Calculus Term Paper: Learn Essential Mathematical Skills

[D H]

In another thread, alec_tronn posted

I am required to write a term paper for my Calc. 3 class about what calculus has been about thus far. ...

My basic reaction: Write a term paper for a calc 3 class?? My first and continued impression is that this requirement is just shovel work. It hinders rather than aids mathematical education. The time taken to write the paper is time not taken to learn essential mathematical skills. The requirement also hinders rather than aids teaching communications skills. The grader (a math professor) most likely does not know how to write well himself. (The evidence is piled in front of me in the form of technical journals.)

 

[waht]

"What Calculus has been thus far"? No way, that's bs. If the paper was about a proof or a mathematical result just like a journal, that could be interesting.


I would write about what a moronic teacher we had thus far.

 

[gravenewworld]

That's the problem with a lot of math education at the university level. Students are a lot of times only given problems to solve after class and take exams, they are never required to write anything. The project is a good idea, professional mathematicians better have good writing skills if they ever want to submit an article to a journal. Two of my math classes (sr. seminar, and real analysis) when I was an undergrad were considered writing intensive (more than 20+ written pages a semester).

 

[D H]

Gravenworld, those two classes you mentioned were upper-level undergrad courses. I agree that a senior seminar or senior research project class should be writing intensive.

On the other hand, lower-level undergraduate classes involve learning orthogonal skills. Most students in technical areas are lacking in basic math skills (introductory calculus, up to "calc level 3") and good communication skills (technical writing 101). Require students to take the basic maths and the basic writing courses, and later merge these separately learning skills in upper-level undergraduate classes.

Does mixing the skills at an introductory level add value, or does it detract? I assert it is the latter. The quality of communications and math skills as demonstrated in the posts of many of the younger members of PF is primae facia evidence of my assertion. (alec_tronn, I am not talking about you.)

 

[Mk]

I would also see like to see more papers to be written in math classes in general, probably on topics picked by the students themselves. But I agree about "What calculus has been thusfar" feels like B.S. as well It's not that bad though, you could write a good paper about calculus in general.

 

[gravenewworld]

That's just the problem. A lot of universities don't require technical writing 101 for their science majors.

 

[J77]

Agree with gnw -- it's a good idea.

It's a skill which goes way beyond making a list of what you've learned so far -- those who would make a list have a lot to learn about science and maths; even, particularly, if they can do every question in the Calculus book so far and think this is learning!

 

[arunma]

Seems like an excellent idea to me. Back in my senior year of high school, I had to write a similar paper for my calculus 2 class, on an application of calculus to some real world problem. I wrote it about the integral form of Maxwell's equations. In most of the classes I took for my math degree, I found that writing was a pretty important skill. Sometimes it was necessary to write a couple paragraphs to explain a proof, when calculution alone didn't suffice. And in two of my classes I had to write final papers (one on an application of complex variables to differential geometry, and another on a mathematical analysis of biochemical pathways in the cell cycle). I only wish that more math teachers and professors would do this.

 

[robphy]

I think such a paper is a good idea because it [hopefully] invites the student to step back and see the big picture of what calculus is about.

Is calculus just a bunch of rules and symbolic manipulations to memorize? Or is there an underlying story? If so, can one at least give a plot summary of the story which conveys some mathematical intuition? (Certainly, one can approach such a story historically or structurally or (say) within the context of a physical application.)

Maybe one can be inspired from expositions such as these [arbitrarily plucked from a google search]
http://www.mathpages.com/home/kmath072.htm
http://www.maa.org/editorial/euler/How%20Euler%20Did%20It%2035%20Foundations%20of%20calculus.pdf