How much understanding is enough to truly master a course?

[Mondayman]

My method was to summarize the class notes with as little words/equations as I could with the goal of using no more than one sheet of letter-size paper. Sometimes, I had to write really - really! - small, but I remember summarizing the statics class in less than half a page.

I like this method as well, summarize every lecture or section into your own notes. Often mine are only decipherable by me.

Full-disclosure: I'm not saying that I've never solved problems except in exams.

But you'd be surprise how easily your example can be done sometimes, if one have already played some other sports (like football or speed skating). Skills are transferable and there are a lot of similarities in different fields.

I can agree with that to an extent. At higher levels there is less chance for success however.

I thought you meant zero problem solving. But you are right in that everyone should find what works best for them. Not focusing on problems got you success.

I find being able to summarize the material into your own notes, as if your were teaching it, and apply it to problems deepens understanding, and helps with long-term retention as well.

 

[Dr. Courtney]

... for most people. The entire point is that it can be counter productive to generalize and tell people ”you have to do this to learn well”. This is particularly true with people who have tested different methods for themselves and found out what works for them.

Physics is about solving problems. Saying one can master a physics course without solving problems is like saying you can learn to play football without practicing football or that one can master a musical instrument without practicing the musical instrument.

Impossible? I'll leave that as an academic question. So exceedingly unlikely that it is excellent advice to say, "You have to practice problem solving to master physics."

 

[Mondayman]

... for most people. The entire point is that it can be counter productive to generalize and tell people ”you have to do this to learn well”. This is particularly true with people who have tested different methods for themselves and found out what works for them.

I suppose it's wrong to generalize like that and tell people what to do.

But really, I don't see much controversy in stating that putting some priority on solving problems is essential for success in STEM. Students who don't do the assigned homework or practice tests and leave it to the exams and finals to find out if they've really mastered the material or not are not doing something bright in my opinion. In my experience, people who don't do problems, don't pass the course.

Some people may get through, but that's not really an indicator that their methods were more effective. I bet most student's don't even know what methods work best for them or not. I believe this is discussed in another thread on active learning.

Plus, to claim mastery, you have to have proven ability to apply the stuff to solve problems in my opinion. If I took a simple problem to my professor for help and he was clueless cause he never solved problems, I would not be happy about paying for that course.

 

[Orodruin]

Physics is about solving problems. Saying one can master a physics course without solving problems is like saying you can learn to play football without practicing football or that one can master a musical instrument without practicing the musical instrument.

Nobody is saying this. Please do not build strawmen.

People require different amounts of practice in solving problems versus going through theory to be able to understand and do well for themselves. It is as easy as that. For some, the problem solving part comes quite naturally from the theory.

I suppose it's wrong to generalize like that and tell people what to do.

But really, I don't see much controversy in stating that putting some priority on solving problems is essential for success in STEM. Students who don't do the assigned homework or practice tests and leave it to the exams and finals to find out if they've really mastered the material or not are not doing something bright in my opinion. In my experience, people who don't do problems, don't pass the course.

Some people may get through, but that's not really an indicator that their methods were more effective. I bet most student's don't even know what methods work best for them or not. I believe this is discussed in another thread on active learning.

Plus, to claim mastery, you have to have proven ability to apply the stuff to solve problems in my opinion. If I took a simple problem to my professor for help and he was clueless cause he never solved problems, I would not be happy about paying for that course.

I agree that the ability to solve problems is a fundamental part of mastering a subject, but so is being able to handle the underlying theory. You should probably be at least as unhappy with your professors if they cannot tell you why the method they applied to solve the problems works, which is something I also see in some students that focus too much on problem solving. (I will leave out the payment part because that is political - I will just say I never paid up front for any education).

 

[Mondayman]

I wish I included that handling the underlying theory is important as well.

Forgive me for making it sound as if problem solving is all there is in science. Striving for competence in both aspects is a good idea. And everyone will have different ways of attaining that.

 

[jack action]

The problem with comparing physics with sports or music is that even if you know what to do theoretically, you still need to develop some physical abilities with the latter, like how much pressure to apply or how to keep your balance. It's impossible to master this without experiencing it.

In physics, problem solving is a head thing, just like theory. The hardest part when reading a problem statement is identifying the different parts, like what are the unknown and known variables. But that is a skill that you usually learn in high school algebra. After that, you only need to know the equations to fit those variables, which is usually easy when you master the theory.

About solving problems, the reason I don't like it is that you often focus too much on getting the right answer and not enough on why you got it right. And when you get a hard one - i.e. you don't master the theory - you begin to do anything to get a good answer, things that make sometimes no sense at all, and when you finally get it right, you're not really sure how you did it, because you're mixing the good with the bad. I need to identifying a method that works before trying to do something.

Of course, if you do enough problems, the theory will sink in and you will perfect your method, but too many of the same problems (especially failing at them) kind of discourage/bore me at some point. On the downside, even if you can solve the problems, you sometimes miss on basic theoretical concepts if you don't have "good" problems (which depends on the teacher or textbook you have).

Physics is about solving problems.

Physics is about understanding how the universe behaves. Applied physics is using that knowledge to solve problems. The fact that you can solve a problem, doesn't mean you used physics. For example, people have been building boats that float way before the physics behind it was understood.

I would prefer declaring someone as "mastering physics" if that person can show he/she understands the different concepts and equations without being good at solving problems way before someone who can solve problems by putting numbers in equations, without understanding why it works. But I doubt the former exists: if you master the theory, you can solve problems.

 

[Dr. Courtney]

Physics is about understanding how the universe behaves.

Sure, but someone who cannot make quantitative predictions about the outcome of specific experiments by solving quantitative problems using theory does not really understand how the universe behaves.

Though they often delude themselves that they "understand the concepts" but "just can't work the problems."

 

[Vanadium 50]

before someone who can solve problems by putting numbers in equations, without understanding why it works.

I doubt the latter exists either, at least once you get past the most elementary level.

 

[Orodruin]

I doubt the latter exists either, at least once you get past the most elementary level.

They do exist. I have seen several examples in master level courses that include both a written exam and an oral exam. It is much more common than you would think.

 

[Vanadium 50]

Let's make sure we are talking about the same thing. I am talking about someone who can work a problem that they have never seen before by coming up with the right equation and solving it, without understanding the physics. I think this is quite rare.

 

[Orodruin]

Let's make sure we are talking about the same thing. I am talking about someone who can work a problem that they have never seen before by coming up with the right equation and solving it, without understanding the physics. I think this is quite rare.

If I understood @jack action correctly, this is not the kind of people he described by

someone who can solve problems by putting numbers in equations, without understanding why it works

In particular, the ”putting numbers in equation” part.

 

[Vanadium 50]

Well, by upper division, there is relatively little putting numbers in equations. Usually the answer to a problem is an equation, not a number.

 

[Orodruin]

Well, by upper division, there is relatively little putting numbers in equations. Usually the answer to a problem is an equation, not a number.

Still in those cases, there are certain motions for certain types of problems. The students I was referring to are at master level and the problems I put in the written exams certainly had expressions as answers, not numbers.

It never ceases to amaze me how some students can do quite bad/well in a written exam, yet when you give them an oral exam they move to another end of the spectrum.

 

[Vanadium 50]

Let's take the case of someone who says, "OK, we need to expand in orthogonal polynomials. Since the geometry is spherical, these will be Ylm's, Turning the crank, I get..."

Is this real understanding? Or is it plugging in?

 

[Orodruin]

Let's take the case of someone who says, "OK, we need to expand in orthogonal polynomials. Since the geometry is spherical, these will be Ylm's, Turning the crank, I get..."

Is this real understanding? Or is it plugging in?

Impossible to tell without asking additional questions in my experience.

 

[symbolipoint]

Arguments like what is going on here miss the kind of assessment that can and does take place - Assessment questions can be for mathematical problem-solving questions, and assessments can focus on concepts and theory. Nothing stands in the way of teaching professor using both kinds of assessment questions/problems.

 

[grandpa2390]

Define master! If I take the word literally, the answer is: As much as it needs to teach it.

I like that definition... I'm going to steal it ;)

 

[George Jones]

It never ceases to amaze me how some students can do quite bad/well in a written exam, yet when you give them an oral exam they move to another end of the spectrum.

When I was an undergrad, we had "oral" final exams in both semesters (same instructor) of fourth-year quantum mechanics. Each student had an appointment in the prof's office to solve problems on the prof's blackboard while the prof watched. The problems were the same as he would have given in a typical sit-down final exam. No consultation with book, notes, or formula sheet was allowed. The more the prof had to intervene to help the student through a problem, the lower the grade on the problem.

 

[grandpa2390]

When I was an undergrad, we had "oral" final exams in both semesters (same instructor) of fourth-year quantum mechanics. Each student had an appointment in the prof's office to solve problems on the prof's blackboard while the prof watched. The problems were the same as he would have given in a typical sit-down final exam. No consultation with book, notes, or formula sheet was allowed. The more the prof had to intervene to help the student through a problem, the lower the grade on the problem.

I could see how someone might do worse under those circumstances. lol. a written exam gives you time to sit around trying things and waiting for a Eureka moment. being stared down the entire time would be stressful.

 

[Orodruin]

I could see how someone might do worse under those circumstances. lol. a written exam gives you time to sit around trying things and waiting for a Eureka moment. being stared down the entire time would be stressful.

My most stressful moment in a professor’s office ocurred after I handed in an assignment. He asked me to take a seat while he corrected it and I was just sitting there waiting while he was staring intently at my assignment and making sounds like ”mhhmmm” and ”aha”.