Math education: It’s not about numbers, it’s about learning how to think
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Re: Math education: It’s not about numbers, it’s about learning how to think
#2As my old boss once said, "never confuse mathematics with mere arithmetic."
Re: Math education: It’s not about numbers, it’s about learning how to think
#3As my old boss once said, "never confuse mathematics with mere arithmetic ."
Exactly. That's why there are three kinds of mathematicians, those who can count, and those who can't.
Re: Math education: It’s not about numbers, it’s about learning how to think
#4I think a major issue with math problems in school is that they're obvious.
By that I don't mean it's easy. But when you're grappling with some problem, whatever it is, eg find some angle or integrate some function, if you don't find the answer, someone will show you, and you'll think "OMG why didn't I think of that?"
And you won't have any excuses for why you didn't think of it. Because math is a bunch of little logical steps. If you'd followed them, you'd have gotten everything right.
Which is a good reason to feel stupid.
But don't worry. There are things that mathematicians, real ones with PhDs, will discover in the future. By taking a number of little logical steps that haven't been taken yet. They could have gone that way towards the next big theorem, but they haven't done it yet for whatever reason (eg there's a LOT of connections to be made).
Re: Math education: It’s not about numbers, it’s about learning how to think
#5I think a major issue with math problems in school is that they're obvious. By that I don't mean it's easy. But when you're grappling with some problem, whatever it is, eg find some angle or integrate some function, if you don't find the answer, someone will show you, and you'll think "OMG why didn't I think of that?" And you won't have any excuses for why you didn't think of it. Because math is a bunch of little log…
Reminds me of this quote:
"The view that machines cannot give rise to surprises is due, I believe, to a fallacy to which philosophers and mathematicians are particularly subject. This is the assumption that as soon as a fact is presented to a mind all consequences of that fact spring into the mind simultaneously with it. It is a very useful assumption under many circumstances, but one too easily forgets that it is false. A natural consequence of doing so is that one then assumes that there is no virtue in the mere working out of consequences from data and general principles."
Alan Turing
Re: Math education: It’s not about numbers, it’s about learning how to think
#6I think a major issue with math problems in school is that they're obvious. By that I don't mean it's easy. But when you're grappling with some problem, whatever it is, eg find some angle or integrate some function, if you don't find the answer, someone will show you, and you'll think "OMG why didn't I think of that?" And you won't have any excuses for why you didn't think of it. Because math is a bunch of little log…
Reminds me of this quote: "The view that machines cannot give rise to surprises is due, I believe, to a fallacy to which philosophers and mathematicians are particularly subject. This is the assumption that as soon as a fact is presented to a mind all consequences of that fact spring into the mind simultaneously with it. It is a very useful assumption under many circumstances, but one too easily forgets that it is fa…
You might want to edit that to fix the name. It's "Turing", not "Turning".
Re: Math education: It’s not about numbers, it’s about learning how to think
#7The true eye-opener for me was reading Number - The Language of Science by Tobias Dantzig. The philosophy part of math as an abstraction layer for what is observed or deducted was a nice touch.
Re: Math education: It’s not about numbers, it’s about learning how to think
#8As my old boss once said, "never confuse mathematics with mere arithmetic ."
A professor of mine who was quite bad at arithmetic used to say, "I'm a mathematician, not an arithmetician."
Re: Math education: It’s not about numbers, it’s about learning how to think
#9> it's about learning how to think
It's about learning a set of thinking skills, not how to think. Many people who know no math can think and function very well in their domains and many people who know lots of math function and think poorly outside of math.
Re: Math education: It’s not about numbers, it’s about learning how to think
#10Exactly, as ordinary hacker i was always afraid of math. But after taking mathematical Analysis I realized how wonderful math is. These day i am in love with pure mathematics. It literally corrected my brain pipeline in so many ways and it continues to do it further and further.
I have thought about changing my major to pure mathematics too.