Calculus Reform 2001-2004:
Final Report

Appendix A
Supplementary Questions

The OEA designed and administered supplementary questions were printed onto the backs of the usual end of quarter student evaluation forms. A slight change in the Math 124/5 questions occurred after year 1. Namely, "questions 9 and 10" during 2001-02 were combined into a single "question 9" in subsequent years.

1. Class sessions (lecture) provided opportunities for student questions.
2. Class sessions (quiz sections) provided opportunities for student questions.
3. Time spent in lecture was useful to my learning.
4. Time spent in quiz section was useful to my learning.
5. The course encouraged student commitment to learning.
6. The instructor made efforts to align instructor and student expectations.
7. The lectures and the textbook worked well together in this course.
8. The textbook was useful to my learning in this course.
9. The textbook homework contributed to my learning in this course.
10. Supplementary homework contributed to my learning in this course.
11. Worksheets contributed to my understanding of course content. (Leave blank if worksheets were not used in your class.)
12. I was satisfied with my learning in this course

Math 124/5 - 2002-03 and 2003-04:

1. Class sessions (lecture) provided opportunities for student questions.
2. Class sessions (quiz sections) provided opportunities for student questions.
3. Time spent in lecture was useful to my learning.
4. Time spent in quiz section was useful to my learning.
5. The course encouraged student commitment to learning.
6. The instructor made efforts to align instructor and student expectations.
7. The lectures and the textbook worked well together in this course.
8. The textbook was useful to my learning in this course.
9. The homework contributed to my learning in this course.
10. Worksheets contributed to my understanding of course content. (Leave blank if worksheets were not used in your class.)
11. I was satisfied with my learning in this course.

Math 126 - 2001-02, 2002-03 and 2003-04:

1. The Monday/Wednesday/Friday lecture class size in Math 126 (160 students) contributed to student learning.
2. The Monday/Wednesday/Friday lecture class size in Math 124 and Math 125 (80 students) contributed to student learning.
3. The Tuesday/Thursday quiz section size in Math 126 (40 students) contributed to student learning.
4. The Tuesday/Thursday quiz section size in Math 124 and Math 125 (27 students) contributed to student learning.
5. The Tuesday/Thursday quiz section time in Math 126 (50 minutes + 50 minutes) contributed to student learning.
6. The Tuesday/Thursday quiz section time in Math 124 and Math 125 (80 minutes + 50 minutes) contributed to student learning.

Appendix B
Small Group Interactive Diagnostic Summary Reports

A Note to Math 124 Students
from the Department of Mathematics

What makes this course interesting?

What makes this course difficult?

You all know from previous math classes how one course will build upon the next, and calculus is no exception. Math 124 will introduce only one genuinely new idea, the concept of a "limit". The course then combines precalculus and algebra tools with "limits" to solve new types of problems. We will soon see that some calculations are very unforgiving, as far as algebra or precalculus mistakes are concerned.

Very few of you will go on to major in mathematics or computer science, but most of you will eventually see how calculus is applied in your chosen field of study. For this reason, we aim for ability to solve application problems using calculus. Some of the homework problems are quite lengthy and building up your "mathematical problem solving stamina" is just one of the aims of this course. If you have taken the Math 120 course at UW, you know what this all means. If you have not, it means that a large number of "word problems" ("story problems") or "multi-step problems" are encountered in the course. This is one key place Math 124 will differ from a typical high school course. In addition, it is important to note that the ability to apply calculus requires more than computational skill; it requires conceptual understanding.As you work through the homework, you will find two general types of problems: calculation/skill problems and multi-step/word problems. A good rule of thumb is to work enough of the skill problems to become proficient, then spend the bulk of your time working on the longer multi-step problems.

Five common misconceptions

Misconception #1: Theory is irrelevant and the lectures should be aimed just at showing you how to do the problems.

The issue here is that we want you to be able to do ALL problems--not just particular kinds of problems--to which the methods of the course apply. For that level of command, the student must attain some conceptual understanding and develop judgment. Thus, a certain amount of theory is very relevant, indeed essential. A student who has been trained only to do certain kinds of problems has acquired very limited expertise.

Misconception #2: The purpose of the classes and assignments is to prepare the student for the exams.

The real purpose of the classes and homework is to guide you in achieving the aspiration of the course: command of the material. If you have command of the material, you should do well on the exams.

Misconception #3: It is the teacher's job to cover the material.

As covering the material is the role of the textbook, and the textbook is to be read by the student, the instructor should be doing something else, something that helps the student grasp the material. The instructor's role is to guide the students in their learning: to reinforce the essential conceptual points of the subject, and to show their relation to the solving of problems.

Misconception #4: Since you are supposed to be learning from the book, there's no need to go to the lectures.

The lectures, the reading, and the homework should combine to produce true comprehension of the material. For most students, reading a math text won't be easy. The lectures should serve to orient the student in learning the material.

Misconception #5: Since I did well in math, even calculus, in a good high school, I'll have no trouble with math at UW.

There is a different standard at the college level. Students will have to put in more effort in order to get a good grade than in high school (or equivalently, to learn the material sufficiently well by college standards).

How do I succeed?

What is the course format?

What resources are available to help me succeed?

• Your instructor and TA will be accessible to help you during office hours, which will be announced early the first week of the term. If you are new to the university, you might have the false impression that professors are aloof and hard to approach. Our faculty and TA's make themselves very accessible to help their students and you should not be afraid to ask for advice or help.

• The math department operates a Math Study Center (MSC), located in B-14 of Communications. This facility is devoted to help students in our freshman math courses only. The center has extensive hours of operation that will be announced the first week of class. The MSC is staffed by advanced undergraduate and graduate students who can help you with difficulties as you work through the course. In addition, many faculty hold office hours there as well. One useful piece of advice: The MSC is often overcrowded the day before homework is due; this is another good reason to spread your study time out over the week.

• Some students use the MSC as a place to meet a small group of fellow students in the course and work through problems together. Explaining solutions to one another is often the best way to learn.

• A large amount of material is available on line (including old quizzes, midterms, finals and worksheets) at

  http://www.math.washington.edu/~m124

• Some students additionally hire a tutor for private help; a list of tutors can be obtain at the math student services office, C-36 Padelford Hall.

Appendix D

Appendix G

Date: Mon, 9 Jun 2003 11:50:02 -0700 (PDT)
From: Ken Bube 
To: Selim Tuncel ,
     David Collingwood 
Cc: Ken Bube 
Subject: Re: Thank you! (fwd)

Selim and Dave --

 Here's a item that might be useful in documenting the effectiveness
of the Community College Visitors Program.

     Marina Frost from Clark College in Vancouver, WA visited UW last
year.  She brought her Math Club to Seattle on Tuesday, June 3, 2003,
to visit the UW campus.  She sent me an e-mail the day before, and I
met with her and seven students for 90 minutes at lunchtime.  They
had lots of questions about UW, majors in general, math courses and
math majors at UW, etc., and we had a lively discussion.  Marina said she
had been using some of our 124 and 125 materials successfully in her
calculus courses at Clark College.  So it sounds like some of the goals of
our Community College Visitors Program are being met: connection between
Community College math courses and how we teach them at UW, and contacts
between Community College Visitors and UW faculty that provide resources
of value to the Community College students.

     Cheers,
     -- Ken

---------- Forwarded message ----------
Date: Wed, 4 Jun 2003 22:34:37 EDT
From: MarinaMorosova@aol.com
To: bube@math.washington.edu
Subject: Re: Thank you!

Dear Ken,
 Thank you so much for meeting with us yesterday.  The students were
very appreciative of your giving of your time to talk with us.  Your enthusiasm
and interest were infectious and your knowledge impressive.  The students were
very excited by the whole experience and were motivated to work even harder
when they returned home.  Most want to attend the U now, so you'll probably be
seeing them again.
       Thank you again, Ken, and have a pleasant summer.

All the best,

      Marina

In the fall of 1997, Doug Lind, Chair of the Mathematics Department, formed 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 calculus taught by this department (Math 111/2 and Math 134/5/6) are not part of this 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 teaching the main calculus sequence for first-year student using locally produced materials, sometimes supplemented by paperback workbooks. As this system has been in place for sometime it was time for a review of the Math 124/5/6. The questions before the committee included:

1.)

Are we teaching the right kind of calculus? The current system emphasizes 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

b. Physical Science and Engineering Calculus

A primary recommendation of this committee is to better integrate the syllabus of the basic service course sequence consisting of the five quarters 124-125-126-307-324. These courses should be regarded as a single, coherent stream, and the computer adjuncts 187 and 387 should be integrated into this stream. This department needs to collectively decide on the content, order of topics, and emphasis for these courses. This examination should begin immediately and it should heavily involve the client departments.

Linear algebra probably needs to be thought about also, but that's a topic for another day.

Here are some specific recommendations on the mechanics of the course.

First, we would respond to the desire for more flexibility in teaching calculus. This would consist of three points: improving and expanding the texts, a loosening of the syllabus, and a moderation of the common final. We emphasize, however, that we must maintain the emphasis on mathematical modeling, which means, among other things, that teachers would be expected to address and assign a significant number of hard word problems. Second, we would also immediately begin to address the problem of assessing student preparation and expectations. Third, we recommend the immediate revival of the Math Services Committee as a vehicle for communication with other departments about these and all our courses.

As far as we can tell, this department is deeply divided on the subject of textbooks for calculus. A lengthy open meeting on a draft copy of this remark did very little to resolve this issue. Some of that ambivalence is shared by the members of this committee. On the one hand, locally developed notes are concise, focused, cheap, and make the course easy to explain to client departments. More specifically, there is no doubt about what is to be covered. On the other hand, a published text is flexible, does not need constant maintenance by members of the department, and could easily be adapted to a year-long sequence for the 100 level courses. We recommend that the department experiment with and then choose one of the following two courses of action.

A. The current notes for 124/5 and, perhaps 126, could be thoroughly reworked and expanded. This could include, but not be limited by, rewriting, re-type setting, indexing, and the addition of some topics and problems. What we have in mind here is the model that was successful in Math 120: the project was begun by one faculty member and carried forward by another. The Math 120 notes continue to evolve on a quarterly basis through frequent instructor discussions of the material. Ken Bube has agreed to work on this, and Ramesh Gangolli has agreed to help. Both feel that there is enough support in the department to start, but to proceed beyond a certain point they would want the guidance of a syllabus committee to proceed, and an explicit agreement in advance that product produced would have to be thoroughly vetted by the rest of the department before going into widespread use. These notes could be cross-referenced to a standard text; however, we note that past attempts at multiple texts haven't worked well. The time estimate is that it would require about a year's worth of work for each of the 100 level courses. There are funds on campus for such projects.

B. The department could choose a published textbook that is mathematically clear and precise, has a significant number of applications, has a wide variety of problems of all levels of difficulty, including many word problems in sections that are, on the face of it, not directly concerned with applications. Some areas of application should be developed early and returned to repeatedly throughout the book. It is difficult to recommend any one text without having used it. Therefore, we would recommend a pilot program using such a text for the year 1998-99. We note that there are texts that are not completely incompatible with the current course we teach, and it would be possible to write a common final of the type we suggest below that covered both the current and experimental versions. Robin Graham and Dan Pollack have tentatively decided to carry out such an experiment in Math 125 in the Fall of 1998.

Whatever the choice this department makes, we would like to see each syllabus pared to eight weeks, leaving two weeks free and at the discretion of the individual instructor. However, we would expect that any new syllabus would supply detailed examples on the type and difficulty of word problems that we would expect any successful student to be able to do. The new syllabus should result from examination process suggested above. As part of this development process, it might make sense to have a period of experimentation, wherein interested professors to try new ideas and approaches.

This forces a change in the common final; in a word, it could not be completely common. However the common final is a very effective method of enforcing the syllabus and for defending the instructor against the pressure to teach an easier course. Therefore, we suggest that 75% of any final be in common, and the the other 25% at the discretion of the instructor. There are some logistic difficulties to this proposal, of course, but we have given it some thought and believe it is feasible. We also recommend that the grading period be slightly lengthened - the current Saturday night sessions are draconian to many - and that there be more flexibility in the types of problems considered. The current finals are very stylized, and in some ways very predictable. This could start immediately.

To address the problem of getting students up to speed in a course that is appropriate for them, we have two suggestions. One is to change the placement test. The current test is not very different from an SAT test and is not suitable for our students. Fred Campbell has indicated that we could design and implement our own test. We are told that the university would help us distribute sample tests to incoming students, including transfers, and to high schools. The test itself and the active dissemination of it contents - Debra Friedman even suggested advisory mailings to new students and high schools - could have a very significant impact on student expectations and the design of prerequisite classes in high schools and community colleges. The second suggestion is to implement a sequence of proficiency and diagnostic tests that the students could take to gauge their abilities. These last could be bought - the University of Nebraska has a battery of on-line tests that would be suitable - and they could be expected of all students.

c. New courses

We suggest the introduction of two new calculus sequences, the first intended for the behavioral and life sciences, and the second - which we envision as much smaller in enrollment, but not in importance - would be intended for students interested in calculus as mathematics.

The largest single program on campus is biology with, in 1997-98, roughly 1850 students in the biology, microbiology, zoology, and botany majors. Furthermore, there are about 400 biochemistry majors and 600 psychology majors. By contrast there are roughly 600 majors in chemistry, physics, and mathematics combined, and 2700 in all the engineering majors. One of the main questions we set out to address was how well this cohort of biologists and psychologists was served by our current calculus.

There are several ways to answer this question. Concentrating on biologists for the moment, these students need certain mathematical skills, including math modeling skills, which our current calculus certainly supplies. They also need certain concepts from statistics and probability which they currently obtain from 400 level QSci courses. So, in some sense, we are doing our job. Nonetheless, the students feel badly used, complaining that they are forced into a mold that doesn't fit them. They vastly prefer the QSci 291-2 sequence, often stating explicitly that they like the biological emphasis of the examples. And, to be fair to them, there is probably more material in the 124/5/6 sequence than they need. Finally, many people on campus look at our block of 24,000 student credit hours in calculus and wonder why we can't break it up to serve this clientele.

We are told that biology majors arrive on campus as such, and rarely change to other scientific majors; hence there would be no pedagogical harm in targeting this audience. Psychology is a different matter, in this regard, as many of these majors arrive late to awareness of Psychology as an intellectual discipline; nonetheless, they may be well served by a different calculus as well.

For all these reasons, we recommend developing a course with this audience. Part of the development would be discussing with the relevant departments exactly what their students need. Note, however, that it is not our intention to recommend an ``easier'' class, and the biologists would be upset if we neglected certain fundamentals.

Any such course should only be developed with thorough consultation with the client departments. We recommend beginning this process as soon as possible.

We also recommend a calculus for mathematicians, perhaps with a slightly higher entrance requirement than our current Math 124, but without the stringent requirements of Math 134. The target audience would be bright, interested students who may not have a strong calculus background. Presumably such a course would be easy to develop and there would be any number of volunteers to teach it.

This ``mathematical calculus'' could have several beneficial effects. The first is that we notices that very few math majors are created by the current hones sequence: at most one or two a year. Designing a good calculus sequence that would appeal to a broader range of students should increase the number of students who are interested in majoring in mathematics, and who are better equipped to enter the ACMS major. Certain physics majors would also easily profit from such a class. The second benefit of a mathematical calculus would be that we could put here the rigor and machinery needed or wanted by certain students while, at the same time, orienting the basic calculus courses in the direction of the client departments. This could give us more latitude to demonstrate to these departments that we are responsive to their students.

4. Toward the ideal calculus

Postulating infinite resources and an ideal world, we would offer calculus as follows. First, we would have an extensive screening and placement system to make sure students are in the right class. Second, we would teach in small classes - no more than twenty-five students. The class would consist of two parts: a four-credit course meeting four times a week, plus a one-credit three-hour ``lab" which would not do homework, but would use worksheets, group work, computer modeling, etc. The model, of course, is a science lab and, as with most science labs, our lab would have its own syllabus and agenda and students from any lecture could register for any lab. (A by-product of this approach would be a week-by-week enforcement of uniformity among lectures.) Labs could trail lectures by a few days to allow lecture instructors some flexibility. Third, we would have on hand an extensive battery of materials - quizzes, worksheets, proposed group projects, exams, interactive computer workouts, and so on - to encourage a variety of teaching techniques and experiments. Indeed, we would do everything possible to encourage an atmosphere where each instructor would seek to teach the course best suited to his or her talents, inclinations, and strengths. Fourth, we would have a wide variety of faculty and graduate students involved in calculus. In short, we would make the teaching of calculus in this department into a living, dynamic process, with broad involvement.

Fred Campbell, Debra Friedman, and Nancy Kenney have all invited us to make a ``radical proposal'' for teaching calculus. The calculus program envisioned in the previous paragraph would certainly be radical. We recommend that this department put together a proposal to find the resources for such a program, using the experiences of the University of Michigan and the University of Nebraska as a guide.

The fundamental obstacle to this program is one of personnel. We emphasize that with the level of freedom we would like to grant individual instructors, we would require successful, experienced mathematicians, or highly-motivated, closely supervised graduate students. It would take about 225 twenty-five-student sections to teach our current Math 124/5/6 sequence. For comparison, it would take 160 forty-student section, and we now have roughly 40 calculus sections, each with a lecturer and two graduate students. There would also be a need for support personnel - staffing the study center, collecting and maintaining materials, including computer materials, enough competent graders to correct the homework accurately, and so on. There would also need to be a faculty member to oversee the entire program, to prevent descent into anarchy.

We make this recommendation knowing full well that, as part of this proposal, this department would have to offer something. We could not expect, for example, that the university would fund a battery of teaching AAPs simply so that we could teach in small classes. The exact nature of what we would be willing to offer and what we could expect in return is something for this department as whole to decide. But we are very aware that the status quo will not serve. If we continued to be perceived as stagnating, aloof, disinterested in our students, and generally doing a mediocre job, we feel certain that this department will fare poorly.

Appendix J
Changes as of September 2000

• 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.

  According to the Department Ratings Summary, prepared by the Office of Educational Assessment, for the period Autumn 1998-Summer 1999, the adjusted mean rating for 100-200 level Math Faculty on ``The instructor's effectiveness in teaching the subject matter" was 4.21 (52 classes). This rating was higher than the average for the sciences (4.08) and higher than the average for the University (4.08). Note that we do not offer 200 level courses, and that essentially all of our 100 level classes are precalculus and calculus. The rating for ``The course as a whole" was slightly lower than the average in the Sciences and the University, but there are many aspects of these courses which are not under the control of the instructor, such as the text and syllabus, and thus this rating should not be used to evaluate instructors. Most of the changes (except in Business Calculus 111-112) listed here had not yet taken effect at the time of these ratings, so we expect that this latter rating will rise.

• 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.

Appendix K
Tools for Transformation Proposal

During the academic year 1997-98, the Math Department conducted an extensive review of its calculus program, including focus groups of students and faculty, surveys of teaching assistants and faculty, and interviews with selected client departments and administrators (Appendix A). In 1998-99, we visited a number of mathematics departments around the country in order to identify ``best practices'' used elsewhere. Last year we experimented with many of the better ideas and suggestions developed over the previous year. At the same time we began implementation of many of the recommendations of the calculus review committee (Appendix B). The change proposed here involves significant contributions from the department in terms of increased teaching load, and from the administration in terms of new resources.

Recommended changes to the class format of the first two quarters of Calculus:

• 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.

Why support smaller classes in mathematics? Math is like a foreign language. Interactive communication is necessary for better teaching. There is a lot of information and technique that must be covered in a small time slot. Students must follow or create a sequence of logical deductions, and many will get stuck at very different places. If you miss a point you may be lost for much of the lecture. But if you have a chance to ask a question, you may get around your difficulties or discover where you need to review prerequisite material. Asking questions is clearly easier in a small class.

English composition courses in some sense provide a similar service role for arts and humanities students as our entry level courses provide for science students. The total enrollment in English composition courses is approximately the same as entry level math classes, yet they are limited to a maximum of 22 students per class. Small classes are also found in foreign language classes.

The smaller lecture sections will allow more flexible formats. For example, one configuration would be a faculty member running the lecture plus one of the quiz sections, while a TA runs the other two quiz sections. This will result in closer contact between the faculty member and at least a portion of the class. We expect that this might have a positive effect on the atmosphere in the lecture section since these students would be more familiar with and hence more comfortable with the faculty member. Organization and synchronization with just one TA would also be easier for the faculty member. Some of the faculty in the past have left the organization of the quiz section up to the TA. In this model, the professor will be more intimately involved. Other benefits might accrue to the students who will in some cases have regular class meetings with full professors in small (27) classes.

Another advantage of smaller classes is increased access. There will be more sections offered at more times through the day. Currently if there are more students needing a 10:30 calculus class, we have to decide if there are enough to warrant adding a full 160-sized class. This is easier to do with size 80. Another way to put it, instead of having to choose to add a 160-sized class at either 9:30 or 10:30, we can put a size 80 class at both. Smaller classes are also easier to add just before classes begin if the demand is there. We can also add one more quiz section to a lecture without much difficulty.

One of the main objections by faculty to teaching calculus is the anonymity of students in large (160) lecture sections. A quick glance at the enclosed table of available classrooms (Appendix C) shows that few are of the size of our current calculus lectures (160). This has led to using even larger rooms, and thus greater distances between the lecturer and the back of the audience. The oft-heard reason for top-notch Washington high school students choosing schools other than UW is the size of classes. We have brought a number of high school teachers on campus this year to discuss their concerns. Some have volunteered that they advise their students to either go to Universities with smaller classes or to take their introductory math at community colleges where they can get more individual attention. Last year we experimented with size 25 (Math 124), size 50-70 (Math 144-145), and size 80 (Math 125) and two hour quiz sections (Math 144-145, Math 124). The instructors were uniformly enthusiastic about the benefits.

Here's a table comparing UW student evaluations in our small classes this year versus large classes 95-99. The ratings are ``unadjusted'' since data prior to last year did not have adjusted means.

The adjusted mean in all of these ratings are higher than the unadjusted mean. See also Questions #3 and #6 in the Autumn and Winter Math 144-145 class survey (Appendix D) showing that the students like smaller classes. That same survey shows very favorable comments by the students about the longer quiz sections, Questions #4, #7. The students were very happy with this change even though it meant more class time without additional credit. The students in Math 144-145 (Calculus for Biological Sciences) performed so well that the instructors (H. Smith, S. Tuncel) were not able to keep the mean grades as low as our traditional mean (2.7-2.9). The faculty and students were enthusiastic about this new class partly because of the format and partly because the material was geared toward the students' interest in Biology, without compromising the difficulty of the course.

In our visitations to other universities we found good pedagogical results obtained with a variety of techniques. Having the students work together in small groups during the TA's quiz section can be managed by one instructor only with small classes, according to faculty at several of the schools we visited. This agrees with an experiment in precalculus done here several years ago. For example, a group can work together on a common ``worksheet'' that leads them through the major ideas in a particular lesson. This has greater pedagogical effect than simply having the TA answer questions on homework. The testing and development of worksheets takes a lot of time, as we saw when observing the implementation in Physics classes by Lillian McDermott's group. Part of the proposal is for a significant effort to develop worksheets and to fine-tune the new syllabus for our new text, including extensive testing during Spring and Summer 2001, by teams consisting of 1 faculty and two teaching assistants, one for the first quarter of calculus (Math 124) and one for the second (Math 125).

Many math departments around the country are moving to smaller classes, though usually much smaller than 80: Minnesota, Michigan, Arizona and Maryland, for example. What we like most is the enthusiasm of our instructors who ran the small experimental classes. Ken Plochinski was one such instructor who had to go back to a size 160 class last spring. He remarked that he can't believe how much worse it is than size 80.

Part of the proposal is to provide partial salary support for community college teachers so that they can spend their sabbaticals at the University of Washington. We are required to accept precalculus and calculus transfer credits from Community Colleges. Thus it makes sense to ensure that their courses are equivalent to ours and to work with the community college teachers to ease the transition for students from community colleges to the UW. If 40% of UW students are transfer students, certainly a large number are coming to UW math classes from the community colleges. We will run weekly seminars where faculty and community college teachers will present the techniques and materials they use in common courses. We will also have faculty discuss the material students would be required to know in subsequent courses to calculus at the UW. The community college teachers who needed additional financial support would gain first hand experience with our precalculus and calculus courses. We would benefit greatly from their ideas and suggestions for improvement, since they have a lot of experience teaching these courses. I had email conversations with a number of very interested community college teachers. Shannon Flynn, Chair of Sciences at Shoreline Community College, was very excited about the possibility and would encourage her math faculty to participate. In fact she had already planned to do something similar for her own sabbatical before taking her current job. This outreach program will also provide the opportunity to community college teachers to ``reconnect'' with mathematics, to rekindle their interest in mathematics through attending seminars and advanced courses, or working directly with a faculty member.

Implementation

Department Contribution

• 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 faculty will run and participate 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.)

Administration Contribution

• 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).

The department and administration contributions are roughly equal: 50 faculty will average a 10% increase in teaching load (2.9 to 3.2 units), which is equivalent to 5 FTE. Five TA positions are equivalent to 2.5 FTE, so including the two positions devoted to sabbatical supplements, the administration would contribute a total of 4.5 FTE. This proposal is limited to the first two quarters of calculus because of the associated costs.

Development

Summer 2000: Hart Smith and Dan Pollack developed suggested homework sets and continued to improve the new syllabus for the new text: Stewart, Early Transcendentals, for 124 and 125. The emphasis on applications problems will set the tone for individual instructors in the autumn quarter. It is important to keep the emphasis of the course on applications, as needed by the client departments. Each quarter thereafter, the syllabus will be revised to reflect the experiences from the preceeding quarter.

A calculus committee of approximately 6 faculty and two teaching assistants will be appointed to oversee the project during the year. Ken Bube has agreed to head this committee. During the autumn and winter quarters, the committee will construct seven basic worksheets for math 124, and seven for math 125 designed to be used in the extended-length quiz sections. Work will also be done on sample proficiency (skills) tests and quizzes. During the spring quarter, these materials will be tested in classes, reevaluated and rewritten by the committee. A second iteration of this process will occur during the summer. We will not be able to test the worksheets completely, since they will be designed for 75 minute quiz sections, yet the quiz sections during the spring and summer will only be 50 minutes long. We'll probably have to divide them into smaller pieces for testing.

Each participating faculty member can choose to receive compensation either in the form of partial summer salary, or partial teaching credit. As I have explained before, our department assigns a value to each course, roughly 0.8 for a large lecture, 0.7 for a senior level or graduate course and 0.6 for sophomore-junior courses. The average faculty load is approximately 2.9 of these teaching units. Each year the load for each faculty member is computed and any excess or debit is carryforward to the next year. The average faculty buyout cost for teaching related activities is approximately $1,000 per 0.1 teaching unit. The committee will decide how to distribute these funds to various faculty depending on how much effort was contributed. A similar process will be developed to compensate the teaching assistants or provide them with release time from teaching. The portion of the funds corresponding to release time will be used by the department to hire part time faculty to replace the lost teaching capacity. Since the total effort will not be known until next summer, each faculty member choosing to take teaching credit instead of partial summer salary, will carry that credit forward into the next academic year.

Annual Symposium for Community College Teachers

On November 17, 2000, we will hold a symposium for Washington Community College mathematics faculty. We expect for this symposium to be an annual event. The purpose of the symposium is to foster cooperation and communication with community college mathematics faculty, with emphasis on courses that we teach in common. This first meeting of the symposium will be devoted to informing CC faculty of recent and planned changes to our curriculum. It is anticipated that future meetings of the symposium with contain sessions on teaching techniques, technology use in the classroom, and roundtable discussions of other timely issues.

There will be a plenary session at 11:00 a.m. giving an overview of our recent and planned changes in first and second year courses. At the plenary session we will also announce and describe the Sabbatical Program. This will be followed by a luncheon and special sessions. Patrick Averbeck has invited those interested to attend his Math 111 class at 12:30. This will be followed by a discussion of issues that arise in teaching business precalculus. There will be a session at 1:00 on Math 120 and a concurrent session on Math 124/5/6. At 2:00 there will be a session devoted to course equivalency questions and a concurrent session on 300 level courses.

The expected cost, including room rental and the luncheon, is $1000.

Assessment

This proposal deals with a revision of math 124 and math 125. A natural subsequent course in which to study outcomes is math 126, the third quarter of the first year of calculus. To reduce the costs of the program, we did not propose reducing the size of math 126 which will continue to be taught in classes of size 160. Thus after taking math 126, students will have had experience in both size 80 classes and size 160, and extended quiz sections versus classes without extended quiz sections. Each June, beginning in 2002, we will assess the effectiveness of the program through interviews and surveys of the students and faculty. The results will be used during the summer to improve the program for the subsequent year. We do not have experience in designing assessment methods, so we will work with CIDR and OEA to design methods of assessing the outcome of this experiment. We will also seek the advice of community college teachers who come here on sabbatical. We will also work more closely with advisors and administrators to assure that we collect all complaints about our calculus courses so that we can understand the problems. Assessment is difficult because there are many variables, and few controls. For example, students will have some knowledge of the effectiveness of the course they take, but generally will not take the same course taught from a different perspective and thus cannot compare. Some of the items we might seek to measure are: What is the level of satisfaction with these courses, by the students and by the faculty? Are the client departments happy with the balance of emphasis on word or application problems versus basic skills? Do the students prefer the longer quiz sections? Do they prefer worksheets or other materials? Do the students and faculty feel that the smaller lecture and quiz sections significantly benefit the learning environment? We will also seek to poll students who take 124 or 125 but do not continue on to math 126. Some of these students are pursing degrees which do not require a full year and some will be students who are not successful in 124 and 125. We will seek to understand some of the reasons that students do not do well in these courses.

Permanent Funding

This program will be run on a trial basis for three years. Given a successful outcome to the trial experience, and informed by analysis of the effectiveness of each of the components of the program, Dean David Hodge has reserved $150,000 of New enrollment funding for this purpose and has agreed to provide an appropriate level of on-going funding, including additional funding if warranted, to continue the program at the conclusion of the Tools for Transformation support. The allocation of funds for the Tools project and the reserved new enrollment funding are independent of other resource issues that may involve the Department and the College.

Karen Freisem and Don Wulff of the Center for Instructional Development and Research (CIDR) and Jerry Gillmore of the Office of Educational Assessment (OEA) have agreed to assist the mathematics department in developing methods of assessment of the success of the program.

This proposal was developed by the math department calculus revisions committee over the course of the academic year 1999-2000 and further revised through a series of open departmental meetings culiminating in a vote 30 for, 7 opposed and 2 abstensions. Departmental contribution beyond the level in this proposal would significantly increase the number opposed.