 'the author is not even close to being competent'

I don't see how your answer relates to my criticism at all. What I'm pointing out is that the author touches on a variety of topics where he clearly exceeds his field of expertise. I'm not saying that he is incompetent as a mathematician at all, nor that he is ill-intended in writing the post.

Re: What is mathematical thinking? (2012)

#16

Post by harry8 »

devnonymous wrote: post #10
hans1729 wrote: post #3

So, so much hubris. - "My analogies are brilliant, but you need to already understand the field for them to be brilliant, which I learned after tons of people told me that the analogy is actually not brilliant. But they are brilliant!" - "You need to identify as an X to be good at X" -- No. Polar opposite. The best people in any area don't identify as anything. If anything, the opposite is the case - once you think y…

I'm not sure you either read the entire post or if you did, you grasped the point of the post. Prof. Delvin [1], the author, has been pushing to make math literacy and mathematical thinking more accessible for a long time now. This post is a guide to what that means. [1] http://profkeithdevlin.com/ ..so much for the irony of calling out hubris and stating 'the author is not even close to being competent'

I remember seeing a talk from him (at least I think so or my memory is going to mush) saying he decided to get into giving MOOCS because Khan Academy was so popular and so absolutely terrible. Seemed like hubris at first blush but I gave him the benefit of the doubt and enrolled.

I've ended up doing quite a bit with Sal Khan & Co and have no hesitation is recommending it. (& Co includes Grant Sanderson who has branched off from multivariable calculus at Khan to the whole 3b1b youtube phenom, which is great and also I believe Ben Eater who is also terrific). I didn't get very far with Devlin's coursera MOOC or see the value myself but others mileage may well vary. If you got something useful out of it, please tell us what so those of us who didn't have some chance of seeing the point we missed? But maybe a lot of these kinds of things come down to style and taste?

Re: What is mathematical thinking? (2012)

#17

Post by devnonymous »

hans1729 wrote: post #15
devnonymous wrote: post #10

Earlier quoted context omitted.

I'm not sure you either read the entire post or if you did, you grasped the point of the post. Prof. Delvin [1], the author, has been pushing to make math literacy and mathematical thinking more accessible for a long time now. This post is a guide to what that means. [1] http://profkeithdevlin.com/ ..so much for the irony of calling out hubris and stating 'the author is not even close to being competent'

>..so much for the irony of calling out hubris and stating 'the author is not even close to being competent' I don't see how your answer relates to my criticism at all. What I'm pointing out is that the author touches on a variety of topics where he clearly exceeds his field of expertise. I'm not saying that he is incompetent as a mathematician at all, nor that he is ill-intended in writing the post.

> I don't see how your answer relates to my criticism at all. What I'm pointing out is that the author touches on a variety of topics where he clearly exceeds his field of expertise. I'm not saying that he is incompetent as a mathematician at all, nor that he is ill-intended in writing the post.

Forgive me, I'm confused. You did claim hubris. Which topics, precisely, does the good professor touch upon that is not within his field of expertise as a mathematician and an educator ? ... within this post that you claimed is full of hubris ?

Re: What is mathematical thinking? (2012)

#18

Post by alberto_ol »

hans1729 wrote: post #3

So, so much hubris. - "My analogies are brilliant, but you need to already understand the field for them to be brilliant, which I learned after tons of people told me that the analogy is actually not brilliant. But they are brilliant!" - "You need to identify as an X to be good at X" -- No. Polar opposite. The best people in any area don't identify as anything. If anything, the opposite is the case - once you think y…

At the end of the post there is a note

"The opening paragraph is a parody of such writing. This comment was added a day after initial publication, when a letter from a reader indicated that he missed the fact that the opening was a parody, and complained that he found it difficult to read."

Re: What is mathematical thinking? (2012)

#19

Post by injb »

>>> It’s one of those analogies that is brilliant if you are sufficiently familiar with all four components, but hopeless as a way to explain one in terms of the other three.

Ah yes, one of those - also known as a completely useless analogy.

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