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Topic: [MATHEDU] Re: homework papers
Replies: 4   Last Post: Feb 3, 1997 2:40 PM

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Chih-Han sah

Posts: 75
Registered: 12/3/04
Re: [MATHEDU] Re: homework papers
Posted: Feb 3, 1997 8:18 AM
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[Although this posting is outside our charter (post-calculus
mathematics education), I am letting it go forward because there are
general principles here that apply in many contexts., mathedu list-owner]
In the case of multi-sectioned courses taught in the format
of Lectures/Recitations (each meeting twice a week with lectures to
150-180 students and recitation sections of 35-45 each), I had
encountered the following kind of problems:

(a) Low and sporadic student attendances in the lectures.
The problem is that there is a large spread in preparation. The
students who are ahead quickly decide that they have seen the material
and there is no reason to *waste* their time coming to lectures. The
students who are behind quickly decide that they are not getting anything
out of the lecture because they are lost so they too stop coming. This
phenomenon was apparently (based on annecdotal reports) independent of
the talent of the teacher as an expositor. The attendance eventually
settles down to between 20-40 students. Some faculty doing the *reformed*
courses mentioned that class attendances were in the 70% range against
the 20-30% range in the *pre-reformed* courses. However, when I asked:
What is the *absolute number* in terms of attendance, the answer turned
out to be about the same. Namely, in the *reformed* courses, the lectures
were limited to about 60-65 students and then divided into two recitations
of about 30-35 each. This could not be sustained for *all* the tracks.
As a result, the later *reformed* tracks remained in the same numerical

(b) Faculty coordinators, for several different kind of reasons,
decided to give no more than about 10% weight to recitations. The reasons
were something of the following type:

Students copy from each other on homeworks.
Teaching assistants are irresponsible in leading the recitations.
Students *ought* to know that recitations are good for them.

The problem here is that, with at most 10% weight, students end up
not attending recitations on a regular basis. Recitation instructors
get the signal that their work is not an important factor (when, in fact,
it is much more important in view of (a)--some 10 years ago, we made
national headline when we were given the resources to run calculus in
the format of small classes (about 35 students) with a single teacher
meeting the class 3 times a week--there was no new content, no new
pedagogy, no new technology, etc. Unfortunately, budgetary problems
made the experiment short-lived in spite of the dramatic turn-around.

One of the major problems involving Lecture/Recitation is that
the lecturer has to keep in close contact with the group of recitation
instructors and the course coordinator has to keep in touch with the
different lecturers in order to make sure that everyone is more or less
doing the same topic at about the same pace--in order to prepare the
students to tackle the *uniform* midterms and the comprehensive final


My experimental solution was to put in place a *maximum principle
grading scheme*. It was carried out for an *introduction to calculus*
course with a total of about 930 students distributed among 6 lecture
sections with a total of about 25 recitation sections. At the beginning
of the term, a uniform syllabus was passed out to all. Students and
recitation instructors were told of the grading scheme:

(i) recitation will count either 20% or 40% of the term grade.
(ii) each of the two midterms will be 15%.
(iii) final exam will be 50% or 30%
(iv) at the end of term, two *curves* will be used on the basis
of the two descriptions, students will then be given
the higher of the two letter grades for the term.

Recitation instructors are told:

(a) recitation grades may be based on a combination of
*weekly* homework and/or *weekly* quizzes.
(b) if collecting homeworks, the instructor may collect
one or two at random--announced at the last minute.
(c) quizzes may be based on a random selection of problems
on the homework assignment part of the syllabus,
or on problems similar to the homework, one or two
problems on each quiz.
(d) at least half of the recitation grades MUST come from
weekly quizzes.
(e) the recitation grades *for each section* must have a
section average that is within +- 10% of the
section average of the two midterms; this means
that recitation instructors are free to adjust
the recitation grades for individual students up
or down, but can not do this for everyone in the
section. Of course, the section averages may
vary from one recitation to another, from one
lecturer to another. Both averages are on the
basis of 100 points. If a student missed one
midterm with valid excuse, the other one will be
used to compute the section average. The recitation
instructor and the lecturer may decide on how to
deal with missed work with or without consultation
involving the course coordinator.
(f) recitation instructors may adopt whatever mode of teaching
in the recitation.

To keep all the sections more or less together, all lecturers
and all recitation instructors are required to get an e-mail account.
It will be used as a bulletinboard for the teaching staffs to post
to everyone problems that were encountered. In particular, the
course coordinator can use this as a way to keep everyone informed.

Unannounced wrinkles:

I obtained permission to include two more weighting schemes:

(v) recitation 0%, each midterm 25%, final 50%
this had been the most common scheme used by other
faculty coordinators.
(vi) recitation 0%, midterm 0%, final 100%
this was used informally by some faculty members
to deal with students with special problems at the
last minute.

Neither the students nor the recitation instructors were told of (v)
and (vi) until the last two weeks of classes (after the midterm
grades were in). They were told *only* when they came in to see me
on an individual basis.

To get around the problem of providing some choices on the
midterm, I constructed the midterm so that the maximum grade would
total between 105 to 110 points and the students were told that the
extra 5 to 10 points were considered as *bonus*. Of course, this
made no difference since the computer computation of the 4 different
schemes and the computer selection of the maximum grade washes out
this. What is does do is to *single out* the top performers at a
glance and it also eases tension because the students do NOT have
to decide which problem to tackle. Finally, it allowed me to include
one to two more difficult problems (but with *lower* weight rather
than *higher* weight when compared with the other problems--so that
skipping over the challenging problems does not cause alarm among the
average students).

Finally, all bucks stopped at the desk of the course


This was the finding at the end of the term:

A. All 4 grading schemes led to class average (for 930 students)
that fell between 60 to 63%. In the grading scheme
used by other colleagues, the average for the final exam
or for the grand total--depending on computations made
(in most cases, this was anecdotal--though I had seen
them when I was a participating lecturer in a number of
cases) had been between 45 to 55%.

B. A total of about 12 students came to see me to complain about
the term grade. In each case, I went over the recitation
record, the final exam, plus the computer generated output
and pointed out that the student had received all possible
benefits of the doubt. In each case, the student left
satisfied. In some cases, the letter grade was perhaps
on the *high* side, but it was not adjusted downward even
though I told the student that it was on the high side.

C. Recitation instructors and faculty lecturers were satisfied
with the arrangement since they could pass the buck to
me as needed. I do encourage and take into account their
inputs--especially on the matter of pace and level of
difficulties of the problems on the tests. They were
asked for suggestions, but did not get to see the tests
until the day before the test. They are encouraged to
provide review sessions, but NO official sample exams
were passed out. At best, they were told the sections
that would be covered on the tests--this was in the
initial syllabus already.

D. For this course, the computer selected term grades fell
evenly on all 4 schemes (the students were typically
new to the university--there were also older students
since the course is also used to meet the distribution
requirement for graduation).

In a later follow up course for 230 students, I tried
it again. The computer selected term grades fell evenly
on 2 of the 4: Option (i)--40 % for recitation and Hidden
Option (v) 0% for recitation, 25%, 25%, 50% on the three

Apparently, students new to the university had not settled down on
a study mode but eventually do settle down after a year or so.

E. Students evaluations of the course included comments of the
form: I liked the grading scheme because there is a
choice. [There were not too many comments in this
direction in part because most of the students were new
to the university and there was no basis for comparison.
The above comments may have come from students who had
been around for a year or more.]


I should emphasize: the experiment was run in the *pre-reformed*
calculus course. I tried to get other faculty coordinators to give the
scheme a try. There was NO takers. The excuses were of the
following type:

Too complicated.
Blatant grade inflation.

In terms of the first, what apparently had happened is that
faculty coordinators typically put the task on *auto-pilot* on the
grounds that lecturers and recitation instructors are *experienced*
teachers. This ignored the fact that most people tend to aim for the
*least effort* because of other duties. The system only sound complicated,
most of the burden falls on the course coordinator who should not be
*stuck* to this task on a *permanent basis* but should only serve on a
rotation basis. I did get one faculty colleague to try this out, but
with me as one of the lecturers. What I discovered was that the colleague
did not trust the computer program designed for me by the system guru
(it took about 20 minutes to put together) and spent the entire term
putting together a new computer program (it did the same thing, but
was fancier in that histograms etc were generated as well). During
the middle of the term, I had to post to the entire teaching staff
comments that should have been posted by the coordinator. This led
one of the recitation instructors to ask me in the common room:

Have you taken over as course coordinator?

At the end the term, the course coordinator told me that he should have been
more *hands-on* but had thought that there was no need because, after
all, the recitation instructors (all TAs) were *experienced* (typically,
they averaged about 2 years in teaching experience).

In terms of the second, I do not believe that it is any worse
than using a *curve*. In fact, the latter may be more of a grade inflator
when the final exam or the entire semester raw scores for the class
average came out to between 45 to 55%.

In any event, it was not tried by other faculty members.
I have not tried it beyond the three times mentioned
since I have not been coordinating multi-sectioned
calculus courses after the *reform* had been put in

To me, the *maximum principle grading* was a very inexpensive
*reform* in terms of *assessment*. It appeared to have changed
the students' study habits. The principal points were:

(I). It gave notice to the students that there were
different paths to pass the course. All of
paths involve their doing works. They had a
choice. Sluffing off is not an option.
Even in the case of unforeseen problems, there
are options.

(II). It gave notice to the recitation instructors that
their efforts are appreciated and are important.
There was no subtantial increase in time-demand
to master *new content*, *new pedagogy*, *new
technology*. They also have rapid access to
help via e-mail.

Han Sah,

P.S. I was warned that

once students have gotten used to the scheme, it may
be necessary to change again.

My reaction was: that is fine. This was a very inexpensive
way to go. There was NO reason why the *hidden wrinkles* had
to be included. That part is at the option of the course
coordinator. Given that they were *unannounced*, the students
would have to *guess*.

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