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Testing Should I feel bad I didn't do well on an exam like this?

  1. Jan 13, 2016 #1
    I just want to give an instance of what happened in one of my examinations. I don't feel bad that I didn't do well because I studied a lot and acquired lots of new knowledge. But, it's hard to explain it to teachers, parents and future employers who unfortunately will just judge the number on the report card.

    Please give me your opinion on this. If the point of an exam is to test the students knowledge, is this exam then structured to not to do this well ? And if it is not possible to have any exam who's marks would accurately predict how much knowledge a student has, is there an unnecessary, overstated emphasis on exams ?

    From the point of view of someone who studies for knowledge, it can be utterly crushing sometimes.

    I have noticed about by personal temperament that I learn better on my own than I do under authority. I learn better when I am reading books and studying on my own than when I am sitting in a class and listening to six hours of people talking.

    So, when I develop an interest in a subject, I learn a lot about it on my own. I had a lot of interest in Maths, not necessarily the Maths taught in college and in the second semester I realised I could indulge my need for learning on my own. Till that time, I always depended on school to learn subjects like Maths and Science and never thought I could do it on my own. With this revelation, I went down the rabbit hole. I started reading lots of Maths books. Books about Maths history (Journey Through Genius, A History of Mathematics by Victor Katz), books about recreational Maths(books by Ian Stewart, Martin Gardner, Ross Hosenberg), books about problem solving(Thinking Mathematically, Arthur Engel, Alan Schoenfeld, Sanjay Mahajan), and books about particular topics in Maths that I had no idea about like Visual Complex Analysis by Tristan Needham. There were many other books that I started reading. I should note that I never finished any of these books. I would read a little bit, and then get scared of not understanding something and then reading another book and returning to it once again (or sometimes not).

    So, I enjoy studying and study topics I like in depth.

    Sometimes, I Go into too much depth. For example, in my discrete mathematics class there was a unit on mathematical induction. I liked it so much that I started working on a book that was entirely devoted to mathematical induction alone. Groups, and rings was another unit mixed with coding theory. Instead of making abstract algebra and coding theory two separate units. They split it unevenly into two. So one unit had groups and homeomorphisms and coding theory. Another had Rings and coding theory. I liked Abstract Algebra a lot and started learning from books that were solely devoted to abstract algebra. I could not do coding theory justice though. In the exam however, there were 3 rather elementary questions about mathematical induction. In the other two questions, the sub questions involving abstract algebra was simple, but I didn't know how to solve the coding theory question. This forced me to answer the question about mathematical logic instead, which I was not very confident in. It bothered me to no end that someone who did not know as much about mathematical induction or abstract algebra, let alone read it's histories and development, who didn't spend as much time as I did learning about it, would score more than me provided they prepared adequately for the system. That too, was a very sad day for me, because I expected all the effort I had been putting into learning Maths independently would come together on the Discrete Mathematics exam. It didn't.

    It seems to me that these kind of university exams discourage learning for its own sake, favour breadth over depth, and test neither intelligence, knowledge, aptitude or hard work but rather the degree of fitting into the system.
     
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  3. Jan 13, 2016 #2

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    let me share my point of view but agree or not its up to you.
    1st- Results from exams always doesnt reflect intelligence level but they do play a role in showing your analysing and problem solving skills
    2nd- I do believe that the one who arrange the academical syllabus put the basics needed knowledge on each topic in order for the learner to use it together to solve problems... an extreme example... if a person who knows the meaning of every single word in a language but doesnt know its grammar cant do well in that language test can he? Do you still thinks he's good in that language? Basics comes first. There's a thin line between genius and proud.
    3rd- a movie that you might want to search for and watch - 3 Idiots with eng sub... and you will realise good results vs real genius
     
  4. Jan 13, 2016 #3
    Regarding your second point, there were no questions which involved combining two units. It wasn't that I couldn't solve that question because I couldn't combine concepts. I couldn't solve it because I didn't know that particular concept well enough. My whole point is should I feel bad when I studied some topics to a great depth (not tested by the exam) and didn't know some topics, while somebody who knew both topics by their bare minimum would have scored more inspite of having lesser net knowledge. I am asking if I should feel bad at all because that number does not reflect my knowledge. It does not adequately represent how much I know because it wasn't tested and moreover, somebody who only learnt one of those concepts to the required level and no further and no more and skipped the other, they would score the same. So, what I was asking is if exams should be given value at all if they are so woefully inadequate at reflecting how much the student knows.

    I gave a very particular example, not a general one. Are you saying there is more merit in knowing basics of abstract algebra and coding theory, than in knowing one in depth ? Your analogy with language doesn't hold because it is possible to use abstract algebra for many applications not touching coding theory, while it is not possible to use language without grammar. And, that's the same case for mathematical induction too.

    I have seen the movie. It was funny but I didn't understand what you meant.
     
    Last edited: Jan 13, 2016
  5. Jan 13, 2016 #4

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    Its an extreme example like i mentioned. Unless you wanna just be an expert on one topic and know nothing about the other. But i cant think of an occupation that is an expert in one topic but know nothing about another topic in the same field. Self fund researcher maybe? But still in a research you cant just solely rely on one expertise.

    What i meant from the movie is the result of exams is not so important if you truly know all the knowledge and how to use it to solve problems that will occur in your future occupation.

    "There were many other books that I started reading. I should note that I never finished any of these books. I would read a little bit, and then get scared of not understanding something and then reading another book and returning to it once again (or sometimes not)."
    Knowing it thereotically and able to use it practically is also another question.
    Jack of all trades, master of none is still overrated for that situation.
     
  6. Jan 13, 2016 #5
    Well, the jack of all trades and master of none, is exactly the kind of person who is scoring more than me. Someone who knows all the chapters to their bare minimum and none to any depth. Someone who spent less hours of effort, and who doesn't have as much interest about it. My whole rant was about how exams don't really test knowledge, or skill, or even hard work, but how efficiently someone can adjust to the system. So in a way if all it tests is itself, maybe there's an overrated emphasis on it.

    Also, I didn't say I want to know only one topic and not the other. Just that when I like some topics, I study a lot about it, and in this case didn't have time to study others. In this case it was mathematical induction and abstract algebra I had a lot of interest it. Also, I could argue that both of those topics, especially the latter is not a narrow speciality but rather a topic wide enough to spend a lifetime studying.

    I never said I want to be an expert in one topic and know nothing about the other, and this thread is not about a real life jobs. It's about exams, their purposes and their inherent design flaws.
    The results of exams is unfortunately important in determining the future occupation even though it may not be critical in its performance

    I was talking about learning some topics in depth and not being able to do some others. And in any case, the depth to which the questions were asked in the exam is far lower than the research levels. It's not like someone who knew enough of all units to score would be able to understand research papers. In fact, even though I studied a lot about mathematical induction, Fibonacci numbers and abstract algebra to a far greater depth than the exam tested, it is still not enough to understand modern research papers. .

    Yes, there were many books I started reading which I didn't finish. I find it difficult to finish books. But, they weren't about diversely different topics. They were all about Maths and they all helped me get insight into each other, and they all were not required by the syllabus.

    I don't understand the theoretical-practical angle. What if I want to be a mathematician or a theoretical computer scientist ?
    That's not an angle I was asking about.
     
  7. Jan 13, 2016 #6

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    "My whole rant was about how exams don't really test knowledge, or skill, or even hard work, but how efficiently someone can adjust to the system."
    Test can never test knowledge level or hard work. Test is just a generalized way to test the basics. Formal education equip you with the basics. That's all.. the additional plus is based on yourself. But you are just to emphasis on the plus which is not the intention of formal education. There no perfect test because everyone is different.. thats why they only test the basics. Learn all the basics and then go in depth on what you like. Then major in a field you prefer although a majoring still covers multiple topics. My guess is only on pHD level that you can emphasis on several topic you love.
    "Also, I didn't say I want to know only one topic and not the other. Just that when I like some topics, I study a lot about it, and in this case didn't have time to study others."
    This simply just means that you recognise the fact that you fail to plan.
     
  8. Jan 13, 2016 #7

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    one more thing is:
    "Well, the jack of all trades and master of none, is exactly the kind of person who is scoring more than me. Someone who knows all the chapters to their bare minimum and none to any depth. Someone who spent less hours of effort, and who doesn't have as much interest about it."
    Its not the right mindset here if you asked me.
    From my experience for test and exams: Smart learner with great knowledge scored the best followed by smart analyst with sufficient amount of knowledge then followed by hardworking learner or lazy geniuses and others.
     
  9. Jan 13, 2016 #8
    I disagree with both your stereotypical division of students and the hierarchy of marks. Since, you're offering anecdotal evidence, I'll retort likewise and say that in my experience, that's not the case. :)

    In fact, I don't ever recall the person with the most knowledge or deepest understanding being the top scorer right from my school days. It was always the person who made the best adjustment to the system by knowing what to write, how to present it, knowing what to skip, etc. It was never the person who knew the most facts about the subject or grasped a deeper understanding of the subjects and its connections. It could be possible we're in different educational systems. I'm in India. Your profile says you're from Germany so I guess what you're saying may be true there.
     
  10. Jan 13, 2016 #9

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    Smart learner with great knowledge is not just the person with the most knowledge or deepest understanding. Note that i used the word smart or maybe in another word= clever not just having most knowledge or plain understanding for the top and second rank in scoring. Smart is quick witted. Basically the person in your statement the person who made the best adjustment to the system by knowing what to write, how to present it, knowing what to skip, etc.
     
  11. Jan 13, 2016 #10

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    my profile stated germany yes for my bachelor studies at the moment. Im in my final semester and im from south east asia so the education throughout is pretty much the same. Like i mentioned... its the smart guy with 2nd amount of knowlegde and understanding that wins over the guy with top knowlegde and understanding. School and society, its the same situation in play =)
     
  12. Jan 13, 2016 #11
    I guess what you're saying is that the resourceful person who adapts and adjusts to the conditions does better than someone with the most raw amount of knowledge and understanding in exams. I agree. Don't you think that it shouldn't be the case ?
     
    Last edited: Jan 13, 2016
  13. Jan 13, 2016 #12

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    sorry that i cant agree with you on that. Im siding the resourceful person who adapts and adjusts to the conditions based on reality. Civilisations and engineerings are created by them. These are the people that able to recognise, analyse and solve problems faster and innovate ór invent new things and also creating new form of studies. Although its just my opinion.
     
  14. Jan 13, 2016 #13

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    There sure is a lot of text here. Is this a fair summary?

    1. You were assigned material.
    2. Some of it you studied in more depth on your own. Some of it you didn't study at all.
    3. You got a poor grade on the test because you couldn't do problems in the area you didn't study,

    Is this accurate?
     
    Last edited: Jan 13, 2016
  15. Jan 13, 2016 #14
    Pretty much. Except we were assigned a syllabus and recommended some material. As to the third point, I won't say I got poor marks. More like average marks that were poor in proportion to both my effort and my knowledge of the subject.
     
  16. Jan 13, 2016 #15

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    This then is the problem. The test doesn't measure how smart you are, or how much you have worked in other areas. It measures how much of the assigned material you have learned. If you decide not to learn material covered in the class so you can learn material not covered in the class, you will do less well.
     
  17. Jan 13, 2016 #16
    That's true. If you do that, then you will do less well. So doesn't that mean tests are an over rated barometer ? If you learn it, you will do well. If you don't, you won't do well. But, just because you didn't do well on a test doesn't mean you don't have a good grasp of the subject. All tests do is see how well someone prepares for them. All it really tests is itself. Knowing this, why is there such an undue emphasis on test scores from parents, teachers, admission officers and interviewers ?
     
  18. Jan 13, 2016 #17
    Because that's the way the majority of the world is most motivated to learn and get things done. Also, there are thousands of very qualified people from all countries now applying for very good positions, jobs, universities etc, and not the same number of seats available, i.e., way too much competition. Admission officers and other such recruiters can't possibly try to individually cater to every person, and seek to differentiate between a slacker who simply didn't study as opposed to someone who studied tons but didn't do too well.

    If getting a good job, financial security, admit to a decent institution (which mind you, have lots of very helpful resources) etc isn't your priority, study what you want, enjoy the learning and don't seek validation from others. If the above is a priority in your life, take out the time to learn it, and put in more time to learn what you love, which is what I do. It's harder and takes more effort, but that's how the world works.
     
  19. Jan 13, 2016 #18

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    erisedk said it well... nobody have time to check on each candidate. like i said exams and test is a generalized way to differentiate who knows the basic well and who doesnt know it well.
    smart people learn the way fast and navigate through it. if future job and other doesnt matter to you, can just study what you like. Able to practice it on society or not is then another question.
    Study to be able to use them alongside with the society and competing to improve or just study for the joy of it.....
     
  20. Jan 13, 2016 #19

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    So a course has been designed with a clear syllabus. This syllabus indicates that, by the time you finish this course successfully, you should know this and this and this.

    You, on the other hand, decide for yourself, that you'd rather study that and that, on your own, rather than what the course and the instructor have outlined. When you are tested on the area that you SHOULD know based on what the course requires, you didn't do so well. So you blame the test for not really testing what you know.

    Is this rational?

    Think about it. If you are hired to do a particular job or task, but you found something else more interesting to do and neglected to do what you were hired for, do you blame your employer for kicking you out? Same thing here! A course has a particular set of goals and syllabus that must be covered. They have to test your knowledge within that area. The exam reflects what you know in that area. If you suck at most of the exams you took, is it a reflection on the exams, or is this really a reflection on YOU?

    Zz.
     
  21. Jan 13, 2016 #20

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    Let's go one step further. You take a Spanish class and decide to study French on your own instead. At the end of the term you are fluent in French and can't speak a word of Spanish. Should you get an A in Spanish?
     
  22. Jan 13, 2016 #21

    Mark44

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    This is a question that is often asked by people who don't do well on tests.
    Not doing well strongly suggests that DON'T have a good grasp of the subject, at least that portion that the test covered. As already stated, you were given some idea of the topics that would be covered in the class (a syllabus), which should have given you an idea of the concepts you would be tested on. If you study other topics instead, and skip over the ones that are listed in the syllabus, it should not be surprising that you don't do well on an exam.
     
  23. Jan 13, 2016 #22

    Choppy

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    Because no one has come up with a better system for efficiently measuring and verifying a person's knowledge and skill set.
     
  24. Jan 13, 2016 #23
    Unless the class is "A Study of Everything," your net knowledge of topics outside of the course is completely irrelevant. Tests are used to evaluate your level of knowledge in that particular course. If you're unable to answer questions about what appears in the course, then you don't earn a good grade in that course (in other words, the instructor deems that you do not have a full mastery of the material). It doesn't mean you're bad at math. It doesn't mean anything except that you didn't learn the course material. Whether you should feel bad about that or not depends on your priorities; other people can't answer that question for you.
     
  25. Jan 13, 2016 #24
    How can you say that the net knowledge of topics outside the course is irrelevant ? That's only with the rather myopic, utilitarian view of making the exam the ultimate prize, which it isn't. Also, let's separate the course from the subject. They're not the same entity. Doing well on the course does not imply a great grasp of the knowledge neither does doing badly on it imply a lack of knowledge. Ultimately, I agree with you that it doesn't mean anything that you did well on the course. My point is since the scope of a test is very limited. It can only test the syllabus, and that too only the part of which questions are asked from on that given day. The domain of knowledge (In this case, Discrete Mathematics) is far bigger. So, if a job required extensive knowledge of Discrete Mathematics, I'm not sure the marks of a standardised test is a good indicator of it. (The whole university has the same paper. My teacher doesn't make or correct it.)

    So, yes, while it is true that if you spend time studying what you like you won't score good in the test, my entire point is if it's worth anything to score on a test like that. A test that almost punishes studying out of interest and not conformity, depth over breadth. No test can actually measure competence over a domain of knowledge, just the syllabus, and even then not the entire syllabus, just the precise questions asked on that day. My point is that this is a serious design flaw in the paradigms of testing.

    Paradoxically, this flaw came to my help in another subject which I didn't like ... Electronic Circuits. I didn't like that subject much and didn't go the extra mile at all. All I did was refer to the standard questions perfectly within the strict boundaries and did well. My guess is somebody who had a lot of interest in that subject, went into a lot of detail in the portions that interested him, read around the subject, built a few electronic circuits in his spare time would not have scored any more than I did because the test is bound by its scope. And there's a possibility that he might have scored a little less than me if he couldn't cover some topics because he was confident in the units he studied, and then found questions from the units he knew and didn't know under the same number. So, the marks would tell you that I know more and am more competent than him in Electronic Circuits, which is of course, totally false. Except in Discrete Mathematics I was that guy. This situation is not totally hypothetical. I have a friend like that who got less than me in Electronic Circuits when he has more knowledge about it than anyone in the class.

    It's like such a system encourages learning dryly with a minimum interest and punishes exploring territories of knowledge out of sheer curiosity. The rewards for learning, as a means to an end, are greater than those for pleasure. It is not good at gauging the level of knowledge of its students, as in the example given above. So, while doing X things would get you a good percentage and doing Y things would not get you a good percentage, my whole question was if getting a good percentage is a worthwhile endeavour, because all the percentage will tell you is that the person took X actions over Y actions. It does not imply that someone who did X things is necessarily more knowledgeable or competent than someone who did Y things. And, if indeed marks are so shallow in their scope, and limited in their powers of predicting the parameters of interest, maybe there shouldn't be such an undue emphasis on them.

    Ultimately, I feel the same points are being made over and over again and this thread is going around in circles.
     
  26. Jan 13, 2016 #25
    It's irrelevant to the course you're taking. I will agree that getting an A doesn't imply perfect knowledge, but not getting an A usually (in most of the cases) does imply a lack of knowledge in the course material.

    Exams aren't perfect, but they can serve as a good indicator of who deserves an A in the course--that is, the people who learned the topics the course is supposed to teach you.

    Example: say you're taking calculus 1 (a typical introduction to differential calculus). Let's say you go above and beyond and read an analysis book instead of the course textbook. You can prove any limit converges to the proper value using the epsilon-delta definition. You can prove the product rule, the chain rule, etc. You've got a deep understanding of the course content, but you're not good at actually taking derivatives. Do you deserve an A in the class?

    No, you probably don't, because one of the main goals of the course is to teach you how to take derivatives. The theoretical stuff has its place in an analysis course. Were you wrong to study extra outside of the course? No, it's never a bad idea to learn more, but if you don't learn the material of the course you're supposed to learn, you won't do well in the course.

    Curricula are designed so that you learn the necessary material in order to succeed in future classes. Had you done as above and skipped out on practicing taking derivatives, you'd be done for when you get to differential equations, or circuits, or whatever.

    By all means, it's a great thing to learn more than the course requires, but you have to learn what the course requires to succeed in it.
     
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