6 ms·

Nothing beats having a (good) teacher. Self-learning, no matter how smart you are, is pitifully slow without a teacher. Half an hour with a good teacher can sav

Nothing beats having a (good) teacher. Self-learning, no matter how smart you are, is pitifully slow without a teacher. Half an hour with a good teacher can save you weeks of table head-butting. (But obviously you can't rely only on the teacher.) As for books, it's not a spectator sport: you gotta do it yourself. Read a sentence, then work it out yourself with pen & paper. You can't get it just from reading alone. Finally: in mathematics there's many many roads to Rome! If something isn't working for you, try another way.

phugoid 9y ago
If OP lives in a city, it shouldn't be hard to find a sharp college kid who will tutor.
iliketosleep 9y ago
I disagree with the general statement that leaning maths is "pitifully slow without a teacher". So long as one has structure (e.g. some kind of syllabus) and has access to google, then learning can proceed very efficiently indeed. In addition, by being able to work through difficulties independently you can "be your own master" so to speak, earning the confidence to solve new and difficult problems without assistance. Having said that, I have come across people who have absolutely no apitutude for maths and definitely need a teacher. In a matsh class, there's usually one one set of people who kind of just "get it" straight away, and another set who struggle despite studying hard. As you said, there are many roads to Rome, and the best road may or may not involve a teacher depending on the individual.
- darkxanthos 9y ago
  An author of a book is still a teacher... we’re just debating the personalization of the teaching at this point.
  - TheTrotters 9y ago
    But then this recommendation becomes vacuous. No one is recommending learning math by deriving everything yourself.
    - darkxanthos 9y ago
      Exactly. What’s really being referred to? Lower cost and more scheduling flexibility perhaps?
  - threatofrain 9y ago
    Maybe, but I think people do mean a literal human, and I do think books were always available, and if that alone were the key... then I hesitatingly make the simple argument that it would've already been done. One might make a similar argument about why Khan Academy isn't a blowout success in the US.
- threatofrain 9y ago
  I think for most people though, not having a teacher doesn't mean "pitifully slow", it means they will eventually forfeit the endeavor. The option to self-study has always been there, and now Khan Academy is here too, but I think there's a reason why we haven't seen an education revolution just yet, and I think it's because an interactive teacher who monitors your state and thinks about the road ahead is key. There are even a lot of math teachers who feel anxiety about basic math. Why don't they simply self-study?
  - iliketosleep 9y ago
    They feel anxiety about basic math because they've lost touch with the basics, and this is a massive problem. They could and should go back and review the basics; otherwise they will not make great teachers.
- chris11 9y ago
  > I disagree with the general statement that leaning maths is "pitifully slow without a teacher". How do you check your work then? I remember specific experiences in college math classes where I thought I understood something, took a test, and then got something wrong. And it was because of a misunderstanding of something I thought I understood. I have those misunderstandings occasionally in math. And that can make self-teaching really difficult. At least with cs/software development you can check your understanding by writing code.
  - iliketosleep 9y ago
    By downloading question papers that have worked solutions. If you get something wrong, check your solution against the worked solution and then error in your understanding should become apparent. This works well up to about college level, after which it's harder to find resources.
    - chris11 9y ago
      That's a good solution, but college-level mathematics was specifically where I had issues learning the material myself. I remember taking an upper-level college class for my cs degree that focused heavily on proof-based mathematics. I decided I wanted a tutor. Online tutoring for the highschool/lower level college classes was easy to find. But not for upper-level proof based math classes that were TA'd by grad students. I finally found one company that was willing to tutor me. They advertised tutors from ivy-league grad schools and started billing at over 100/hr. Fortunately I found a grad student to to tutor me at my university for a much more reasonable price. But I definitely noticed a difference in the type of tutoring offered. I'm much less confident self-teaching myself mathematics if it involves proofs, or material that would show up in grad school or an upper-level undergrad class.
realharo 9y ago
>Half an hour with a good teacher can save you weeks of table head-butting. That says more about the poor quality (or bad fit) of the book/video/material than it says about the skill of the teacher. I guess online courses where students can post comments and talk to each other partially address this. These comments may help point out the parts that the material failed to convey properly (and in an ideal world, such feedback would then be incorporated into the next revision of the material).
- learnstats2 9y ago
  Yes, the quality of the material you use is important. A good teacher can quickly direct you to appropriate materials for your personal needs. A novice learner is generally unable to identify what is or isn't poor quality (hence the OP's question). [Edited to add: This forum has recommended certain materials, but we have no idea whether they suit the OP's needs. There has not been enough two-way communication with the OP, even if the OP has made a good effort to clarify their question.] Using a teacher to bypass this step of identifying materials is way more efficient and... saves you weeks of table head-butting.
  - realharo 9y ago
    For very specialized subjects, I would completely agree. But when it comes to lower-level math - a group of topics that surely have been done to death countless times over, there really should be well-known books (or online courses) by now that learners don't get stuck on. If there aren't, that begs the question why. Though now I'm getting into pointless theorizing territory - as far as practical advice goes, it's true that having regular in-person lessons can also help a lot with discipline - so that's definitely a plus compared to self-learning. On the other hand, just like with identifying quality materials, you need to be able to identify a quality teacher.
    - learnstats2 9y ago
      There aren't universally well-known books or courses that suit everyone studying math at this level, and the why is because everybody has their own needs. What you are calling "lower-level math" includes everything that you might expect people could learn in primary and secondary education, from age 2 to age 16 - that's 15 years in which everyone takes their own path and ends up at a different place. It is specialized.
deleted 9y ago
[deleted]
munin 9y ago
> Half an hour with a good teacher can save you weeks of table head-butting. I spent a year and change trying to teach myself calculus from a textbook. Eventually I signed up for a class at a community college and learned more in a month than I had all year. I think this says more about my learning style than anything else, though, but my experience was shared (on other topics) with lots of other people. I think you benefit a lot from having other people working on the same thing, and you benefit a lot from having a teacher/mentor who can interactively explain to you where you are going wrong. You can definitely find some hard-ass who taught themselves measure theory in a cave, but...
bjourne 9y ago
I'm curious about the need for a teacher. Because I'm learning math by myself and I don't have a teacher. Except for math.stackexchange.com, essentially. How many hours of tutoring/hour of self-study do you recommend? What can tutors help you with that is hard or impossible to learn on your own?
- InitialLastName 9y ago
  An experienced teacher, in a one-on-one situation, can identify the areas you're struggling with much more quickly than you can, and can guide you on a path out that you might not be able to see. I've found that sole self-study can make it easy to convince yourself you're more comfortable with some set of material than you are, which can make it hard to see why you're struggling with the next conceptual layer up.
nicoburns 9y ago
> Nothing beats having a (good) teacher. True. But good teachers can be hard to find, and a lot of things (for example, a good textbook / notes) beat a bad teacher...

phugoid 9y ago

If OP lives in a city, it shouldn't be hard to find a sharp college kid who will tutor.

iliketosleep 9y ago

I disagree with the general statement that leaning maths is "pitifully slow without a teacher". So long as one has structure (e.g. some kind of syllabus) and has access to google, then learning can proceed very efficiently indeed. In addition, by being able to work through difficulties independently you can "be your own master" so to speak, earning the confidence to solve new and difficult problems without assistance. Having said that, I have come across people who have absolutely no apitutude for maths and definitely need a teacher. In a matsh class, there's usually one one set of people who kind of just "get it" straight away, and another set who struggle despite studying hard. As you said, there are many roads to Rome, and the best road may or may not involve a teacher depending on the individual.

darkxanthos 9y ago
An author of a book is still a teacher... we’re just debating the personalization of the teaching at this point.
- TheTrotters 9y ago
  But then this recommendation becomes vacuous. No one is recommending learning math by deriving everything yourself.
  - darkxanthos 9y ago
    Exactly. What’s really being referred to? Lower cost and more scheduling flexibility perhaps?
- threatofrain 9y ago
  Maybe, but I think people do mean a literal human, and I do think books were always available, and if that alone were the key... then I hesitatingly make the simple argument that it would've already been done. One might make a similar argument about why Khan Academy isn't a blowout success in the US.
threatofrain 9y ago
I think for most people though, not having a teacher doesn't mean "pitifully slow", it means they will eventually forfeit the endeavor. The option to self-study has always been there, and now Khan Academy is here too, but I think there's a reason why we haven't seen an education revolution just yet, and I think it's because an interactive teacher who monitors your state and thinks about the road ahead is key. There are even a lot of math teachers who feel anxiety about basic math. Why don't they simply self-study?
- iliketosleep 9y ago
  They feel anxiety about basic math because they've lost touch with the basics, and this is a massive problem. They could and should go back and review the basics; otherwise they will not make great teachers.
chris11 9y ago
> I disagree with the general statement that leaning maths is "pitifully slow without a teacher". How do you check your work then? I remember specific experiences in college math classes where I thought I understood something, took a test, and then got something wrong. And it was because of a misunderstanding of something I thought I understood. I have those misunderstandings occasionally in math. And that can make self-teaching really difficult. At least with cs/software development you can check your understanding by writing code.
- iliketosleep 9y ago
  By downloading question papers that have worked solutions. If you get something wrong, check your solution against the worked solution and then error in your understanding should become apparent. This works well up to about college level, after which it's harder to find resources.
  - chris11 9y ago
    That's a good solution, but college-level mathematics was specifically where I had issues learning the material myself. I remember taking an upper-level college class for my cs degree that focused heavily on proof-based mathematics. I decided I wanted a tutor. Online tutoring for the highschool/lower level college classes was easy to find. But not for upper-level proof based math classes that were TA'd by grad students. I finally found one company that was willing to tutor me. They advertised tutors from ivy-league grad schools and started billing at over 100/hr. Fortunately I found a grad student to to tutor me at my university for a much more reasonable price. But I definitely noticed a difference in the type of tutoring offered. I'm much less confident self-teaching myself mathematics if it involves proofs, or material that would show up in grad school or an upper-level undergrad class.

realharo 9y ago

>Half an hour with a good teacher can save you weeks of table head-butting. That says more about the poor quality (or bad fit) of the book/video/material than it says about the skill of the teacher. I guess online courses where students can post comments and talk to each other partially address this. These comments may help point out the parts that the material failed to convey properly (and in an ideal world, such feedback would then be incorporated into the next revision of the material).

learnstats2 9y ago
Yes, the quality of the material you use is important. A good teacher can quickly direct you to appropriate materials for your personal needs. A novice learner is generally unable to identify what is or isn't poor quality (hence the OP's question). [Edited to add: This forum has recommended certain materials, but we have no idea whether they suit the OP's needs. There has not been enough two-way communication with the OP, even if the OP has made a good effort to clarify their question.] Using a teacher to bypass this step of identifying materials is way more efficient and... saves you weeks of table head-butting.
- realharo 9y ago
  For very specialized subjects, I would completely agree. But when it comes to lower-level math - a group of topics that surely have been done to death countless times over, there really should be well-known books (or online courses) by now that learners don't get stuck on. If there aren't, that begs the question why. Though now I'm getting into pointless theorizing territory - as far as practical advice goes, it's true that having regular in-person lessons can also help a lot with discipline - so that's definitely a plus compared to self-learning. On the other hand, just like with identifying quality materials, you need to be able to identify a quality teacher.
  - learnstats2 9y ago
    There aren't universally well-known books or courses that suit everyone studying math at this level, and the why is because everybody has their own needs. What you are calling "lower-level math" includes everything that you might expect people could learn in primary and secondary education, from age 2 to age 16 - that's 15 years in which everyone takes their own path and ends up at a different place. It is specialized.

deleted 9y ago

[deleted]

munin 9y ago

> Half an hour with a good teacher can save you weeks of table head-butting. I spent a year and change trying to teach myself calculus from a textbook. Eventually I signed up for a class at a community college and learned more in a month than I had all year. I think this says more about my learning style than anything else, though, but my experience was shared (on other topics) with lots of other people. I think you benefit a lot from having other people working on the same thing, and you benefit a lot from having a teacher/mentor who can interactively explain to you where you are going wrong. You can definitely find some hard-ass who taught themselves measure theory in a cave, but...

bjourne 9y ago

I'm curious about the need for a teacher. Because I'm learning math by myself and I don't have a teacher. Except for math.stackexchange.com, essentially. How many hours of tutoring/hour of self-study do you recommend? What can tutors help you with that is hard or impossible to learn on your own?

InitialLastName 9y ago
An experienced teacher, in a one-on-one situation, can identify the areas you're struggling with much more quickly than you can, and can guide you on a path out that you might not be able to see. I've found that sole self-study can make it easy to convince yourself you're more comfortable with some set of material than you are, which can make it hard to see why you're struggling with the next conceptual layer up.

nicoburns 9y ago

> Nothing beats having a (good) teacher. True. But good teachers can be hard to find, and a lot of things (for example, a good textbook / notes) beat a bad teacher...