Question about calculus and education

[Jkohn]

Hello all, so my question boils down to why in the MIT OCW (http://ocw.mit.edu/courses/mathematics/18-01-single-variable-calculus-fall-2006/) single variable calculus lectures such little time is spent on limits and why in for example community college so much time is spent on limits.
-cheers

 

[raxAdaam]

I thought about this myself - because at the university where I teach, a great deal of time is spent on limits and infinite sums (in the integral calc course). I think it boils down to the fact that, as a practicing physicist or engineer, MIT graduates will mostly use applications of calculus itself and not so much the limits themselves (nb. they *do* use limits, but I think it would be safe to say that the limits they use are generally much simpler - esp. at an undergraduate level - than the limits involved in analysis/calculus).

However, because limits are fundamental to the ideas in calculus, an older, standard pedagogical approach deems it extremely important that students understand limits and be able to manipulate them.

In my own experience, this latter method is not really effective (if the goal is to underline the relevance of limits in calculus): when I ask students why they study limits in calculus, not one of them can explain their relevance to the rest of the material, which means that - even with all the emphasis & extra examples - the message isn't being communicated effectively.

It seems to me MIT has taken this same stance and attempted to stress the conceptual relevance of limits without ceding excessive learning time to developing the technical skills required for their manipulation - though I'm certain many will disagree with this approach.

I should add, that I expect limits are revisited or addressed in greater detail at a later time - for example in 18.01 I believe they circle back to limits at the end of the course. So they may have simply chosen to address limits more completely at a later point in the ugrad course schedule.

 

[HallsofIvy]

Generally speaking, a four year college- and particularly a college such as M.I.T.- will assume that students who are taking Calculus already have been exposed to "limits" even if they have not taken a Calculus course before.