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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

#71

Post by ClashTheBunny »

wwweston wrote: post #16

I can recognize some of my experience in what she's saying -- as I've been told several times in math/stats "you don't understand this, you just get used to it." That's a bit of troubling statement at first, but I think it's sortof a shorthand way of saying that much of the understanding available comes through the process of repeated manipulation and observing outcomes. I've also noticed that a decade or two after g…

It's interesting that that famous quote about math is a von Neumann quote. I always use the same quote with language and I think that there is a strong connection between language learning, especially ultra logical and systematized ones like Russian. Still, for the sake of saying the full quote:

    Young man, in mathematics you don't understand things. You just get used to them.

Re: How I Rewired My Brain to Become Fluent in Math

#73

Post by eric_bullington »

Verdex wrote: post #66
kenjackson wrote: post #28

I 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 recen…

> I couldn't spell was because at the time I did not understand the rules behind how the letters form together to get words.

One of the main goals of this kind of learning (at least for me) is to recognize patterns and rules on your own. When I repeat something often enough, patterns and rules began to jump out at me.

Re: How I Rewired My Brain to Become Fluent in Math

#74

Post by kamaal »

>>student may have thought he’d understood it at the time, and perhaps he did, but he’d never practiced using the concept to truly internalize it.

I'm changing jobs and I've interviewed at quite a few places off late. Having faced with so many Algorithm and Data Structure questions, I took it upon myself to read upon a good deal of material before I started interviewing. So I did the usual approach one takes while studying math, understand all the basic concepts and look for places where you could apply them, rather than studying individual problems.

Recently I interviewed at one place, where I guess a guy who was just out of college asked a few questions. My general approach is to look for how the problem would fit in the concepts I've learned. I gradually derived the solution out of the concepts I knew. And to my surprise, the solution was simply unacceptable to the interviewer, he just clung to his position that I was wrong. He then proceeded to write the answer, he even wrote the test cases.

Now I go back home and check it out of the internet and it was hardly surprising for me to see what I had suspected. The guy didn't want the answer to the question. He wanted exactly the same answer he had memorized. The guy had even memorized the variable names, even the exact input values.

Most people interviewing you on your Algorithm and Data structure skills. They are simply testing your algorithm and data structure rote memorization skills. The same goes in exams.

Re: How I Rewired My Brain to Become Fluent in Math

#75

Post by ClashTheBunny »

blazespin wrote: post #36
oldbuzzard wrote: post #11

I found the article rambling and mostly pointless... However, if you have a weak background in math and want to get up to speed before going into calculus and beyond, I have 2 suggestions. 1) Lial's Basic College Math[1] is adequate and will get you up to speed. 2) Serge Lang's "Basic Mathematics" is great and will cover all you need to go into a rigorous theory based college math class. [1] http://www.amazon.com/s?i…

The article wasn't pointless at all. He's saying that a conceptual understanding is important, but so are things like flashcards. I know growing up my ability to quickly do simple math and recognizing patterns quickly always helped me speed along quickly.

The problem is that unless you are also able to approach things like a constructivist, you will end up with a bunch of disjoint facts. I think that most people just don't understand math well enough to understand this key. The more math I know, the more I wish I hadn't memorized anything, but derived more things. There are many cases these days that I will have to go back and derive an equation for the first time because I was never taught the equation.

Her department is "Industrial & Systems Engineering", she doesn't need to know much more math than how to do arithmetic and a Chai squared. Not that I know more math than she does, it's just not a true part of the mathematical disciplines. She and I probably both just use the tools handed to us and don't understand the beauty or the ugliness. One of the big problems with math today is that nobody understands that arithmetic isn't math. It would be like a baseball player being called a woodworker because she used a wooden bat.

Re: How I Rewired My Brain to Become Fluent in Math

#76

Post by ivansavz »

oldbuzzard wrote: post #11

I found the article rambling and mostly pointless... However, if you have a weak background in math and want to get up to speed before going into calculus and beyond, I have 2 suggestions. 1) Lial's Basic College Math[1] is adequate and will get you up to speed. 2) Serge Lang's "Basic Mathematics" is great and will cover all you need to go into a rigorous theory based college math class. [1] http://www.amazon.com/s?i…

Since we are on the topic of math textbooks, I will suggest the No bullshit guide to math and physics which is a math textbook written specifically for adult learners. See http://minireference.com/ for more info.

I'm the author

Re: How I Rewired My Brain to Become Fluent in Math

#77

Post by anigbrowl »

stdbrouw wrote: post #24
eric_bullington wrote: post #13

I come from a very similar background as the writer. As a young man, I showed high potential for languages. So when I went to college, I loaded up on languages, graduating with 6 different languages at at least the 200-level and fluency in 3 of those languages. Unlike the writer, I chose neither military nor government work upon graduation, but instead worked as an ATA-certified translator for 10+ years, primarily tr…

> But I am in total agreement with the writer that modern education does a grave disservice to young learners by discarding rote learning and repetition. I've come to appreciate the importance of rote learning over the past couple of years... but despite its simplicity, I would call it a very advanced technique. You don't need rote learning to get to understand something. You don't even need rote learning to become v…

Even though I chafed a bit at the delays it imposed and kept asking the teacher about other more advanced topics, I do not regret a single minute of the time spent chanting 12-times tables in my first couple of school years. Same deal for written exercises and homework - I don't think I'd be so good at mental math, estimating, and 'back of the envelope' calculations done in pencil if it weren't for all that practice as a child.

Re: How I Rewired My Brain to Become Fluent in Math

#78

Post by ivansavz »

My observation from years of experience teaching calculus and mechanics is that every student has a different learning style. In particular, there are "theory people" who need to understand the reasoning behind the concepts first and "practice people" who best understand concepts by looking at worked examples. There may be other subdivisions, but these are the main types.

I had two cases when my students showed no signs of progress after hours of theory-style training, and then became Einsteins after solving some practice problems. I was like... why did we waste so much time with the theory???

I don't necessarily agree with the OP that rote memorization is for everyone. Ultimately both the theoretical/symbolic understanding and the "doing"-experience are necessary, but the order in which students acquire these skills is up to them.

Here's a nice quote:

    不闻不若闻之，      Not having heard is not as good as having heard,
    闻之不若见之，      having heard is not as good as having seen,
    见之不若知之，      having seen is not as good as mentally knowing,
    知之不若行之；      mentally knowing is not as good as putting into action;
    学至于行之而止矣    true learning is complete only when action has been put forth
           -- 荀子                                    -- Xunzi

Re: How I Rewired My Brain to Become Fluent in Math

#79

Post by [deleted] »

anigbrowl wrote: post #77
stdbrouw wrote: post #24

Earlier quoted context omitted.

> But I am in total agreement with the writer that modern education does a grave disservice to young learners by discarding rote learning and repetition. I've come to appreciate the importance of rote learning over the past couple of years... but despite its simplicity, I would call it a very advanced technique. You don't need rote learning to get to understand something. You don't even need rote learning to become v…

Even though I chafed a bit at the delays it imposed and kept asking the teacher about other more advanced topics, I do not regret a single minute of the time spent chanting 12-times tables in my first couple of school years. Same deal for written exercises and homework - I don't think I'd be so good at mental math, estimating, and 'back of the envelope' calculations done in pencil if it weren't for all that practice…

[deleted]

Re: How I Rewired My Brain to Become Fluent in Math

#80

Post by Expez »

ivansavz wrote: post #78

My observation from years of experience teaching calculus and mechanics is that every student has a different learning style. In particular, there are "theory people" who need to understand the reasoning behind the concepts first and "practice people" who best understand concepts by looking at worked examples. There may be other subdivisions, but these are the main types. I had two cases when my students showed no si…

“Tell me and I forget, teach me and I may remember, involve me and I learn.” - Ben Franklin
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