Employment Opportunities for Undergraduates

Rutgers Students Shine in Putnam Competition

Effectiveness of Calculus Reform Documented

#### Editorial

Since I am stepping down as vice chair effective May 31, 1999, this is my last issue of the Newsletter. This issue summarizes the administrative changes taking place in the department. There are also descriptions of employment opportunities for undergraduates in the instructional program, reports of honors received by both students and faculty, and information about the effect of recent changes in our approach to teaching calculus.

Charles Sims

Undergraduate Vice Chair

#### Employment Opportunities for Undergraduates

Over the last few years, the Mathematics Department has increased its hiring of undergraduates dramatically. We now employ students in three different jobs: peer mentors, graders, and senior peer mentors.

Peer mentors assist in first-year calculus workshops and perform some grading. To be peer mentors, students should have completed Math 251, or at least done very well in Math 152. They must also have completed at least two semesters at Rutgers with a GPA of 2.75 or better. There is a peer mentor web page. To find it, go to the Math Department page, sites.math.rutgers.edu and follow the peer mentor link. On this page, it is possible to obtain more information and to apply for a position. It is also possible to contact the peer mentor coordinator by sending e-mail to mentor@math.rutgers.edu. Assignments involving only grading, primarily grading of Maple homework in Math 244 and 251, are also available. Graders should have completed the course for which they are grading with a grade of B or better and be familiar with the aspects of Maple used in the course. Students interested in these assignments should contact the peer mentor coordinator at the above e-mail address.

Senior peer mentors serve as recitation instructors in precalculus classes. To be considered for appointments as senior peer mentors, students must be math majors entering their senior year and must have a GPA in math courses of at least 3.4. They must also have served as peer mentors for two or more semesters. Applications may be made by e-mail to sims@math.rutgers.edu or in writing to the Undergraduate Office, Room 303, Hill Center.

#### Administrative Changes

Two important changes in the administrative structure of the Mathematics Department are in the works.

Professor Antoni Kosinski, who has served two 3-year terms as chair, is relinquishing that position at the end of this academic year. By vote of the department Professor Richard Falk has been nominated to take his place. The final decision will be made by Dean Foley, but it seems very likely that Professor Falk will be the chair on July 1.

Professor Falk is an applied mathematician whose research deals with the numerical solution of partial differential equations. For the last two years he has been a member of the Committee on Standards and Priorities for Academic Development (CSPAD) and has chaired the New Brunswick Computing Advisory Committee, which is appointed jointly by Vice Presidents Haska and Seneca.

Professor Charles Sims, who has been Vice Chair for the Undergraduate Program for the last seven years, is also stepping down. His replacement has not yet been named.

#### Rutgers Students Shine in Putnam Competition

By Professor Michael Saks

The William Lowell Putnam Exam is a highly competitive nationwide mathematics contest for undergraduate students held each December. This year, Rutgers students made an excellent showing among the 2600 students who took the exam. Senior Amir Shimoni scored high enough to rank in the top 5%, while sophomore Dan Wilckens and senior Khvenkin Kirill were both in the top 8% and sophomore Vitaliy Gyrya was in the top 12%. Three other Rutgers students, seniors Brigitta Vermesi and Steven Schirripa and first-year student Rajeev Rao were all in the top 30%. The Rutgers team finished 38^{th} out of the 321 schools that entered teams. [Ed. Note: Professor Saks acted as "coach" for the Rutgers Putnam participants.]

#### Math Faculty Honored

Three members of the faculty of the Mathematics Department recently received recognition for outstanding accomplishments.

Professor Amy Cohen, who is a former dean of University College and currently serves as treasurer of the Association for Women in Mathematics, received the Award for Distinguished College or University Teaching from the New Jersey Section of the Mathematical Association of America.

Professor Feng Luo was given the Rutgers Board of Trustees Fellowship for Scholarly Excellence.

Professor Jean Taylor, who is president of the Association for Women in Mathematics, received the Rutgers College Class of 1962 Presidential Public Service Award.

#### Effectiveness of Calculus Reform Documented

As part of recent efforts to improve the teaching of calculus at Rutgers, the Mathematics Department has experimented with several instructional formats. Recently Professor Charles Weibel and Dr. Lewis Hirsch, Director of Basic Skills, undertook a two-part study to determine whether these innovations produce significant, positive results. This article summarizes briefly the first part of their study. A more detailed report is available from Professor Weibel, whose e-mail address is weibel@math.rutgers.edu.

The two-semester sequences Math 151-152 and Math 153-154 use the same text and cover basically the same topics. Students in Math 151 and 153 take the same common final, as do students in Math 152 and 154. Since its creation in 1990, Math 153-154 has been taught in an intensive, 6-credit format, which involves two 80-minute lectures and three 80-minute workshops each week. In workshops, students work in small groups on specially designed problems whose solutions, written up outside of class, are graded for both mathematical correctness and quality of exposition.

Since 1996, Math 151-152 has been taught in two formats, carrying 4 and 5 credits, respectively. In the 4-credit format students have two 80-minute lectures and one 80-minute workshop each week. Lecture classes typically have 75 students while workshops have about 25. All classes in the 5-credit format have about 25 students. In addition to the two lectures and one workshop, there is a 55-minute "practicum", which is similar to a traditional recitation and provides an opportunity for students to go over previously assigned homework.

Students are not assigned to sections of Math 151-152 and Math 153-154 randomly. For example, although open to all students, the 6-credit format is recommended for students who are ready for calculus but who are at risk in the sense that their preparation may be somewhat weak or they may need help with study skills. The purpose of the first study undertaken by Weibel and Hirsch was to determine whether, for students with the same preparation and ability, the 5-credit and 6-credit formats produce better results than the 4-credit format as measured by scores on the common final exams.

The study looked at students who took Math 151 or 153 in fall 1997 and students who took Math 152 or 154 in spring 1998. To simplify the analysis, only students who were first-year students in fall 1997 were considered. The numbers were as follows: 408 students in the 4-credit format, 152 students in the 5-credit format, and 45 in the 6-credit format. To assess a student's preparation and ability, Weibel and Hirsch had the following data: the Math and Verbal SAT score, the high school rank in class, and the score on the New Brunswick Placement Test. The Verbal SAT turned out not to be a reliable predictor of final exam scores for students in Math 151 and 153 and was not used in the study.

In fall 1997, students in the 4-credit and 5-credit format classes of Math 151 had roughly the same profile: an average Math SAT of about 655, an average rank in class of about the 82^{nd} percentile, and an average score on the placement test of about 27 out of 40, where 19 is need to qualify for calculus. The profile for students in the 6-credit format Math 153 was noticeably different. The average Math SAT score was 570, the average rank in class was the 74^{th} percentile, and the average score on the placement test was 23.

The students in Math 153 scored on average about 15 points higher (out of 200) on the final exam than students of comparable preparation and ability in the 4-credit format classes. This improved performance of at least half a letter grade is consistent with early studies of the effectiveness of Math 153. Students in the 5-credit format classes of Math 151 scored on average about 9 points higher on the final than comparably prepared students in the 4-credit format classes. This improvement, as well as that observed in Math 153, was statistically significant.

The analysis of spring 1998 students was complicated by the fact that not all students in Math 152 or 154 that semester had taken calculus in the fall, and even when they had, for some that calculus course was Math 135. Also, some students in Math 154 had taken Math 151 in the fall and some students who took Math 153 in the fall switched to Math 152 in the spring. The reader is referred to the full report for the details, but one interesting result is that students who were in 4-credit format classes both semesters averaged 130 out of 200 on the common final for Math 152 and 154, while students who had been in 5-credit format classes both semesters averaged 153 on the same test.

The second part of the study, comparing the 4-credit and 5-credit format classes in Math 135-136, is still in progress.

#### A Final Thought

By Charles Sims

I had not originally planned to make any formal statement as I prepared to hand the leadership of the undergraduate program over to someone else. Farewells tend either to be gushy, describing how enjoyable the job has been and how much it will be missed, or angry, cataloging the frustrations of the position. Neither tone seemed appropriate. In the end, because I have put so much effort into trying to maintain and strengthen the undergraduate program, I decided to write something.

Rutgers faculty generally and faculty in the Math Department in particular tend to believe that it is the quality of their research and the excellence of their contributions to the graduate program that justify their presence on campus. The mathematics research done at Rutgers is first rate and our graduate program has brought some very talented students to Rutgers. However, if it were not for our service role to roughly 8,000 undergraduate students each semester, we would be a very small department.

Those students deserve the best program we can provide, a program in which all instructors teach with the energy and compassion with which they would want their own children, or those of their friends and neighbors, to be taught. We have made some progress and we frequently come close to this goal, but we can do better.

#### Useful Information

Here are the telephone numbers and e-mail addresses of Mathematics Department administrators, at least for the next month:

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.

Associate Vice Chair, Michael O'Nan, 445-2390, monan@math,rutgers.edu.

Head Undergraduate Advisor, William Sweeney, 445-2390, wsweeney@math.rutgers.edu.