- Thread starter
- #1

- Jan 17, 2013

- 1,667

- Thread starter ZaidAlyafey
- Start date

- Thread starter
- #1

- Jan 17, 2013

- 1,667

- Thread starter
- #2

- Jan 17, 2013

- 1,667

- Admin
- #3

- Jan 26, 2012

- 4,198

- Feb 21, 2013

- 739

For some reason I can't really study good at morning... I can really focus when it's late and dark out side. Is it only me?

Regards,

\(\displaystyle |\rangle\)

- Admin
- #5

I'm the same way...I get my best work done when "decent" folks are asleep.

For some reason I can't really study good at morning... I can really focus when it's late and dark out side. Is it only me?

Regards,

\(\displaystyle |\rangle\)

For me to truly learn something mathematical, first I need to understand the derivation or proof, then it's a matter of being able to apply it to as broad a scope of problems as possible.

- Feb 21, 2013

- 739

Hello MarkFL,I'm the same way...I get my best work done when "decent" folks are asleep.

For me to truly learn something mathematical, first I need to understand the derivation or proof, then it's a matter of being able to apply it to as broad a scope of problems as possible.

I agree with you but if I am honest. I know this is not really something good but I bet many student can admit. In my school we read math really fast, and I can't really do that fast so I will be a litle behind, then their is moment when you get close exam and you got some part left to understand and you don't really got time to fully understand and want to know the 'method to solve' because you wanna succed exam. Well those part I done I really understand and feel safe but their is part that take more time.. That is why summer will be a great time where you can really careful read and understand without have any pressure

Regards,

\(\displaystyle |\rangle\)

- Admin
- #7

- Mar 5, 2012

- 9,416

- Skim through all the
**bold**and/or*italic*words and try to absorb what they mean (and/or write them down).

With little time this is all I do.

It's the difference between being considered an expert and being considered someone who shouldn't be present in a meeting. - Skim through any examples or other concrete stuff (often at the end of a chapter).
- Try a couple of exercises if present (or think up my own).
- Try to make sense of propositions.
- Skim through proofs, although I usually don't get that far until confronted with the need to do so.

Whenever I'm teaching, the first and foremost thing as far as I'm concerned, is definitions, definitions, definitions.

If someone doesn't know the words and symbols, there is nothing to talk about in a sensible manner - it's like trying to make sense of Chinese (assuming you don't know the language).

- Thread starter
- #8

- Jan 17, 2013

- 1,667

For me , when I first study something I take theorems for granted . But if I want to go deep in a certain subject then I have to understand the proof and be able to derive it .

- Admin
- #9

- Mar 5, 2012

- 9,416

Yep. For most purposes there's no need to know or understand the proofs.

For me , when I first study something I take theorems for granted . But if I want to go deep in a certain subject then I have to understand the proof and be able to derive it .

That usually only becomes important if you're actually studying math with an accent on the theoretical side.

IMO, in math it

- Thread starter
- #10

- Jan 17, 2013

- 1,667

Absolutely , I think everyone should take a course in logic and methods of proofs . It will make your life just easier .Yep. For most purposes there's no need to know or understand the proofs.

That usually only becomes important if you're actually studying math with an accent on the theoretical side.

IMO, in math itisimportant to know which methods you can use to proof something (mostlydeductionandproof by contradiction).

- Jun 26, 2012

- 45

- Mar 4, 2013

- 188

I think the best way to study a theorem is by keep deriving it(rather than simply byhearting).For me , when I first study something I take theorems for granted . But if I want to go deep in a certain subject then I have to understand the proof and be able to derive it .

- Feb 29, 2012

- 342

I try to do that as well - the problem is that it takes too much time, and when you're hard pressed it's quite tough to digest everything properly.

That also happens, but when you have major theorems (whose proofs take pages) it's somewhat impractical to continuously keep deriving it.I think the best way to study a theorem is by keep deriving it(rather than simply byhearting).

I'm not sure my way of learning has been established it, but what I do know is that it doesn't match tests here. I'm so frustrated about my bad results, despite often knowing the material.

- Thread starter
- #14

- Jan 17, 2013

- 1,667

Yes , it sometimes happens to me . When you get a bad grade in a subject which you think you understand, your confidence becomes less.I'm not sure my way of learning has been established it, but what I do know is that it doesn't match tests here. I'm so frustrated about my bad results, despite often knowing the material.

But , I think it is difficult to measure how well we understand a certain topic. Exams don't usually measure that , they , for the most part, measure how well you read the book or listened to your professor . Sometimes , exams measure how many problems you solved (this is the worst for me ).

- Feb 29, 2012

- 342

Everything you said is so true; yet, how can counteract the fact that you will, in the end, be measured by people who don't know you by those same grades?Yes , it sometimes happens to me . When you get a bad grade in a subject which you think you understand, your confidence becomes less.

But , I think it is difficult to measure how well we understand a certain topic. Exams don't usually measure that , they , for the most part, measure how well you read the book or listened to your professor . Sometimes , exams measure how many problems you solved (this is the worst for me ).

- Admin
- #16

- Mar 5, 2012

- 9,416

Questions verifying you know the definitions.

A couple of checks if you can reproduce an example.

If you can do both, you may already have a sufficient grade.

Then more questions for which you may need to know a proof.

And more questions, requiring deeper understanding of the matter.

You can only get a perfect grade if you can do all.

- Feb 29, 2012

- 342

Interesting, you should give that piece of advice to my teachers. I haven't seen such a set up for my exam in a LONG while. Right now, most of my examinations require fierce memorization of lists of exercises set forth, and those who fail to memorize all the details score poorly. In fact, that happened in cases where we had the teacher choose a set of problems.

Questions verifying you know the definitions.

A couple of checks if you can reproduce an example.

If you can do both, you may already have a sufficient grade.

Then more questions for which you may need to know a proof.

And more questions, requiring deeper understanding of the matter.

You can only get a perfect grade if you can do all.

When I took multivariable analysis the set was "all exercises from 'Calculus on Manifolds' by Spivak"; when I took real analysis (measure theory) the set was "all problems from 'Elements of Real Analysis' by Bartle". It also happened that both teachers did not know how to solve said exercises. The first constantly used the solutions manual found in the internet, the second didn't care. We didn't know topology when we took measure theory, and the teacher made constant use of it. At some point he realized people weren't exactly following his 'explanations' (read: copying the book on the board). He promptly asked: "Everyone knows point-set topology, right?" The answer was an unanimous "no." He replied with "Well, Bartle does," followed by a shrug and continuing to copy the book on board.

I am taking Metric Spaces Topology this semester. My lecturer has decided that this course is useless and instead chose to use Munkres' General Topology as the textbook. Frequently he does not know what he is doing in front of the class and claims absurdities until somebody points out the huge flaws in them (he once said that projections weren't continuous in the product topology). He confessed that while he chose some problems of the book he didn't know how to do most of them.

Yet, can you guess what happened on the test? That's right: rote memorization of certain problems he had chosen on the lists. And not quite so easy ones: one of the questions reminded you about the uniform topology on $\mathbb{R}^{\omega}$ (the cartesian product of the real line with itself "real" times), and defined the metric as $$d(x,y) = \left( \sum_{i=1}^{\infty} (x_i - y_i)^2 \right)^{\frac{1}{2}},$$ assuming that $\sum_{i=1}^{\infty} x^2_i \leq \infty$. The problem: show that this defines a metric on $\mathbb{R}^{\omega}$ and that it produces a topology finer than the uniform topology but coarser than the box topology.

There were 4 other questions to be done within a period of 2 hours. Can you imagine proving this in necessary detail and still having feasible time to answer the other four? I could tell you them, but I believe this already gives quite an idea of what is common around here.

tl;dr All this ranting is to say one thing: if the exam isn't "carefully set up in different difficulty levels" but rather "sloppily set up with arbitrary criteria", how does one get by? I have a hard time not getting pissed off about all of this. It goes against my nature to just see things hitting the fan and going unpunished. Later, the same incompetent professor will be the one to evaluate your skills, and when he sees the numbers without the accompanying background he'll be likely to say "well, not so skilled, are we?"

- Thread starter
- #18

- Jan 17, 2013

- 1,667

- Feb 29, 2012

- 342

I apologize if I have sounded rude to you, I Like Serena. It's just that it hit my berserk button pretty hard that one adopts the position that tests are carefully set up the way you mentioned and therefore failure to acquire the desirable grade was basically a failure to understand the concepts and prepare yourself for such standard test. That, unfortunately, seems to be pretty far from my frequent reality that it's not even funny.

Addressing your points, Zaid, I want to point out that I try hard to conform to what reasonable testing should be. I work a lot to maintain subjects as close to continuous practice as I can (although I may not always be successful), and it breaks me when I get surprised with unfair or completely off the rails tests.

It's pretty much the rule that most people get close to zero out of lectures. In the video I posted of Eric Mazur there is a discussion about that and it clarifies many points regarding this issue. The main problem seems to lie in that lecturing almost always implies passivity from us students, and that makes the transfer of knowledge way harder. It's not unusual to realize that when you participate in class by asking questions or debating with teacher generates greater comprehension of the material. That happens because the stance adopted requires active work on our part and thus our brains manage to retain more information.

Anyway, the thread is about the best way of learning. Regardless of the events I mentioned, there is much to learn about how to study. Let's keep the dice rolling!

- Admin
- #20

- Jan 26, 2012

- 4,198

I totally agree with this one. Which is why Socratic dialogue is, in my opinion, one of the most effective ways to teach. I ask slightly leading questions, hoping the students will do the heavy lifting in their thinking. I don't go so far as the modern education fads, which say that the teacher is an equal. No, the teacher knows the subject or art or lesson to be taught, and has to know it. But if the teacher can get the student to rediscover it, then the student owns that.It's pretty much the rule that most people get close to zero out of lectures. In the video I posted of Eric Mazur there is a discussion about that and it clarifies many points regarding this issue. The main problem seems to lie in that lecturing almost always implies passivity from us students, and that makes the transfer of knowledge way harder. It's not unusual to realize that when you participate in class by asking questions or debating with teacher generates greater comprehension of the material. That happens because the stance adopted requires active work on our part and thus our brains manage to retain more information.

There's an old book, originally published in 1884, called

- Admin
- #21

- Mar 5, 2012

- 9,416

I guess I should have added that it has been that way in my experience.I apologize if I have sounded rude to you, I Like Serena. It's just that it hit my berserk button pretty hard that one adopts the position that tests are carefully set up the way you mentioned and therefore failure to acquire the desirable grade was basically a failure to understand the concepts and prepare yourself for such standard test. That, unfortunately, seems to be pretty far from my frequent reality that it's not even funny.

On high school, on university, and for all the people I've been tutoring.

What you write sounds pretty bad.

Rote memorization? IMHO, that's no way to learn math!

It's pretty much the rule that most people get close to zero out of lectures. In the video I posted of Eric Mazur there is a discussion about that and it clarifies many points regarding this issue. The main problem seems to lie in that lecturing almost always implies passivity from us students, and that makes the transfer of knowledge way harder. It's not unusual to realize that when you participate in class by asking questions or debating with teacher generates greater comprehension of the material. That happens because the stance adopted requires active work on our part and thus our brains manage to retain more information.

Interesting.I totally agree with this one. Which is why Socratic dialogue is, in my opinion, one of the most effective ways to teach. I ask slightly leading questions, hoping the students will do the heavy lifting in their thinking. I don't go so far as the modern education fads, which say that the teacher is an equal. No, the teacher knows the subject or art or lesson to be taught, and has to know it. But if the teacher can get the student to rediscover it, then the student owns that.

I have found most lectures in my higher education near useless.

Now work group sessions - those were useful!

My own favorite way of teaching is indeed the Socratic dialogue.

But I can see that it's not feasible to do on a great scale.

- Feb 29, 2012

- 342

I think you'd be amazed if you watched part of the video I posted in the thread Peer Instruction. While the advice is sound for all, it's mostly directed at physics. I agree with what you said about the teacher not being an equal: someone needs greater experience than the rest so he can guide the discussion in a fruitful manner, or else venues that are a waste of time will be explored rather than interesting problems.I totally agree with this one. Which is why Socratic dialogue is, in my opinion, one of the most effective ways to teach. I ask slightly leading questions, hoping the students will do the heavy lifting in their thinking. I don't go so far as the modern education fads, which say that the teacher is an equal. No, the teacher knows the subject or art or lesson to be taught, and has to know it. But if the teacher can get the student to rediscover it, then the student owns that.

There's an old book, originally published in 1884, calledThe Seven Laws of Teaching. I have one quote from it in my signature. The entire book is filled with pithy statements like that. The gold in that book, are all the violations of the laws that John Milton Gregory points out. You won't find a single violation he mentions that does not occur in many schools.

Also, I didn't get the "violations" paragraph.

I agree! I wish I had a similar experience, I'm sure I'd be learning more.I guess I should have added that it has been that way in my experience.

On high school, on university, and for all the people I've been tutoring.

What you write sounds pretty bad.

Rote memorization? IMHO, that's no way to learn math!

That's because most lectures are designed as simple transfer of information from the professor speaking to the student. The problem is that it doesn't work as effectively as we hoped. Eric Mazur even mentions that he once saw someone define lecture as the process where the notes get transferred from the professor's book to the student's. Work group sessions are amazing - if done right. What I mean is that I often don't get much from those unless I'm levelled with others in terms of material, even if I'm not confident about it.Interesting.

I have found most lectures in my higher education near useless.

Now work group sessions - those were useful!

My own favorite way of teaching is indeed the Socratic dialogue.

But I can see that it's not feasible to do on a great scale.

About your great scale, I must point out the peer instruction link above. I think you may find it an interesting option for your classes.

- Banned
- #23