This is sort of a shower thought because this morning I was using some shaving cream and I thought, if it turns out in 5 years this was giving me cancer, I wouldn’t be surprised.
Comes out a goo, ejected from a can with force, immediately becomes a foam?
Do you have anything you use that you think might be too good to be true?
I think that comes down to your desire to learn. One person might just repeat a google answer but another person might spend some time thinking about why it’s the right answer.
Google is how people get degrees after all, it’s the modern day version of hunting down books in libraries
I think there are many questions where it’s very easy to convince yourself the solution is obvious after you’ve been shown it, but it’s less obvious for someone who is taking the time to try to figure it out on their own.
I teach college math courses (usually around calculus-level), and for every exam I give I will write a practice exam to post online a week before, and I’ll devote the lecture prior to the exam to reviewing those problems. I try to make every problem that appears on the exam very similar to one that was on the practice. The students who attempt the problems before the review session, even the students who get incorrect solutions in the process, will bulldoze their exams and will say it was essentially identical to the practice, while the students who just watch me give the solutions and copy down what I’m writing will tell me the practice was easy but this was barely similar at all.
When you see an obvious solution immediately, you completely bypass seeing potential stumbling blocks which might have tripped you up.
I get what you’re saying about how people establish stronger pathways when they discover something on their own rather than copying something down but at the same time, that’s how education works. You have something explained to you simply first, whether that’s by human instruction like a prof or written instruction/visual demonstration like doing your own research on google. Of course there are low quality/high quality internet sources just like there are low quality/high quality professors and that goes back to how much of a desire the student has to learn, whether they just want to copy and paste answers or actually understand why it is that answer.
As a math teacher I’m sure you can agree that high level academics depends on having a understanding of the fundamentals. If I don’t understand algebra or polynomials then It’s going to take me a while to get a hang of derivatives or calculus and that doesn’t mean I’m stupid or lazy, I just haven’t devoted my life to that specific field because I have 9 other courses to study at the same time. Graduation numbers would be insanely low if we expected kids to figure everything out on their own without access to previous knowledge like the internet. Having the world’s library at your fingertips gives you the ability to copy and paste but also the ability to be an autodidact, it really depends on that specific person’s desire and goals.
I had a lot of foreign students as TA’s for my calc courses, I know it’s not their fault but it was really difficult for a lot of us to understand their accents and we didn’t want to be rude by asking them to repeat themselves all the time. If I didn’t learn google-fu for explanations on concepts I would have failed those classes easily.
I was trying to use an example from personal experience to illustrate the benefit, but my point is that immediate answers wasn’t an option not too long ago, so curiosities you actually did want answered would necessarily have that delay. Being able to learn things well in spite of this shift is becoming a skill not everyone has. It’s something that needs to be nurtured, and it’s now easy to neglect, which really can affect everyone, although obviously some attitudes and lifestyles will be hit harder than others.
Something of a tangent but honestly I hate the way academia works here in general and I resent my role in contributing to math being used as a barrier to a better life. Unfortunately, I do need a career of some sort and there are worse things I could be doing. So I play by the rules well enough to keep my job and just try to do my best to be understanding.
I didn’t even enjoy math myself until I took an analysis course because I thought a math minor would help with job prospects. I always had an easy time with math and when I took analysis I got a D the first time and barely scraped by with a C the second. Math is actually interesting when you feel there’s creativity required in problem-solving, but it’s not reasonable to demand that in a lower-level math course because it doesn’t mesh well with a course existing primarily as a roadblock for students.
A hardworking student might still struggle to develop that creativity quickly enough to get through the course unscathed, which is fine if you’re enrolled because you just want to learn, but not fine for students trying to get good grades or at least pass everything to get through as quickly as possible. A student might have the crazy idea that failing is a financial hit or something. The result is you’re simply put through a grind until you voluntarily take on a course beyond the calculus sequence.
What I’m getting at is that I think your complaints all stem from the fact that, in spite of what we’re all forced to pretend, education is not the main purpose of academia.