[BUG] some thoughts towards the end of the course

[Smith, Alexander J.]

I have had students work through just about every lab at this point. (One more to go.)
Their write ups count for 10 points, while their daily homework counts 5 points. 
You can see some of the implementation and what I required for lab writeups by using the guest access/Preview feature at this Blackboard Web site: http://blackboard16.imt.uwm.edu/?bbatt=Y/
Look under theMath 216 Fall 2003 course. 
 
It would be useful to have some labs that support the development of multiple integrals.
Our course is multivariable calculus, which is vector calculus plus directional derivatives,  multiple
integrals, etc. So there were some "gaps" in the pedagogy of the course, because there was no material for the multiple integrals, etc. This is not really a big deal.
 
One thing I did to save time was to skip the section on the surface area differential for a surface that is the graph of a function z=f(x,y).  You know...the stuff with cos(gamma) and grad(f) etc. 
I justified this for a few reasons: 
1) the following section goes over expressing the surface area differential for parametric surfaces and since this is more general, forget the special graph case.
 
2)  I made it a point to assigned homework problems in the vector calculus part that involved spheres and cylinders, where one should >geometrically<  work out (sans parametrization) normal vectors and surface area differentials.   
 
So what did students do? Somehow the textbook examples steered them into this cos(gamma) and grad(f) nonsense! When students come and ask for help, I kindly point out that we skipped this method, and suggested that there must be another perspective on the problem. Weaker students fell back to the parametric surface methods, and stronger students used the simple geometrical reasoning.
 
It seems that no matter what you do, you end up running interference between the evil textbook and the high minded principles of the Bridge Project. 
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