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> how I always find maths and particularly statistics - I always just want to answer ‘but why’ and then people lose interest in explaining after a while. Unles

by acqq 7y ago

> how I always find maths and particularly statistics - I always just want to answer ‘but why’ and then people lose interest in explaining after a while. Unless you try to solve more problems yourself, you won't understand the advantages or disadvantages of some methods in solving the problems. So the real answer is: construct the examples, compute and compare, don't approach it "philosophically." All the methods used today survived because they were the solutions to some problems. It doesn't mean that everybody applies them properly: for that you have to get some experience yourself. Learning about the historical development of the methods is also for me satisfying experience: e.g. logarithms aren't a concept devised for philosophical purposes, Napier developed them to save astronomers time and limit "slippery errors" of (their) calculations: https://www.thocp.net/reference/sciences/mathematics/logarithm_hist.htm https://www.thocp.net/reference/sciences/mathematics/logarit...

pnutjam 7y ago
I think you just described the common core method. The main problem is teachers don't understand all the methods they are teaching and kids pick up on this. Then the parents don't understand all the methods and the few intellectually curios help their kids figure it out; but he vast majority of people just tell their kids it's stupid.
- acqq 7y ago
  I didn't address the topic of what and how children learn, I've given some ideas to the one who wrote: "I have a PhD in computer science but I cannot understand long division" For that, personal experience in devising the examples, evaluating them and comparing the results is the only way to get the understanding. One can't complain that one doesn't understand Greek texts if one personally never tried to learn the Greek letters. One could have learned "about" Greek but at the end one hasn't done the inevitably necessary preconditions to actually read Greek texts. The error in thinking is believing that because one already learned about something else somewhere else he should somehow "understand" something without doing the necessary work on that something. The solution is "make your own homework" to fill the gaps. The topic of what, how and why children learn in schools is much more complex. Edit: Also, now reading the Wikipedia article: https://en.wikipedia.org/wiki/Long_division https://en.wikipedia.org/wiki/Long_division I do understand why people don't understand it: the taught notation for the process, used in many countries, is utterly confusing to me, so my reason for confusion when looking at various notations is not that I don't understand the nature of the method but that I haven't spent time analyzing what was built on top of the basically simple idea -- I can also "understand" all the notations but I'd also need more time for that. Still, having enough experience, I can claim that I understand the idea and the process even if I never learn all the notations and conventions in different countries (which part of the process you write where, what you write and what you don't when etc). The idea is simple, the conventions enforced don't have to be. Those who only learned the conventions maybe never invested any time to figure out what's behind the conventions: what is actually being done.

by acqq 7y ago

pnutjam 7y ago

I think you just described the common core method. The main problem is teachers don't understand all the methods they are teaching and kids pick up on this. Then the parents don't understand all the methods and the few intellectually curios help their kids figure it out; but he vast majority of people just tell their kids it's stupid.

acqq 7y ago
I didn't address the topic of what and how children learn, I've given some ideas to the one who wrote: "I have a PhD in computer science but I cannot understand long division" For that, personal experience in devising the examples, evaluating them and comparing the results is the only way to get the understanding. One can't complain that one doesn't understand Greek texts if one personally never tried to learn the Greek letters. One could have learned "about" Greek but at the end one hasn't done the inevitably necessary preconditions to actually read Greek texts. The error in thinking is believing that because one already learned about something else somewhere else he should somehow "understand" something without doing the necessary work on that something. The solution is "make your own homework" to fill the gaps. The topic of what, how and why children learn in schools is much more complex. Edit: Also, now reading the Wikipedia article: https://en.wikipedia.org/wiki/Long_division https://en.wikipedia.org/wiki/Long_division I do understand why people don't understand it: the taught notation for the process, used in many countries, is utterly confusing to me, so my reason for confusion when looking at various notations is not that I don't understand the nature of the method but that I haven't spent time analyzing what was built on top of the basically simple idea -- I can also "understand" all the notations but I'd also need more time for that. Still, having enough experience, I can claim that I understand the idea and the process even if I never learn all the notations and conventions in different countries (which part of the process you write where, what you write and what you don't when etc). The idea is simple, the conventions enforced don't have to be. Those who only learned the conventions maybe never invested any time to figure out what's behind the conventions: what is actually being done.