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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

#121

Post by jxm262 »

icantthinkofone wrote: post #112

I remember struggling with Calculus in high school. I sat in the library next to the smartest guy in the class and explained to him that I couldn't figure out why a certain formula was to be used to solve a problem. It went something like: Steve: "You have to use that formula to solve this." Me: "I understand that but why do we use that formula?" Steve: "Cause that's the only formula that works." Me: "OK but how did…

I've constantly struggled with something along these lines too. I've always had a difficult time in Chemistry because i wanted to know the why's of things as opposed to just memorizing things. Even in programming, my intro Java class everyone learned the basic public static void main(String[] args){} and we were expected to take it for granted. The first Hello World assignment took most students a few minutes to complete, but sent me researching the Oracle docs, which led me to the java trail, which made my assignment like a week late lol.

If there's any life hacks on how to minimize this mindset, I'd love to hear about it. I'm constantly struggling to find this balance of memorizing abstractions vs digging in the details.

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

#122

Post by sAuronas »

icantthinkofone wrote: post #112

I remember struggling with Calculus in high school. I sat in the library next to the smartest guy in the class and explained to him that I couldn't figure out why a certain formula was to be used to solve a problem. It went something like: Steve: "You have to use that formula to solve this." Me: "I understand that but why do we use that formula?" Steve: "Cause that's the only formula that works." Me: "OK but how did…

Perhaps the reason most people don't think memorization is important is because they don't realize they already did it through practice outside of school. Usually (if you will), the kids who are more successful in math and science during K-12 education and who pursue STEM in university are the ones exposed to more math early-on ...and often. Having a parent with those skills to help you - even if only ten mins a night after school - is a huge difference-maker. Those who succeed may not realize the advantage those extra ten or so minutes a day over 6 to 12 years have given them over the peers, whose parents were math illiterate and, therefore, ignorate of the process of accumulated study.

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

#123

Post by _RPM »

jxm262 wrote: post #121
icantthinkofone wrote: post #112

I remember struggling with Calculus in high school. I sat in the library next to the smartest guy in the class and explained to him that I couldn't figure out why a certain formula was to be used to solve a problem. It went something like: Steve: "You have to use that formula to solve this." Me: "I understand that but why do we use that formula?" Steve: "Cause that's the only formula that works." Me: "OK but how did…

I've constantly struggled with something along these lines too. I've always had a difficult time in Chemistry because i wanted to know the why's of things as opposed to just memorizing things. Even in programming, my intro Java class everyone learned the basic public static void main(String[] args){} and we were expected to take it for granted. The first Hello World assignment took most students a few minutes to comp…

I think some things you just have to accept as is. If you do not, you will find yourself constantly looking for why something is the way it is. Why does the sum of 1 and 1 equal 2? I couldn't tell you why. I just know that the sum is 2 because I know.

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

#124

Post by Bahamut »

_RPM wrote: post #123
jxm262 wrote: post #121

Earlier quoted context omitted.

I've constantly struggled with something along these lines too. I've always had a difficult time in Chemistry because i wanted to know the why's of things as opposed to just memorizing things. Even in programming, my intro Java class everyone learned the basic public static void main(String[] args){} and we were expected to take it for granted. The first Hello World assignment took most students a few minutes to comp…

I think some things you just have to accept as is. If you do not, you will find yourself constantly looking for why something is the way it is. Why does the sum of 1 and 1 equal 2? I couldn't tell you why. I just know that the sum is 2 because I know.

That is simply because + is defined such that 2 is 1 + 1

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

#125

Post by w8rbt »

icantthinkofone wrote: post #112

I remember struggling with Calculus in high school. I sat in the library next to the smartest guy in the class and explained to him that I couldn't figure out why a certain formula was to be used to solve a problem. It went something like: Steve: "You have to use that formula to solve this." Me: "I understand that but why do we use that formula?" Steve: "Cause that's the only formula that works." Me: "OK but how did…

I asked similar questions. My instructors always encouraged us to just follow the rules and memorize the formulas. We never really were encouraged to understand. Doing that took too long!

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

#126

Post by spion »

jxm262 wrote: post #121
icantthinkofone wrote: post #112

I remember struggling with Calculus in high school. I sat in the library next to the smartest guy in the class and explained to him that I couldn't figure out why a certain formula was to be used to solve a problem. It went something like: Steve: "You have to use that formula to solve this." Me: "I understand that but why do we use that formula?" Steve: "Cause that's the only formula that works." Me: "OK but how did…

I've constantly struggled with something along these lines too. I've always had a difficult time in Chemistry because i wanted to know the why's of things as opposed to just memorizing things. Even in programming, my intro Java class everyone learned the basic public static void main(String[] args){} and we were expected to take it for granted. The first Hello World assignment took most students a few minutes to comp…

YMMW, but I use "I can always fill in that gap later if I have the time" and move on. Later, if I do indeed have the time or I find out that I'm struggling because of missing details, I'll get back to it.

Its like making a temporary mess in a project while trying to understand the problem you are solving and making a promise that you will refactor it later, once you get to something that works.

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

#127

Post by jxm262 »

Bahamut wrote: post #124
_RPM wrote: post #123

Earlier quoted context omitted.

I think some things you just have to accept as is. If you do not, you will find yourself constantly looking for why something is the way it is. Why does the sum of 1 and 1 equal 2? I couldn't tell you why. I just know that the sum is 2 because I know.

That is simply because + is defined such that 2 is 1 + 1

Well yes, you're correct. And I wouldn't obviously struggle with simple addition like 1+1. But... for me, the hard part is the "accepting as-is" on more complex things. Especially on topics that I'm new to, or some higher level concepts. I'm currently learning Scala and really trying to learn FP for the first time and have similar issues.

Also, fwiw, you can take anything to the extreme. Even simple addition :)

http://math.stackexchange.com/questions/321939/proof-of-the-...

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

#128

Post by TwiztidK »

vidarh wrote: post #97
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…

I first understood symbolic derivation after implementing code to apply the rules we'd learned (then I derailed completely and turned the expression evaluator I'd written for it into the core of a compiler). All through primary school and most of high school, I stayed well ahead of the curve in maths because I could figure most things out from what we'd already learned, and finding algorithms was easier than memorisa…

That sounds better than a good portion of my K-12 math education. Starting in 7th grade and going to 10th grade, I would walk into class and the teacher would have a list of problems on the board for us to complete and turn in. That's it. Zero instruction at all, we were expected to read the book to figure out how to do everything on our own because the teacher barely knew how to do the problems. These were the "upper level" math classes too.

This situation was actually pretty terrible. My classmates and I hated this setup and most of us were barely learning the material, those of us who did figure it out usually had to teach those around us since the teacher wasn't. During this time my math grades were low compared to my normal grades, mostly in the B to D range.

Eventually, I found a teacher who would spend class teaching instead of having us work on "homework" the whole time. We would go over all of the relevant theories to the chapter for a few days, showing us, in a way that most of us could understand, mostly how they worked but without getting too in depth. At this point, I went from being the guy barely skating by in math classes to being a straight A student, just because my teacher was willing to put in the effort.

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

#129

Post by cgag »

conistonwater wrote: post #61

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.

There isn't one, all titles like this do is perpetuate the myth that you need some sort of specially wired brain to learn math. I hate the spin of learning as some sort of hack. Surprise, learning something involves repetition and practice.

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

#130

Post by wfunction »

kalid wrote: post #119
wfunction wrote: post #90

Earlier quoted context omitted.

Is there really an intuition for i^i? I can give you the answer but I have nearly zero intuition for it.

Yep, I think so. My philosophy, at least, is that any idea can eventually be intuitive, no matter how difficult at first, if we find the right analogies. I see any exponent like a^b as starting at 1.0, intending to apply a rate of change of (a), but modifying that rate by (b). For example, 3^2 is an initial rate of change of 3x, which is then applied for 2 units of time [leading to 9]. So, 1.0 would turn into 9.0. Mo…

Your intuition is nice for figuring out the directions, but not so nice for explaining the numbers. By which I mean, I can understand why it's real, but I can't explain why i^i = e^(-pi/2)... I would expect it to be a nicer number instead (like 1/2, or 1/e, or something like that). I can't really explain why both pi and e end up int he formula.
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