Students should know how their work is graded. Then they can better understand the relative importance of various requests in the assignment. They also can more knowledgeably review the correctness of the grading.
The first Maple assignment
Here are the instructions the graders were given:
There will be a total of 10 points.
The first workshop problems
Here is the body of a message I sent to the recitation instructors,
who read and graded twothirds of the workshop problems. I graded one
section for each lecture. The contents of the message should
provide some background on the grading.
I just finished grading the workshop problems for section ¶ taught by
Mr. ¶¶. Here are some observations about the student work and my
grading which almost surely will be true for all of the sections.

Problem  #1  #2  #3  #4  #5  #6  #7  #8  #9  Total 

Max grade  8  12  10  12  12  12  12  12  12  96 
Min grade  0  0  0  0  0  0  0  0  0  8 
Mean grade  5.69  5.31  6.03  6.49  7.43  7.44  2.16  6.25  7.54  54.35 
Median grade  6  2  6  6  8  9  0  6  8  54.5 
140 students took this exam. Numerical grades will be retained for use in computing the final letter grade in the course. The different versions did not seem to have very different statistical results. Here are approximate letter grade assignments for this exam:
Letter equivalent  A  B+  B  C+  C  D  F 

Range  [80,100]  [75,79]  [65,74]  [60,64]  [50,59]  [45,49]  [0,44] 
Problem 1 (8 points)
a) (5 points) 1 point each for finding two vectors (say pq and pr, for
example). 3 points for finding the cross product.
b) (3 points) Students may use their answer (even if incorrect) to a)
in this part if the answer is not trivial (such as the 0 vector
or just <1,0,0>). 1 point for not knowing the the triangle's area
should be half of the magnitude of the cross product.
Problem 2 (12 points)
2 points for computing the dot product of V and W
correctly. 2 points for computing the magnitude of W
correctly.
A correct value of V_{1} gets 4 points, and
a correct value of V_{2} gets 4 more points.
Students certainly may use any of the formulas on the formula sheet,
provided that the answers are correct. If a student makes a mistake
early in the problem but does not trivialize the problem (for example,
makes an error in computing the dot product) then the student will be
penalized for that error but can earn all the points in the balance of
the problem, working as if the earlier answer were correct.
Problem 3 (10 points)
a) (4 points) 2 points for recognizing the correct normal vector. 2 more
points for writing the correct parametric equations.
b) (4 points) 2 points for recognizing the problem: that is, addressing
the distance question correctly. 2 more points for getting a correct
point (either correct point earns the points!).
c) (2 points) This is earned for writing the correct equation for the
plane. 1 point off for either a wrong "point" on the plane or for a
wrong normal vector. The student may use an incorrect point from b)
and still earn 2 points here.
Problem 4 (12 points)
2 points for a correct r´(t).
2 point for computing (and recognizing the "need" for) r´(t).
Students do not need to "simplify" this expression, or any other in
the problem.
2 points for a correct result for T(t) and then for T(1).
3 points for T´(t) (take off a point for each error but continue
to read for other results!).
3 points for N(t) and then N(1): any "mess" (if correct!) will earn
the points.
Quoting from the formula sheet (even relevant formulas!) will not earn
credit.
Problem 5 (12 points)
4 points for the graph: the graph should be "unimodal": down then up,
with good limits (2 points). And it should be 0 on an appropriate
interval in between. (2 points). Since I'm convinced that the curve
sketched is smooth 1 point will be deducted for graphs of
curvature which seem offensively nonsmooth to me.
4 points for the limits: the limit as s goes to + (or ) infinity are
each worth 2 points.
4 points for the explanation. What's needed is an explanation,
not a description in words of the graph of the limiting
behavior. There must be some reasoning or explanation given. Ideally,
the word circle should occur, and some relationship between the radius
of a circle and the curvature of that circle. Then the relationship
between circles A and B and the curve should be mentioned.
An acceptable explanation need not be long. Certainly some students
received full credit with just one or two wellwritten sentences. When
the word "it" was encountered, an effort was made to identify the
referent (what the "it" means). If this identification was ambiguous
or impossible, credit was reduced. I read what students wrote. Such
phrases as "the curvature of a point" or "the definition of curvature
is 1/R" are meaningless or incorrect, and don't earn credit.
Students whose only error is somehow systematically interchanging
+infinity and infinity will be penalized 2 points only.
Comment I meant to ask for an explanation of both the
graph and the limits, but did not. Then I would have wanted a
statement about why curvature is 0 for an interval around s=0 (the
curve is a straight line segment there, and straight lines have
curvature 0.) I didn't phrase the question as I should have, however!
Problem 6 (10 points)
1 point for computing f's value at (2,1).
2 points each (total: 4 points) for computing the first partial
derivatives of f correctly.
2 points (1 each) for evaluating these first partial derivatives.
3 points for the linear approximation formula. It does not need
to be explicitly stated. A numerical version is o.k. Students who
insist upon doing numerical work incorrectly should lose a
point. Realize that there is no need to do any numerical work
in this (or any!) problem  answers do not need to be simplified.
Problem 7 (12 points)
a) (6 points) 2 points for a correct z_{x} and 2 points for a
correct z_{y}. 2 points for assembling these into a correct
verification of the PDE. Working with a specific function f earns
no points (!).
b) (6 points) 4 points for a correct use of both the product rule and
the chain rule (2 for one of them not correct). Then 1 point each for
stating explicitly what the two functions (A and B) are (that
is requested!).
Comment This problem had the worst results. Therefore either
the chain rule wasn't taught well and/or it wasn't learned well. There
will be a similar question on the next exam.
Problem 8 (12 points)
a) (6 points) 1 point for F(x,y,z). 1 point for the correct value of F at p. 2 points for the maximum
directional derivative stated correctly and 2 points for the correct
unit vector.
b) (6 points) C's value earns 1 point. Realizing that F at p is a normal vector earns 2
points (so incorrect data from a) can still earn these
points). Writing the equation of the tangent plane earns 3 points.
Students may use their result from a) if incorrect and nontrivial
without penalty.
Problem 9 (12 points)
a) (4 points) 2 points for the correct computation of f (the correct computation of the
partial derivatives alone earns 1 point  assembling them into the
gradient earns the other), and then 1 point for f(2,1,2) and 1 point
for f(2,1,2). The gradient of
this function should be a vector in R^{3}, not in in
R^{2}. A twodimensional answer loses a point.
b) (4 points) 2 points for the correct computation of g (the correct computation of the
partial derivatives alone earns 1 point  assembling them into the
gradient earns the other), and then 1 point for g(2,1,2) and 1 point
for g(2,1,2).
c) (4 points) 2 points for realizing that the cross product (or
something equivalent!) is needed were rewarded, and 2 points for the
computation. Students could use their results from a) and b) even if
incorrect without penalty provided that the resulting problem was
nontrivial. A correct geometric observation such as "The tangent
vector of the curve is perpendicular to both surface normals" would
earn at least a point.
Maintained by greenfie@math.rutgers.edu and last modified 2/28/2006.