Last revised 26jan16

Policy Concerning Grades and Preparations for the Final

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The following question was posted on Piazza. Since not everyone has logged into Piazza yet I am posting a copy of my answer here.

Question:

Since the midterm and final are 50 pc of the whole grade, I was wondering would there be any past exams posted online which can help us prepare them? Thanks!

I hope not. If you find any such postings online, they are unauthorized. Please let me know if you find one.

There are two reasons why I do not publish my finals.
First, on lower level math courses like calculus, which depend on memorization and
drilling techniques of solution, it is easy and cheap to produce thousands of variants of a problem set. Indeed,
experiments have shown that robots can create such variations, and the answers can be graded by robots, relieving
instructors and armies of graders from the tedium of producing and grading tests.

Second, higher level math courses (those with 400 numbers at UIUC) require mathematical thinking for which
memorization is largely useless. To asses the skills students must acquire to do mathematics is relatively easy
with oral interrogation (office conversations, class discussions, group problem sessions, etc). But public universities do not have the resources to teach in this way, and written tests are used for summative assessment. Such tests are very difficult to create because they are the wrong tool for the job. Publishing past finals is counterproductive, because it is possible to study for strictly for the tests without demonstrating the knowledge taught in the lectures. It is not necessary to study the subject over an entire semester to pass such examinations. In fact, many higher
level coursehave proficiency exams you prepare for and pass without ever going to class. This type assessment is
handled by the administration, not the instructors.

Math 347 is a transition course between the lower level math courses where rote memorization is preferred, and
upper level math courses, where independent and critical thinking is preferred. Thus I teach you how to make this
transition. My job at the end of the semester is to determine to what degress you have achieved that. That is
why you may use a Journal even on the final, because I am not interested in what you have memorized. I am interested in whether you can explain and elaborate a certain body of math, and combine and connect many different mathematical ideas. My finals place heavy emphasis on an hour long essay you may prepare, but which
is written during the examination. Only a small portion of the course can actually be "covered" on the final. So the
final is only a sample of what is covered over the entire semester. Therefore, an essential preparation for it is to learn
how to answer the questions I ask all along, in the midterm, the quizzes, the homework, and the filecards.

Remember, you have a B coming into the course based simply on the fact that you are intelligent enough to be
eligible for the course, and have mastered the prerequisites. This expected grade can drop if you cannot keep
up with the course, perhaps because you do not have skills to progress beyond drill and memorization, or
you are over committed with too much work. I hope, however, that all of you will strive to achieve an A. You
cannot accumulate points to reach this mark. An A+, A, or A- in my courses mean that the student truly knows the mathematical ideas, methods and can prove this fact. And it is my job to assess this in whatever manner my 58 years of experience of teaching university mathematics permits.

Finally a word about the distribution you mention. The University requires that we publish such percentages. So I
set the value of the very last chance you have to prove to me your mastery of MA347 so high. It is what you can do
on the last day of the course that matters to me, not what you do at the beginning. Some students have prior knowledge and can do well on the first test. They become overly confident and do not synthesize the entire course
in their minds. They depend on their good memory and neglect learning the course in a timely manner, cramming
for the final. My finals are designed not to reward this ineffective kind of learning.

Other students struggle at first, but diligently do what they can to improve steadily over the semester.
This is much closer to the real world, where you are your own teacher and acquire knowledge over a period of
time. So, a poor grade on the first test is no predictor of the final grade. It indicates a spectrum of mishaps,
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