Postings to email@example.com. (un)subscribe to firstname.lastname@example.org. (un)subscribe mathedu <type in your email address here> -------official header above------posting from subscriber below------- [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. D.Epstein@warwick.ac.uk, 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 format.
(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 exams.
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.
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 coordinator.
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 exams.
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 place.
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, email@example.com
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*.