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My observation from years of experience teaching calculus and mechanics is that every student has a different learning style. In particular, there are "theory p

by ivan_ah 12y ago

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

Expez 12y ago
“Tell me and I forget, teach me and I may remember, involve me and I learn.” - Ben Franklin
- Eiriksmal 12y ago
  Very interesting. "I especially thought “involve me and I learn” didn’t sound very Ben-Franklinish, or very 18th century. So I did a little poking around. I found out that while the quote is generally believed to have come from Franklin, it might actually have originated with Xun Kuang, a Chinese philosopher who lived from 312-230 B.C." [0] http://www.gazettextra.com/weblogs/word-badger/2013/mar/24/whose-quote-really/ http://www.gazettextra.com/weblogs/word-badger/2013/mar/24/w...
nl 12y ago
This is so true. I work best from examples, and find learning computer languages from documentation very hard. OTOH, I'm very quick at looking at examples, generalising behaviour, finding edge cases and then looking at the docs to understand those edge cases. One of the best programers I know is the polar opposite. He will spend days reading every. single. piece. of documentation on something, and then 5 minutes writing a perfect piece of code.
- wfunction 12y ago
  Do you end up writing perfect code when you learn from examples? Just like you, I learn from examples rather than by reading documentation... and I suspect that just like me, you don't end up spending 5 minutes writing perfect code. If true, to me, that means your friend's method is superior.
  - nl 12y ago
    After the same amount of time I'd say our code is of the same quality (ie, after say X days working on something new). I'll have written lost of lesser quality versions first and slowly approached an optimal solution. He'd never write anything until he understood it well enough to write the optimal solution first time. Sometimes getting lesser quality versions done quickly is a good thing - certainly I was much more useful at getting a quick messy mostly working solution done (and sometimes that's all that is needed). OTOH, if there is job big enough to amortise that startup cost and important enough that it had to be of the highest possible quality then I'd often give it to him.
pbhjpbhj 12y ago
I'd say the prime proof of true learning is to have taught someone else to put in to action what you have learnt. The "put forth" in the above is not entirely clear to me but I imagine that fits in there as a sub-division.
vidarh 12y ago
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 memorisation. E.g. I remember being given the task to sum all numbers from 1 to 100, and figuring out the algorithm for summing any series from 1 to n in time to be able to be intolerably smug about how quickly I had the result (I must have been 14-15 at the time so it was nothing out of the ordinary - the teacher assigned the task explicitly to see if anyone would find shortcuts or the formula). I then proceeded to spend the rest of the lesson figuring out how to modify it for all odd numbers, even numbers and various other classes of numbers. Up until then, that was how I spent most of my lessons, and my teachers tended to encourage it. I lost most interest in maths when the teaching turned to become more about memorisation, and I was not taught the skills needed to figure out the underlying rules to be able to compensate for not memorising. If I'd been more interested, and invested the time in finding suitable resources myself, I'm sure I could've kept up, but it was still "just school" to me, even though I enjoyed math lessons until then. It went from being my favourite topic to being something I actively avoided because of this.
- TwiztidK 12y ago
  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.
Create 12y ago
"Young man, in mathematics you don't understand things. You just get used to them." -- John von Neumann
xsace 12y ago
不: not 闻: hear 若: good 见: see 之: have 知: know looks easy :)
- akavi 12y ago
  '若' is closer to 'as' or 'equivalent to'
- dmytrish 12y ago
  That's not as easy as it seems. 若 literally means [some kind of] "if", 之 is not "have" but rather "the" [?]. The last line is completely obscure for my very beginner Chinese skills. I'd be glad if someone explained this.
  - ivan_ah 12y ago
    My chinese is probably more rudimentary than yours, but I often use a firefox plugin that helps you get some idea of what the sentence means: https://addons.mozilla.org/en-US/firefox/addon/perapera-kun-chinese-popup-tra/ https://addons.mozilla.org/en-US/firefox/addon/perapera-kun-... (note it recognizes expressions, instead of working only character by character ... )

by ivan_ah 12y ago

Expez 12y ago

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

Eiriksmal 12y ago
Very interesting. "I especially thought “involve me and I learn” didn’t sound very Ben-Franklinish, or very 18th century. So I did a little poking around. I found out that while the quote is generally believed to have come from Franklin, it might actually have originated with Xun Kuang, a Chinese philosopher who lived from 312-230 B.C." [0] http://www.gazettextra.com/weblogs/word-badger/2013/mar/24/whose-quote-really/ http://www.gazettextra.com/weblogs/word-badger/2013/mar/24/w...

nl 12y ago

This is so true. I work best from examples, and find learning computer languages from documentation very hard. OTOH, I'm very quick at looking at examples, generalising behaviour, finding edge cases and then looking at the docs to understand those edge cases. One of the best programers I know is the polar opposite. He will spend days reading every. single. piece. of documentation on something, and then 5 minutes writing a perfect piece of code.

wfunction 12y ago
Do you end up writing perfect code when you learn from examples? Just like you, I learn from examples rather than by reading documentation... and I suspect that just like me, you don't end up spending 5 minutes writing perfect code. If true, to me, that means your friend's method is superior.
- nl 12y ago
  After the same amount of time I'd say our code is of the same quality (ie, after say X days working on something new). I'll have written lost of lesser quality versions first and slowly approached an optimal solution. He'd never write anything until he understood it well enough to write the optimal solution first time. Sometimes getting lesser quality versions done quickly is a good thing - certainly I was much more useful at getting a quick messy mostly working solution done (and sometimes that's all that is needed). OTOH, if there is job big enough to amortise that startup cost and important enough that it had to be of the highest possible quality then I'd often give it to him.

pbhjpbhj 12y ago

I'd say the prime proof of true learning is to have taught someone else to put in to action what you have learnt. The "put forth" in the above is not entirely clear to me but I imagine that fits in there as a sub-division.

vidarh 12y ago

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 memorisation. E.g. I remember being given the task to sum all numbers from 1 to 100, and figuring out the algorithm for summing any series from 1 to n in time to be able to be intolerably smug about how quickly I had the result (I must have been 14-15 at the time so it was nothing out of the ordinary - the teacher assigned the task explicitly to see if anyone would find shortcuts or the formula). I then proceeded to spend the rest of the lesson figuring out how to modify it for all odd numbers, even numbers and various other classes of numbers. Up until then, that was how I spent most of my lessons, and my teachers tended to encourage it. I lost most interest in maths when the teaching turned to become more about memorisation, and I was not taught the skills needed to figure out the underlying rules to be able to compensate for not memorising. If I'd been more interested, and invested the time in finding suitable resources myself, I'm sure I could've kept up, but it was still "just school" to me, even though I enjoyed math lessons until then. It went from being my favourite topic to being something I actively avoided because of this.

TwiztidK 12y ago
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.

Create 12y ago

"Young man, in mathematics you don't understand things. You just get used to them." -- John von Neumann

xsace 12y ago

不: not 闻: hear 若: good 见: see 之: have 知: know looks easy :)

akavi 12y ago
'若' is closer to 'as' or 'equivalent to'
dmytrish 12y ago
That's not as easy as it seems. 若 literally means [some kind of] "if", 之 is not "have" but rather "the" [?]. The last line is completely obscure for my very beginner Chinese skills. I'd be glad if someone explained this.
- ivan_ah 12y ago
  My chinese is probably more rudimentary than yours, but I often use a firefox plugin that helps you get some idea of what the sentence means: https://addons.mozilla.org/en-US/firefox/addon/perapera-kun-chinese-popup-tra/ https://addons.mozilla.org/en-US/firefox/addon/perapera-kun-... (note it recognizes expressions, instead of working only character by character ... )