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How I Overcame Learning Challenges That I Faced Studying STEM

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For the past few days, during my summer break, I have been intensively self-studying mathematics (namely number theory) for several hours each day without having prior experience in theoretical math.  The struggle of learning is not unique to mathematics; during my first year of computer engineering (which I had just completed at the time of writing this article) I faced many similar challenges that I continue to face now. There are many difficulties we face that we must overcome in order to succeed.  In this article, I will discuss the challenges that I faced, which are likely common to others with varying academic backgrounds, and how I overcame them.  I will also discuss a challenge that I have not yet been able to overcome.

Challenge #1: Doubt

The first and by far the most destructive obstacle to self-learning is that of doubt.  Whenever I encountered difficult material, I felt like giving up. I had the nagging thought that I wasn’t smart enough to be able to do the content; that I would fail, and that I should stop wasting my time and give up.  Unfortunately, there was no easy solution to this problem.  However, I feel like this issue existed because I often compared myself to other people who seemed to breeze through the material (despite the fact that many of these people have much more experience than I).  To lessen the impact of this challenge on myself, I had to change the way that I thought, and I had to stop comparing myself to other people.  I never gave up, and thanks to my persistence, I always figured out whatever troubled me, and when I did, I knew that I could continue to overcome challenges that came my way.   Although these feelings may never go away, their impact on you will lesson with time and experience, so as long as you stay persistent.

Challenge #2: Losing Interest

The second challenge that I faced was losing interest with the material that I studied.  I felt like this challenge was a direct consequence of the first obstacle to learning: doubt.  When I struggled in specific academic topics, or felt as if I wasn’t progressing with the material fast enough, I often became frustrated with myself.  This frustration led me lose interest in the material that I studied.  I started to rationalize the purpose of learning the areas I struggled in; such as telling myself that number theory was useless as it had no real life application, and that I shouldn’t bother learning it, that I should focus my efforts on more important things.  However, thinking like this was destructive and caused me to lose interest in my studies.  After overcoming the first learning challenge: doubt, I had found that I started to regain interest in number theory, because I knew that I was capable of doing it.  I also started keeping track of my progress throughout my studies, and I began looking forward to what learning number theory will bring me: more mathematical maturity, which I feel is applicable to every aspect in science (specifically theoretical computer science).  I feel that one should always make something to look forward to which will result from the topic that they are currently studying, especially if they start losing interested in said topic.

Challenge #3: Time Management and Unrealistic Goals

The third challenge that I faced was time management and unrealistic goals.  I had a vision of all of the books that I would have completed by the end of summer, as well as all of the topics I would have completed.  Therefore, I set a goal of completing a certain number of pages per day.  This forced quota of “pages to complete per day” ironically caused me to become even less productive.  When I encountered a difficult proof in my book that I did not understand, I would simply skip it and continue on.  However, there would come a point in the future that understanding this proof was critical.  This essentially forced me to either continue skipping material, or to go back and actually learn the difficult material.  I have now realized that my goals were unrealistic, and vowed to spend as much time as I need.  I feel like an important lesson to share is what follows: don’t set unrealistic goals.  Know what you can and can’t do.  Be satisfied with what you can do, so as long as you vow to put in 100% effort.  However, it is important for one to know their limits.  Having never written a math proof before in my life nor knowing anything about math logic before I had started studying number theory, I had come to the conclusion that I was not yet ready to continue studying number theory, because I could not satisfy the demanded prerequisite knowledge.  I decided it was best to start learning more basic mathematics (namely about proofs, math logic, sets, etc), so that I will be ready to return to studying number theory at some point in the future.

Challenge #4: Understanding Difficult Problems

The fourth challenge that I faced was that of actually understanding difficult problems.  I found that the majority of problems I encountered were due to the fact that I was missing some prior knowledge.  Whenever I didn’t understand something, I would find out what I struggled with and then return to previous lessons to relearn what they had taught me.  In the case of number theory, I had difficulty approaching certain proofs because they had seemed very complicated and long.  It was as if these questions had absolutely no relation to anything I had previously learned, and I felt like I had to use some foreign skill to solve these problems.  However, I found that I could often break these problems up into little subproblems, and then use the solutions to previous questions to solve these little subproblems, as well as some thinking to glue everything together.  This often transformed giant scary problems into problems with laughable difficulty.  However, I found that the key to being able to break up problems is to have a firm grasp of prior knowledge and knowing the content that you must know in order to be competent in your studies.

Challenge #5: Lack of Feedback

The last challenge is one that I have not yet been able to overcome.  It is the lack of feedback regarding problems I solve.  Despite resources being available to ask for help (such as the internet), often the feedback was not available in a timely manner.  There is no debugger for math proofs or physics problems, like there is for software.  Most of the time, I could not figure out if my proof was incomplete, or even flat out wrong.  This caused me difficulty as I didn’t know how to proceed.  This is true even in the case of physics or engineering problems when the numerical answer is provided.  Since it often takes a very long time to solve these problems and includes numerous steps, if your answer is wrong, you know that you made a mistake. However, you don’t know what kind of mistake you made. Did you make a calculation error, or is your process/logic just plain wrong? It can be very frustrating, especially in engineering when you only have limited time to learn specific topic, due to the fact that you have a very heavy workload.

Conclusion

All in all, overcoming challenges is a vital part of in life, and affects everyone with varying academic backgrounds and experience.  I found that in general, to overcome almost every challenge I faced, all I had to do was the following: never give up, constantly have something to look forward to which result from the topic I was currently studying, be satisfied with my limits so as long as I put in 100% effort, know when to retreat and regroup, and have a firm grasp of prior knowledge.

 

I have just completed my first year of computer engineering at UofT. My interests include: computer science, mathematics, physics, and reverse code engineering.

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  1. Greg Bernhardt
    Greg Bernhardt says:

    Nice article x86! I definitely struggle with lack of interest at times. I have severe modification swings. I can be pumped about something and not get any sleep and then next day I am so-so about it.

  2. Chestermiller
    Chestermiller says:

    I liked your article quite a bit.  Regarding Challenge #5, that's where Physics Forums can help.  Regarding Challenge #4, you have discovered that, in solving problems (e.g., modelling), a very effective practice is to start simple.  Why?  If you can't solve a simple version of the problem, then you certainly won't be able to solve the complicated version.  Plus, after you has solved the simple version, you have "something under your belt" with which you can compare your more refined solutions.Chet

  3. uselesslemma
    uselesslemma says:

    Challenge #1 is my main issue personally. Not comparing yourself to others is difficult, but once you decide to ignore the progress of others learning becomes much easier, and you'll find yourself leagues ahead! Nice article.

  4. Monsterboy
    Monsterboy says:

    Challenge 6: How to avoid pessimistic people who constantly bug you and tell you to give up and you are not in a position to snap back at them and tell them to shut up.

  5. Monsterboy
    Monsterboy says:

    Challenge 3: How is it even possible to know your limits early on?   have you heard of this saying ?"To know your limits you must try to cross them"

  6. x86
    x86 says:

    Try to surround yourself with more positive people who believe in you.  Changing your environment really helps, if it is possible.  I've been through this before, and I can't lie, it is a tough thing to go through, especially since what they say will always be a nagging thought at the back of your head whenever you fail.  You need to find people who believe in you and support you, as well as do something you have a passion in.

  7. x86
    x86 says:

    Well, I think it is important to have a rough idea of your limits before starting.  I.e., It may not be wise to jump into a calculus course if you don't yet know precalc algebra and trig.

  8. x86
    x86 says:

    I felt the exact same way when I had to take material sciences, dynamics, and thermodynamics this semester, given that I'm not in mechanical or chemical engineering.  However, you're going to have to force yourself to get excited about this content.  Look in the mirror and tell yourself you enjoy it.  (It works best for me).I don't know much about academic research, but perhaps it is possible to talk to someone who is an expert in this field?

  9. jedishrfu
    jedishrfu says:

    Nice insight. It mirrors the same problems researchers in all fields  have when breaking new ground. They often have no one to turn to, doubt their results and struggle to verify things before publishing so in a sense the self-learning exercise prepares you for the real world where you will have to self learn difficult things to solve difficult problems in novel ways.

  10. VoteSaxon
    VoteSaxon says:

    Unfortunately, you need strong self-discipline to get studying stuff you don't have any interest it. My shocking lack of self control has meant I have probably sabotaged my first year at uni.

  11. Docscientist
    Docscientist says:

    That was very useful !I would plan to do so many things for my vacation like learning a programming language,master high school math and science (I just completed my middle school ).But I would end up spending most of my time learning science since I love it more that math and computer science.The lack of interest was as you said "self doubt" I think I should dive into this freaking math and master it before my vacation ends so that I could crack my medical entrance !

  12. Kitaev_Model
    Kitaev_Model says:

    Nice article x86! I definitely struggle with lack of interest at times. I have severe modification swings. I can be pumped about something and not get any sleep and then next day I am so-so about it.

    Yeah, that’s me. One day I can stay up all night learning about topology in condensed matter physics, not get any sleep, the next day I’ll spend goofing off on the Internet or doing meaningless coding, and I just get so hyperfocused on that…

    That’s part of what I’m trying to solve now, dealing with the roller coaster of my emotions.

  13. Greg Bernhardt
    Greg Bernhardt says:

    Yeah, that’s me. One day I can stay up all night learning about topology in condensed matter physics, not get any sleep, the next day I’ll spend goofing off on the Internet or doing meaningless coding, and I just get so hyperfocused on that…

    The bouncing around shouldn’t be that troubling especially if you are young. You should be trying as many different things as you can to figure out your true path. Get some sleep though. It’s very important to your health and happiness.

  14. blue_leaf77
    blue_leaf77 says:

    To me the true challenge of self-studying is when you have to study something you have no genuine interest in to begin with, like for example there can be certain part in doing thesis where one is sometimes obliged to learn something out of his field. This especially can become quite painful when this stuff out of your field actually belongs to some not-so-easy graduate level courses in its own field. Such experience has occurred to me at least once.

  15. Kitaev_Model
    Kitaev_Model says:

    The bouncing around shouldn’t be that troubling especially if you are young. You should be trying as many different things as you can to figure out your true path. Get some sleep though. It’s very important to your health and happiness.

    Yes, my new academic counsellor (I was too proud, too bull-headed, and too stupid to ask for any help from anybody as an undergraduate, which was a serious mistake) and I are trying to devise ways of me getting uninterrupted sleep. I think I might just have found a formula.

    I’ve noticed my productivity is generally better. And it’s like a muscle-as you train it, you’ll need less, though never none.

  16. Kitaev_Model
    Kitaev_Model says:

    Challenge 6: How to avoid pessimistic people who constantly bug you and tell you to give up and you are not in a position to snap back at them and tell them to shut up.

    That’s a tough one, but if necessary, simply change who you hang out with.

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