I know the material inside and out, but then make dumb mistakes on tests

[Cyrus]

it was this comment of yours that set me off:

"Who honestly has the time to do all this (make and take practice exams)? I just don't see this happening and think its a bad way to study. sorry.
"

that seemed a bit foolish and smartalecky, and i felt you were ignoring good advice from someone with vastly more experience than you.

If you do NOT do this stuff, I guarantee you are even not in the ball game with the best students, even if you do stay up until 4 am.

peace.

I said I agree with you on going over problems. What I don't see myself doing is writing exams to take. I'm sorry, but not everyone does this. It takes time to write a good exam. And even then, how do you know the exam you write will be anything at all close to what the professor will write? You just can't. It takes a huge amount of time to write a quality exam to practice off of.

 

[leright]

it was this comment of yours that set me off:

"Who honestly has the time to do all this (make and take practice exams)? I just don't see this happening and think its a bad way to study. sorry.
"

that seemed a bit foolish and smartalecky, and i felt you were ignoring good advice from someone with vastly more experience than you.

If you do NOT do this stuff, I guarantee you are even not in the ball game with the best students, even if you do stay up until 4 am.

peace.

I see a lot of students that have a better GPA than me, but their GPAs are where they are because they spend no time just thinking about the concepts to tie things together and get the big picture and never ask insightful questions to the professors, but spend tons of time just memorizing facts and steps, and doing problems. These people cannot even explain what it is they are doing, or the point of doing it. If you can't explain it to your great grandmother, you don't understand it, and these people couldn't even explain it to their professor, or another student. I am not impressed by people that say they have high GPAs. You need to show more than that. GPA is meaningless.

It is just as important to think about concepts as it is to work problems, in my eyes. Problems don't necessarily provide conceptual insight, but only provide mechanical technique to solving a particular problem. I suppose if I need to give up problem solving time to think about concepts and as a result, take longer to work problems on tests since I didn't work as many problems, it is a good trade off. Also, this results in a somewhat depressed GPA than the other students that work just as hard, but devote more time to working problems and less time to thinking.

 

[mathwonk]

for example, in preparing for a history test, you should write a sample essay on a topic that is likely to come up on the test. then you can either use it directly or draw upon it for other questions on the actual test.

It amazes me that this is such a strange concept to people here as it was well known at Harvard when i was an undergrad there. I aced some graduate courses in math using this method as an undergrad. I walked out of lynn loomis real analysis final e.g., 30 minutes early with an A.

This is also the method we used in high school when I was mid state or state math champ 2 years out of 4 in high school. At Harvard there were collections of old final exams in all the house libraries and we studied them before finals. I myself took in advance every test written by a single prof before going into his final.

I expect my phd students in algebra to work every old prelim for the last 10 years before attempting the prelim in january. anyone who does not do this is not trying hard enough to pass.

 

[mathwonk]

I am sure you are right that not everyone around you is doing these thigns. I am telling what poeple do who win postdocs to harvard, research grants, and international conference invitations,...

if this is your goal, he who has ears to hear,...

 

[vanesch]

I'll add my two cents to the discussion here.
As I started out as an engineering student, "small errors" on tests were severely punished. Many professors said: "I couldn't care less whether you understood the problem and the principles of the solution ; I want to see the right answer come out. If, as an engineer, you design a power plant, and it blows up half of the city, you can always try to tell the judge that you knew the principles, but that you made some minor errors making the final answer come out wrong."
This is often different in a maths or physics department, where the professor usually wants to find out whether you knew the principles, and the problem at hand is just a way for them to analyse your reasoning. Although not entirely: Feynman is known to have said to a student: "if you don't get the last 2 pi factor right, you've understood nothing!"

Now, everybody makes errors, and indeed the worst ones are those where you misunderstood the principles of the problem and the solution, but you should consider it also a serious error not to be able to find the right answer.
I think there are several factors playing here, and there are ways to avoid this. The most straightforward one is probably this:
Work tidy . Often wanting to write quickly and sloppy introduces silly errors. Take your time to write nicely, don't do 20 steps in one line. Ok, this takes some exam time, but tell yourself that it might save you a lot of time "looking for the error". (and even looking for the error will be more efficient that way).
Master the basics blindly. This is often a vexing thing, but if you don't remember exactly your trigonometry relations or so, you'll make silly errors that way. Be sure to master them, and don't be afraid to do some drilling problems on them if you think that there's a problem. It is study time well invested.
Regularly check your intermediate results Often, there are simple ways to test the consistency of intermediate results: units, if it are real-world problems: are the results realistic ? Can you easily derive some side result from your intermediate result which verifies something about it (by re-deriving something given in the problem or so) ...
If you find something fishy, track back before continuing. If you don't find an error, write down on your copy what you find strange. (in engineering class, a professor found it a positive attitude that you signalled something "strange", meaning that as a real-life engineer, you'd probably want to double check things).

If you're pretty sure that the final answer cannot be, say so on your copy.

And then, practice, practice, practice. But practice in a realistic situation: don't be happy during your practicing that you make small errors: work as tidy and serious on your training exercises as you would on your exam: you don't get bad habits that way.

 

[leright]

I am sure you are right that not everyone around you is doing these thigns. I am telling what poeple do who win postdocs to harvard, research grants, and international conference invitations,...

if this is your goal, he who has ears to hear,...

If a student that does the things that you are saying to do, and can work every problem that could be on a test, but cannot explain to someone else what it is they are doing, or what the point is, then they aren't going to be win postdocs at harvard.

If you can't explain something in a simple, yet complete way, you don't understand it, no matter how good you are at doing the problems.

 

[Cyrus]

This is also the method we used in high school when I was mid state or state math champ 2 years out of 4 in high school. At Harvard there were collections of old final exams in all the house libraries and we studied them before finals. I myself took in advance every test written by a single prof before going into his final.

Unless a professor here gives you a sample exam, they do not want old exams being handed out. Why? Because people study the exams to see what is asked and not the material itself.

To me, that is studying verrry biased to what the teachers going to ask you. It's learning what the teachers going to ask, as opposed to what do you really know.

 

[leright]

I'll add my two cents to the discussion here.
As I started out as an engineering student, "small errors" on tests were severely punished. Many professors said: "I couldn't care less whether you understood the problem and the principles of the solution ; I want to see the right answer come out. If, as an engineer, you design a power plant, and it blows up half of the city, you can always try to tell the judge that you knew the principles, but that you made some minor errors making the final answer come out wrong."
This is often different in a maths or physics department, where the professor usually wants to find out whether you knew the principles, and the problem at hand is just a way for them to analyse your reasoning. Although not entirely: Feynman is known to have said to a student: "if you don't get the last 2 pi factor right, you've understood nothing!"

Now, everybody makes errors, and indeed the worst ones are those where you misunderstood the principles of the problem and the solution, but you should consider it also a serious error not to be able to find the right answer.
I think there are several factors playing here, and there are ways to avoid this. The most straightforward one is probably this:
Work tidy . Often wanting to write quickly and sloppy introduces silly errors. Take your time to write nicely, don't do 20 steps in one line. Ok, this takes some exam time, but tell yourself that it might save you a lot of time "looking for the error". (and even looking for the error will be more efficient that way).
Master the basics blindly. This is often a vexing thing, but if you don't remember exactly your trigonometry relations or so, you'll make silly errors that way. Be sure to master them, and don't be afraid to do some drilling problems on them if you think that there's a problem. It is study time well invested.
Regularly check your intermediate results Often, there are simple ways to test the consistency of intermediate results: units, if it are real-world problems: are the results realistic ? Can you easily derive some side result from your intermediate result which verifies something about it (by re-deriving something given in the problem or so) ...
If you find something fishy, track back before continuing. If you don't find an error, write down on your copy what you find strange. (in engineering class, a professor found it a positive attitude that you signalled something "strange", meaning that as a real-life engineer, you'd probably want to double check things).

If you're pretty sure that the final answer cannot be, say so on your copy.

And then, practice, practice, practice. But practice in a realistic situation: don't be happy during your practicing that you make small errors: work as tidy and serious on your training exercises as you would on your exam: you don't get bad habits that way.

Thanks for the insightful advice Vanesh.

I was talking to a professor of mine today and he said that same thing about getting the right answer in the real world is imperative. I told him that the exact same problem I could do correctly in less time while sitting at home, but on the test it takes me LONGER to do the problem, and I get the wrong answer! He said that for him, any time he got a problem wrong it was because he didn't know how to do the problem and not because he made silly mistakes. He is simply a good test taker, and I am not. I also told him that it frustrates me when I can do the problems at home in a timely manner and understand the concepts, yet when I take the test I come up short. I told him that I strive for As and get A-s and B+s and Bs. He said not to worry about it and he got As all his life and they really did him no good in the end. However, I told him that they help get you into grad school. He agreed and that was the end of the conversation.

Overall though, the guy gives good advice. However, he knocks points off for things like rounding 9.981 to 10.0, but in many cases the extra accuracy is needed to get a meaningful answer, so I understand where he's coming from.

 

[imabug]

mathwonk's advice is excellent. how do you expect to become good at problem solving if the only problem solving you do are the 5 or so questions a week the prof assigns as homework.

Look at any of the standardized exam (GRE, USMLE, LSAT, etc) prep materials you'll find in the bookstore. What are they filled with? Practice exams. What's the first thing they tell you in all of those books? Take the exam under exam conditions. There are many reasons for this:

• Get you to practice problem solving techniques
• Get you used to solving problems under exam conditions
• Get you more familiar with the material
• Gets you familiar with various types of problems
• Better familiarity means being able to estimate what your answer should be (at least within an order of magnitude
• You'll learn to recognize different types of problems and the solutions that go with them

You don't even have to spend time making up your own exams. Work out the questions in textbooks. Check the department or your students union to see if they have an exam bank you can buy old exams from. Ask senior students if they have copies. Your library probably has several decades worth of physics textbooks just loaded with questions at the end of each chapter (where do you think profs get most of their questions anyway?.

 

[JasonRox]

I agree with mathwonk here.

It sounds crazy, but that's the reality to doing well. I haven't done all of that, but I wouldn't be surprised if I did in Graduate School.

The whole purpose of writing your own exams is to force you to stop using the information at hand. This forces you think, and solve without help. In the end, if you get anything wrong, you now know your limit to the information you know. Therefore, study that for a bit, then write another practice exam and see where you can't get through.

If you already solve problems without looking at the information at hand, then it's all good. I think you're totally fine here because you aren't being dependent on the information at hand. The only problem now is basically how fast you solve the problem. Basically, I just ask myself realistically, am I fast or not? If not, then work FASTER! If you don't know, write a practice exam and find out if you're fast.

The only problem that comes from writing practice exams for me is that once I write/read the question I probably already know how to solve it and/or a method to do it. Plus, I'll remember the question 100%. I'd still remember it if I wrote it a month ago! Another problem is that if the solution does not pop into my head, I'll ponder about it until I got it because I love the challenge. Of course, I can always put hard questions on, but then that goes beyond the difficulty of the midterm, which is fine, but I like to do these on my own time rather than for study time.

Anyways, my philosophy to doing well in classes is to focus more on the understanding and learning of the material. It's not so easy these days because the focus is shifting into learning-how-to-pass-the-midterm rather than learning the material itself. As well as professors are teaching-you-to-pass-the-midterm rather than teaching the material itself. I don't blame anyone for this because that's just the result of having so many people in university focused on getting the degree for the job and not for the learning or actual education.

Like, for example, I suck in probability. But in reality, I'm probably one of the better students in the class. I say I suck because my understanding of it is weak. I can solve problem after problem, but give me one problem that is vastly different (but same material) and I'm probably screwed. Of course, I'm probably ready for the midterm and can do well, this isn't my goal. Why? Because if I understand it, I'll probably never forget it for awhile and that's what counts. (Even though I hate probability, the remembering part is beneficial because when I study for finals, I'm half way done.)

I met students with higher marks than me in Linear Algebra, but yet in a third year class a linear transformation question came up and I was the only one able to understand it or even answer it. As a TA, I feel fairly comfortable that you can ask me anything with regarding to the text because I did it, I understood it, I remember it, I studied it, etc...

I met students with higher marks than me in Calculus, but yet I understand it more than them. Some forgot Green's Theorem!

The more I understand it, the less I need to study. And so, that's my method.

 

[mathlete]

I agree with mathwonk here.

It sounds crazy, but that's the reality to doing well. I haven't done all of that, but I wouldn't be surprised if I did in Graduate School.

The whole purpose of writing your own exams is to force you to stop using the information at hand. This forces you think, and solve without help. In the end, if you get anything wrong, you now know your limit to the information you know. Therefore, study that for a bit, then write another practice exam and see where you can't get through.

If you already solve problems without looking at the information at hand, then it's all good. I think you're totally fine here because you aren't being dependent on the information at hand. The only problem now is basically how fast you solve the problem. Basically, I just ask myself realistically, am I fast or not? If not, then work FASTER! If you don't know, write a practice exam and find out if you're fast.

The only problem that comes from writing practice exams for me is that once I write/read the question I probably already know how to solve it and/or a method to do it. Plus, I'll remember the question 100%. I'd still remember it if I wrote it a month ago! Another problem is that if the solution does not pop into my head, I'll ponder about it until I got it because I love the challenge. Of course, I can always put hard questions on, but then that goes beyond the difficulty of the midterm, which is fine, but I like to do these on my own time rather than for study time.

Anyways, my philosophy to doing well in classes is to focus more on the understanding and learning of the material. It's not so easy these days because the focus is shifting into learning-how-to-pass-the-midterm rather than learning the material itself. As well as professors are teaching-you-to-pass-the-midterm rather than teaching the material itself. I don't blame anyone for this because that's just the result of having so many people in university focused on getting the degree for the job and not for the learning or actual education.

Like, for example, I suck in probability. But in reality, I'm probably one of the better students in the class. I say I suck because my understanding of it is weak. I can solve problem after problem, but give me one problem that is vastly different (but same material) and I'm probably screwed. Of course, I'm probably ready for the midterm and can do well, this isn't my goal. Why? Because if I understand it, I'll probably never forget it for awhile and that's what counts. (Even though I hate probability, the remembering part is beneficial because when I study for finals, I'm half way done.)

I met students with higher marks than me in Linear Algebra, but yet in a third year class a linear transformation question came up and I was the only one able to understand it or even answer it. As a TA, I feel fairly comfortable that you can ask me anything with regarding to the text because I did it, I understood it, I remember it, I studied it, etc...

I met students with higher marks than me in Calculus, but yet I understand it more than them. Some forgot Green's Theorem!

The more I understand it, the less I need to study. And so, that's my method.

I agree with this 100%. I feel that lectures cover way too much material. I don't have a problem with the pace, but I'm not learning anything. I got two As in my E&M courses, but my understanding is very weak... why? For example, we'd cover Gauss' law and then do a most basic example and then move on. Like you said, any problem out of the ordinary dealing with E&M will be tough for me if I can't just plug numbers into the equation.

I know it's up to the student to learn more about something, but it's tough to find a time when you can devote yourself to learning something on the side when you probably have other work you can be doing for your classes.

Basically, I'd rather do less material and cover it more in-depth than just flying by learning the bare minimum.

 

[unit_circle]

I've thought it over and I thought that maybe the reason I make dumb mistakes is because I am dumb. I dunno.

Your not dumb. You chose the "true light" which is science and mathematics. That makes you smarter that all of the post-modern, truth-denying liberal arts majors out there . I'm only half-joking, English and history majors feel free to flame me.

 

[JasonRox]

Your not dumb. You chose the "true light" which is science and mathematics. That makes you smarter that all of the post-modern, truth-denying liberal arts majors out there . I'm only half-joking, English and history majors feel free to flame me.

WOW! Ignorant in so many ways.

I'm a mathematics major, and consider myself to be a man of science, but there is no way to I relate to what you're saying.

I appreciate history, arts, language, philosophy, and so on. All beautiful subjects on their own.

 

[balletomane]

Leright,
When you are taking an exam, do you feel anxious? I know that I make really stupid mistakes and blank on problems because I get really nervous what with the time pressure and perceived high stakes and all.
If that's the case, maybe working on staying calm in addition to the strategies suggested above can help.

good luck.