1998 - Volume 5 Number 2: February 18, 1998

Editorial

New Full-Time Recitation Instructors

Spring Mathematics Enrollment

A New "Math for Physics" Course

1 Point Quizzes

Rethinking Precalculus

Math Instruction and the Web

Useful Information

Editorial

This issue of the newsletter is one of the longest since publication began five years ago. A lot is happening in the undergraduate program. There are job opportunities for full- and part-time recitation instructors. We continue to teach more and more students. There are important developments in our courses and in the instructional strategies used by our teachers. Finally the Word Wide Web is having a dramatic impact on the entire educational process, not just in mathematics but across all disciplines.

Charles Sims, Undergraduate Vice Chair

As noted in the previous issue of this newsletter, last fall the Mathematics Department used four undergraduates as recitation instructors in precalculus. Each instructor was responsible for two sections.

All the evidence available indicates that this experiment was very successful. The evaluations from the students in the sections taught by undergraduates rated the instructors above the average for the course. Comments from the lecturers were uniformly positive. Three of the four instructors are teaching precalculus recitations again this semester. The fourth was unable to continue because of scheduling difficulties.

For next fall, the department would like to increase the number of undergraduates teaching recitations. Current math majors who are juniors, who have a GPA of 3.4 or better in mathematics courses, and who will have completed at least two semesters as a peer mentor by the end of this term are urged to apply by calling 445-2390 or sending email to sims@math. The pay will be $$1300 for two sections. New Full-Time Recitation Instructors For several years, the most difficult staffing problem facing the Mathematics Department has been finding enough qualified recitation instructors, particularly for fall classes. The number of mathematics teaching assistants is much too small to permit all recitations be taken by TA's. Last fall 27 part-time instructors taught a total of nearly 90 recitations. Almost all of these individuals were recruited during the month of August. One way the department has moved to create a larger pool of qualified recitation instructors is by the use of undergraduates. (See the previous article.) For next year, another innovation should be very helpful. The FAS Dean's Office has approved four full-time recitation instructor positions. The new positions will carry the title assistant instructor and have an annual salary of slightly over$$24,000. Assistant instructors could be considered for summer teaching assignments, which could bring the total annual compensation to nearly \$30,000. Assistant instructors will be appointed for one year, but renewals may be made for a total of up to four years. The preferred qualifications are a master's degree in mathematics and prior mathematics teaching experience. However, persons with a bachelor's degree and substantial teaching experience will be considered.

The normal teaching load for these assistant instructors will consist of 12 recitation classes per semester, primarily in precalculus. The spring assignment may sometimes be 9 recitations and one class of Math 103. Candidates must be prepared to work long hours during the final exam periods. Recitation instructors are expected to help with the grading of all major exams, including finals, and the assistant instructors may have over 400 students in their classes!

Spring Mathematics Enrollment

Again this semester enrollment in undergraduate mathematics courses is up over last year. The increase is nearly 6% compared to spring 1997.

As has been the case for several years, growth is occurring in first and second year courses. One notable change occurred in Math 250, Introduction to Linear Algebra. In spring 1997 there were 356 students enrolled in this course. Currently there are 453 students. The only significant decreases in lower-level courses were in Math 136 and 138. The lower enrollment in these courses is apparently due to a change in the requirements for biological sciences majors, which now permit statistics to be substituted for a second semester of calculus.

The following table summarizes enrollments on February 4, 1997 and February 12, 1998:

   Spring 1998 Spring 1997 Noncredit 741 655 Liberal Arts 392 363 Precalculus 1322 1145 Other 100-Level 2389 2369 200-Level 1161 1107 300- & 400-Level 594 594 Total 6599 6233

Reports at the recently held national mathematics meetings in Baltimore spoke of decreases in mathematics enrollments at many institutions. Thus Rutgers appears to be bucking the trend. However, one must be careful in drawing conclusions since not all departments collect data in the same way. In particular, they may not include noncredit courses, where the growth at Rutgers continues to be high.

The undergraduate class schedule in mathematics for fall 1998 has been designed for about 9300 students, or roughly 4% more than took mathematics in fall 1997.

A New Math for Physics'' Course

The professional physics major at Rutgers-New Brunswick is intended to prepare students for graduate study in physics at the highest level. This major requires a large number of courses in mathematics and physics for its highly motivated students. Last year the Physics and Mathematics Departments discussed how to reduce this number while still giving these students a reasonable opportunity to learn the important mathematical information they would need for their careers.

The two departments have begun an experiment designed to see if students can successfully learn the relevant material from ordinary and partial differential equations and complex analysis in only two semesters. An appropriate amount of linear algebra will also be introduced during the two courses, although almost all of the students attending the course have had Math 250. It is expected that students will take these courses after completing with distinction the basic three-semester calculus sequence and a similar sequence of physics courses.

This semester the course instructors are Professor Michael Stephen of the Physics Department and Professor Stephen Greenfield of the Mathematics Department. They will alternately present material, and will try to illustrate the mathematics discussed with interesting physical examples. Recently, an analysis of the motion of a carbon dioxide molecule led naturally to diagonalizing a certain 3-by-3 symmetric matrix, and then to a discussion of which eigenvalues of that matrix could be observed because of the dipole moment of the motion — not an ordinary Math 250 example!

The success of the course is not yet clear, but at least one math faculty member is learning a good deal. It is also interesting to see whether the intense and lively interaction between mathematics and physics in research and graduate education at Rutgers can be extended into a part of the undergraduate curriculum.

1 point quizzes

By Professor Stephen Greenfield

Math 135 is our largest course, with students gathered by compulsion rather than attraction. Almost all students in Math 135 take the course because their anticipated major requires one semester of calculus. These students usually believe they will major in business, finance, biology, pharmacy, etc. They usually don't have a strong background or interest in mathematics. Math 135 is rarely their highest academic priority.

Low or inconsistent attendance seems to decrease the chance of success in Math 135. I wanted students to get an immediate reward for coming to class, I wanted to know what students were or were not learning, and I wanted to give students some feedback about their work in the course. Therefore I gave and graded short quizzes during every Math 135 lecture class, a strategy suggested by Professor Brenda Latka of Lafayette College. For each quiz taken I gave the students 1 point towards their final grade accumulation in the course, whether or not the answer to the quiz was correct. The total credit that any student could earn towards their term grade was the equivalent of about two problems on an exam (there were three exams, two during the semester and a final at the end, with a total of about 30 problems).

I had several concerns before starting the 1 point quizzes. First, how much class time would they take? Each quiz took about 5 minutes of an 80-minute period. I'm rarely able, however, to use all 80 minutes effectively. Second, would students take the quizzes seriously? I note happily that they generally did. They saw other advantages earlier than I did. The instructor gave them questions after each lecture, gave them the chance of answering these questions under conditions as close as they wished to exam restrictions, and graded their work with comments: a good rehearsal. I also sometimes asked students to work in pairs to encourage them to meet each other and perhaps help the formation of study partnerships outside of class.

My greatest concern, though, was for my own time and effort. I worried slightly about how much time invention of questions would take (almost none –– a good 1 point quiz is rarely clever or intricate but asks straightforwardly about an important fact or idea from that day's lecture). I worried a great deal about how much time grading and recordkeeping would take. I kept a diary, now available on the web, listing the questions, student performance, and grading time. The time I needed to grade and keep records for this class of 100 was about 20 hours over the whole semester.

I recommend that other instructors consider giving 1 point quizzes, although any increase in instructional time is a difficult issue. This increase may be balanced in Math 135 by the fact that students rarely come to office hours. I am teaching Math 135 again this semester and again am giving 1 point quizzes. My last quiz of the fall semester asked, "How useful have the quizzes been to you?" I was struck by the almost unanimous positivity of the answers and the variety of reasons given.

More information about what I did can be found on the web, linked through my teaching page or directly.

Rethinking Precalculus

A committee chaired by Professor Amy Cohen has been appointed to review the three precalculus courses offered by the department, Math 111, 112, and 115. This is the next step in the curricular reform that began with the introduction of the intensive calculus sequence and has included the addition of workshops to Math 311 and 351, substantial modifications to the sequence Math 151-152-251, more modest changes in Math 135, and the introduction of a five-credit format for some sections of several first-year calculus courses.

The most urgent charge to the committee is to recommend a new text. However, it is likely that the committee will call for substantial changes in the syllabus and a new name.

The title "precalculus" suggests that the primary purpose of these courses is to prepare students for calculus. However, only about half of the students who take Math 115 go on to take calculus. Math 115 is a prerequisite for General Biology and a graduation requirement for psychology majors. Thus there is a need for the course to have significant intellectual content by itself.

High school students take a course labeled "precalculus". When they come to college and have to take a course with the same name, they react negatively. Nationally, the trend is to build the course around the concept of a function, a concept that many of our calculus students still have difficulty with. Thus a title like "functions and their graphs" might help remove the stigma from placement into Math 115 and indicate more clearly the content of the course.

Anyone with suggestions about precalculus at Rutgers is encouraged to contact Professor Cohen. Her email address is acc@math.rutgers.edu.

Math Instruction and the Web

The growth of the World Wide Web is having a significant impact on instruction in a wide variety of disciplines. It is almost certainly going to change the way Rutgers mathematics students and instructors interact with each other and with the department's undergraduate office.

At Rutgers, one of the leaders in the use of the web in instruction has been Professor Douglas Blair of the Economics Department. Professor Blair regularly teaches Economics 102, Microeconomics, to classes of several hundred students. All supplemental materials for his class are made available on the web, including copies of the slides used in every lecture. Use of the web by students is a requirement of the course. To view this material, go to Professor Blair's home page and follow the link to Economics 102.

The Rutgers Art History Department has digitized its collection of visual images and made them available to its students on the web. The images are accessed through the link to course materials from the department's home page. Unfortunately for the casual art lover, the images are password protected to prevent infringement of copyright. Passwords are issued to students by their instructors.

Use of the web in mathematics instruction is increasing rapidly. A consortium of universities including Ohio State and Illinois is offering a calculus course on the web. The course incorporates the symbolic package Mathematica. More information is available. This is only one of a number of web-based mathematics courses.

The use of the web in the Rutgers Mathematics Department is also growing. There are now web pages for several large courses. These pages contain syllabi, review materials, and copies of actual exams, some with solutions. The home page for the Mathematics Department contains a link to course materials. From that page, the links to material about Math 135 and Math 152 are the most important.

Many faculty members provide information about the courses they are teaching on their personal web pages. These pages may be found by following the link to faculty information on the department page.

There is a significant problem with using the web for mathematics. Most tools available for displaying information on web pages do not provide good support for mathematical notation. Mathematicians prefer to develop a document in TeX or LaTeX and print it using Postscript. Most web browsers, particularly the ones readily available to students, are not able to display Postscript. Help is on the way. The presentation at the Baltimore meetings about the proposed mathematical additions to HTML drew a standing-room-only audience. However, these additions are several years away. For the moment, various less than ideal alternatives are available.

One of these alternatives is to convert Postscript files to GIF format. Most browsers support GIF files. The GIF format is not as precise as Postscript, sometimes leading to mathematical content which can be difficult to read. Professor Greenfield has created a page discussing one way to produce GIF files.

The web is also likely to change the way students request special permission to get into closed sections of mathematics classes. Currently students must fill out a paper form to submit a request. Each semester the department handles roughly 2000 such forms and the number is growing along with enrollments in math classes. The processing of the forms requires the heavy involvement of three staff members and an average of more than eight hours from each of five faculty members.

For fall 1998 the department wants to put the special permission process on the web. Students would submit requests by filling out a form on the web. Deans would be able to support selected requests using another web page. From yet another page, mathematics faculty would be able to review all requests for a specific course and to make adjustments to the initial priorities assigned to requests by the system. Once a decision was made on the number of requests to be granted, the distribution of special permission numbers would be automatic. Students would check the status of their requests using the web.

Intensive discussions are currently underway with the Registrar, the Scheduling Office, and RUCS to resolve a number of technical issues. Some funding has been found and more is being sought. The goal is to have a system ready for large-scale testing in July and fully operational in August.

We are rapidly reaching the point at which all Rutgers mathematics students will be expected to use email and to be able to locate, download, and print material from the web. Students can reasonably expect that their instructors will have these skills as well.

Useful Information

Here are the telephone numbers and e-mail addresses of Mathematics Department administrators:

Chair, Antoni Kosinski, 445-2393, kosinski@math.rutgers.edu.

Undergraduate Vice Chair, Charles Sims, 445-2390, sims@math.rutgers.edu.

Graduate Director, Peter Landweber, 445-3864, landwebe@math.rutgers.edu.

Director of Basic Skills, Lewis Hirsch, 445-2288, hirsch@math.rutgers.edu.