How best to learn? How to get 100%?

[IneedA]

Homework Statement: I see people saying to understand concepts instead of memorizing.
Relevant Equations: Barely gonna start calculus-based physics. My question is how do i understand concepts and when do i know i have understood them fully? I would like a step by step to this with no room ambiguity or imagination. A video would be amazing. I would like examples, too. Like show where a concept is learned and used to solve difficult problems that would like otherwise be impossible to solve or something like this.

Basically like, if it was your job to make a C student get an A in calculus-based physics. What would you tell them to do if you wanted to guarantee they would get an A?

 

[berkeman]

Welcome to PF.

if it was your job to make a C student get an A in calculus-based physics. What would you tell them to do if you wanted to guarantee they would get an A?

It's hard to make such a guarantee, but there are some things you can do to improve your chances of doing well. One of the biggest ones is to do as many problems as you can. Spend the time to do the work and do lots of problems. If you aren't willing to spend the time to put in all that work, then you probably aren't really interested in doing well in your classes.

 

[sbrothy]

I know apsiring doctors use mnemonic tricks like The memory Palace because they have to learn so much by rote. I'm not sure that'll work with mathematics though; but as someone else said: if you're looking for shortcuts you may be on the wrong path.

The best of luck though.

 

[sbrothy]

Well, as usually I stand corrected:

https://en.wikipedia.org/wiki/Rote_learning

 

[Mark44]

I'm not sure that'll work with mathematics though; but as someone else said: if you're looking for shortcuts you may be on the wrong path.

Maybe you're referring to something like this:

whether there was in geometry no shorter way than that of the elements and he replied, “There is no royal road to geometry”.

 

[symbolipoint]

Basically like, if it was your job to make a C student get an A in calculus-based physics. What would you tell them to do if you wanted to guarantee they would get an A?

First thoroughly review study Intermediate Algebra, and Trigonometry; maybe also extend into "College Algebra". Next,...., I will leave that for later, or maybe for somebody else to respond.

 

[kuruman]

NEVER use AI tools to get answers. If you do, you will not gain the confidence that you can solve problems on your own and without help.

When you get stuck, go to a real person (teacher, fellow student, physics forums) who can get you unstuck and, most importantly, diagnose why you got stuck and what to do in order not to get a stuck when something related comes up again. That's called learning. AI gives you answers but it does not teach you how to get answers on your own.

 

[Mark44]

I'm not sure that'll work with mathematics though

As is stated in the wiki page you cited, rote learning is useful for certain foundational concepts. In arithmetic, it's crucial to know what are referred to as addition facts such the sums of single digit numbers, as well as the "times table." In trig, rote knowledge of at least some of the identities is also very important, although if you know that $\sin^2 \theta + \cos^2\theta = 1$, you can derive the other five circular trig identities. It's also useful to have a few of the derivative formulas and integration formulas under your belt.

 

[sbrothy]

Maybe you're referring to something like this:

Well, I had the distinct feeling that rote learning wouldn't help you learn mathematics (as it wont help you learn figure-skating). Music scales perhaps, but that a very limited usage:

https://www.betterhelp.com/advice/memory/why-rote-memory-doesnt-help-you-learn/

 

[symbolipoint]

when symbols arranged on the page express precise meaning

edit: I guess I should say more than that.
Symbols written on a page in a purposeful ordered way are a transcription of language.
I know the thought may still be incomplete but that's all I feel I can say on it right now.

 

[Mark44]

Well, I had the distinct feeling that rote learning wouldn't help you learn mathematics (as it wont help you learn figure-skating).

Generally speaking, I agree with the above. However, it's important to have certain facts hard-wired, such as the examples I cited earlier.

 

[sbrothy]

Yes, I agree in almost all STEM-disciplines there are a lot of rules to remember, like right-hand and left-hand rules of electromagnetism for instance. And a ton of others. Remembering them is not the whole story though. If you don't actually use them you don't internalize them. If it was that easy I'd just read Penrose's "Road to Reality" and be done with it!

 

[IneedA]

I may have figured something out. I am doing my logic final and I am determining whether the fallacy being committed in an argument is a Hasty Generalization or a Composition. I looked at past problems I solved or examples and none match the problem I am working on.( This method seems like memorizing how to solve problems). So to solve this problem, I have to read what each fallacy actually means. Is this how it will be for physics? If so, how do I learn these definitions effectively in physics? I will have to take the class to see whats going on, but if i could just get an idea of what tasks to perform to give me the best chances of getting an A, I would greatly appreciate it.

 

[CrysPhys]

Well, I had the distinct feeling that rote learning wouldn't help you learn mathematics (as it wont help you learn figure-skating). Music scales perhaps, but that a very limited usage:

<<Emphasis added.>> In figure skating, as well as in other sports, there is the concept of muscle memory. The "figure" in figure skating comes from the aptly named school figures: specific precise geometric patterns that skaters had to repeat over and over to register foundational skills into muscle memory. School figures fell out of favor, and compulsory figures were dropped from competitions in 1990. But less demanding patterns remain in a sequence of tests for figure skaters in training. And some coaches have been pushing for a revival of school figures: they see too many skaters rushing to advanced jumps without having mastered foundational skills.

 

[sbrothy]

I know about muscle memory. Nevertheless I think there's a valid analogy hidden there. You can't read a book about math and get good at it, like you can't read books about figure-skating and get good at that. You have to apply yourself. Granted, mathematics is perhaps not muscle memory per se, but if you don't solve the problems again and again it wont stick. At least that's my experience.

EDIT: As an added bonus you wont hurt yourselves horribly applying yourself at math!

EDIT2: Hit the wrong button. That was hardly funny, thinking about all the poor young girls breaking bone after bone trying to get good at that. Oh and young men too. Ech these #metoo-times!

 

[kuruman]

I may have figured something out. I am doing my logic final and I am determining whether the fallacy being committed in an argument is a Hasty Generalization or a Composition. I looked at past problems I solved or examples and none match the problem I am working on.( This method seems like memorizing how to solve problems). So to solve this problem, I have to read what each fallacy actually means. Is this how it will be for physics? If so, how do I learn these definitions effectively in physics? I will have to take the class to see whats going on, but if i could just get an idea of what tasks to perform to give me the best chances of getting an A, I would greatly appreciate it.

You seem to focus too much on what to do to get an A and not enough on learning. You seem to think that if you only memorized all the rules, you will get that coveted A. That's not how it works. The rules are there to provide the infrastructure and starting points for processing and resolving problems. It's like driving a car. When you learned how to drive, your driving instructor did not cover all the possible situations that you might face in a lifetime of driving. It's up to you to apply and creatively extend what you learned. For example, if your car dies on a railroad crossing with a freight train coming towards you, you should leave the car and get the hell out of there, not to scratch your head and think "Hmm, my driving instructor never covered how to restart my car when it dies on railroad tracks. What do I do now?"

When you do introductory physics problems, you are faced with a physical situation and are required to cast it in mathematical form (it's called modeling) and then answer the question that is posed by the problem. Consider this, for example

Problem
A car is stuck on a railroad track intersection. The driver sees a freight train at distance 100 m moving towards him at 60 km/h. He needs 5 seconds to unbuckle his seat belt, open the door and get out. Will he make it before the train hits? Justify your answer.

Can you provide a solution to this problem on your own? If so, please post it. There are many people in Physics Forums who can look at it and assess where you stand by the way you approached it. However, if your immediate thought is something like "I don't know how to tackle this problem because I haven't taken physics yet", I would say forget about that A in physics and settle for something lower.

Humans can learn to perform adequately in almost any endeavor, but reaching the top requires talent (in my opinion). One can learn how to play the piano adequately, but to become a concert pianist one needs the innate ability to do so. The same is true for physics. The talent required to get an A in introductory physics is the ability to recognize how the solution to a new problem can be assembled from bits and pieces of solutions to problems that you have already seen. Incidentally, that would be an indication that you have understood the old concepts.

Also, when you take introductory physics be aware that there is a learning curve. By this I mean that you should not expect instant understanding at the time you are presented with the material. There is a delay of about 3 weeks until the material becomes your property. I should add the well-known fact that getting an A in introductory physics does not mean that you have really understood it. That happens, and I'm sure most PF users will concur, when you have to teach it.

 

[Mark44]

I am doing my logic final and I am determining whether the fallacy being committed in an argument is a Hasty Generalization or a Composition. I looked at past problems I solved or examples and none match the problem I am working on.( This method seems like memorizing how to solve problems).

More important than the past problems you've solved or the examples are the various types of logical fallacies, a couple of which you have listed. You need to have this catalog of logical fallacies committed to memory, at least for the short term, since these are the tools you'll need to use in order to solve problems. As an analogy, a carpenter who is tasked with building a house always arrives at the job site with tools such as hammers, saws, and so on, together with the knowledge and skill necessary to use them so as to solve the larger problem of how to put the pieces together to make the house.

So to solve this problem, I have to read what each fallacy actually means. Is this how it will be for physics? If so, how do I learn these definitions effectively in physics?

Yes, you have to read and understand each fallacy and retain them in memory in order to categorize the particular problems you need to solve. In physics, you need to memorize the definitions and formulas in order to solve problems they apply to. Back when I was studying Engineering Physics, my housemate and I came up with this saying, "If you don't know that F = ma, then F = your grade."

 

[sbrothy]

You seem to focus too much on what to do to get an A and not enough on learning. You seem to think that if you only memorized all the rules, you will get that coveted A. That's not how it works. The rules are there to provide the infrastructure and starting points for processing and resolving problems. It's like driving a car. When you learned how to drive, your driving instructor did not cover all the possible situations that you might face in a lifetime of driving. It's up to you to apply and creatively extend what you learned. For example, if your car dies on a railroad crossing with a freight train coming towards you, you should leave the car and get the hell out of there, not to scratch your head and think "Hmm, my driving instructor never covered how to restart my car when it dies on railroad tracks. What do I do now?"

When you do introductory physics problems, you are faced with a physical situation and are required to cast it in mathematical form (it's called modeling) and then answer the question that is posed by the problem. Consider this, for example

Problem
A car is stuck on a railroad track intersection. The driver sees a freight train at distance 100 m moving towards him at 60 km/h. He needs 5 seconds to unbuckle his seat belt, open the door and get out. Will he make it before the train hits? Justify your answer.

Can you provide a solution to this problem on your own? If so, please post it. There are many people in Physics Forums who can look at it and assess where you stand by the way you approached it. However, if your immediate thought is something like "I don't know how to tackle this problem because I haven't taken physics yet", I would say forget about that A in physics and settle for something lower.

Humans can learn to perform adequately in almost any endeavor, but reaching the top requires talent (in my opinion). One can learn how to play the piano adequately, but to become a concert pianist one needs the innate ability to do so. The same is true for physics. The talent required to get an A in introductory physics is the ability to recognize how the solution to a new problem can be assembled from bits and pieces of solutions to problems that you have already seen. Incidentally, that would be an indication that you have understood the old concepts.

Also, when you take introductory physics be aware that there is a learning curve. By this I mean that you should not expect instant understanding at the time you are presented with the material. There is a delay of about 3 weeks until the material becomes your property. I should add the well-known fact that getting an A in introductory physics does not mean that you have really understood it. That happens, and I'm sure most PF users will concur, when you have to teach it.

Tried to solve it:

Spoiler

Is he able to make with it ~10 seconds to spare?

EDIT: But I see you're talking about fallacies now, so I probably got it wrong. Embarrassing. But there 's nothing wrong with my fallacy!

 

[sbrothy]

I know about muscle memory. Nevertheless I think there's a valid analogy hidden there. You can't read a book about math and get good at it, like you can't read books about figure-skating and get good at that. You have to apply yourself. Granted, mathematics is perhaps not muscle memory per se, but if you don't solve the problems again and again it wont stick. At least that's my experience.

EDIT: As an added bonus you wont hurt yourselves horribly applying yourself at math!

EDIT2: Hit the wrong button. That was hardly funny, thinking about all the poor young girls breaking bone after bone trying to get good at that. Oh and young men too. Ech these #metoo-times!

What, specifically, made you react like that @symbolipoint? My dinosaur access to #metoo or that I think skaters hurt them themselves horribly training?

 

[symbolipoint]

sbrothy, I do not understand the post #19, you wrote. Suspecting you made major posting compositional mistakes. Big quote of one of your posts, tiny imprecise sentences of yours. Try again but carefully.

 

[sbrothy]

What I meant was that you reacted to my post #17 with a "Wow"! I just wondered what precisely in that post made you react like that. Make no mistake, you're of course entitled to your opinion. As I said, I just wondered what it was in that post that you felt warranted that response?

Also, perhaps this should've been a personal message. Ah well, here we are....

 

[IneedA]

(60km/h)(1h/3600s)(1000m/1km)=16.667 m/s

5sx16.667 m/s=83.335 m

100m>83.335m

. Well, I live next to ucla, usc, and caltech. These schools don't like B’s. The pressure is intense. I get stressed when I see a 90% as opposed to 100%.

I got a B on a midterm. I was stressed seeing my grade at 91% the rest of the semester.

Physics is not until fall so i have time to learn. I have calculus 1 in summer.

I know physics will be my most difficult course. Some people at my college are just going to take physics with easier professors at another college. I am not about it. I want to take physics as it was intended. I just need to know exactly what steps I should to give me the best chance for an A.

 

[berkeman]

(60km/h)(1h/3600s)(1000m/1km)=16.667 m/s

5sx16.667 m/s=83.335 m

100m>83.335m

I did it in my head, so I used a simpler method that is more intuitive to me. $60 \frac{km}{hr} = 1 \frac{km}{min}$ So 1000m in a minute is 100m in 6 seconds. That means the driver has a second to spare.

It's good to get used to trying to work problems in your head to look for simplifications, or at least to get a ballpark estimate of the answer before you start writing out a problem to solve it. That is a part of getting good at working problems...

 

[kuruman]

(60km/h)(1h/3600s)(1000m/1km)=16.667 m/s

5sx16.667 m/s=83.335 m

100m>83.335m

. Well, I live next to ucla, usc, and caltech. These schools don't like B’s. The pressure is intense. I get stressed when I see a 90% as opposed to 100%.

I got a B on a midterm. I was stressed seeing my grade at 91% the rest of the semester.

Physics is not until fall so i have time to learn. I have calculus 1 in summer.

I know physics will be my most difficult course. Some people at my college are just going to take physics with easier professors at another college. I am not about it. I want to take physics as it was intended. I just need to know exactly what steps I should to give me the best chance for an A.

I see a lot of numbers but no answer. Will the driver be able to get out in time and why? You need to supply words explaining what the numbers mean.

It looks like you used a calculator to answer this question. Here is how you can do it in your head.

1. The train moves at 60 km/h. Since 1 hour has 60 minutes, the train travels one kilometer every minute.
2. One kilometer has ten one-hundred-meter intervals.
3. One minute has ten six-second intervals.
4. Therefore the train will cover the one hundred initial distance in six seconds.
5. Thus, the driver can get out with one second to spare.

As far as problem-solving in physics is concerned, I would advise you to use the SIMA step-by-step method, Strategy, Implementation, Manipulation, Answer which I used in my classes.

Strategy (Must contain words and only words; no symbols no equations, no numbers)
Here you explain the logical path that you will follow to answer the question.
Implementation (Must contain words and equations but no numbers)
Here you model the physical situation and use equations to describe mathematically what you said you will do in the previous step. The words that you use must justify the use of the equations, e.g. why this particular equation and not some other equation.
Manipulation (Must contain mostly equations and some words but no numbers)
Here you manipulate the equations algebraically, to get an algebraic expression where the quantity you are asked to find is on the left side and a whole bunch of symbols on the right side.
Answer (May contain numbers if a numerical answer is required)
Here you state the answer to the problem so that the person who evaluates your solution will not have to dig into your scribblings to find it.

So let's illustrate the use of the SIMA method to the stranded car problem.

Strategy
I will calculate the time it takes for the train to travel the initial distance to the stranded car. If this time is more than five seconds, the driver will safely make his escape.
Implementation
We know that the displacement $\Delta x$ of the train moving at constant speed $v$ as a function of time $t$ is given by the equation $$\Delta x=Vt.$$ Manipulation
Solving this equation for the time gives $$t=\frac{\Delta x}{V}.$$ When I replace the initial distance and train speed in this expression, I will get the collision time.
Answer
$$V=60~\left(\dfrac{\text{km}}{\text{h}}\right)\times 1000~ \left(\dfrac{\text{m}}{\text{km}}\right)\times \dfrac{1}{3600} \left(\dfrac{\text{h}}{\text{s}}\right)=\dfrac{100}{6}~\left(\dfrac{\text{m}}{\text{s}}\right). $$ $$t=\frac{\Delta x}{V}=\frac{100~\text{m}}{\dfrac{100}{6}~\left(\dfrac{\text{m}}{\text{s}}\right)}=6 ~\text{s}.$$ Since the train reaches the car in 6 s, the man can escape with one second to spare.

Presenting clearly what you plan to do, explaining what you are doing as you go along, using symbols so that your algebraic manipulations are transparent will get you better grade than just throwing numbers around. Instructors are not mind readers. It is your job to demonstrate to them the extent of your knowledge and understanding.

"Well", you might ask, "who has the time during a physics exam to lay out the solution using the SIMA method?" The student who needs an A, that's who.

The SIMA method is not new. If you think about it, several professions rely on it to solve problems. A doctor will listen to your health problem and suggest a strategy to address it, e.g. we have to do a bunch of tests. At the implementation stage blood is drawn and x-rays taken. At the manipulation stage the doctor assembles the collected evidence to come up with the cause of your health problem. At the answer stage, you are given a supply of pills to take once a day.

Police detectives work the same way. When they find a dead body say, they first develop a strategy, canvas the neighborhood, look for surveillance camera footage etc. Then they implement the strategy by doing just that, then they digest the information to see if it points to a suspect and in the end they find whodunnit.

 

[kuruman]

I did it in my head, so I used a simpler method that is more intuitive to me.

That is why I picked those particular numbers. I gave this problem to my wife and she figured it out the same way. She is a professional historian with analytical skills.

 

[berkeman]

Presenting clearly what you plan to do, explaining what you are doing as you go along, using symbols so that your algebraic manipulations are transparent will get you better grade than just throwing numbers around. Instructors are not mind readers. It is your job to demonstrate to them the extent of your knowledge and understanding.

"Well", you might ask, "who has the time during a physics exam to lay out the solution using the SIMA method?" The student who needs an A, that's who.

I remember an undergrad thermo test (I was doing very well in the class and the instructor knew me pretty well from my class participation) where the hardest question was going to require an iterative approach to the solution. I finished the rest of the test and went back to that problem and explained what I was doing and why, and made it through about 3-4 iterations getting closer to the solution when I ran out of time. I ended that problem with "out of time, another couple iterations should do it...".

I got close to full credit for that problem, and I think I got the top grade on the exam and finished in the top couple of students in the course. So yeah, it's worth the time to explain what you are doing and why so the grader/instructor does not need to try to guess.

Spoiler

Having said that, I was a grader for an undergraduate E&M class where a friend of mine was a student (one year behind me). He is one of the 3 most intelligent people I've ever met or worked with -- he regularly competed in and won Math Olympiads and aced all of his technical classes on the way to his EE degree. He had a habit of not writing much down in his solutions to homework problems, but after talking with the professor about him, I was allowed to give him full credit for his solutions despite the lack of shown work. I wish I had a mind that amazingly strong!

 

[berkeman]

That is why I picked those particular numbers. I gave this problem to my wife and she figured it out the same way. She is a professional historian with analytical skills.

If I tried to give a problem like that to my wife, she'd smack me upside the head!

 

[vela]

I just need to know exactly what steps I should to give me the best chance for an A.

You need to learn how to learn. For each person, it's different, so asking exactly what steps you have to take is misguided. Assess if what you're doing is actually working. If it's not, try something different.

Quit obsessing over grades. You want primarily to focus on learning, not getting an A on a test. Keep a teaching mindset: approach understanding the material as if you're going to teach it to a class.

Algebra and trig are basic subjects you're expected to have mastered. If you're making frequent errors or always having to look things up, e.g., using SOHCAHTOA to resolve a vector into components, you'll be wasting a lot of time you could better spend on learning physics.

Understand that learning takes time and effort. If you give up too easily or if you misuse videos, AI, Chegg, and other resources on the internet to short-circuit the learning process, you won't be doing yourself any favors.

 

[symbolipoint]

What I meant was that you reacted to my post #17 with a "Wow"! I just wondered what precisely in that post made you react like that. Make no mistake, you're of course entitled to your opinion. As I said, I just wondered what it was in that post that you felt warranted that response?

Also, perhaps this should've been a personal message. Ah well, here we are....

What is where going-on? Post #19 or posts #17? I best imagine you mismatched which posts I responded or reacted. So very many more posts from other members are now added, if I say much more doing so will just make this topic messier and messier. I'll try to compose a private response, if I can figure one.

 

[symbolipoint]

ineedA said,

I know physics will be my most difficult course. Some people at my college are just going to take physics with easier professors at another college. I am not about it. I want to take physics as it was intended. I just need to know exactly what steps I should to give me the best chance for an A.

NO. That is quoted wrong! The bottom needs to be OUTSIDE of the quote tag. I will try to put it here now.
EDIT: OK fixed the problem myself.

Be careful with that kind of thinking. The Course is the course, almost no matter who teaches it. You should best decide, who teaches the Course well; who generally teaches well. As far as trying to decide by judging yourself and what other students believe, try to pick the teacher/professor who is level-headed, who is not insane and not a psychopath.