How is "rewiring your brain to become fluent in maths" different from "learning maths"? Can someone explain this? I read the article, and I don't understand it. To me it sounds like she learned maths, in much the same way one learns anything else.
How I Rewired My Brain to Become Fluent in Math
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Re: How I Rewired My Brain to Become Fluent in Math
#62Author makes generalizations based on her own individual experience - the process which she doesn't understand.
Rot-learning in music (mentioned as example of good practice) produces millions of classically-trained musicians that don't understand anything about music, and can't play even Christmas song by ear.
Re: How I Rewired My Brain to Become Fluent in Math
#63Earlier quoted context omitted.
I got tired of not having an intuitive understanding of particular mathematical concepts. The rote memorization was very limiting for be because I wasn't as easily able to grasp when it might apply to certain concepts. Pretty sure Kalid is a commenter here, but I have to give him a huge thanks and plug for BetterExplained.com--really helped me grasp some of these higher-level concepts in a more intuitive manner, even…
Wow, thanks for the plug and the kind words! Glad to hear the site is helping -- most of the time I miss the intricacies too, and end up adding things years later [after a re-read] or in response to a comment from the article. As a more general reply to the article, I was fortunate enough to work with Prof. Oakley on her Coursera Class ( https://class.coursera.org/learning-001/lecture , I'm the last guest interview a…
Very happy to give the plug--the quality of your content and your generosity for putting so much out there for free is something I wish more people did.
I hope the business side of it is going well for you.
Side note--have you considered trying to work with Khan Academy? I feel like Salman's style flows well, but sometimes substitutes learning tricks vs. internalizing the underlying logic. Khan Academy could benefit from a touch of BetterExplained.
Re: How I Rewired My Brain to Become Fluent in Math
#64How is "rewiring your brain to become fluent in maths" different from "learning maths"? Can someone explain this? I read the article, and I don't understand it. To me it sounds like she learned maths, in much the same way one learns anything else.
Authors usually don't get to pick the titles of their articles. That's the editor's job and they try to pick headlines which will attract readers.
Re: How I Rewired My Brain to Become Fluent in Math
#65How is "rewiring your brain to become fluent in maths" different from "learning maths"? Can someone explain this? I read the article, and I don't understand it. To me it sounds like she learned maths, in much the same way one learns anything else.
[deleted]
Re: How I Rewired My Brain to Become Fluent in Math
#66I think those of us who aren't a fan of "memorize/repeat" is that it is extremely inefficient. And you lose as many people as you gain. The classic example is long division. In elementary school I did a thousand long division problems, but I never understood it. I just knew the pattern. I didn't really know the math. It wasn't until much later did I learn how and why it worked. Having done those thousand problems did…
I can relate to your long division example. In grade school my mom helped[1] me put in a ridiculous amount of effort in order to get through my school's spelling tests. I have come to believe that the reason that I couldn't spell was because at the time I did not understand the rules behind how the letters form together to get words. Simply memorizing how words are spelled took a lot of painful practice.
A more recent example is when I was first learning lambda calculus I wanted to understand how church encoding worked to allow basic integer operations with just function abstraction and application. Most of the operators are easy except for predecessor, which is absolutely nightmarish to get on your own. I tried memorizing the definition I found on wikipedia for over a year to no avail, but once I understood how it was working ...
pred = λ n . λ f . λ v.
n ( λ a . λ b . b (a f) )
λ k . v
λ i . i
[1] - well, basically dragged me kicking and screaming
EDIT: formatting
Re: How I Rewired My Brain to Become Fluent in Math
#67Just saw that the author, Barbara Oakley, has a (free) Coursera course titled "Learning How to Learn" starting Oct 3. Sign-up here - https://www.coursera.org/course/learning
Re: How I Rewired My Brain to Become Fluent in Math
#68Assuming the author's convictions are true, how would one apply a 'rote learning' technique to programming? I believe in repetition, but, personally haven't been able to find a useful way of implementing it to become a top-notch programmer. Why? Well, take calculus. Buy a book, pound problems. Do 1,000 derivatives. Next chapter. 1,000 integrals. Is there a similar "exercise" for programming?
Drop in to the REPL, this is why languages that have Read, Eval, Print, Loop are super popular. BASIC, Python, LISP, SQL, Ruby, etc. You can get proficient in such languages faster than C, Java
Re: How I Rewired My Brain to Become Fluent in Math
#69Earlier quoted context omitted.
Wow, thanks for the plug and the kind words! Glad to hear the site is helping -- most of the time I miss the intricacies too, and end up adding things years later [after a re-read] or in response to a comment from the article. As a more general reply to the article, I was fortunate enough to work with Prof. Oakley on her Coursera Class ( https://class.coursera.org/learning-001/lecture , I'm the last guest interview a…
Very happy to give the plug--the quality of your content and your generosity for putting so much out there for free is something I wish more people did. I hope the business side of it is going well for you. Side note--have you considered trying to work with Khan Academy? I feel like Salman's style flows well, but sometimes substitutes learning tricks vs. internalizing the underlying logic. Khan Academy could benefit…
Thanks! The business side of things is coming along, I've just finished up a hectic few months (wedding, honeymoon) and am looking to crank on the site again. Long term I want the site to be an ever-growing part of my life.
I'm very interested in collaborations, and helping people sprinkle an intuitive approach into whatever teaching they are doing. (I like Bret Victor's approach, where he provides guidance on what programming tools could look like, which might work its way into new programming languages like Swift, etc.). I'm in touch with an internet buddy at Khan Academy and have been meaning to work together, I'll be reaching out soon I think :).
Re: How I Rewired My Brain to Become Fluent in Math
#70Earlier quoted context omitted.
I got tired of not having an intuitive understanding of particular mathematical concepts. The rote memorization was very limiting for be because I wasn't as easily able to grasp when it might apply to certain concepts. Pretty sure Kalid is a commenter here, but I have to give him a huge thanks and plug for BetterExplained.com--really helped me grasp some of these higher-level concepts in a more intuitive manner, even…
Wow, thanks for the plug and the kind words! Glad to hear the site is helping -- most of the time I miss the intricacies too, and end up adding things years later [after a re-read] or in response to a comment from the article. As a more general reply to the article, I was fortunate enough to work with Prof. Oakley on her Coursera Class ( https://class.coursera.org/learning-001/lecture , I'm the last guest interview a…
The entries on complex number, exponential functions & e, and many other subjects at betterexplained.com are simply amazing! It helped to clear my decade-long confusions or fears when dealing with them, Thank you for the great work.
In my opinion the three essential characteristics of a great teacher are expert level in the subject at hand, great communication skill and enthusiasm for teaching. Possessing two of them already makes a good teacher. You have all three.