Testing I in studying and taking tests at university

[trees and plants]

Hello there.I am and undergraduate student in math and I have problems, a little anxiety and doubt about taking tests in math courses at my university.I am trying to pass my exams and i have improved myself at that.So, what am I doing wrong about the preparation before taking tests?I am reading for example an introductory course in ordinary differential equations and I try to learn for example about first order linear differential equations, i start with the theorems, perhaps learn some proofs of them, then the examples.How will I know that I am well prepared for the course?This is a basic question, but I am a little confused.Then I have another course in topology about metric spaces and perhaps also topological spaces.The same thing with this course, the same problem I have.It is a period of taking exams and I want some advice, as well should i make predictions about what will be on the tests or what I will need to prove the exercises at the tests?Thank you very much.Have a good day.

 

[fresh_42]

A frequent obstacle beside a good technical preparation is the psychological factor. Have a read:
https://www.physicsforums.com/insights/10-math-tips-save-time-avoid-mistakes/

You should do as many exercises as you can beforehand for the technical preparation, either from books or from the countless resources on the internet. Search for "lecture notes + ..." or "... + exam + solution".

 

[trees and plants]

Thank you fresh_42.After reading the theorems, proofs and examples on a chapter and try to solve some exercises, what happens if i get stuck?Because I get stuck sometimes.Should I read the related theory about i them and solve them?In addition to this, will the exercises at the exams be of the same level of difficulty with the ones I do during preparation?What if some theorems will be needed at the exams when I have not previously worked on them with exercises?I feel better now having made those questions.I will be waiting for replies.

 

[fresh_42]

what happens if i get stuck?

Make use of our homework forums. Only requirement: show some effort and if possible where you got stuck. And don't say "no idea where to start" since we have even fewer knowledge of the chapter you have just learnt.

Don't lose too much time. Clock management is important. It's better to ask for help or join a learning community than to run at a wall over and over again. If you have enough time, make a break, have some fun, e.g. sports, and try again later or even better, the next day. And if you have read the essay, then you will know that a kind of triage at the beginning helps. Start with those questions you're familiar with. Thinking costs much more time than people would think.

 

[trees and plants]

In some courses I try to solve some examples or exercises with the solutions but without seeing the solution.I know related theorems to what the exercise asks but they do not fit.Then I look at the solution and new elements and techniques have been used to solve the exercise.After that I learn the solutions although I did not solve the exercises in the first place.Is this normal?Is it normal to have new elements and techniques that I do not know and for example it defines new abstract objects, then uses them with theorems and definitions I do not think I would use.It has happened more times than someone would think.

 

[fresh_42]

In some courses I try to solve some examples or exercises with the solutions but without seeing the solution.I know related theorems to what the exercise asks but they do not fit.Then I look at the solution and new elements and techniques have been used to solve the exercise.After that I learn the solutions although I did not solve the exercises in the first place.Is this normal?Is it normal to have new elements and techniques that I do not know and for example it defines new abstract objects, then uses them with theorems and definitions I do not think I would use.It has happened more times than someone would think.

Well, a bit of flexibility is normally required. If there was no variation to the application of a theorem, then there would only have been the theorem itself, which was already dealt with in the lecture. Mathematics is often similar to a playground. There are the tools around, but how you play with them is up to you.

There is a natural gap in the learning process which is difficult to shorten: Learning is not understanding. Yóu can learn a theorem but understanding takes further insights which can be achieved by teaching it yourself to others (and therewith being forced to be prepared for many silly questions) or a lot of experience and practice.

Here is another pool of questions and answers (although not sorted by subject):
https://www.physicsforums.com/threads/solution-manuals-for-the-math-challenges.977057/

 

[Lnewqban]

... So, what am I doing wrong about the preparation before taking tests?

My hat is off to you, I was always terrified by Math during my school years.
Because of that, my advice is about getting prepared and taking tests in general, not about taking Math tests.
The above posts are excellent.

A mind that is not calmed can't learn much or demonstrate that have learned via tests.
Try to reduce your level of anxiety as much as you can, during your times of studying and while taking tests alike.

Anxiety comes from your capability of imagining disastrous consequences from poor performance.
My experience has been that no outcome is as fatal or as terrible as we imagine, life has a way to open alternate opportunities to laborious persons like you.

Do what you can, but be easy on you and understand that your time at the university is unique and enjoyable, which hard work and difficulties are preparing you for future challenges that will be equal or more difficult that these tests.
For that reason, you need to develop the ability to become comfortable with learning (rather than getting ready to pass a specific test), being tested and dealing with the results you get.

Study as hard as you can in order to learn and understand the subject, but avoid imagining ghosts that come from a tired and exhausted mind.
Dedicate some time each day to exercise your body (more oxygen flowing into your brain improves its performance, always) and to do some recreational and social activities, even if it is time that you steal from studying (there is an optimum amount of that time, too much is bad).

... How will I know that I am well prepared for the course?

You will never be well prepared, those who put tests together have the advantage of time.
Flow with the questions of the test and never use too much time in any particular one, time that you may lack latter to properly respond another question.
Never believe any reason is a good reason to steal sleeping time, a tired brain is a dull brain and you need yours to be very sharp now.

... should i make predictions about what will be on the tests or what I will need to prove the exercises at the tests?

That never worked for me.
Right before taking any test, I avoided any contact with other students that "knew" what will be on the test, just to anxiously discuss it with other terrified students a few minutes before taking the test.
Many of those students suddenly realized that they did not know how to deal with "what will be on the test", resulting in reduced self-confidence exactly at the time they needed it the most.
Instead, I used that previous hour to swim twenty invigorating laps, consistently obtaining decent results in the test.

My very best wishes for success in these tests and during your future career.

 

[trees and plants]

Perhaps trying to solve exercises of similar difficulty and style with those of the exams could help? When i get stuck in an exercise should i open the books or the material of the subject and read it and try to solve it then? For example by reading the examples and theorems or proofs to help me solve the exercise?

 

[haushofer]

For me, what helps is to describe the problem as accurately as possible. Many times I require insights by merely typing my topic about a question I have here. Being accurate takes you out of your comfort zone; that's why being sloppy is so comfortable.

So, if you're stuck: try to formulate your problem as precise and concrete as possible.

See also the "Feynman method" to learn new stuff.

 

[trees and plants]

I think some people confuse the physical dependent knowledge with what-they-know-and-read dependent knowledge in math and physics. Math and physics have their definitions, theorems and proofs for things someone may work only with them when memorising or solving problems and questions. If some things from the physical reality help it is ok, but i think many times it is like i said.

The execution of solving the problems and questions is where i get stuck. I need to start solving problems similar to those of the exams. If i do this , perhaps i will gain more experience and fear and stress about the exams will decrease or even not have an effect on me.

 

[mpresic3]

How will I know that I am well prepared for the course?This is a basic question, but I am a little confused.

I did not read the earlier threads so I do not know if anyone has mentioned this specifically. One way to see if you may be prepared for the test is to attend every class lecture, lab, and recitation, and take notes, like everything that appears on the blackboard, whiteboard, or powerpoint or whatever is used these days. The textbook is not always enough. The notes along with the problems assigned indicate what your instructor thinks is important, and it is likely problems on the test are going to be similar, with maybe a little twist.
I used to hear stories about people who skipped classes, and just read the textbook and got all A's. I found out in all cases, they were just stories. In many years in school, I found who was there at the end. It was the people that attended classes.

 

[member 587159]

I used to hear stories about people who skipped classes, and just read the textbook and got all A's. I found out in all cases, they were just stories. In many years in school, I found who was there at the end. It was the people that attended classes.

I know many examples of such people, myself included. At some level, you just have to put in the effort yourself and a teacher is only important if you have questions. Everyone must just find out whatever works for him/her, there are no absolute golden rules that work for everybody. For me, attending classes is time wasted.

 

[WWGD]

A good technique for taking tests is to read every question before starting to answer. That way you have an idea of what you will be getting yourself into, and you start breaking down the questions in the back of your mind. EDIT: Other suggestions are taking care of the basics: make sure you're eating right, exercising, getting enough rest, etc. overall.

 

[Mark44]

Perhaps trying to solve exercises of similar difficulty and style with those of the exams could help?

Yes, provided that you know in advance the types of problems that will be on the exam. A good instructor will include questions on the exam that are at least similar to the kinds of problems that have been assigned as homework prior to the exam.

For example by reading the examples and theorems or proofs to help me solve the exercise?

Since your thread is about a class that is devoted differential equations, my advice is to read and understand the theorems and proofs, but you should put a larger percentage of your effort on working the problems at the end of the section. Do not just look at the worked examples. Seeing how someone else solved a problem is not the same as working through the problem yourself. If you get stuck, see if there is a worked example that is similar.
To a large extent, solving differential equations entails experience in a number of solution techniques, so you should be able to categorize a given differential equation so as to be able to apply an appropriate solution technique.

The execution of solving the problems and questions is where i get stuck. I need to start solving problems similar to those of the exams. If i do this , perhaps i will gain more experience and fear and stress about the exams will decrease or even not have an effect on me.

Yes. The more problems you solve, of a variety of types, the less fearful and stressed you should be.

 

[trees and plants]

Ok, so what should be a schedule or program to maximise the probability of getting good grades like 8's or 9's or 10's in courses at my math department? How much time should i give at each of my courses per day for reading theory and working on exercises and problems?

I also perhaps have a problem. When thinking of how theorems are applied to solving exercises i think of it mostly as combinations of them or analogies. Is that wrong?

Geting stuck even beginning solving problems or not even looking at similar worked examples to help me? Or not looking at theorems that perhaps i forgot or did not think of using to help me? What should i do about those? Thank you.

 

[symbolipoint]

@trees and plants
Almost been 1 year - anything changed or improved? Done any differently?

 

[trees and plants]

@trees and plants

Almost been 1 year - anything changed or improved? Done any differently?

I think i have less fear and sadness now for the mistakes i made and the mistakes i will probably make and the expectations of my grades, the examinations i am about to participate in and my attitude towards the efforts i am about to make when giving exams.

I still have difficulty in trying to solve exercises or problems at my courses of the math department, especially many of different variety types of exercises and problems.

I should better see my efforts and works when studying for the courses and giving exams as my profession. It is like this is my profession , but i am not getting paid for doing it.

Any advice you want to give me about at least me making the efforts of solving exercises at the courses, studying more than i do at the courses and lessening the fear and sadness and stress of taking exams and getting good grades or me having negative expectations about the exams and the grades?

Also, i think very much of not having the opportunity to continue for postgraduate studies if i get the degree, what should i do?

Thank you for all your efforts and time that you give to me, teaching me and giving me advice.

 

[MidgetDwarf]

Do as much as you can without looking at solutions. From personal experience, you may get by looking at solutions and acing certain courses due to the teacher not challenging students. Maybe not even carrying.

I have seen a lot of my friends flunk out of grad school due to relying on solutions too much. Grades are meaningless. What is important is the understanding of the material, and to be honest with oneself. Ie., where do I stand on the mathematical number line in terms of knowledge, what are my goals, and how do I improve.
If a person barely studies and gets crap results. Then its obvious why said outcome occurred. If a person tried there best, and still did poorly, then the just means more wok/effort/self-evaluation is needed. If a person gets in A in the course, but the material was babied, then a responsible student would cover the information in more depth.

 

[mpresic3]

I said in an earlier post that it is important to attend classes and got contradicted, so I will cite a case from personal experience. My calculus professor (an honors course), assigned problems from a textbook, and I did every problem completely and carefully. When I used to get the tests, I would severely underperform, until I realized his test questions were always on the theory behind calculus, (e.g. state and prove Rolle's, theorem, state and prove the intermediate value theorem by a bisection argument, etc) His homework problems assigned were nothing like the test problems. I suppose he thought between the tests and the homework, all the bases were covered.

You say you are learning the proofs first, and then trying to do the applications, and it isn;t working. It seems for the intro to diff eq class, maybe it is better to look at worked problems and begin with the applications first, before concentrating on the theory. It seems in the topology class, beginning with applications might be harder, but I think it was a prominent mathematicians Gorenstein, who said when he was confronted with trying to solve a proof in algebra, he first tried to think up as many examples as possible. This is unlike many mathematician friends of mine that say you should work from definitions, first.

You probably should review your notes and get an idea of what your professor thinks is important. You should not be trying to "guess" the problems on the test, but to establish the priorities important to the professor. He or she is presenting the course and the test material.

 

[trees and plants]

Do as much as you can without looking at solutions. From personal experience, you may get by looking at solutions and acing certain courses due to the teacher not challenging students. Maybe not even carrying.

I have seen a lot of my friends flunk out of grad school due to relying on solutions too much. Grades are meaningless. What is important is the understanding of the material, and to be honest with oneself. Ie., where do I stand on the mathematical number line in terms of knowledge, what are my goals, and how do I improve.
If a person barely studies and gets crap results. Then its obvious why said outcome occurred. If a person tried there best, and still did poorly, then the just means more wok/effort/self-evaluation is needed. If a person gets in A in the course, but the material was babied, then a responsible student would cover the information in more depth.

It is like something prevents me from trying to solve the exercises. I have very much difficulty trying to solve exercises. I think that if i try to give exams, when giving exams i think i will not be able to concentrate at what i am reading and what i should use to help me solve the exercises. What should i do?

What do you mean by more depth when covering the information?

 

[fresh_42]

What should i do?

Download the solution manuals from
https://www.physicsforums.com/threads/solution-manuals-for-the-math-challenges.977057/
look for the problems which are relevant to you, and then start to practice, practice, practice, before you look up the correct solution.

 

[trees and plants]

I said in an earlier post that it is important to attend classes and got contradicted, so I will cite a case from personal experience. My calculus professor (an honors course), assigned problems from a textbook, and I did every problem completely and carefully. When I used to get the tests, I would severely underperform, until I realized his test questions were always on the theory behind calculus, (e.g. state and prove Rolle's, theorem, state and prove the intermediate value theorem by a bisection argument, etc) His homework problems assigned were nothing like the test problems. I suppose he thought between the tests and the homework, all the bases were covered.

You probably should review your notes and get an idea of what your professor thinks is important. You should not be trying to "guess" the problems on the test, but to establish the priorities important to the professor. He or she is presenting the course and the test material.

So, i better should attend classes? And i should listen, read and write very carefully what the professor teaches? What am i missing when i am getting prepared for the exams?

 

[trees and plants]

I am sorry for asking you all these things about preparation for exams and the exams. i do have difficulty in these things, but at the past years of my undergraduate studies i failed most times and sometimes i did not even go to the exams in some courses. I think i have very much fear, doubt , sadness, stress and i think i will fail at the exams that i am about to give in some weeks or in some other future exams.

 

[fresh_42]

I am sorry for asking you all these things about preparation for exams and the exams. i do have difficulty in these things, but at the past years of my undergraduate studies i failed most times and sometimes i did not even go to the exams in some courses. I think i have very much fear, doubt , sadness, stress and i think i will fail at the exams that i am about to give in some weeks or in some other future exams.

I'm sure I said this before, but you should read
https://www.physicsforums.com/insights/10-math-tips-save-time-avoid-mistakes/
and think about it. It might help you in exam situations.

 

[trees and plants]

It seems like for myself almost impossible to get my degree or even pass one two or three courses at an exam period. I do not know how to surpass this. I would want to teach at a junior high school or high school if i had my degree but how would i teach after failing so many times after so many years at my courses at the department?

 

[Mark44]

You say you are learning the proofs first, and then trying to do the applications, and it isn;t working. It seems for the intro to diff eq class, maybe it is better to look at worked problems and begin with the applications first, before concentrating on the theory.

This is something I've said before -- that you (trees and plants) should spend more time working the problems at the end of each section. It's important to understand the theorems, but if you spend all your time on the theorems and none on the problem sets, that seems like a sure recipe for doing poorly on exams.

It is like something prevents me from trying to solve the exercises. I have very much difficulty trying to solve exercises.

So, i better should attend classes? And i should listen, read and write very carefully what the professor teaches?

After many years in college, you are just figuring this out now? It's no wonder that you are failing in these classes.

but at the past years of my undergraduate studies i failed most times and sometimes i did not even go to the exams in some courses.

See above for why this might be so. Also, since you have not been successful in working toward a degree in mathematics, maybe it's time to think about pursuing some other area of study.