Why I failed an exam? (problem solving vs lecture note reading)

[marellasunny]

I failed an exam recently,90% of which comprises solving numerical problems based on formulae.(mechanical engineering)

During this recent exam,I remembered the formulae well but didn't know how to connect them to the given problem. (although I use formulae in work everyday and have no problems with doing machine diagnostics).

I asked my study buddies about their views on my failure and they think I spent too much time reading lecture notes and not solving all the exercises at the end.

Can I put this down 'only' to laziness in not solving the exercises at the end?OR do you think it better to solve numerical problems and read the theory side-by-side?

Does one need to make a separate time and routine for solving exercises-at-the-end also?I'm trying to learn from failure.

 

[lisab]

In my experience, the students who got the best grades were the ones who worked the most problems. Really good students go well beyond solving just the homework problems.

Knowing the theory is very important, of course, but remember you will be tested on how well you solve problems.

 

[Erythro73]

What I always tell my students : just do your exercices. You don't learn physics by only reading / listening to the teacher.

 

[ZapperZ]

The more things change, the more things remain the same. While this is mentioned for mathematics, it applies to practically all of science and engineering as well.

From Mary Boas' "Mathematical Methods in the Physical Sciences", 2nd Ed:

One point about your study of this material cannot be emphasized too strongly: To use mathematics effectively in applications, you need not just knowledge, but skill. Skill can be obtained only through practice. You can obtain a certain superficial knowledge of mathematics by listening to lectures, but you cannot obtain skill that way. How many students have I heard say "It looks so easy when you do it," or "I understand it but I can't do the problems!" Such statements show lack of practice and consequent lack of skill. The only way to develop the skill necessary to use this material in your later courses is to practice by solving many problems.

And this was written back in 1983.

This is also what makes studying science, math, and engineering different than "liberal arts/humanity" subjects. You can't just sit and read, and hope to understand things.

Zz.

 

[marellasunny]

Q1.So,do you guys set-up a separate schedule to solve the exercise problems after each theory reading?One very disconcerting things with studying advanced engineering(esp.mechanical engineering) is that some of the concepts require practical experience to visualise the flow process,something which is not always possible ofcourse. So,what would you do in these cases?Just trudge-on,memorise the methodology of solving a numerical problem and hope you'll understand the concept later-on in life? Its kind-of disheartening to study like this-"when you start something,finish it nevertheless" kindof way.

 

[DrummingAtom]

I can feel your frustration. In previous semesters, I have always took the problems seriously and let the theory come from osmosis or reflection after the semester. In some cases, the theory never clicked but I still got good grades in those classes.

When this semester began, I made the decision to focus on the theory/concepts during the semester. I haven't been working many problems and I do feel like I'm understanding concepts well but honestly my grades are suffering bad.. very bad. I experimented with my methods and now I'm paying for it. Now I know, it's problems > theory during the semester. If it doesn't click during the class I have to just take things for face value and move onto the problems as quick as possible. After I do a lot of problems I can then focus on the theory.

For things that I can't visualize, I focus on the math to get the answers. Engineering has a "get the answer and move on" attitude. I still struggle with this attitude because I like to try to connect the dots of what's going on. Usually the reason for moving quickly through the material is time. My engineering classes have a lot of homework and projects. The projects are a pure time sink. I learn a lot from the projects but I'm not getting tested on them so I need to finish asap move on and start studying for the exams. Get it done and get it out.

Here's an article that sums up engineering to me:

http://technet.microsoft.com/en-us/magazine/hh921911.aspx

 

[ChaseDuncan]

As a fellow student this is a near constant conflict for me. Grinding problems is the best way to get good grades but I don't think it necessarily promotes understanding. For that reason it can be unsatisfying.

On the other hand, I can easily find myself down the rabbit hole trying to 'understand' something for which I do not yet have all of the proper tools to understand. Also, sometimes the thing that makes the understanding 'click' is just working a bunch of problems. It's tricky.

What I've been doing recently is attempting to incorporate the activity of pencil-to-paper-problem-solving into my study. For instance, instead of just reading/memorizing/contemplating the characteristics of some mathematical object I challenge myself to come up with an example of my own. Then I might try and see how different examples I can come up with. Then I might find other ways to challenge myself to manipulate what I've written down so I effectively create my own problems.

I've found this to be pretty satisfying. After I've done that for a while then it's just problems, problems, problems. However, I still take the approach of 'this is mine to play with'. I like to try and turn a given problem inside out as many ways as I can before moving on. For me, it's more personal and satisfying.

Good luck to you.

 

[djh101]

Here's how I study physics:
1) Take notes in class
2) Read the book and take separate notes (lecture notes are my sloppy notes, book notes are my reference notes)
3) Copy important lecture notes and examples into reference notes
4) Do most of the homework problems
5) Reread parts of book until understanding is pretty solid
6) Do more homework problems
7) Browse Wikipedia/Google for further insight on concepts

Adding to what others have said, you need to really understand the concepts to do the homework problems and know the subject, but ultimately, it's the amount of homework problems done that really determine your grade. You can balance it out depending on how your professor teaches. In my E&M class, the homework problems are fairly simple and the exams take them to the next level so having a really solid grasp on the concepts is a must.

 

[Vanadium 50]

. Grinding problems is the best way to get good grades but I don't think it necessarily promotes understanding.

But that is understanding. Understanding is being able to quantitatively describe the behavior of a physical system.

 

[ChaseDuncan]

But that is understanding. Understanding is being able to quantitatively describe the behavior of a physical system.

I must respectfully disagree. In my experience it's entirely possible to learn how to solve problems in an academic context yet have no real understanding of what's going on outside of that structure. I've done it and some of the most accomplished students I know will gladly admit they don't 'understand' the material they're just good at doing the problems.

Even one of my TAs, now doing his PhD at my school, told me that despite his great success in undergrad as a mechanical engineer the only thing he really learned was to recognize and solve problem types. He told me this when I was having some issues in the class he was TAing last semester. His advice was to not waste time trying to understand the material just learn to recognize and solve the problem types. He was right, it turned out. I got a 68 on my first test then, after talking to him, I got a 99 on my second midterm an 86 on the final -- well above average for the rather tough test.

It's entirely possible to leave aside trying to understand, learn to solve problems, do well, but still not have an real intuition about the material. Obviously the ideal is to do both, which was the point of my post, yet when you're chips are down (and getting a good grade is the goal) the best bet is to just focus on the types of problems the class are doing and worry less about 'getting it'.

 

[djh101]

In my experience it's entirely possible to learn how to solve problems in an academic context yet have no real understanding of what's going on outside of that structure.

The problem is that most of the book problems are just simple grind problems that really only test that you know how to solve book problems. Some of the challenge problems, though, although they might not be entirely realistic, do really force you to understand the concepts pretty well in order to solve them.

 

[Vanadium 50]

Being able to parrot back only the exact problems you have seen before isn't understanding either.

 

[ChaseDuncan]

The problem is that most of the book problems are just simple grind problems that really only test that you know how to solve book problems. Some of the challenge problems, though, although they might not be entirely realistic, do really force you to understand the concepts pretty well in order to solve them.

I agree. That's why my advise was to make your own problems as you study and to take the book problems to another level by exhaustively analyzing in every one can think of.

Being able to parrot back only the exact problems you have seen before isn't understanding either.

Absolutely, and this is exactly why I said that grinding problems doesn't necessarily promote understanding. Yet, many of the most successful students I've known in engineering, math and physics would happily admit they did not know what they were doing rather they were just doing what they're told.

 

[AlephZero]

Yet, many of the most successful students I've known in engineering, math and physics would happily admit they did not know what they were doing rather they were just doing what they're told.

I note you say "successful students", not "successful engineers". The real world doesn't often give you a nice string of textbook-sized problems to solve!

Of course some of them may just perpetuate the cycle as poor teachers - like your TA.

 

[ChaseDuncan]

I note you say "successful students", not "successful engineers". The real world doesn't often give you a nice string of textbook-sized problems to solve!

Of course some of them may just perpetuate the cycle as poor teachers - like your TA.

Yes, but we're talking about doing well on exams, right? You guys just don't let up, heh.

My whole point is that it's a nuanced thing but the tests, in general, favor knowing how to solve problem types not necessarily really deep understanding of the material. So, if one is interested in really understanding the material then there's balance to be sought.

Also, my TA was awesome but your arbitrary judgement is duly noted :) Helping me learn to navigate the academic bureaucracy as it is is not a bad thing. I certainly wasn't going to get anywhere with Ds on my exams and he helped me to get As. Come test time no one cares if the reason you can't perform is because you've over thought the material. All they care is that you can't perform. Some times it is necessary to just take it on faith and learn the procedure for solving the problems. Again, there's no one shoe that fits every class.

 

[carlgrace]

Classes focus on problem solving skill because "understanding" is difficult to measure quantitatively.

In the real world you'll find that actual "understanding" is a really slow process (I'm 15 years post-BS and I'm still re-learning things every day). That said, problem solving skills are what make you successful in a job. Really, that's why they're paying you.

 

[mal4mac]

This is also what makes studying science, math, and engineering different than "liberal arts/humanity" subjects. You can't just sit and read, and hope to understand things.

Zz.

I think that makes the humanities seem easier than they are. Have you tried just "sitting and reading" Kant's First Critique? I had to continuously take notes, and continuously refer to philosophical dictionaries and secondary literature. If I'd just sat and read I'd have got nowhere. And actual philosophers say you need to be involved in philosophical discourse, and read the classics, to *really* get anywhere with philosophy - although I'm not a professional philosopher, I've dabbled enough to believe them! So the idea of the necessity of skill development is also there in the humanities.

 

[marellasunny]

I think that makes the humanities seem easier than they are. Have you tried just "sitting and reading" Kant's First Critique? I had to continuously take notes, and continuously refer to philosophical dictionaries and secondary literature. If I'd just sat and read I'd have got nowhere. And actual philosophers say you need to be involved in philosophical discourse, and read the classics, to *really* get anywhere with philosophy - although I'm not a professional philosopher, I've dabbled enough to believe them! So the idea of the necessity of skill development is also there in the humanities.

True mal4mac. Engineers do look down on the humanities. It is a pity.