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Also, you don't get instant, positive feedback, and immediate indication of whether your solution is correct as you do when programming.
Earlier quoted context omitted.
Perhaps an apprenticeship-system might be worth a try? Let them work together with adults---that might put some sense into them.
I've long believed the master-apprentice system to be the most effective type of teaching system. Unfortunately, it doesn't scale.
Teaching math from a programming perspective (or vice versa) should work since you must (as opposed to 'shall') model problems you care about in terms of math.
I had a rather bruising experience last fall "teaching" precalculus to a lecture of 180 students. Although I'd try to engage the students and explain how the stuff is useful, the students would have none of it. I got scathing reviews about how I was teaching stuff that wouldn't be useful until calculus 2 (which is, of course, a feature and not a bug). We're fundamentally talking about 18-year-olds with bad attitudes…
I had a rather bruising experience last fall "teaching" precalculus to a lecture of 180 students. Although I'd try to engage the students and explain how the stuff is useful, the students would have none of it. I got scathing reviews about how I was teaching stuff that wouldn't be useful until calculus 2 (which is, of course, a feature and not a bug). We're fundamentally talking about 18-year-olds with bad attitudes…
I say that as someone who was once so motivated to learn math, I lied to a highschool precalculus teacher in order to take proof-oriented calculus at a university. (Though she thought she forebade me, I gained prerequisites in a summer-school, running as fast through the material as I was allowed, passing the maximum 3 tests per day — one test per chapter — once I hit my stride. This allowed me to take classes at a university with a highly regarded undergrad math program).
Yet... the university class was boring. Producing "rigorous" epsilon-delta proofs (and whatever else we did) was a tedious exercise which improved my abilities in no significant way. Probably made me dumber. I took only one more math class after that. All of it was a waste of time. Didn't "teach me how to think better" or any of that paternalistic claptrap.
I wish you did not blame your students for their "bad attitude." I sincerely don't mean to be rude, but maybe your attitude could also use some modification. In a better world, you might have been teaching an intro to enjoying one's inborn mathematical abilities, with a crack team of TAs from the psychology dept undoing everyone's damage from earlier schooling.
WTF? Math has specific content and method. A proof is not a program. A for loop is not an integral. Your vaguely technical subject is not a substitute for math just because your students seem more engaged. Teaching people to think logically isn't the point of math, any more than it is the point of history, biology, literature or, yes, even programming. If your students have fuzzy feeling when problem solving, they probably have fuzzy ideas about math. They haven't been taught clearly. If they're uncomfortable with reasoning in math, they haven't been forced to develop intellectual independence. And foisting of "check the steps" on a computer won't help. And don't get me started on how naive an ideas of correctness that is.
A common gripe from young students when learning math is "I'm never going to use this!" With programming, it's much easier to motivate the subject matter - students want to learn the math so they can improve their projects. Similarly, I found linear algebra and linear programming much more interesting when I was studying economics, and classical physics much more fun when writing little javascript animations. So mayb…
I could never understand some people's obsession with only learning things of immediate and obvious use. You should study math for much the same reason you study Shakespeare: to learn to think about things you had never thought about before, in ways that you had never imagined to exist.
I had a rather bruising experience last fall "teaching" precalculus to a lecture of 180 students. Although I'd try to engage the students and explain how the stuff is useful, the students would have none of it. I got scathing reviews about how I was teaching stuff that wouldn't be useful until calculus 2 (which is, of course, a feature and not a bug). We're fundamentally talking about 18-year-olds with bad attitudes…
I think your employers set you up for failure. Nearly all educational institutions make math seem like something only weirdos could enjoy, for their later employment as tools of industry. I say that as someone who was once so motivated to learn math, I lied to a highschool precalculus teacher in order to take proof-oriented calculus at a university. (Though she thought she forebade me, I gained prerequisites in a sum…
I'm sorry that your introduction to real math left you sour, but I assure you that epsilon-delta proofs are not a conspiracy by the industrialist class to brainwash kids away from critical thinking--or whatever you are alleging.