Exams, Homeworks, and Grading
Students are
responsible for understanding all of the policies on this page.
These policies are subject to change at any time by the instructor.
Topics:
Assumptions and Intent in Exam Problems
Grading and Exams
"Fair Game" Material
Rough Cutoffs
Grading Comment Codes
Homework
Reading Quizzes
Attendance Quizzes
Regrades
Studying
"Log Confidence" Exam Problems
Improving Your Performance
Additional Comments
Assumptions and Intent in Exam Problems
Students should be very careful about what formulas are used in the
solution to a problem. Points will not be awarded if students
simply cite formulas that were not intended to be used in the solution
to the problem.
For example, consider the problem of finding the antiderivative of the
function (1-4x^2)^(-1/2) with respect to x. There are multiple
expectations that an instructor might have for solutions to this
problem:
1. Some instructors might allow students to cite formulas
from integration tables. In that case, an acceptable solution to
the problem would consist only of plugging in to a memorized formula.
2. Other instructors might allow students to cite the
formula for the derivative of the arcsine function, in which case an
acceptable solution to this problem would require the student to
perform a substitution.
3. Another instructor might allow neither of the above, and want the student to do a trig
substitution -- thus assuming even less and showing more work in the
derivation of the solution.
This choice is entirely at the discretion of the instructor. If
it is not explicitly clear in the statement of the problem or from the
course materials or lectures, the student should clarify before making
an assumption that might well turn out to be wrong.
Misunderstandings on this do not excuse inappropriate solutions.
For most Duke math classes, students can rule out certain possibilities
by some simple reasoning. In the example above, for instance,
note that the first option allows the student to come to a correct
answer by having memorized a formula, without any demonstration of
understanding of significant ideas or techniques. This is not
typical of math classes at Duke, and so students should not assume that
such a solution would receive credit. Both the second and third
solutions above though do demonstrate understanding of important
techniques, and either could reasonably be what the instructor expects;
students should get clarification from the instructor.
Other conclusions can be drawn by thinking about the motivation for a
given exam problem. Suppose for example that a problem asks you
to compute the derivative of the composition of two functions, h(x) =
g(f(x)), where f and g are given. The clear intent of the problem
is for students to demonstrate their understanding of the chain rule by
using it to derive the solution. As this is the clear intent,
students should suspect that they are supposed to do the problem that
way. Now, a correct final answer can be computed by first
computing h(x) explicitly and then computing its derivative directly,
with the usual shortcut rules -- but, as this method circumvents the
clear purpose of the problem, students should not expect to receive
credit for this.
Remember, your solution is not graded on the correctness of the final
answer, but on the extent to which you have demonstrated comprehension
of the corresponding techniques and concepts. So you should make
sure to identify what those are as you work any problem. Again,
in any situation where you are unsure, you should make sure to clarify
before making what might turn out to be an importantly wrong assumption.
Of course sometimes there are multiple ways to solve a problem, several
of which are substantial and appropriate. In those cases, it is
not expected that the student will necessarily make the same selection
as the instructor.
Grading and Exams
Final grades for the class will be determined by the total number of
points earned in the class. These points are given based on
performance on the items below, with the following maximum possible
scores:
Tests:
~300 possible points (3 exams x ~100 points each)
Final Exam: 200 possible points
Homework average: 50 possible points
Reading Quizzes ~30-40 possible points
Attendance TBD
------------------------------------------------------------------------------------------------
Total:
~580 possible points
The student should be prepared for the fact that the grading system for
these exams is NOT the same as the one most students became accustomed
to in high school. There are two main properties in particular of the
high school system that will not be used in this class :
1) In most high school grading systems, there are fixed, arbitrary
numbers that determine the cutoffs between different letter grades --
these cutoffs were invariant, and independent of the exam. The problem
with this that it forces the instructor to create exams that are always
the same difficulty; in other words, the instructor must make sure that
all exams will yield the same mean score. Furthermore, it requires that
the distribution of scores also be roughly constant. Achieving both of
these goals is not only difficult, but impossible to perform perfectly.
This system ties the instructor's hands severely, and is totally
unnecessary! Of course it is important that final letter grades for a
class follow a prescribed plan, so that those letter grades have some
meaning outside of the context of that class. Ensuring that is actually
easier if the instructor chooses the cutoff numbers after having seen
the distribution of student scores. The cutoffs can then be chosen
while incorporating important considerations such as the difficulty of
the exam, or any other points about the exam that may be relevant.
2) The class average on exams in most high schools was usually expected
to be somewhere in the mid-eighties. While this is reasonable
considering the nature of high school, it is not always appropriate for
a college setting.
In this class, certainly, there are expectations for the student that
are much more demanding than those of most high schools. We expect that
the student will achieve much more than the mere ability to reproduce
what he or she has seen in class. In particular, we expect that the
student will achieve an understanding of the ideas that are at the
foundation of the methods -- and thereby gain the ability to apply
those ideas to situations that he or she has not already been exposed
to.
Since the expectations of this class are more difficult than those of
high school, it stands to reason that the exams, designed to test the
students mastery of these more lofty goals, must involve more difficult
questions; and therefore, the exams must be more difficult. Clearly
this will result in class averages that are lower than what one would
expect if the exams were more like those of high school. It will also
tend to result in score distributions that are more broad, since the
students responses can be expected to be more varied.
The student should be fully aware of these points before taking an exam in this class.
"Fair Game" Material
This class, as with most math classes, is largely "vertical", in the
sense that the material covered later in the course usually depends on
the material from earlier in the course. Because of this, it is
not possible to make an exam that is entirely non-cumulative.
Questions on topics from later in the course unavoidably will require
proficiency in topics from earlier in the course.
Nevertheless, we can still note that most problems have a primary
focus, which can usually be associated to a topic covered at a specific
point in the course. Each midterm exam will have an associated
range of topics from the syllabus that are declared to be "fair game"
as a primary focus for problems on that exam. These fair game
ranges will be specified by the instructor, and will not overlap; that
is, if a topic is fair game as a primary focus for the
first midterm, it will not be for the second midterm. (Note,
these ranges refer to material from all aspects of the course -- the
book, the lectures, the homework problems, the recitation sections (for
courses with recitation sections), and any other official part of the
course.)
This makes the midterm exam as non-cumulative as possible. Still,
of course, students must be sure to retain proficiency in topics that
were fair game for earlier midterms, because even though those skills
will not be the primary focus of problems on later midterms, they still
should be considered as necessary skills in solving such problems
completely.
The term "fair game" is used as an acknowledgement that for most
midterms, there is not enough time to allow for testing all of the
skills and concepts relevant to that exam. Midterm exams will
cover a representative sample of the relevant material, but not all of
it. Calling a topic "fair game" means that the instructor might
choose to create an exam problem testing a particular topic, but makes
no explicit promise.
To summarize then: On each midterm exam, the primary focus of
each problem on that midterm will be from the fair game material for
the exam, which includes all of the material in the course up to a
certain point in the syllabus (to be specified by the instructor) that
was not declared as fair game for a previous exam in that same
term.
Unlike the midterm exams, the final exam is cumulative. All of the material from the course will be fair game.
Rough Cutoffs
It is very dangerous to associate letter grades with performances on
individual exams, because it is very difficult to predict how the
distributions for those exams will interact when the total score
distribution is formed. Therefore, the class will usually be informed
only of the class median and mean for a given exam -- letter grades
will not be assigned.
On the other hand, I believe that it is desirable to give students some
idea of their position in the course. To this end, I will
sometimes assign "rough cutoffs" for current total scores.
Students might find them helpful for roughly interpreting their
performance, and they also might find them useful in communicating with
others, perhaps parents, about their position in the course.
Usually I will not make such rough cutoffs after the last midterm exam,
since it is so close to the end of the semester.
Given the "roughness", these numbers will not account for
incidentals. So, if the rough cutoffs are given as 173 for an A,
141 for a B, 107 for a C, one might interpret a total score of 170 as a
B+; and likewise, one should probably view a 145 as a B-, and a 111 as
a C-.
I will usually not give a rough cutoff for the grade of D. Any
score below the rough cutoff for a C should be interpreted as
unacceptable, and precariously close to failing.
Critically however, students should understand that THESE ROUGH CUTOFFS
WILL HAVE ABSOLUTELY NO SIGNIFICANCE IN THE DETERMINATION OF LETTER
GRADES AT THE END OF THE COURSE.
Students should also be aware of the statistical fact that positions in
the rankings do not behave as might be expected when distributions are
added. Certainly, rankings do not "average". Even more, it
is not hard to create a scenario showing that a student can score in
the top half of the class (above the median) on all of the exams, and
yet still be in the bottom half of the class for total scores.
This phenomenon is not even particularly rare.
A closely related point is that very often a student might be above the
rough cutoff for a B- after the second exam, score approximately the
median on the third exam and the final exam, and yet still end up with
a C+ for the course. (And likewise near other cutoffs.) Of
course this goes the other way equally often, but students are usually
far less inquisitive in those cases.
One point of view that can be taken on this is that a student is mostly
in competition with only a small fraction of the students in the class,
and much less with the entire class. Specifically, a student is
mostly in competition with the other students that are nearby in the
distribution of current totals. If on an exam you score above
most of the students that are near you in the distribution, then you
would pass them in the totals and would expect to move up in the
rankings; and likewise if most of those students score above you, then
they will pass you in the totals and you would expect to move down in
the rankings. On the other hand, scoring higher on an exam than
some student that is way above you in the totals would probably not
move you up or down in the rankings.
As a result, it is impossible to draw conclusions about movement in the
rankings based on how your score compares to the mean or the
median.
While this difficulty in predictions might seem undesirable, the more
important point is the simple reality that grades in this course are
based on the total number of points earned. The difficulty in
predictions should be interpreted as part of the unreliability of the
rough cutoffs, and not as a flaw in the grading system.
Grading Comment Codes
Graders in this class might choose to use the shorthands listed on the Grading Comment Codes webpage.
If you see a code on your graded exam paper that is not self evident,
check this webpage and see if it is one of those listed shorthands.
Homework
Homework exercises are assigned for every lecture, and students should
ideally complete each assignment on the day of the lecture. The
assigned exercises for each lesson are listed on the syllabus.
(Note, we might find ourselves behind or ahead of the posted schedule;
if so, you should do the exercises as we actually finish the sections.)
Make sure you staple your homeworks! We cannot give credit to
students for work that was lost as a result of not being stapled.
Also, make sure to put at the top of the front page your name, the
section number(s) for those exercises, and the course information (Math
XYZ, Clark Bray)
In order to give flexibility to students, the assignments for about one
week of lectures will be picked up about once per week, usually on Fridays, and
will be graded and returned as soon as
possible. You will turn in the homeworks to your recitation TA; talk to your TA for those details.
The exercises due on a given due date will be those from sections
on
the syllabus that we finished talking about in lecture at least two
days prior to the due date. For example, for a course in which
the homeworks are due in Thursday recitations, then the exercises to be
collected will be those from sections we finished talking about in
lecture on or before that Monday. For a course in which the
homeworks are due on Fridays, the exercises to be collected
will be those from sections we finished talking about in lecture on or
before that Wednesday.
No late homework will be accepted without filling out the Short-Term Illness Notification form, or obtaining a Dean's Excuse.
In calculating homework grades, the lowest of your homework scores will
be dropped. The purpose of this policy is to handle exceptional
circumstances. Please do not request to have late homework
accepted without filling out the Short-Term Illness Notification
form. Also, it is inadvisable to skip a homework unless
absolutely necessary, since only one homework will be dropped.
On Sakai you will find a collection of solutions to some exercises from
our textbook. Please be sure to note the following important
comments about those solutions:
These solutions were written by a recent Math 107 instructor. He was kind enough to allow us to use them in this course.
Note, you should use these solutions
ONLY as a guide on problems where you are stuck, or to confirm your own
solution. Of course every solution that you turn in should be
your own work.
You should also make a point not to
rely too heavily on these solutions -- remember, they will not be
available on the exams, and you don't want to mislead yourself into
overestimating your level of preparation for the exams.
The author of these solutions makes
no claim about their accuracy in any way (nor do the instructors or
TA's for this course). Also, every instructor makes different
choices about how topics are covered, notation, what methods are
allowed and/or encouraged; these solutions do not account for these
sorts of differences between this Math 107 and the one for which they
were written. Also, you will note that not all problems are
represented.
So, use them at your own risk!
Working together in groups on homeworks is strongly
encouraged! You will find that the people you are working
with either (1) understand something you don't, in which case they can
explain it to you; (2) understand something that you do understand, but
from a different point of view -- these additional perspectives can
prove to be very useful; or (3), don't understand something that you do
understand -- in which case you have the opportunity to explain it to
them... I think you will find that in the process of explaining
something, very often you will achieve a better understanding yourself.
Of course, it goes without saying that even though you may work in
groups, the homeworks you turn in must be your own work.
You may share ideas, perspectives, approaches to problems, but copying
is not allowed. Furthermore, keep in mind that the homeworks are
primarily a learning tool, and count for a fairly low percentage of
your grade. Do not deprive yourself of this invaluable learning
opportunity!
Note, because of the sheer numbers involved, usually the grader will be
asked to grade only a specific subset of the homework assignment.
The homework score will be entirely based on the evaluation of your
answers of just those select problems. The grader will not look
at the other problems -- so, you cannot assume from the lack of any
marks that the solution you submitted is correct. Also, note that
students are required to turn in a complete homework assignment.
If you turn in an incomplete assignment, then you subject yourself to
the risk that some of the problems you did not submit might have been
the ones that were graded, resulting in a score that might be
disproportionately low.
Reading Quizzes
Students are required to read the corresponding sections of the book
before they come to class. This gives students a rough idea of
what will be covered in class, allowing for a more thorough treatment
during class time.
Sometimes, reading quizzes will be set up on Sakai to test that students have
done this reading on time. These quizzes will be short --
typically only one or two questions, typically worth one point apiece
-- and should be easy questions if the student has read the sections in
question. Students will be informed of the creation of these
quizzes by email. Make sure that you take the quiz AFTER doing
the reading and BEFORE class -- because these are timed tests, and
furthermore are available only before class time.
Attendance Quizzes
Attendance in lectures is required, and is part of your grade for this
course. Your attendance record will be combined with your other
scores for the course, in a way that will be determined by the
instructor.
It is not feasible to check attendance in class; instead, attendance
will be checked by "attendance quizzes" which will be administered on Sakai.
Most days in class I will write an "attendance code" on the board at
some point during the class. The quiz on Sakai to be posted
that day will have only one question, the correct answer to which will
be that attendance code. Students simply have to write down
that number during class, and then later that day log into Sakai
and enter that number as the answer for the quiz. The grade will be entered
automatically into the Sakai gradesheet.
Ideally, students should take each attendance quiz on the date of that lecture.
Else, students should be sure to take the attendance quizzes for a
given week during that week; for example, you might choose to take all
of the quizzes for a given week on that Friday after class. The
attendance quizzes for a given week will continue to be available
through the weekend as a buffer, in case a student might forget on
Friday; but they will be removed immediately after that weekend.
It is the responsibility of the student to make sure to take the
attendance quiz and obtain credit while it is still available.
Students are encouraged to form a regular plan on when to take the
attendance quizzes that will minimize the chances of forgetting before
they are made unavailable. Please do not request credit for a
quiz that you failed to take while
it was available.
At the end of the semester, your total score on the attendance quizzes
will be factored in to your course total by a system to be determined
by the instructor.
Note, this system is deliberately flexible and allows a student to skip
a class occasionally with only minor grade impact. But students
who skip regularly will find that the missed points on attendance
quizzes will make a substantial impact on their grades. Of
course, more importantly, students who skip regularly will find their
grade even more substantially impacted by their decreased performance
on exams.
It is not allowed to communicate with other students about the
attendance code, or in any way to attempt to undermine this system of
determining who was in actual attendance in class. Such
communication (either giving or receiving) or other attempts to
undermine the system will be viewed as a clear violation of the Duke
Community Standard.
Evidence of violations of this rule will be
presented to the Office of Student Conduct. Students should be
aware that such evidence can be obtained by a variety of methods, which
will be employed periodically, without announcement, and which are
surprisingly effective at identifying students who have cheated on
these quizzes. These methods have led to identifying multiple
such students; those cases have been directed to the Office of Student
Conduct and classified as cases of academic dishonesty. Students
should be aware that the potential sanctions for cases of academic
dishonesty are extremely serious, even in cases involving only a minor
impact on the student's grade for the course.
If you have information about other students who are not following the
rules regarding the attendance quizzes, please let me know, as per the
"obligation to act" component of the Duke Community Standard.
If you are unable to attend class due to an illness, you must submit a Short-Term Illness Notification
form
in order to receive credit for the corresponding attendance quiz or
quizzes. Submit an STI form for each lecture that you miss due to
illness -- or, for an illness that covers several days, you can submit
a single STI form and indicate clearly in the comments section exactly
which lecture dates you missed for that illness. On those
quizzes for which I will manually enter your score due to your illness,
I will enter a grade of "1.01" instead of "1.00". The decimal
part will be used only to allow me to keep track of how many times each
student has missed class due to illness -- it will be eliminated before
grades for the course are computed. Absences due to university
representation and religious observance will also be excused (athletes
missing class due to athletic events should submit a NOVAP
form). Other absences will be excused only in extreme
circumstances, and at the discretion of the instructor. If you
anticipate a possible absence and are not sure it will be excused, you
should communicate with the instructor in advance of the class in
question. Note, absences due to holiday travel are voluntary and
will not be excused; students must make their own decisions about
choosing to travel before the official beginning of the university
holiday in question.
Regrades
Here is the procedure we will use this semester for homework regrades:
(1) Write a clear and complete description of why
you feel your paper deserves more points than you originally received.
(2) Attach that description to your homework paper.
(3) Put that paper into the pile in the following week, when the next week's homework is being collected.
(4) The grader will receive your note and original paper, will give
it fair consideration, will consult with me (or the TA) if necessary, and then will
make a change to the score if that is deemed appropriate. He or she will then
also make the change on the homework gradesheet.
(5) The grader will put the paper back in the pile
and it will be returned to you along with those other homeworks.
For exam regrades, the policy is similar except that you will give the
exam paper either to me or the TA instead of putting it into the
homework
pile. Also, exam regrade requests will be accepted NO EARLIER
than 24 hours after papers are returned in class (or recitation
section) to ensure that students have compared their papers to the
posted solutions before
requesting regrades; and NO LATER than one week after papers are
returned in class (or recitation section). If you are not in
attendance when exam papers are
returned, it is your responsibility to come collect it; note, the TA
(or I) will probably not bring it to the next class or recitation
simply on the chance that you might be there, so you will need to make
an arrangement to come to pick it up from the appropriate office.
You will still be required to wait 24 hours before making a regrade
request, but the deadline remains as one week after the papers were
returned to the rest of the class. No requests for regrades of midterms can be accepted after the final exam.
For the final exam, regrades are made only in exceptional
circumstances. Note that it is Trinity policy that grade changes
for the course can be made only in the case of "an error in calculation
or an error in transcription"; I interpret this as excluding subjective
choices on grading of particular problems. Students may view
their final exams after the grading is completed and grades are in, but
should be aware of this Trinity policy on grade changes.
Here are a few thoughts to keep in mind about regrades:
(a) It is entirely possible and reasonable that the grader might have
misread your paper, and with your explanation realize that you do
indeed deserve more points. In such a case, he or she will be very happy to
award more points.
(b) It is also very common for a student to feel simply that too many
points were taken off for a given error. In these cases, the student
should be prepared for the likely conclusion that no additional points
will be awarded. The point here is that this is a subjective
situation, and a choice has to be made. The grader makes the decision
based on his feeling about the importance of a given aspect of the
problem, and the grader's opinion on this question is the standard.
Common examples of these types of disagreements involve the amount of
explanation that should be given, and the relative importance of
different parts of the problem. These are highly subjective questions,
and reasonable people will come to different conclusions.
Remember that this is a curved class. So, when it comes to questions
about too many or too few points being taken off, it is far more
important that the grader's scheme be applied consistently across the
board for all students than that it be something other people might or
might not agree with.
(c) When you submit your paper for a regrade, the grader might possibly
come to the conclusion that too many points were awarded in the first
place. In such a circumstance, your score could go down. Of course
the grader will always make such decisions dispassionately and fairly,
but certainly you should only submit for a regrade in a situation where
you feel you have a comfortably strong claim.
(d) The grader is a very reasonable and intelligent person, and
absolutely deserving of being addressed politely and treated with
respect. Make sure to phrase your requests calmly and reasonably. And
of course, always be prepared for the possibility that the grader might
have a different point of view than you on a given question, and that
his or her fair and reasonable consideration of your request might yield no
additional credit.
Studying
This course covers a huge amount of material, and so each exam requires
an enormous amount of preparation. In fact, it is not reasonable to do
all of that preparation in the few days before an exam, in the way that
students usually think of "studying for an exam". Students who
procrastinate their studying for the exam until the few days before
will find themselves completely overwhelmed, and are far less likely to
do well on the exam.
Rather, a much better way to prepare for the exams in this class is to
prepare for the exam continually throughout the semester. That is,
after each lecture, the student should study that material sufficiently
thoroughly that he or she feels prepared to take an exam on the topic.
Note, this requires substantially more work than merely working the
homework problems. (See the previous discussion of the expectations in
this course.)
In addition to spreading out the effort, there are more advantages to
this strategy. First, the concepts in question will have enough time
to "sink in" -- this is a phenomenon of learning, that it just takes
time for a student to become comfortable and fluid with an idea. If
you wait until the day before the exam, that "sink in" time just will
not be there.
Second, by being thoroughly comfortable with the content before the
next lecture, that next lecture will make more sense to the student
because the foundations have already been understood. Remember, this
is a largely "vertical" course in that most of the ideas covered in
this course depend on an understanding of those presented previously.
If a student does this consistently throughout the semester, then in
the few days before each exam the student can concentrate on memorizing
needed formulas, refreshing ideas that have already been thoroughly
learned, and the total effort is something that is reasonable to do in
those few days.
"Log Confidence" Exam Problems
In some of my classes, I will employ a type of exam problem that I call
a "log confidence" problem. If you are not certain whether these
types of problems will be used in the class you are taking, please ask
me.
Log confidence problems are similar to multiple choice problems, except
that instead of choosing only one of the possible responses, you can
indicate next to each one your confidence that this is the correct
response. These problems allow students to remove the randomness
normally associated with multiple choice problems. You can read
more about these types of problems on my Log Confidence Problems webpage.
Note, there is much to say about this type of exam problem. If
the class you are taking from me will employ this type of exam problem,
you should make sure to read all of the contents of the Log Confidence Problems
webpage to make sure that you are fully prepared and aware of how the
problem works and how to respond to your own advantage, so that you
will not have to spend valuable time during the exam doing this.
If after reading this webpage you still have questions about how best
to respond to this type of question, make sure to ask me well before
the exam during office hours. (Email is probably not a good
choice for this type of conversation.)
Improving Your Performance
Sometimes, students receiving low scores on exams feel that they
understand the material better than the score would suggest.
There are several possibilities that might explain this.
The most common explanation is that the student simply does not
understand the material well enough -- and very likely, not as well as
he or she might think. These students need to find ways to "raise
the bar" on their comprehension, as per the earlier comment on this
page. There are several ways that you might do this.
- Most obviously, some students need to increase the amount of time
that they spend working on this class. Sometimes, this can be
achieved with better time management techniques. Sometimes this
time must come at the expense of other classes. And of course
sometimes the time can be found by reducing time spent on social and/or
extracurricular activites.
- Students should also make sure to spend study time
efficiently. Make sure that you are not just memorizing
algorithms, but that you are also understanding the underlying ideas,
developing comfortable familiarity with their use and with their
connection to related ideas. Remember, this is a course about
comprehension, not memorization.
- Some students might simply not have a good idea of how to gauge
whether they understand the material well enough or not. One good
way to gauge your understanding was discussed earlier on this page --
that is, for some given topic, you can consider the prospect of giving
an oral presentation to a group of people on that topic. If you
feel that you can give a comfortable and thorough presentation of the
topic, including the background, relevant derivations/proofs,
connections to other ideas, and example applications, and that you
would be comfortable answering potential questions from the audience,
then that is a good sign that you do have a good understanding.
If the prospect of such a presentation makes you nervous, this might be
a sign that you do not have the necessary level of understanding
yet. In fact, the part of the presentation that you would be the
most nervous about might give you specific clues to suggest what you
need to study more thoroughly.
In fact, as discussed previously, you might consider actually giving
such presentations. If you work in a group, the rest of your
group might be willing to listen to your presentation, ask questions,
and give constructive criticism afterwards. This could be a good
learning experience for everyone involved.
- Make sure to use all of the resources for this course. If
recordings of the lectures have been made, you should re-watch some of
those lectures, particularly those on material that you do not feel as
comfortable with. While watching those recordings, you can of
course make extensive use of the rewind button and the pause button to
give yourself the exposure and time to be able to absorb the ideas
completely. And note, if you are stuck on one topic, it is very
likely that this is a consequence of not having a sufficient
understanding of some earlier material; before continuing then, you
should make sure to go back and solidify your understanding of that
earlier material.
- If you feel that you need more practice materials than are
presented in the book, remember that in many of my classes there are
some old exams from previous semesters available for your use.
Some of those old exams might also have solutions available -- you
might want to try working the problems first on your own, and then
comparing your solutions with the posted solutions. Make sure to
compare both the final answer, and the method, and the clarity of
presentation.
You can also generate your own practice materials, especially if you
study sometimes in a group. Each member of your group could
generate some hypothetical exam problems. You can then exchange
the problems, work on them separately, and then come together as a
group to discuss them. Good questions to discuss would be:
- Was this problem too hard or too easy?
- Does the problem focus on important ideas from the course, or is it tangential and/or irrelevant?
- What important idea does this problem allow the tester to gauge in the student?
- What other ways might this problem be rephrased, while still being basically the same problem?
- Are there other types of problems that might be created that test this same underlying idea?
I think you will find that in trying to generate hypothetical exam
problems, you will be forced to think about the underlying concepts in
a way that will help you organize the ideas, and uncover areas you do
not understand thoroughly. Of course working on your group
members' problems will also give you good practice. Finally, the
discussions afterwards should help generate good dialogue about the
ideas in the course, which should give opportunities for some students
to hear explanations of ideas they don't understand, and opportunities
for other students to practice giving explanations of ideas they feel
they do understand.
Another possible explanation is that the student might not be using
good test taking skills. These are unavoidably important, and
every student should make sure to have a reasonable competence with
them. For example, don't spend all of your time on one question
on the exam. If a problem is taking a long time to work out or if
you don't think you know how to do it, consider that you might be able
to get more points per unit time working on other problems first.
Make sure to flip through the entire exam to have a general idea of how
many points are available for what problems, and take the best of those
opportunities (the ones with the most points, that you can solve in the
least amount of time) first.
Yet another possibility is that the student might be allowing nerves to
affect his or her ability to think efficiently and creatively during
the exam. If this is the case, you will need to find a way to
take control over your thoughts so that you can concentrate and work
efficiently and creatively during the exam time. Of course there
is no substitute for full and appropriate preparation; if you are well
prepared then you are less likely to have anything to be nervous about
in the first place. Also, it is important to block out all
thoughts that are not directly relevant to the problems on the
exam. Don't allow yourself to think about what is going to happen
after the exam is over, what your grade might be, how that will affect
your final letter grade for the course, what you are going to major in,
how much you are going to need to study for some other class -- for the
duration of the exam period, all of these topics are nothing more than
distractions from what you should be doing, which is to be thinking
actively, efficiently, and creatively about the problems on the
exam.
You might also do some of your own independent research on how to overcome nerve related issues on exams.
Whatever the explanation might happen to be, students should be sure to
understand though that letter grades in this course must be determined
strictly from the exam scores. Exceptions to this rule would be
unfair to the other students in the course. So, one way or the
other, if your scores are not in the range that will lead to the letter
grade you are hoping for, the only solution is to find a way to bring
up your scores. Remember, it is your responsibility to identify
and solve the problem or problems that are preventing you from
achieving your goals.
1. For a course in which the exams are graded objectively, based merely on
the correctness of the final answer, it is possible to make a grading
system that can be advertised in advance, serving as evidence of the
objectivity and complete impartiality of the system.
However, in a course such as this one, this is simply not the case.
Grading on any individual problem is intrinsically subjective, based on
the view of the grader as to how well the student communicated in the
written solution his or her clear understanding of the method, theory
and technique relevant to solving that problem.
Of course, fairness is still critical. In order to ensure as much
fairness as possible, the grading on any given problem will always be
done by the same grader for each student in the class. If the grader
is generous, then this generosity will affect all students equally in
expectation value, and then because of the curve it effectively does
not have any systematic influence on grades at all. Similarly, if a
grader is harsh, but applies the same harsh grading system to all
students on that problem, then again after the curve the effect is that
there should be no systematic influence on the grades.
Because of this subjectivity it is likely that the student might have
his or her own opinion as to whether the grading on a given problem is
too harsh or too lenient. Certainly students have their rights to
their own opinions on this question. But when it comes to regrades, in
preserving the fairness discussed above, it is essential that regrades
be based on that grader's consistent view of the grading. Thus,
requests for regrades based on an assertion simply that it is your
opinion that too many points were taken off for the acknowledged error
will generally not be granted. (Similarly unlikely to yield extra
points is an appeal based on your claim of what your high school math
teacher used to do.)
Of course students are always welcome to submit their papers for
regrades, but in those instances that boil down to a simple difference
of opinion, further argument will not yield any benefit. In such a
circumstance, the student will be far better off trying to understand
the grader's perspective, so that necessary adjustments can be made
that will avoid such problems in future exams.
2. Very often, a grader will establish a system for grading in order to
aid in the consistency of evaluation over large numbers of students.
For example, the grader might decide that one particular part of the
problem is worth some number of points, or certain steps (or errors)
are worth some number of points. Similarly, a system is in place
regarding the accumulation of points in this course and the process by
which final letter grades will be determined.
These sorts of systems are useful tools for graders.
It should be emphasized however that these systems are decided on by
the grader voluntarily, and for the purpose of assisting the grader.
It is not to be assumed from the existence of such a system that the
grader abdicates his or her right to form any opinion about the quality
of a student's work.
For example, note that on a given problem (on an exam, for instance),
there might be multiple ways to work the problem; and even worse, there
are countless ways that a student can make mistakes. A given system
might allow the grader conveniently to determine grades for most
papers, but for another the system might not have been set up to
account for the pecularities in that particular paper. In such a case,
the grader is entirely within his or her rights, and in fact obligated,
to award points based on his or her true opinion of the work, and not
based on the system.
The grades on homeworks, exams, and the letter grade for the course
will be determined entirely by the corresponding grader's considered
opinion as to the quality of the work done by the student. Systems are
useful tools to help the grader achieve that goal, but ultimately it is
only the opinion of the appropriate grader that determines the grade
awarded.
4. During an exam, if you have a question you may come up and ask me.
However, I will only answer questions that concern a clarification of
what the question is asking -- I will not give any information that
will help you formulate a solution to the problem.
For example, suppose the question says, "Bob is pushing a 20-pound box
up a ten foot ramp angled at 30 degrees. How much work does it take to
get the box to the top?" Questions that I can answer include:
- Should we ignore friction?
- Is ten feet the length of the surface of the ramp, or is it the height of the ramp?
- Is it 30 degrees from horizontal or from vertical?
However, I cannot answer questions such as:
- What is the sine of 30 degrees?
- What is the formula for work?
5. If you ask me a question during an exam -- MAKE SURE THAT YOU WHISPER
YOUR QUESTIONS! When you speak in a normal speaking voice in a
virtually silent room, everyone in the room can hear you. So, for one
thing, speaking above a whisper is a distraction to all of the other
students.
More importantly though, if your phrasing of your question itself
contains any content, and if another student overhears you, then you
may have communicated assistance to that student! For example, if you
ask, "Is this where we use the formula about force times distance?" in
a voice that can be overheard by another student, then you have
communicated to that student some assistance in the solution to that
problem.
This is entirely avoidable of course, and I expect that all students
will take simple and obvious precautions in order to avoid this sort of
thing. Failure to do so might be viewed as a violation of the Duke
Community Standard.
6. I try to be available to students as much as I possibly can. But
students should be aware of the fact that I tend to be extremely busy
on the day of exams, and also on the day before -- I have the exams to
write (in all of my classes, not just this one!), to be copied,
checked, solutions to write, scan, and post, and lots of other little
minutia that must be dealt with.
Tragically, many students leave it until the day of the exam, or the
day before, to come to me with their questions. Again, I make every
effort to be available, but sometimes the reality is that I just don't
have the time to answer questions so close to the exam when I too am so
very busy. All too often such students find themselves with very
little time left before the exam, and significant concepts not yet
understood.
Please do not procrastinate like this and create for yourself a no-win situation.
Of course I have already promoted the idea that students should be
preparing for the exams continually throughout the semester; students
who take my advice on this will have the further advantage of being
able to come and ask me substantial questions well before the exam,
when I am far more likely to have time to answer those questions.
7. Try to make sure that you get good sleep on at least the night before
the exam. Inconvenient though it may be, the reality is that sleep is
an important factor in a student's ability to think analytically and
quickly, both of which are critical to doing well on a math exam.
Obviously study is critical too, and students have to make their own
decisions about the trade-offs; but do not underestimate the importance
of sleep. In fact it would be best to get good sleep every night, and
having a regular and full sleep schedule makes it easier to get the
sleep when you need it.
Ideally of course students should not have to make trade-off choices
between sleep and study. With good time management, you should be able
to plan your study time well in advance, and arrange to be thoroughly
prepared still in time to get a full nights sleep.
8. You may NOT bring in scratch paper to use during the exam. All of your
responses must be written on the exam paper itself, ideally in the
space provided. You are welcome to use the backs of those pages also
if needed, but if you do this please make sure to indicate very clearly
in the intended space for the problem exactly where the remainder of
your solution is located. All together this should be more than enough
space to solve each of the problems.
DO NOT tear the pages out of the staple or remove the staple. All of
these pages must remain attached to ensure that pages are not lost.
9. This is a curved class, in that the determination of your letter grade
at the end of the course is based on your performance relative to the
rest of the class -- not based on arbitrary cutoffs determined
beforehand. Specifically then, your grade in this course depends in
some part on the scores of the other students in the class.
Because of this, it is particularly important in this class that,
during each exam, all students must have the same amount of time to
work on the problems. If one student should somehow have more time to
work, the extra points that student gets in that extra time will
negatively affect the relative performance of the other students; and
clearly this is not acceptable.
Making sure that all students get the same amount of time on the exam
is accomplished by two steps -- starting everyone at the same time, and
ending everyone at the same time. At the beginning of the exam I will
pass out the exams and tell students not to turn over the cover page
until everyone else has a copy of the exam and I say "begin". At the
end of the exam, when I say "stop", students should immediately put
down their pens/pencils, and bring their papers up to me.
Note the following, from the Duke Community Standard In Practice: A Guide for Undergraduates (2010-2011 version), specifically in the section on Academic Dishonesty, among the list of forms of cheating:
• working on any examination, test, quiz or assignment outside of the time constraints imposed;
Note also the following from the same document, specifically in the section on Failure to Comply:
Some students seem to feel that they can get away with continuing to
write for a minute or two after the official end of the exam -- perhaps
because they feel they will be unnoticed in the hustle and bustle of
other students getting up and turning in their papers, or perhaps
because this sort of thing was condoned or even accepted in their high
school math courses.
Students should be very clear that it is critically important to the
fairness of the course that they do indeed stop when instructed to do
so. I will allow students a few seconds to finish a thought, but after
that I strictly require that no more writing on the exam paper should
take place. If any writing on the exam paper should take place
significantly after I have very clearly called the end of the exam, I
will consider this to be a clear and deliberate violation of both of the above cited aspects of the Duke
Community Standard, and I will notify the Office of Student Conduct.
10. Performance at the end of the
semester is reported in the form of a letter grade with
incidentals. Of course these letter grades are determined by the
instructor based on numerical scores on the graded items from the
course. There are several facts about this conversion that
students should be aware of.
- The spectrum of total scores for the course is hundreds of points
wide, filled with a very large number of students, and yet there are
typically only 11 or 12 different letter grades (counting incidentals)
awarded -- and fewer that are awarded commonly. As a result, it
is unavoidable that sometimes students with somewhat different total
scores will receive the same letter grade for the course. It is
also unavoidable that sometimes students with very similar total scores
will receive different letter grades.
Students should be prepared for these possibilities, and aware that
such occurences are not reasonable grounds for requesting
reconsideration of letter grades.
- It is the responsibility of the student to make sure that scores
on graded items for the course have been recorded correctly.
Please make sure that you have confirmed these records as they are made
throughout the term. Corrections such as this must be made before
the final exam -- after grades for the course have been submitted, it
is too late to make such corrections.
- As discussed previously in the above section on rough cutoffs,
students should be aware that those rough cutoffs have absolutely no
role in the determination of letter grades at the end of the
course. Please make sure to read carefully the discussion of this
in the section on rough cutoffs.
- Since the third midterm is usually extremely close to the end of
the semester, I will usually not report any rough cutoffs after that
exam. At that stage of the course, a student's only concern
should be studying as much as possible and doing as well as possible on
the final exam.
- Duke University policy
(http://trinity.duke.edu/academic-requirements?p=grade-changes) clearly
indicates that, with only a very few exceptions, letter grades are
final after they have been reported. Please do not request
reconsideration regarding letter grades based only on previous
expectations, appeals based on effort exerted, appeals based on the
personal consequences of your letter grade, or subjective
interpretations of how letter grades for the course should have been
determined.
- Final exams are not returned to students in this course. It
is Department policy that all final exams remain secured. You may
come and look at your final exam in your instructor or TA's office, but
you may not remove it from that office, even temporarily. Because
of the Duke University policy linked above, regrades for the final exam
are considered only in the instance of an extreme error of grading;
students should be aware that this is very rare, and should not come to
look at the final exam motivated by the hope for a regrade.
11. Sometimes there might be material that is fair game for an exam, but
for which the homework problems are not due until after the exam due to
the way the schedule and due dates are set up. Make sure to
consider this possibility when you are studying for the exam, and if
this should be the case you are strongly encouraged to do the
corresponding homework exercises before the exam in question, so that
you can get the needed practice for the exam.