Mathochism: Becoming independent
One woman’s attempt to revisit the math that plagued her in school. But can determination make up for 25 years of math neglect?
I went to office hours today before class, because I had a few questions. I’ve been going over limits again, helped by a take-home review supplied by the professor.
The problems on this review are far more challenging, and far more rigorous, than what I encountered in the book. And boy, I wish I had had it before the test! Mastering these problems would have prepared me so much better, really reinforcing my understanding of limits.
Oh well. I feel somewhat vindicated by the fact that the Calc Professor told me she wished she had given us that review during my office visit. I also felt vindicated when she agreed that the homework problems in the book are at times too simple.
She also told me that this “simple homework, harder tests” thing is part of a larger departmental policy. By Calculus 1, students are expected to be more “independent,” and expected to seek out information on their own. Bottom line: There will be no more spoon-feeding or hand-holding.
Side note: The Calc Dementor appears to take this policy to the extreme. The Calc Professor, while abiding by this policy, seems to sympathize and try to smooth over the transition, so students like me won’t be completely demoralized. Can you guess which approach I appreciate more?
Considering calculus is a college-level course (in spite of many high schools offering it), I can understand the policy. In college, you’re responsible for your own learning and are expected to have good study habits. Help is available, but you have to identify what you need, and to have made an effort first.
However, I don’t think it is effective to teach concepts using the simplest examples, give homework featuring examples that are just a bit harder, then testing on the hardest examples. Why not teach the simpler and harder examples, give homework featuring the harder and hardest examples, followed by helping students with the hardest examples as needed, i.e when they’re well and truly stuck, and then test on the hardest examples?
I mean honestly, why is it so wrong to want a better idea of what you’re facing? If I may resort to metaphor, while I suppose it is possible (though certainly painful) to run a marathon when you’ve only ever run a 5K, it seems more productive to run a half-marathon before attempting a marathon.
In preparing for this calculus marathon, I’ve been looking for harder examples involving limits. I’ve been looking for ones involving fifth roots and absolute values and other often nasty permutations that make the clear murky. I’ve also been looking for more examples of piecewise function limits, because I really, really need to practice those.
I can’t say I have been wildly successful at finding either. The book, as mentioned before, is useless, at least in the first chapters. Excellent resources like Khan Academy, Wolfram Alpha, etc. have been disappointing, though I appreciate the videos and practice problems. The review, like I mentioned above, helped a lot, but I wish I could dip deeper into that well. A UC Davis website had some interesting stuff that really helped my understanding of infinite limits and sandwich theorems and delta epsilon intervals. If only they had one on piecewise functions!
I know many of my kind readers are math professors. Can any of you recommend a book, or site, or series that gives me some semi-nasty to truly nasty examples of limits to labor over? I’m not asking for worked-out solutions to go with them, but answers would be nice, so I know if I’m on the right track. If I get truly stuck, I will go to a tutor or the professor.
Sigh. I never thought I would see the day where I would be begging to solve harder math problems. Are the seas boiling? The four horsemen galloping? The locusts swarming?
All text copyrighted by A.K. Whitney, and cannot be used without permission.