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(Disclosure: I taught college mathematics courses (almost entirely from the calculus sequence on up) for one semester as an undergrad, 4.5 years in grad school,

(Disclosure: I taught college mathematics courses (almost entirely from the calculus sequence on up) for one semester as an undergrad, 4.5 years in grad school, and 4 more years as an assistant professor.) > Math (I'm talking about the US based university approach) changes dramatically once you get to "upper division" coursework. It's not just a dramatic change; for most, it's a cliff thrown in the middle of the learning curve. There are many reasons for it: some high schools passing students along when they shouldn't, some professors doing the same thing when students get to college, and the ever-so-fetishized focus on applications over concepts. In short, it's a cultural problem. And at this point, I have no idea how--or if--it can be resolved.

Cowen 13y ago
> It's not just a dramatic change; for most, it's a cliff thrown in the middle of the learning curve. When I transferred to a new university I was placed in their first year calculus program over my own protests. I had already done AP Calculus in high school, and completed the first year calculus course at my previous college, which was admittedly of much lower quality than the university I was transferring to. I thought this new one would be a complete waste of my time. The first thing we covered in this new course were limits. I rolled my eyes; everyone knows how to find a limit. Was this really the kind of thing we were going to cover in this class? Then the professor said these words I had never heard in relation to limits before, "epsilon" and "delta." And here my troubles began. That turned out to be one of the hardest courses I've ever taken, I had to relearn almost everything I thought I knew about math.
- jackmaney 13y ago
  [nod] Yep, sadly, there are too many "calculus" courses that don't mention epsilon and delta at all (I'm looking at you, Business Calc). Without thinking about epsilon and delta, it's prettymuch impossible to have anything but a vague, fuzzy notion of what a limit is. In Calc I, I kept my eyes out for two groups of students: those who did really poorly on the first exam, and those who did really well. The first I watched for obvious reasons, but some of the folks in the latter group--especially those who took some calculus in high school--would start to think "Oh, I know all of this now! Cool. Easy A." and then coast. And they'd be mincemeat somewhere in between implicit differentiation and related rates.
zyxley 13y ago
For me, this cliff came with discrete mathematics, where the appearance of proofs, induction, set theory, and so on left me completely foundering for some time. They were all topics that I had literally never touched before except in the most brief, informal ways, and none of them seemed to have any relation to material I'd previously learned. None of it really made any sense to me, and in retrospect, the only reason I even managed a passing grade in the course was because I'd been taking a statistics course at the same time that covered many overlapping topics (sets and relations, discrete probability, etc) in a "use these things to calculate this other thing" way that actually meshed with my previous education. Proofs were the real killer out of all of it. I still today have barely any idea how to manage a formal proof or what elements are involved in one, because at the time trying to figure out what the hell was going on with this notation and formatting and abbreviations everywhere that I'd never seen before and trying to make any sense of the weird self-referencing logic of it was unpleasant enough that I just fumbled through the bare minimum to get a passing grade whenever they were involved.

Cowen 13y ago

> It's not just a dramatic change; for most, it's a cliff thrown in the middle of the learning curve. When I transferred to a new university I was placed in their first year calculus program over my own protests. I had already done AP Calculus in high school, and completed the first year calculus course at my previous college, which was admittedly of much lower quality than the university I was transferring to. I thought this new one would be a complete waste of my time. The first thing we covered in this new course were limits. I rolled my eyes; everyone knows how to find a limit. Was this really the kind of thing we were going to cover in this class? Then the professor said these words I had never heard in relation to limits before, "epsilon" and "delta." And here my troubles began. That turned out to be one of the hardest courses I've ever taken, I had to relearn almost everything I thought I knew about math.

jackmaney 13y ago
[nod] Yep, sadly, there are too many "calculus" courses that don't mention epsilon and delta at all (I'm looking at you, Business Calc). Without thinking about epsilon and delta, it's prettymuch impossible to have anything but a vague, fuzzy notion of what a limit is. In Calc I, I kept my eyes out for two groups of students: those who did really poorly on the first exam, and those who did really well. The first I watched for obvious reasons, but some of the folks in the latter group--especially those who took some calculus in high school--would start to think "Oh, I know all of this now! Cool. Easy A." and then coast. And they'd be mincemeat somewhere in between implicit differentiation and related rates.

zyxley 13y ago

For me, this cliff came with discrete mathematics, where the appearance of proofs, induction, set theory, and so on left me completely foundering for some time. They were all topics that I had literally never touched before except in the most brief, informal ways, and none of them seemed to have any relation to material I'd previously learned. None of it really made any sense to me, and in retrospect, the only reason I even managed a passing grade in the course was because I'd been taking a statistics course at the same time that covered many overlapping topics (sets and relations, discrete probability, etc) in a "use these things to calculate this other thing" way that actually meshed with my previous education. Proofs were the real killer out of all of it. I still today have barely any idea how to manage a formal proof or what elements are involved in one, because at the time trying to figure out what the hell was going on with this notation and formatting and abbreviations everywhere that I'd never seen before and trying to make any sense of the weird self-referencing logic of it was unpleasant enough that I just fumbled through the bare minimum to get a passing grade whenever they were involved.