Timeline for Why does undergraduate discrete math require calculus?
Current License: CC BY-SA 2.5
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 2, 2019 at 11:55 | comment | added | Walter Mitty | Your second sentence says a great deal. Knowing how to multiply may be a strictly mechanical skill, one you don't need when you have a calculator handy. But knowing what multiplication means, and when to apply it in the real world is fundamental to numeracy. Someone who doesn't know what multiplication is for is partially innumerate. There is an analogous situation for differential and integral calculus. Someone who doesn't grasp the purpose of these two cannot understand the history of ideas for the last 300 years or so. | |
| Sep 12, 2011 at 17:47 | history | made wiki | Post Made Community Wiki by S. Carnahan♦ | ||
| Jun 5, 2010 at 18:38 | vote | accept | johntantalo | ||
| Jun 5, 2010 at 12:57 | comment | added | Steven Gubkin | (At the risk of starting a discussion) I agree that most students do not understand multiplication of integers, and hardly any at all understand multiplication of fractions. Why are we (mathematicians as a community) not giving elementary school concept tests to our incoming freshmen, and teaching them to their level of understanding? Why do we make them memorize pages of calculus formulas when they do not understand the basics of arithmetic? So we don't have to deal with them for more than a year? That is incredibly sad. | |
| Jun 4, 2010 at 23:15 | comment | added | Victor Protsak | @Deane & Alexander: Paraphrasing a well-known quip, you can't help all the people all the time. I think it makes sense to require people aiming for a math or science degree to take a college level calculus course first; if they decide that science is not their thing, after all, I see nothing wrong with that. I also think that there should be a different track for liberal arts majors who may never take calculus, with a discrete mathematics course that does not emphasize sets and structures; many schools do have such a course to satisfy the quantitative reasoning requirement. | |
| Jun 4, 2010 at 22:47 | comment | added | Alexander Woo | @Deane: Frequently they don't, but the cynic in me says that instructors or programs which don't notice and try to solve this problem the right way are just as happy to have this problem solved the wrong way, which is to say that the student struggles for reasons unclear to him or her and is discouraged from taking further mathematics. (Given constraints on resources, solving the problem the right way for most students frequently isn't a viable option.) | |
| Jun 4, 2010 at 22:14 | comment | added | Deane Yang | The diagnosis is correct, but do they really acquire the necessary skills in the calculus course? | |
| Jun 4, 2010 at 21:39 | comment | added | Victor Protsak | Excellent diagnosis! I might add that struggles in calculus and ODE courses are often due to poor algebra preparation, whereas struggles in discrete mathematics and abstract algebra are due to complete lack of experience with abstract concepts and abstract reasoning. So it makes sense to start with calculus. | |
| Jun 4, 2010 at 20:09 | history | answered | Alexander Woo | CC BY-SA 2.5 |