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Until this point I have felt inspired to study math and looked forward to my classes. But lately I've been having difficulty with my math skills, where I keep making errors over problems I had absolutely no problem with some months ago - errors I never thought I'd make so frequently. Mistreating constants as variables, neglecting coefficients, neglecting bounds, forgetting basic trig identities, forgetting integration techniques, etc.

It doesn't help I landed a professor that is extremely strict. I'm thinking I might be hitting a temporary setback, a few bad months because of covid-19. But part of me is also concerned I'm losing my drive for math. The prospect of me having to retake a class has made me almost always sleep deprived and unable to focus and enjoy my study sessions like I did previously (because I already failed it once last summer). I used to be the student happily helping other students solve problems and trying to get them to get their aha moments on my own free time, but these days I've stopped interacting with my classmates because of these issues.

I guess the question is, when do I know to call it quits? Do I change majors or drop out after having to retake the same class a couple times? Do I chalk this down to a bad semester and a bad time to be a student?

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    $\begingroup$ Are you just having trouble with your math courses or other courses too? It sounds like you are an undergraduate. What year of study are you in? $\endgroup$
    – Amy B
    Oct 3 '20 at 16:19
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    $\begingroup$ That sounds like part of a grouping of topics often taught under the name discrete mathematics, although it can include other topics and proof writing is sometimes taught in a separate bridging course to more abstract mathematics. Anyway, if structures is going at least okay, are there any aspects of Calc 2 you are finding particularly difficult? What are the topics covered there? $\endgroup$
    – J W
    Oct 3 '20 at 18:19
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    $\begingroup$ You say you've stopped interacting with your classmates because you can't help them. Maybe it's time to ask them to help you? Or is everyone having trouble? In that case maybe it's just a tough class and no reflection on you. It sounds like you are having a lot of stress and that's causing careless mistakes. If you work with someone else - a classmate or tutor maybe they can get you past this. $\endgroup$
    – Amy B
    Oct 3 '20 at 19:29
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    $\begingroup$ Can it be that you used to have teachers who went extra mile to make sense of your work (is it "9" or "a"? Have you forgot the negative sign in an equation? When calculating $ \sqrt {27 \times 12}$ you multiplied the numbers instead of breaking them into primes separately, which is more efficient), and now you have a prof who marks your work down not only for wrong answers but for ineffective calculations or lost signs and coefficients? Can it be that you used to produce sloppy work but haven't paid attention to that until you got a prof who does not fix your errors for you? $\endgroup$
    – Rusty Core
    Oct 3 '20 at 19:41
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    $\begingroup$ Calc II is traditionally a very tough class that many otherwise brilliant students struggle with. As far as carelessness goes, there's a lot more opportunities to do something wrong versus say Calc I. $\endgroup$
    – Isaiah
    Oct 3 '20 at 20:14
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To add to Daniel Collins' thoughtful and considered advice, another helpful book could be Lara Alcock's How to Study as a Mathematics Major. It offers tips on calculation procedures, transitioning to proof-based mathematics, dealing with others and time management.

In my experience, many students hit a wall at some point. It can be very frustrating and cause you to doubt yourself, but it can also be a chance to take a breather, reflect, evaluate, and gather the courage to try again/keep going, possibly with an adjusted strategy. The wall may not be as insurmountable as it seems at first glance. Be patient with yourself and do not assume you are not cut out for studying mathematics. Ultimately, you might decide to chart a different course in your degree, or maybe not, but it's early days yet.

Also, life circumstances are not to be underestimated. The Covid-19 pandemic has made life more challenging for many students and their family/friends. This is on top of all the other difficulties life can throw at you at times. Make sure you investigate (and use) the resources offered to you by the university: study skills training, counselling, tutors, TAs, etc.

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  • $\begingroup$ The first part of the Alcock's book is an indictment to the way math is taught in American schools. Most of the stuff she writes about should be taught in school, like polynomials, their factorization and dividing of polynomials, math symbolics, basics of proofs, etc, and the most important skill of them all — the ability to work with textbook and with own notes. My son did not have math textbook from K to 8 grade, he had EngageNY workbooks. He was not required to write homework in notebook to preserve the history, he filled out worksheets. The system is at fault, it is broken. $\endgroup$
    – Rusty Core
    Oct 5 '20 at 3:59
  • $\begingroup$ @RustyCore: Am I correct that "indictment" is your term and not a description of Alcock's tone? I do not get a sense of strong criticism when reading her it or the UK equivalent How to Study for a Mathematics Degree. Rather, she is just being helpful, as can also be seen in her book How to Think About Analysis. $\endgroup$
    – J W
    Oct 5 '20 at 7:52
  • $\begingroup$ (Too late to edit my comment; "her it" should be "her book".) $\endgroup$
    – J W
    Oct 5 '20 at 7:58
  • $\begingroup$ Yes, this is my takeaway. Cops don't rat out other cops, but I can read between the lines when she lists topics and skills and writes, "professors expect you to be fluent in procedures you already learned, they expect you to be able to accurately manipulate algebraic expressions, to solve equations ... without having to stop every time to find a rule". Not everyone takes calc at high school, but at least algebra, basic geometry and trig should be standard and should be taught well. There should be a coherent curriculum, good textbooks, a culture of using notebooks, and no calculators in sight. $\endgroup$
    – Rusty Core
    Oct 5 '20 at 17:36
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It sounds like OP is in their first year, and likely first semester, of a college math program. One's first year in college has traditionally been a very large changeover point. College courses (good ones, at least) require a lot more study, rigor, and precision in writing -- especially in fields like math and computing. Admittedly, they're not for everyone. Furthermore, college life and courses require that the student take control of their own goals and become self-directed and reasonably disciplined without as much hand-holding or safety net supports from family or instructors. The combination of new challenges can be burdensome for many or most people.

For your program, also bear in mind that the discrete math/discrete structures course is generally used as a "transition" and introduction-to-proof course, which is the gateway to the rest of the studies in the math discipline. This switch from calculation-based to proof-based courses is therefore a third big hurdle that you're facing right now. The calculus II course shouldn't be difficult for a math major, exactly, but it's not the most important thing. In the far future it's possible that you may use little to none of that content; but the concepts of logic and how to read and write a proof are essential skills used always by any math practitioner. Do you like the discrete math content, does it fire your imagination? That's the best sign that the math major is the right choice (and that's what most later classes look like).

For the math courses, I would encourage you to start learning to read the textbook itself. One of the most formative experiences I had was, in my first college calculus course, realizing that the classroom experience itself wasn't doing much for me (delivered at distance via closed-circuit television), and I started reading the book very carefully and slowly on my own. The fact that I could do this was a revelation and was the primary tool I relied on to get through an undergraduate math program. Arguably, my job today is basically to apply that same skill: read an arbitrary textbook and summarize it in digestible chunks for current students.

For time-management skills, I recommend that you read the first 3 chapters of Eva Lantsoght, The A-Z of the PhD Trajectory. You're not going for a PhD (now), and neither am I, but recently I've found the time-management procedures there to be extremely helpful. Lantsoght says she developed most of them while she was flailing as an undergraduate science student.

More generally, I would encourage you to use your undergraduate experience (esp. the early part) to take courses from as wide an array of disciplines and departments as possible, and see if any open your mind in ways you didn't expect. You likely at least have general-education requirements, and you should look at these as opportunities and essential college experiences. Do any of the areas excite and intrigue you more than mathematics? Possibly areas you'd never even heard of before now (many of which don't exist in the high school curriculum)? If so, then you should follow the path of greatest excitement (balanced by considerations of resource and career potential). You can change paths any time in life, but it's certainly easiest at the point where you are right now. Early undergraduate years should be a time of broad exploration.

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I guess the question is, when do I know to call it quits?

Having been in shoes, I will give you the advice I wish someone would have told me since the beginning: seek a mental health professional. Lack of motivation, sleep deprivation, inability to focus, no longer enjoying activities that used to be fun, retraction from social interactions, feeling like a "fraud" could all be symptoms of depression or anxiety.

The COVID pandemic has been shown to exacerbate those issues. Don't quit before being sure they're being caused by math itself, instead of external factors. Once you get your mental health in order, the appreciation for learning (not because you need to "pass", but because it makes life more fulfilling) should return gradually.

It might mean you'll need to lower your expectations and take on a lighter load for a while. I don't know where you live, but most Western colleges offer counselling for those situations, since they're far more common than they're willing to admit. Try not to think of it as a a setback, but rather as a pit stop: when you're in it for the long run, some refuelling is bound to happen time to time.

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  • $\begingroup$ Right. You've already spent thousands on your education, why not splurging some more on "mental health professional", who will heal your hurts by pretending to listen to you. These are the most useless "doctors" out there. $\endgroup$
    – Rusty Core
    Oct 5 '20 at 17:45
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    $\begingroup$ @RustyCore I used to think the same and it only made me take longer to get better. I could have graduated 1-2 years sooner had I sought out help when the first signs appeared. But I didn't mean it as a silver bullet, just a threshold before quitting, which could end up being just as expensive. $\endgroup$
    – Ramon Melo
    Oct 5 '20 at 18:16

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