Math 124/5 Calculus Reform:
Summary Report for 2001-2002

Autumn 2001 SGID summary
Winter 2002 SGID summary
Spring 2002 SGID summary

Appendix D
Goerss Report (June 1998)

In the fall of 1997, Doug Lind, Chair of the Mathematics Department, for med an Ad Hoc Committee on Calculus to review the Math 124/5/6 sequence and to recommend ways to improve calculus instruction. The other versions of calcu lus taught by this department (Math 111/2 and Math 134/5/6) are not part of thi s review. The committee consisted of Paul Goerss (Chair), Ken Bube, Ramesh Gangolli, and Don Marshall.

After a transition period in the early 1990s, this department began teac hing the main calculus sequence for first-year student using locally produced materials, sometimes supplemented by paperback workbooks. As this system ha s been in place for sometime it was time for a review of the Math 124/5/6. Th e questions before the committee included:

1.)

Are we teaching the right kind of calculus? The current system emphas izes mathematical modeling and word problems. Is this best emphasis?

2.)

Are the topics and ideas we now cover best for our client departments ? Are they good for the math department?

3.)

Are the instructional materials the best possible?

4.)

What is the level of instructor satisfaction with these courses?

5.)

How can we improve instruction?

1.

Summary of Results of Interviews

(a)

Physical Sciences

(b)

Engineering

(c)

Life and Behavioral Sciences

(d)

The Drop Policy Committee

(e)

Debra Friedman and Fred Campbell

(f)

Mathematics

(g)

Student

2.

Conclusions on the State of Calculus

3.

Recommendations

(a)

Summary

(b)

Calculus for Physical Sciences and Engineering

(c)

New Courses

4.

Toward the Ideal Calculus

1. Summary of results of interviews

In deciding who to talk with about our calculus program, we began by making a list of who took Math 124 and what majors they eventually graduated with. Then we looked at the departments and programs with large representation. Some, such as English and Music, simply reflected the fact that these are popular majors. Discarding these, we talked with members of the following departments, offices, and programs.

a. Physical Sciences

In Chemistry we talked with Professors Mike Heinecky and Leon Slutsky. The former is chairman of the undergraduate program committee, the latter a physical chemist. Surprisingly, chemistry in general uses little calculus. Physical chemistry uses a great deal, often couched in notation we would find vague and confusing. Professor Slutsky concluded that the best service we can supply these students is training in mathematical sophistication. The chemistry department in general is deeply aware of the great range of students on this campus, and strongly supports the efforts of this department to teach sophisticated first-year courses. Professor Heinecky did mention the Mathematics Study Center, calling it a ``class operation'' and mentioning that Chemistry had adopted the model for its own study center.

From Physics we received a report from a committee consisting of Professors Oscar Vilches (Undergraduate Program Director), Vic Cook, Steve Ellis, and Stamatis Vokos. They need a lot of calculus, often earlier than we can possibly supply it, but in general they were not dissatisfied. They would definitely like vectors introduced earlier, and would certainly not like to see multi-dimensional material moved from the first to the second year. In general, they were supportive of the idea of introducing mathematical concepts in the context of applications, as they hope their students will be adept at this skill.

b. Engineering

Perhaps our most illuminating interview was with Professors Uy-Loi Ly and Adam Bruckner of Aeronautics and Astronautics. Professor Bruckner is the Undergraduate Program Advisor for that department. The meeting began with criticisms of calculus. Professor Ly felt the students were deficient in various routine skills, and Professor Bruckner was critical of what might be called standard, old-fashioned calculus courses. Upon examining the Koblitz notes, however, they ended by praising what we were trying to do with the emphasis on word problems, applications, and modeling. This experience emphasized to us the value of communication with other departments - by the end we had their sympathy and support. We did, however, continue to hear lurid tales about the inability of many students to do even basic differentiation and integration.

We also talked with Professors Per Reinhall and Duane Storti from Mechanical Engineering. Reinhall is the chair and Storti a member of the committee that oversees the second year introductory engineering courses. They also underscored the importance of problem solving skills.

An examination of the second-year engineering texts was very illuminating. From the very start, the students are asked to do calculus in the setting of concrete applications - in particular, they must be conversant with the language of vectors. If the books are any guide, these courses are quite difficult.

From Computer Science and Electrical Engineering, we had an extensive e-mail communication from Professor Paul Beame. Their concerns were more with various kinds of discrete math.

At about the same time, Jim Morrow talked with Professor Jim Reilly, chairman of Mechanical Engineering, who had some scathing criticisms of the calculus course we taught ten years ago (and which he thought we still teach), and of the differential equations course we now teach. He said, among other things, that differential equations should be taught by the people who use them. Indeed, from all the engineers we got the sense that our Math 307/8/9 sequence could use a thorough revamping. In light of a national trend for engineering schools to absorb these classes into themselves, it behooves us to pay attention to this warning.

Finally, we talked with Dave Prince of the Minority Students in Engineering Program. Deeply aware of the needs of his students in the second year engineering courses, he is very supportive of the emphasis of word problems and applications. In general he is very supportive of the emphasis and direction of our current notes. However, his students find our current course materials difficult, or even impossible, and Dave has written an extensive supplement of his own for their use.

c. Life and Behavioral Sciences

On different occasions we met with Professors Johnny Palka, Tom Daniel, and Gary Odell of Biology, and Professor Mark Cooper, chair of the Zoology undergraduate program committee. While no concrete proposals were made, the first three seemed to agree that a two-quarter calculus sequence emphasizing biological examples and including some multi-variable techniques would sit very well with their students. They also agreed that such a course would be mostly to make the students happier, and not necessarily make them better biology students. Mark Cooper seconded this last thought, and it was from him that we had a warning about not diluting fundamentals. All four were pleased we talked with them and would welcome further dialogue.

From Biology, we also talked with Joyce Fagel, head undergraduate advisor. While very polite, she was highly sceptical of our current calculus, as she perceives a high failure rate among otherwise good students. (We have a hearsay report that Dean Hunt, of the medical school, has expressed a similar sentiment: too many otherwise good students are derailed by calculus.) She has warm things to say about the QSci 291/2 sequence. We also talked with Jay Johnson, Professor of Wood and Paper Science, who teaches that sequence. It was from him, among others (see part d. below), that we heard the idea we are regarded, on campus, as being unresponsive by not addressing the needs of life science students.

We talked with Professors Beth Kerr (Vice Chair) and John Miyamoto (head of the quantitative group) of Psychology. Their requirements are difficult to summarize and even more difficult to fulfill. A large proportion of their students enter the university thinking they will be business majors; thus, for better or worse, they accept Math 111/2. What they really need is some mixture of statistics, probability, and linear algebra.

At a later date we also talked with Bus Hunt, professor and a former chair of the psychology department. He offered his expertise in developing placement and gateway tests.

d. The Drop Policy Committee

During this process, Paul Goerss and Brooke Miller were asked to meet with the University's Oversight Committee on Student Services and Administrative Changes, known as the Drop Policy Committee for short. We were asked a number of questions about our drop rates (which do not deviate much from the national norm), why we don't teach in small classes, what we were doing in response to administrative changes, and so on. We were invited to make a radical proposal to improve our classes in general and our calculus courses in particular. However, a significant portion of the meeting dwelt on the question of why we don't offer some calculus course more appropriate to life and behavioral sciences. Even members of the committee, such as Jerry Gilmore, the director of the Office of Education Assessment, who were sympathetic to strains on our program, wondered why we were tardy in doing this. Among the committee members were Jay Johnson, who waved away the idea that there might be some conflict of priorities with the QSci program, and an undergraduate, a biology major, who was openly hostile to our department. She was, not to put to fine a point on it, sarcastic, patronizing, and rude. If she reflects the general opinion of our department among biology students, we have trouble.

e. Debra Friedman and Fred Campbell

Of the University's top level administrators, these are the two most concerned with undergraduate teaching. Debra Friedman is the Associate Provost for Academic Planning and Fred Campbell is the Dean of Undergraduate Education and Vice Provost. We met with them separately, but both meetings began with the assertion that Campbell's office gets more complaints about first-year math courses than all other entry-level courses combined. Feeling that a systematic review of these complaints would be valuable to the work of this committee, we asked to see them, but Campbell said he doesn't actually keep them on file after he deals with them and that, in fact, many were not written. (There are only two in Doug Lind's files.) Nonetheless, Campbell and Friedman were happy to summarize the substance. The salient points, according to them, were these: 1.) the calculus courses we teach are too different from what students expect and the students often misjudge how prepared they are; 2.) students with good credentials often do badly; 3.) the math faculty is not respectful of the students - in particular, we are not interested in student success; 4.) math courses are as much a ``screen'' as an intellectual endeavor; 5.) the approach is objectionable - specifically, students complain about the huge leap in difficulty, the lack of a text book, the difference between exams and class, the lack of easier problems building to the hard ones, and the large lecture/quiz section format; and 6.) old study habits no longer work. Many of these complaints, whatever their source, could be addressed by better screening the students and better informing them of what to expect. Both Campbell and Friedman underscored the importance of this, and both offered resources to make it work. Fred Campbell specifically mentioned that we could change the placement tests and if we needed the approval of the HEC board, he could arrange it. Campbell strongly suggested we think about other kinds of calculus. Both Friedman and Campbell solicited a radical proposal from us, one that ``takes some risks and allows for experimentation.'' They suggested that the President and the Provost would look favorably upon such a proposal. Both also invited us to work with them. The influence of these two administrators is enormous, and an effective partnership with them or their successors could yield enormous benefits.

f. Mathematics

In the fall we solicited the comments of the faculty of the math department. We got a large number of responses, ranging from detailed criticisms of the syllabus, to polemics for or against the current system. Rather than try to build a consensus where none seemed evident, our major conclusion is that we needed introduce more flexibility in the system. Hence one of our major recommendation is for greater independence, within carefully prescribed boundaries. Other criticisms centered on the extremely tight grading schedule of the common final. Perhaps the one comment on detail we heard the most often is that there is need for many more and different problems, that currently our problems are all of a type and neglect some fundamentals and other aspects of calculus. It is also possible to learn the type of problems without learning calculus. Other remarks addressed topics that have been omitted, but should be included. There were a number of such, but several people pointed out that in Math 307 the students are assumed to have a working knowledge of limits and continuity.

One of the main questions we set out to answer, was the following: Why are so few professors volunteering to teach calculus? The responses were varied. Certainly large classes, low pay and ambiguous teaching evaluations are all factors. However, there were a variety of responses to the effect that the problem wasn't calculus itself, or even calculus in large lecture format, but the rigidity and style of the current system. Among other remarks, we had echoes of Debra Friedman's sentiment that we don't respect our students.

We also sought the opinion of the graduate students. Larry King gathered a group of students who, in turn, went around and interviewed every graduate student in the department. As can be imagined, the results were widely spread. In general, though, there is a substantial preference for increasing the amount of drill and the amount of theory in our courses, and at least half of the respondents were in favor of using fewer word problems. Moreover, the grad students were nearly unanimous in agreeing that potential math majors are not being well-served by the current program. Indeed, a majority of grad students who responded stated that, had they been undergraduates in the current U.W. program, they would not have chosen to go into mathematics.

One aspect of the current program that was regarded as a success by almost everyone in the department is that Math Study Center. This corresponds to remarks we heard from others on campus, most notably from the undergraduate advising office.

g. Students

We tried various ways to gauge student responses to our calculus courses, but, finally, we resorted to focus groups, run by Tom Taggert, Assistant Director of the Office of Education Assessment, and Ken Etzkorn of Undergraduate Education. There were two groups of students: one had recently completed a calculus class, and the other had done so some years earlier and were using it their majors. There was a cross-section of abilities, but we excluded students with final grades below 2.0. There were nine students in the former group and six in the latter. These groups are very small, and the results should be balanced by other means, perhaps by follow-up groups. These focus groups were held on May 12 and 13 and we received the report on May 22.

First, both groups of students felt that story problems were important and were not critical of that approach. They felt the emphasis on them should continue.

Second, in contrast to the ratings on the student evaluations, the general feeling was that the present text for Math 124/5 was adequate, but would be greatly helped if it could be cross referenced to a good, standard, more traditional text that included additional explanations and problems. (This was a spontaneous suggestion, not one we included in our questions as a possibility.) This would take care of several objections to the current text:

1. Not enough examples, sample solutions, and explanations.

2. Difficult to use as a reference. Students complained about having to read the entire chapter in order to find the point they were particularly interested in. An index would be helpful here.

3. Dense type-setting.

This would also speak to student's concerns that they have a reference that they could keep, and use easily in the future. An $80 price didn't seem to bother them, assuming the text would be used for the whole sequence.

Third, there were a number of comments about the Math 126 text. Specifically, some students felt that there were not enough problems, and that some of the materials could be easier to read.

Fourth, several students mentioned that it was nice having a smaller text.

Fifth, student misunderstand the point of the common final, and there is a myth that the final is written by a small number of the instructors, giving an advantage to the students of those professors. Whereas in fact problem submissions come from all instructors and the exam is compiles by someone not instructing the course in that quarter.

Finally, the student reaction to the TA sections was very mixed. Some said the TA was better than the lecturer. Others regarded the sections as basically ``busy work''. This perception seemed to be independent of what the TA actually did, whether it be going over homework or worksheets. Indeed, worksheets not fully integrated into some sort of lecture drew very mixed responses from the students. Even quizzes drew mixed responses. Unless they were graded and handed back very quickly, students felt they were not performing the feed-back function we'd like them to fulfill. (As a side note, an early, hard quiz designed to help the students gauge their chances of success in the class is regarded, instead, as an attempt to ``scare'' them out of over-full courses.) One of the major recommendations of these focus groups is that there should be more TA training. This may not be practical or even advisable, but this recommendation is a reflection of student perceptions and sentiment.

2. Conclusions on the state of calculus

First, the form of our current calculus is highly suitable for students going into engineering and the physical sciences. Beyond basic calculus techniques, the most important skill these students need is the ability to model real-world problems and the current emphasis on this skill in our calculus class serves them well. However, the percentage of such students in our Math 124/5/6 sequence is not as large as one might think. Roughly the same number go into the behavioral and life sciences, and these students might be better served by a different mathematics track, one that might not even be entirely calculus. We also note that one department that might not be so well served is mathematics, for the art and rigor of our subject is de-emphasized in the current version of calculus. At the level of instructional material, we did hear from a variety of sources that all students would benefit from working a greater variety of problems than we now supply. This would include, but not be limited by, more problems that are purely mathematical or even manipulative in nature. As one engineering professor put it, ``They can model okay, but they can't integrate sin(2x).

Second, the other members of the university community have only a hazy idea of what we are doing and why we are doing it. A number of the people we talked with had a very clear idea of what our calculus was, and it was false; indeed, these ideas more suitably described what calculus was like when they took it. Another common perception is that we should face the biology clientele more squarely. And, with the current scrutiny of ``high demand-high drop'' courses, we are marked across campus as teaching one of the problem courses. Most people recognize that we have a difficult job, but it is probably fair to say that these same people think we are doing a tough job in a mediocre manner. Whether or not we are providing a good service, we are not necessarily seen as doing so. There is a need for communication and outreach. As a side note, everyone we approached was pleased and happy to talk to us.

Third, there is a certain amount of dissatisfaction in this department with teaching calculus. This has many sources. For example, the large lecture sections and concomitant student incivility is draining to many people, as are the poor skills and unrealistic expectations of many of our students. The TA/Professor relationship can range from trying to rewarding without much predictability. However, one central complaint turns ultimately on the following point. For many of us, learning calculus was a central intellectual experience, one that informed the direction of our lives. We have taught it often and many of us have loved it. The current text and materials do not let us, in our own ways, express what we find beautiful about the subject. In sum, faculty and graduate student morale would improve considerably if there were more freedom and independence in the curriculum.

Finally, the largest impediment to teacher and to student satisfaction is the poor preparation and unrealistic expectations of our students. Our classrooms hold an incredible mixture: students newly out of high schools, transfers, returning students, and so on. The first group - those newly out of high school - is surprisingly small, as over 40% of the students on campus are transfers, and the trend is for these students to postpone their mathematics until arrival here. (Math is seen as hard and adversely affecting qualifications for admission.) Many have not had math for several years and even those right out of high school may not have taken math in their last year. The skills tested on the placement test are very different from what we expect our students to be able to do and someone with a three-year-old community college credit for Math 120 (and who is thus eligible for 124) can easily have forgotten many fundamentals. The level and amount of work we expect from our students is far higher than anything they've ever seen before. And yet the students think that an adequate score on the placement test or transfer credit should be a guarantee of success. The dissonance that results from thwarting this expectation is enormous. By some estimates, as many as a quarter of our students do not belong in Math 124.

3. Recommendations

Before detailing our recommendations, this committee would like to reaffirm the commitment of this department to high-quality calculus courses emphasizing word problems and mathematical modeling. Such a course is necessarily difficult for many students, but an easier course does neither the students nor client departments the service they need. There are many ways to try to keep the standard up, but none will be effective without widespread support or without a commitment by the regular faculty to teach the class. A course taught be a jumble of adjunct faculty or disaffected professors will necessarily be of less than the highest quality.

a. Summary of Recommendations

• Review the role of the placement test; change it if necessary
• Broadcast our expectations to state high schools
• Buy (or devise) and implement gateway and proficiency tests
• Revive the Mathematics Services Committee
• Rework the syllabus for the sequence Math 124-5-6-307-324
• Institute a new course for life and behavioral sciences
• Institute a new mathematical calculus
• Implement the following changes to the current calculus:
• Substantially revise or replace the text
• Introduce more flexibility for instructors

• Math 111-112: We reduced the size of Business Calculus classes from 300-500 to a maximum of 160 (Autumn 1998). This does not impact our Student Credit hours, but does increase the number of classes we teach. We did this without an increase in our faculty. In fact, our faculty was reduced in size that year. During the academic year 1998-99 we offered 7 classes of math 111, and 4 classes of math 112, each limited to 160 students, an increase of 7 classes.
• Placement tests: These tests are written by a statewide committee, but we do have one representative on it. Many of our suggestions about the content of the exam were accepted, though some suggestions about the mechanics were not. I do think that the exam will be a better method of placing students in the correct class. We will continue to work toward future improvements.
• Math Study Center: Thanks to help from the College, the Office of Undergraduate Education, and Classroom Support Services, we have been able to expand the Math Study Center to cover our Business Calculus classes in a remodeled classroom from noon to closing time. We now require all teaching assistants in all calculus and precalculus classes to hold at least one office hour in the study center. Most faculty for these courses do this as well. A number of TAs have found this sufficiently beneficial that they are holding all of their office hours at the Center. Incidentally, the Office of Educational Assessment is doing some in-depth studies of the experiences of undergraduates. I was told recently that one of their questions asks the students how they would advise a friend who is having difficulty in a required math class. The answer seems to be: they would tell their friend to go to the Math Study Center (not drop or switch professors as I might have guessed). A frequent volunteered comment is that they like having their TA's office hours at the Center.
• Calculus for Mathematical Sciences: Last year we introduced this new sequence intended for students interested in majoring in Mathematics and other mathematical sciences. Our standard calculus sequence is heavily oriented toward applications, which is the desire of our client departments. However, many of our faculty feel that there is too little mathematics for our majors. A survey of our graduate students revealed that they feel that many of the interesting, more rigorous mathematical topics have been removed, to the extent that they guess that they would not have majored in math if this had been their calculus class. Hopefully this new sequence will overcome these objections. It may also serve as an ``honors'' version of calculus for students seeking greater challenge and depth. With this new course in place, there will be fewer math faculty objections to making syllabus changes to the other versions of calculus, so as to better fit the needs of our client departments.
• Calculus for Biological Sciences: We consulted with 6 departments and programs to design a calculus class with emphasis on biological examples, and on the material appropriate for those students. While the course remains as difficult as our standard calculus classes, the students seemed to be much better motivated by material related to their major. The Psychology Department is also very interested in the material in the first quarter of this course for their students who only needed to take one quarter of math (not the more scientific tracks of psychology where more calculus is required) and they now advise these students accordingly. We will change the name to Calculus for Life Sciences in all likelihood as a result.
• Math Services Committee: we have reconstituted this committee (it has not met for many years) consisting of representatives of departments served by our freshman and sophomore courses. The discussions are useful for indicating to us where we need to concentrate our reform efforts. They are also useful to the client departments so that they can see the many, sometimes conflicting, requests from the various departments. Jim Morrow, our Undergraduate Program Coordinator, and I have now begun meeting with representatives of each engineering department. We are finding that these meetings with individual departments are a more effective method of working with the departments, though the larger meetings are helpful for the global picture. While these discussions began with freshman calculus, they have expanded to include 124-5-6-324-307. This quarter we will begin meetings with the physical sciences departments.
• Teaching Evaluations: During Winter 1999, we switched from form G to form B. We found that questions 1 through 4 were the same on all relevant forms except for form G which had a different set of questions. The math department was essentially the only user of form G. The Office of Educational Assessment found that scores on items 1-4 were highly correlated, except for form G where item 2 is not correlated with the other items. Item 2 on form G is a rating of the textbook. Our textbook decisions are made by the undergraduate program committee, with the exception of the calculus sequence which is a departmental decision. Thus it should not be used as a method for evaluating the instructor, since the instructor has no control over this item. The mathematics department had been using item 3, which is an instructor rating, for its internal evaluations. However, we have seen a number of outside comparisons, even ones appearing in the Daily, which use an average of item 1-4 to compare departments. It is not unusual to see instructor ratings above 4.00 on item 3, yet the textbook is rated in the 2's, resulting in a poor average. This change should lead to a fairer evaluation of the math department and higher ratings. At the end of Autumn 1999 quarter, the Office of Educational Assessment changed the first four items of form G, eliminating the textbook question, though we will keep using form B since the questions are still slightly different. After reading the studies published in scholarly journals on the effect of workloads and expected grades on the evaluations, we have come to believe that the adjusted mean, which attempt to remove these influences, are a much fairer assessment of student ratings, and we will use those adjusted ratings from now on.

• New Text for 124-125-126-324: Our standard 124-5 calculus sequence has been using notes written by one of our colleagues, Neal Koblitz, as our textbook. There were several advantages to this text. It was written prior to the recent nationwide calculus reform, and as such was one of the first to have heavy emphasis on application word problems. The students however had a number of complaints about the text, as did the teaching assistants and faculty. Through interviews and focus groups we determined that the main difficulties were with the lack of an index (so that it was difficult to find anything), the terse explanations, the scarcity of easy problems on which to test initial understanding and develop confidence, as well as some specific complaints about the types of applications. There were also complaints about the text written by another colleague, Caspar Curjel, used in the third quarter (Math 126) and the first quarter of the second year (Math 324). These complaints were of a different nature. For example, there were few if any applications to areas outside of mathematics. Over the past year, we have experimented with several different textbooks, and found that Stewart's Calculus, Early Transcendentals, was a great improvement. This book is used at over 100 other institutions around the country, including many of the top mathematics departments. On March 7, the department voted 29-4-5 to adopt the new text for Math 124-5-6 and 324, after many committee meetings and open departmental meetings. We will need to be vigilant to keep the emphasis on word problems, as our client departments want, but also spend time on math skills which were underemphasized in the Koblitz Notes. I should point out that we certainly will not return to proofs or theorems in this course, but rather leave those topics for the Calculus for Mathematical Sciences. During the past year we have had students who took courses with all 3 books, Koblitz, Stewart, Curjel, and recommended Stewart strongly.
• Syllabus: We also decided to alter our syllabus to be more like the rest of the world. Our third quarter calculus had become almost exclusively a course in several variables. This forced us to move sequences and series into the differential equations class, 307. With the new text, we will put sequences and series back into math 126, moving some of the several variables material into math 324. We will move the integration out of math 124 and into math 125, and move some of the differential equations material in 125 into math 307. This will give us a little more time at the beginning of math 124 to get first quarter freshmen up to speed, and it will ease the plight of transfer students whose courses at other institutions many times fit better into this new syllabus.
• High School Calculus: Through the UW extension office we have begun to offer UW credit for calculus taught in the high schools by their teachers. Two major problems we face are a lack of adequate high school preparation for our calculus and precalculus classes, together with the related problem of `faux' calculus taught at some high schools. A significant number of students feel they have already learned calculus, yet when the get to the UW they are not only not prepared to go on past calculus, but they do not know enough to get into calculus and must repeat precalculus. By having calculus taught in high schools at the level of UW courses, the better students will not need to take calculus here. Moreover, the high school teachers will also understand the level of understanding of precalculus required in order to master the course. We hope this will have a trickle-down effect on incoming students. One worry is that the UW extension overhead costs are so high that many high schools will not be able to afford it. A UW professor will approve the credentials of the high school teacher, assist the teacher in writing exams and monitor the results.
• Web tests and homework: Several faculty have evaluated available packages for instantly graded homework and tests administered on the web. Their unanimous conclusion is that software is not yet mature enough to offer to all students.

• Reduce maximum lecture size from 160 to 80.
• Reduce maximum quiz section size from 40 to 27 (Three sections per lecture).
• Increase the length of one of the two quiz sections from 50 minutes to 75 minutes.
• Develop worksheets for calculus quiz sections.

• To implement smaller classes, the math department will add 22 additional lecture sections and 44 additional quiz sections.
• Increase the average teaching load from 2.9 to 3.2 teaching units. Currently we compute each faculty member's teaching load with 0.8 units for each large 100 level lecture, 0.6 units for 300 level courses and 0.7 units for graduate level courses.
• Longer quiz sections: 75 minutes one day, 50 on the other instead of two 50 minute sections. (TAs agree to this so long as we have the next item.)
• Faculty prepare worksheets and quizzes so that the TAs have less preparation, and so that there is more uniformity in the quiz sections.
• Math faculty will take over the duties of the TAs in 6 quarter long graduate classes, so that the 6 TA quarters can be reassigned to calculus. We will partially offset the extra effort by increasing the value of graduate classes by .05 to 0.75 teaching units.
• Math department will give release time each year to a faculty member to be the coordinator of these calculus classes (1.0 teaching units). With a total of 44 lecture sections and 132 quiz sections it is imperative that we have someone organize the effort. Quality control will be provided by common final examinations, organized and written by the coordinator. This will assure comparable courses so that a student who takes Math 124 from one instructor is ready to take Math 125 from another. Students are usually not able to take both from the same instructor.
• Math facparticipate in seminars and other activities surrounding the sabbatical program for Community College Math teachers.
• Math faculty will run some of the quiz sections. (TAs will not run the lecture section.)

• 5 new TA positions devoted to calculus.
• 2 positions, each funded at approximately $45,000 per year. These will be used first to supplement sabbatical salaries of the Community College teachers, who will teach a proportional amount. For example, if a community college teacher received 2/3 pay from their home institution, we would provide 1/3 pay in exchange for a teaching load equal to 1/3 that of a full-time lecturer. Any remaining portion of the 2 positions would be filled by full-time lecturers, with salary supplemented from our recapture budget if less than a full position is available from these funds.
• Funds for calculus course development (worksheet development and testing).