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How I Rewired My Brain to Become Fluent in Math

nautil.us

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

#41

Post by notduncansmith »

rubicon33 wrote: post #33

Assuming 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?

Depending on what you want to learn, sure. Googling for "[someLanguage] practice problems" appears to turn up good results for most languages.

For data structures, write some unit tests and then make them pass.

I personally wouldn't recommend you bother learning the implementation details of algorithms: just learn the names and use-cases. Make some Quizlet flash cards and you're good. If you're having trouble finding some to learn, try Googling "sorting algorithms" or "sorting algorithm for [someDataStructure]". Go from there. I'd recommend a similar approach for design patterns.

If you want to get better at building applications, practice by reimplementing apps you use every day in your favorite language (or just come up with your own). "Building applications" encompasses a wide variety of things not mentioned above that you'll only be exposed to by building stuff, so do that.

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

#42

Post by Dylan16807 »

MilnerRoute wrote: post #25
dubcanada wrote: post #14

Earlier quoted context omitted.

This is why the education system will never ever change. Too many people learn too many different ways. Some people can read a formula and instantly memorize it. Other's need a connection to that formula. Some need to figure out how that formula was derived in order to understand and memorize it. And some know the formula before you even show it too them. Not to rehash what you hashed, but it depends who you are. If…

This is very true. A corporate trainer once told me there's specific kinds of learners. They've actually identified each type, and which specific methodologies you need to reach each one. The best teachers find a way to synthesize it all into an effective single presentation. (This may also be why tutors are so helpful -- they can customize their material to the audience...)

Although there is ample evidence that individuals express preferences for how they prefer to receive information, few studies have found any validity in using learning styles in education.[2] Critics say there is no evidence that identifying an individual student's learning style produces better outcomes. There is evidence of empirical and pedagogical problems related to the use of learning tasks to "correspond to differences in a one-to-one fashion".[3] Well-designed studies contradict the widespread "meshing hypothesis", that a student will learn best if taught in a method deemed appropriate for the student's learning style.[2]

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

#43

Post by goodJobWalrus »

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.

she. the authors name is barbara oakly.

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

#44

Post by Chinjut »

was_hellbanned wrote: post #40

As someone who graduated with a math minor and promptly forgot the vast majority of what he learned, something that really messed me up were gaps in my education. For example, I took a graduate level course in the foundations of mathematics (proving natural numbers and arithmetic). I grasped the lectures, but one day I was completely stumped by a step in the proof where algebra was performed across an inequality. I h…

What do you mean by "algebra across an inequality"? (Does this mean things like "x < y is equivalent to 5 + x < 5 + y"?)

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

#45

Post by jdbernard »

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…

I disagree. We are expecting students to learn more than ever before. Math is a great example. Their ability to handle even a simple concept like multiplication requires fluency in addition. The ability to learn algebra requires fluency in arithmetic. The ability to learn calculus requires fluency in algebra. Tons of kids pass one grade but emerge unprepared for the next. The author hits the nail on the head: they understand the material at the time, but never develop fluency. Then next year when they try to build on that foundation it has evaporated. Rote learning should begin in elementary. I am thankful that I was required to learn my multiplication tables.

Yes, we need to tailor our teaching to the attention span and abilities of our students, but that doesn't mean we shouldn't be using this powerful tool of fluency through rote learning.

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

#46

Post by edwinespinosa »

I liked her point of repetition being the main problem. It makes sense as we strengthen the new synopsis that are made. Josh Foer author of moonwalking with Einstein proposed an interesting theory that, essentially fucked up imagery of any kind helps increase and strength synaptic connections.

Interesting watch (first 5mins gives good context) http://books.google.com/books/about/Moonwalking_with_Einstei...

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

#47

Post by e12e »

rubicon33 wrote: post #33

Assuming 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?

> Is there a similar "exercise" for programming?

Project Euler?

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

#48

Post by michaelcampbell »

aeharding wrote: post #7

What an incredibly short-sighted sentence: "Sorry, education reformers, it’s still memorization and repetition we need.". I could not disagree more with this article. Memorization helps, but MAKING CONNECTIONS between concepts is _HOW YOU MEMORIZE EFFECTIVELY_. Memorizing is great for learning different languages. NOT MATH. Sure, maybe students are bullshitting in understanding concepts, and forgot quickly since they…

> Memorization helps, but MAKING CONNECTIONS between concepts is _HOW YOU MEMORIZE EFFECTIVELY_.

This is the essence of the article. It is chunking.

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

#49

Post by e12e »

robaato wrote: post #23
MisterBastahrd wrote: post #21

Memorization is not learning. It is a part of learning. Being able to memorize things and understand their relationships in context is learning.

My German teacher at school did an accelerated course from scratch at university (no previous knowledge) - a full language degree. It involved rote memorisation of German texts. It worked! She said that the advantage was that you later recognised phrases and grammar and were able to analyse what was previously just rote memorisation. I spent a couple of years in Italy in my early 20s and learnt fluent Italian in that…

From experience with exchange students, staying with families and going to regular local secondary school (ages 15-18, look at www.afs.org for more information) -- that sounds typical for an adult in a non-native work setting, making an effort.

Generally students starting at zero will use 3/5/7 months to approach fluency, approaching native level at the end of a stay. The difference being the "jump distance" -- so German to Norwegian or Spanish to Italian is 3 -- Arabic to Norwegian might be 5 -- and Japanese to Norwegian might be closer to 7.

Coming to Norway, sometimes students with poor English skills will do better - not being tempted to fall back to English, breaking the immersion - and not having such a hard time "forcing" class mates to speak Norwegian.

Having spent a year in Japan myself, it's fascinating how one can go from seemingly "nothing" to fluent after those months of no apparent progress. But language learning tends to be like a staircase -- you can feel stuck at one level for a long time (and being in a foreign setting it can be incredibly frustrating to be constrained to a preschool level of speech) -- only to seem to jump up a level. And then you'll be stuck there... etc

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

#50

Post by mw67 »

For those interested in this learning approach, I recommend the book "The Talent Code" by Daniel Coyle [1] which covers 3 areas for mastering new skills.

Here the author only mentions about the importance of repetition (which she refers to as fluency). In the Talent code book Repetition is the first step, but we can learn that the brain is wired to master new skills by taking advantage of 2 others areas as well: A/ Ignition (or passion and motivation), and B/ Discipline and long term commitment.

[1] http://www.amazon.com/The-Talent-Code-Greatness-Grown/dp/055...

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