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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 w

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 they come up with that one formula?" Steve: "Cause it just works!!" He didn't know. That's when I first realized a lot of his knowledge was just memorization while I needed to know the why. It wasn't till my first year in college that I finally found a math instructor who always shows us the reasons why that I was able to take off and grasp math by connecting the dots. So, no, I do not think memorization is the key but, like most zen things, understanding is.

Taek 12y ago
The point of this article is that they need equal emphasis. If you don't know why you're using a certain formula, you're missing half the picture, but you're still going to be able to solve problems faster than someone who has to redo the derivation every time they see a problem. In professional life (as a programmer), it's very valuable to be able to look at a problem and think 'hash table!' before even fully understanding what sort of problem I'm approaching. I can get things done a lot faster because I've practiced my algorithms and data structures and I have strong intuitions for where each is useful. At the same time, having a well explained, fundamental understanding of how everything works is critical to innovation. If you're staring at a problem that nobody has ever been able to sovle before, it means that the general basket of tools isn't going to help, because if it would somebody would have already solved it. The point of this article is that both styles of learning are critical, but America has largely thrown one of them out the door.
mafafu 12y ago
You have a good point, but I think the author was making the case that a conceptual understanding AND memorization/repetition are required to make the learning stick. I don't see a case for not explaining concepts, but a caution to not go too far the other way. And I saw repetition as being more important than memorization. That by repeating the application of your understanding of some concept, as being the key to making it stick.
clueless123 12y ago
Right on man.. When you think you know something, you earned your Bachelors. When you realize you dont Know a thing, you get your Masters. When you realize no one else knows either you get a PHD!
jxm262 12y ago
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.
- _RPM 12y ago
  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.
  - Bahamut 12y ago
    That is simply because + is defined such that 2 is 1 + 1
    - jxm262 12y ago
      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-standard-algorithm-for-addition http://math.stackexchange.com/questions/321939/proof-of-the-...
- spion 12y ago
  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.
sAuronas 12y ago
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.
w8rbt 12y ago
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!
Zelphyr 12y ago
I feel like this touches on the Montessori Method quite a bit. Most schools assume the student is an empty vessel and that the knowledge needs to be poured in. Montessori takes the approach that humans are naturally curious and that we in fact LOVE to learn so it encourages understanding through exploration. I would say the rote memorization that the author of this article lauds is actually unnecessary. When one is learning through exploration of a subject and subjects you in fact are exposed to the same concept many times (like with memorization) but you have the added benefit of association with other concepts. In other words; learning doesn't have to be boring to be effective!

Taek 12y ago

The point of this article is that they need equal emphasis. If you don't know why you're using a certain formula, you're missing half the picture, but you're still going to be able to solve problems faster than someone who has to redo the derivation every time they see a problem. In professional life (as a programmer), it's very valuable to be able to look at a problem and think 'hash table!' before even fully understanding what sort of problem I'm approaching. I can get things done a lot faster because I've practiced my algorithms and data structures and I have strong intuitions for where each is useful. At the same time, having a well explained, fundamental understanding of how everything works is critical to innovation. If you're staring at a problem that nobody has ever been able to sovle before, it means that the general basket of tools isn't going to help, because if it would somebody would have already solved it. The point of this article is that both styles of learning are critical, but America has largely thrown one of them out the door.

mafafu 12y ago

You have a good point, but I think the author was making the case that a conceptual understanding AND memorization/repetition are required to make the learning stick. I don't see a case for not explaining concepts, but a caution to not go too far the other way. And I saw repetition as being more important than memorization. That by repeating the application of your understanding of some concept, as being the key to making it stick.

clueless123 12y ago

Right on man.. When you think you know something, you earned your Bachelors. When you realize you dont Know a thing, you get your Masters. When you realize no one else knows either you get a PHD!

jxm262 12y ago

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.

_RPM 12y ago
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.
- Bahamut 12y ago
  That is simply because + is defined such that 2 is 1 + 1
  - jxm262 12y ago
    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-standard-algorithm-for-addition http://math.stackexchange.com/questions/321939/proof-of-the-...
spion 12y ago
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.

sAuronas 12y ago

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.

w8rbt 12y ago

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!

Zelphyr 12y ago

I feel like this touches on the Montessori Method quite a bit. Most schools assume the student is an empty vessel and that the knowledge needs to be poured in. Montessori takes the approach that humans are naturally curious and that we in fact LOVE to learn so it encourages understanding through exploration. I would say the rote memorization that the author of this article lauds is actually unnecessary. When one is learning through exploration of a subject and subjects you in fact are exposed to the same concept many times (like with memorization) but you have the added benefit of association with other concepts. In other words; learning doesn't have to be boring to be effective!