Understanding theory before practice

[cs23]

I've been told many times that to improve understanding, one should practice many problems. I've tried that but failed miserably. I end up referring back to worked examples for guidance, rather than thinking. When a more difficult problem arises, I'm finished( if there is not similar problem)

I think I'm lacking in my theoretical knowledge. I usually read/sit though a lecture/book and don't understand a thing. Then i convince myself that if i work problems it will make more sense. Sadly, that doesn't help and i refer back to the solved examples. It's a cycle.

What am I doing wrong?? I do good in school, because i can memorize the solutions(steps) to problems( but have no idea what I'm doing)

 

[victor.raum]

Can I ask which year of high school or college you're in?

 

[cs23]

I'm in second year of mechanical engineering.

I do well, but as soon as the courses are over I remember nothing. I want to change this.

 

[therealnihl]

The way I started to get an intuition about physics is whenever I was bored I would look at all the mechanical phenomena around me and try to explain it using physical concepts (you do not have to do actual calculations) How am I walking? What forces are responsible for giving the torque on my leg to make a step? How can explain walking using energy? How does that bus move? How does that building stay upright? What if there is an earthquake, what would happen to the building? If I'm standing in an elevator, what if I had a weight scale with me, how does this relate to the apparent weight/equivalence principle? If I'm on a train what would happen if the speed of light were 30 mph instead of 3e8 m/s? How do colors work (photoelectric effect+compton scattering)?

The nice thing about this approach is eventually you'll get to phenomena you can't explain using the physical concepts you've been taught so far and then you'll look it up and learn something new! If you continue with this line of questioning, before long you'll be asking questions no one has asked/answered before--then you have an idea for a honors thesis/PHd thesis.

This has worked well for me now I can't even watch one sports show without attempting to visualize the velocity and acceleration vectors.

 

[SophusLies]

I've been told many times that to improve understanding, one should practice many problems. I've tried that but failed miserably. I end up referring back to worked examples for guidance, rather than thinking. When a more difficult problem arises, I'm finished( if there is not similar problem)

This might seem strange but when I begin studying anything I first look at the problems and never read anything beforehand. This way I am 100% on my own to try and experiment what my intuition tells me. Being a good guesser is an extremely value skill, especially in science and engineering. After doing this, you might find out that you were on the right track for solutions or at least you found ways that you know will not work. The next time you see the problems you can immediately rule out what didn't work because you tried it yourself.

You can even do this for math, which most students usually think that math can not be done this way because it's "axiomatic blah blah." One of my math professors once told our class that when he is doing research on a difficult problem he guesses over and over then sees if anything works. From here he said he can get a feel for a solution then tries things closer to the good guesses. On our homework he would usually give a problem or two that he knew we wouldn't be able to solve and we were told to write down our guesses and then try them. This definitely solidified my method of learning and still use it in grad school.

 

[Travis_King]

This is a problem that many people have. It is essential that you understand the theory behind your calculations. The real world is more about understanding the process than doing the math.

question where every part of the equations come from and seek to find the answers. WHY is Moment = F*L, WHY is Pressure = F / Area, etc. You have to work on developing an intuition for these problems as the problems in the real world will not be standard texbook problems (they also probably won't require such rigorous math, but they will require more understanding of the theory).

 

[cs23]

Update: I think i know my problem. I don't ask any questions, so the information doesn't stick. Now I'm trying to question everything

 

[Dembadon]

Update: I think i know my problem. I don't ask any questions, so the information doesn't stick. Now I'm trying to question everything

Beautiful discovery!

Asking yourself questions about what you're doing instead of just going through the motions is, I believe, extremely important to the learning process. I understand things much better when I force myself to answer my own questions.

 

[cs23]

Beautiful discovery!

Asking yourself questions about what you're doing instead of just going through the motions is, I believe, extremely important to the learning process. I understand things much better when I force myself to answer my own questions.

It's unfortunate that I learned this so late. Even from high school I had this problem. I would sit in class, and just listen. But I wouldn't understand anything that went on. If i had asked myself questions, it would have got me thinking.

I've done well and at times very well. But that came from practicing over and over, until the solution was engraved in my head. Though, if a different problem came i was toast.

thanks everybody

 

[victor.raum]

<snip> I would sit in class, and just listen. <snip>

Note that most of the deep learning has to happen outside of the classroom. Sadly, a lot of the time all you can really do in a modern day lecture hall is sit and listen. Don't get me wrong, sometimes questions totally work. Like for example you can ask a Chemistry professor during a lecture on heat how it is that metals can have heat if theyr molecules are supposedly in a rigid and non-moving lattice structure. He'll tell you real quick that the atoms sort of jiggle about "in place," that'll clear your confusion, and that'll be great.

However, for another large class of questions, namely questions of great depth, the answers you get on the fly during a lecture are likely to be shallow or abbreviated.

I mean, if you're still in the process of coming to grips with some core idea in a subject, that has to be figured out with deep contemplation and solitude. Like for example try asking a calculus professor exactly why a definite integral evaluates to F(b)-F(a), or a linear algebra professor why a 3x3 matrix determinant is defined as it is, or a physics professor why central forces create an ellipse. These are of course hugely important questions for a student to ask, but they're never going to get satisfactorily answered unless the professor is willing to throw the rest of the whole rest of his lecture time into answering your question, and then some. He might just give you a hint at the answer and the move on, but you're always going to have to do the heavy lifting and really learn it outside of the classroom. But hey, that's the fun part :D

 

[jeebs]

If you're just memorizing steps to solutions then that's only going to get you so far. You've got to start out with a solid understanding of what each basic concept is about, what each physical quantity actually is, before you can do problems that involve a combination of these things. If you don't understand a book or your notes then read them again until you do understand them, or find different learning materials.

 

[cs23]

what's goes on in your head when sitting through a lecture.

How do you get the information that the professor is saying into your head and make it stick, so you can solve problems later.

For example, when i would sit in a lecture the teacher would be talking about heat transfer, he would show a diagram and the direction of heat flow and the subsequent equations. I see all this, but does it mean i understand it?

how can i actively get the knowledge into my head, without sitting there passively?

 

[victor.raum]

How can i actively get the knowledge into my head, without sitting there passively?

You can't. Well... you could start asking tons of questions to build out your understanding, but that would require literally entering into a one-on-one socratic conversation with the professor right in the middle of the lecture, which probably wouldn't be doable.

Large lectures sadly can't be much more than sessions of passive listening. They aren't where the real learning happens.

 

[atyy]

At least in physics, large lectures can be where real learning happens. A few words from a master can be worth a thousand books giving all the gory details but using the wrong big picture.

 

[victor.raum]

If my opinion appears to differ from atyy, it's because my definition of "real learning" is synonymous with the "gory details." Whereas his doesn't seem to be.

I agree with atyy that a few succinct words from a master on the big picture of an idea can be a great thing, but in my experience such big picture words are a good only in that they motivate you to be curious about gory details so that you'll then want to go home and actually learn the depths of whatever idea was overviewed during the lecture.

And on the other hand, if you have sufficient motivation to study the gory deals just for the pure joy of it, then the big picture stuff will usually pop out at you even without any words from on high.

I would continue to maintain that lectures are mostly superfluous to the task of gaining a real understanding of a subject, expect in so far as they serve as motivators and entertainment sessions. To use c23's example, no matter how many pearls of wisdom are offered during a lecture about heat you're not going to really feel comfortable with the subject until you go home and sit in quiet contemplation pondering on a plethora different heat related situations. You sit and think about what predictions the heat equations make about each different situation, and in this way you develop your deeper visual-spatial and mathematical understanding of relevant equations. You give yourself some difficult problems to solve, and that builds out your comfort level with the relevant paper-based symbol manipulation. Only then do you really feel content and happy with things. That sort of learning (the real learning) just doesn't happen happen in a lecture.