I'm in the (un?)fortunate position of teaching a terminal level technical calculus course. I find the material very interesting, and it's nice that this course incorporates features from Calc 2, Calc 3, Differential Equations and Linear Algebra (because I don't usually get to teach Differential Equations or Linear Algebra), but it's bad in the sense that I'm not teaching the first technical calculus course and up until this semester, I wasn't teaching any precalculus courses.
Which means that my students are in no way prepared for the course they are taking.
Ignoring the fact that students that have passed Calc 1 should know how to do limits and take derivatives, I can already tell that my students are struggling to tread water in the course.
Over the last week, we've been working on methods of integration, which is quite a bulky portion of the text and would possibly be the majority of a non-technical calc 2 course, but the thing that has apparently started drowning a significant number of students is algebra.
Specifically, being able to rewrite powers of cosine and sine using the Pythagorean Identity and the double-angle (or half-angle) identities.
I know, and I've always taught, that the hard part of calculus isn't calculus, it's everything that we assume you know how to do before calculus that you now realllllllly need to be able to do without thinking about it.
But when confronted with an algebraic problem, even if you're rusty or lacking, why would you let algebra be the thing that makes you give up on a course?
This is the type of thing that is easily rectifiable! It's not like it's some obscure portion of mathematics, it's expanding binomials, but those binomials have cosines and sines in them instead of x's and y's.
It's been a very rough week for my teacher's heart.
When a student completely gives up, shuts down, and refuses to attempt to learn, I may find that the most frustrating of every frustration in this job. I can help if you let me.
If you clamp up and give up on the material though, there's not much I can do to break through that shell in the time we have available to us.
In high school, a single course normally takes something along the lines of 36 weeks, meeting 5 hours a week. That's 180 hours of instruction, with regular reinforcement and steady homework and homework checking. In college, we are lucky to get 15 weeks of 5 hours a week, and non-attendance, non-participation, and completely avoiding the material are significant obstacles. That's less than half of the time. It really hamstrings you in what you are able to do with students. It doesn't force a lecture-based course, but you definitely have your work cut out for you if you want to be more dynamic. It's one of the reasons why many people consider college material to be a teach-yourself sort of thing with professors guiding you and showing you new things, but relying on you to force yourself to master the material.
And yet, there's this idea amongst college students (particularly freshman), that they don't have to work hard outside of class. What the fuck is that?
I shouldn't need a ramrod to shove the material down your throats. If there is a lack in your education, let's address it. I will help you, but I won't force you.
Yet, here I am considering what remediations I am able to provide. Considering working more hours for the same amount of money to try to get students to understand material they don't care about and that they refuse to acknowledge they need.
I wonder how much longer I will be able to continue to get up in front of classrooms full of students. I've already been spoiled by finding out what it's like to help teachers instead of students (although they have their own sets of obstinacies that are sometimes mind-numbingly frustrating).
I'd like to idealize math majors since I don't normally get to teach them, thinking that maybe that would be a different case, but from my own experience as an undergraduate and even graduate student, I know there are possibly a majority of students that still don't care about the material or have a natural curiosity for the field they chose for themselves.