Stright Lines

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The Official Newsletter of the IUP Mathematics Department

January, 1999___________________Volume 2, Issue 1

Welcome to Stright Lines. The Math faculty chose this name for our newsletter to replace the name "The Addition" which was used in the last Volume. The second choice, in case you are curious, was "IUP Math News", and the third choice was "Math Matters". We hope you enjoy this issue and look forward to hearing from you.

Our lead article is by Joe Angelo, who retired in December after 35 years of teaching at IUP. Former students can drop him a note at 2591 Warren Road; Indiana, PA 15701 or by email: JANGELO@grove.iup.edu. You can also write him care of the Mathematics Department.

Jim Reber, Editor.

**How Time Flies When Having Fun**

by Joseph Angelo

When I retire from the IUP Mathematics Department Faculty in December, I will take many memories with me. My memories go back to 1952 when I became a student at Indiana State Teachers College (ISTC). I had one professor for almost all of my mathematics courses, I.L. Stright. Now, I am privileged to teach in a building named for him. He was a terrific teacher who was tough, but really cared about his students.

My undergraduate years were pre-Sputnik, so topics like sets, logic, mathematical induction and formal proof were seldom, if ever, discussed in my undergraduate classes. (By the way, Sputnik was the first satellite to orbit the earth, and it was put up by the Russians, so it encouraged a drastic change in the curriculum for mathematics and the sciences.) When I finally entered the teaching profession in 1959 (post Sputnik), my undergraduate education was out dated because of the so-called "revolution" in school mathematics. I knew I needed a masters degree, and returned to Indiana State College (ISC) in 1960 as a part time graduate student. I got my M.Ed. degree in 1963.

As an undergrad, I belonged to Sigma Tau Gamma Fraternity which had a great reputation then, but has subsequently been suspended, then expelled, and now is re-instated as a non-drinking fraternity. My fraternity brothers included math majors Len Holliday, Roy Chrisman and Larry Gallagher. We held many study sessions in the Sig Tau house (where the HUB is now). Most of our fraternity brothers couldn't understand why we worked so hard for our mathematics classes, but Ike Stright wasn't their teacher. We simply couldn't let him down.

When I arrived on campus in 1952, the classroom building (old Leonard Hall) had just burned down. Classes were held in some houses that the college purchased in the immediate vicinity of the campus. There were no chalkboards, so Dr. Stright used an overhead projector for all of his classes.

I think there were about 2400 students then, and the ratio of women to men was about 3-1. Finding a date was never a problem (for the men), but math majors were really too busy to have much of a social life.

In October 1963, Dr. McKinley, the chairperson of the Mathematics Department, called me at home in Pittsburgh to encourage me to apply for a teaching job at ISC, starting in January 1964. I was teaching at Duquesne University at the time, but was struggling financially, and Dr. McKinley's offer of $6,600.00 per year represented a $1,200.00 increase. Though I loved Duquesne University, I knew I could be happy at ISC and knew that Shirley and our four children would have it better, so I took the offer. That raise allowed me to buy our first station wagon, which was a wise move since we eventually had seven children. Mathematicians know how to multiply!

(Continued on page 2)

(Angelo, continued from page 1)

In January 1999, I will complete my 35th year at IUP. That is the longest I have ever held a job! It has been great, and I have many memories that I could share from my teaching experiences. Perhaps I will write again for the next newsletter.

I do want to tell you about some of my very first students at IUP. I had a student named Jerry Buriok in a Theory of Equations class during my first year at ISC. Jerry was one of the two best students I had in that class. A few semesters later, I had another student, Marcia Cosgray, in my Foundations of Mathematics class, also a very good student. Jerry, of course, is our current Department Chairperson, and Marcia is his wife.

Several of the students in the Theory of Equations class found teaching jobs in Pennsylvania, and I have seen them at PCTM or NCTM meetings. One of them, Jim Prymak has been retired from teaching for a few years.

Since my students are retiring, I guess it is time for me to leave IUP, too! I will leave with a great sense of gratitude to my colleagues and my students for making my 35 years here so very pleasant.

**Changes in the Geometry Curriculum Over the Years**

by John Busovicki

The geometry of yesteryear was usually presented from a synthetic viewpoint where proofs were done in a two column format. Analytic Geometry was usually treated as a separate course with geometry courses focusing on the geometry of the plane with little or no interaction with other mathematical courses. The proofs by deduction of plane geometry were extolled in an isolated environment.

Today's approach to geometry presents deductive arguments in sentence or paragraph form. Although the deductive nature of geometry is not overlooked, the organization of geometric facts from a deductive perspective receives less emphasis, whereas the interplay between inductive and deductive experiences are strengthened. Deducing properties of geometric figures, for example, is often easier for students using coordinate representation rather than synthetic proof. We also want our students today to gain an appreciation of Euclidean Geometry as one of many axiomatic systems. This goal is achieved by investigating properties of other geometries, both finite and infinite, to see how different definitions and axioms lead to different results. Looking at Euclid's fifth postulate provides an opportunity to develop non-Euclidean approaches to geometry.

The study of geometry through the use of transformations -- the geometric counterpoint of functions -- has changed the subject of geometry drastically. Transformations serve as powerful problem-solving tools and permit us to develop a broad concept that applies to all geometric figures. For example, we no longer have to limit our discussion on congruences to showing only triangles are congruent. We can now show through transformations that certain circles, parabolas, trapezoids, pentagons, etc. are congruent. We can define two geometric figures to be congruent if and only if there exists a special transformation (a motion) that maps the one figure onto the other. Through the use of similarity transformations, geometric figures can be shown to be similar as well. Transformations are now used to represent slides (translations), flips (reflections), turns (rotations), and stretches (dilations). Students are encouraged to compose translations with rotations or reflections or slide-reflections and to identify them. Invariant properties of these isometries or similarities are stressed. Although we continue to work mainly in two-dimensions, students are expected to explore the third dimension as well. Transformational geometry in three dimensions is rather easy -- usually extensions of their two dimensional counterparts. The use of computers today also helps us explore the two dimensional and three dimensional figures of geometry. Translations represented as vectors can help us explore physical phenomenon such as velocity and force.

In conclusion, geometry today focuses on more than deductive reasoning and proof. We try to integrate geometry across topics at all grade levels using coordinate and transformational approaches in two and three dimensions utilizing modeling when possible. This approach should provide students with the ability to recognize and effectively apply the geometric concept or method most appropriate to the given situation.

**________________**

**Thoughts from the Chair**

by Jerry Buriok

When I began serving as chairperson of the Mathematics Department in June 1990, I had no idea I would have the position through the millennium. At IUP, the faculty in the department elect a chairperson every three years and it is rare that anyone wants to serve more than two terms. I'm not quite sure what this says about me.

As I look back on the past nine years, three aspects of being chairperson stand out in my mind. Number one among these is the change we underwent in going to a new registration system for students to sign up for classes. Who can forget the chaos of Arena Registration at Memorial Field House! Likewise, I don't think any students or faculty have fond memories of long lines of students attempting to complete drops and adds of classes at department offices for a week after the arena. I recall attending a meeting with some other chairpersons, the Registrar, and several IUP administrators, at which I kept a pile of about one thousand drop/add slips for math classes (about eight inches high) on the table in front of me the entire meeting. At that time, IUP had a very bad reputation regarding scheduling. Now student registration for classes is handled almost entirely by telephone (TELREG) or computer terminal (TERMREG). This technology, along with some changes in how the system is administered, have immensely improved registration. Changing the registration system certainly changed my feelings about the chairperson position.

The second aspect of being chairperson that stands out in my mind deals with the changes in personnel on our faculty. We have thirty-six faculty positions in the Mathematics Department and we replaced eleven people during the nineties. I watched as many talented teachers (whom I considered good friends) retired from our department during that time. There was a camaraderie among that group that is unlikely to be matched in the near future. It was a difficult transition for me, but I am really pleased with, and proud of, the people we added to our faculty to replace the retirees. As a group, they are highly motivated professionals. They are interested in teaching and research, but they all do their share of service, too. They have been a big help to me, but they have also added significantly to my workload. Each of them had a probationary period of five years in which classroom observations were conducted and evaluation reports were written. Eventually, tenure and promotion recommendations also had to be written. Much the department chairperson's time is spent verifying what we already know is true, namely that the faculty we hire in the Mathematics Department are a conscientious, dedicated, and talented group of teachers.

Technology is the third item that stands out as I survey the past decade. A number of faculty who joined our department during the eighties provided superb leadership with regard to integrating computer technology into teaching and learning. Building on this work, a number of the new faculty who joined us during the nineties have broadened our perspective and incorporated new technology based ideas into our curriculum. They have shared their knowledge with us and helped determine new directions for the department. They have helped to write grants to pay for computers for classrooms and laboratories, and helped us make the most of the computer equipment each of us has in our office. We have a classroom holding thirty students where each one has a computer. We've used, or are using, Derive, Matlab, *Mathematica*, and most recently VRML in courses. We require TI-92 graphing calculators in our calculus course for majors, and some instructors use the TI-83 in courses for non-majors. Our math education majors are learning to use Geometer's Sketchpad, as well as everybody's favorite, Microsoft Powerpoint. Use of the Internet is commonplace and we are on the brink of distance education becoming a reality. But it hasn't been without a price. We spent a lot of time in the nineties struggling with the question of how technology can be used most effectively in the classroom. We had some lively discussions and a battle or two, but the same thing was happening across the mathematics community nationally. It has been an interesting and challenging time and I feel fortunate to be part of it.

**________________**

**Note**

Dale Peterson joined the IUP mathematics faculty in August 1996. Prior to that he taught at Embry-Riddle Aeronautical University in Daytona Beach, Florida. He also spent ten years in the aerospace industry, working on advanced space systems projects such as the Strategic Defense Initiative (SDI) and Anti-Satellite program (ASAT). He did his undergraduate work at Stanford University, received an M.S. from Brigham Young University, and was granted a Ph.D. from Rutgers University.

Changes to the M.S. program in Applied Mathematics

by Dale Peterson

Mathematicians are employed in many industries, including scientific research, financial service, and even movies. The work that mathematicians do on movies is described in a July 14, 1998, Los Angeles Times article entitled "Math Whizzes Want Respect in Equation: Mathematicians are behind-the-scenes workers for Hollywood, shuttle launches and crime scenes". The work applied mathematicians do truly is varied and dynamic.

Because of the new types of problems that so frequently arise in industry, it is necessary to occasionally update programs in mathematics. Here at IUP we have just undergone a major change in our Masters program in Applied Mathematics so that our graduates will be better prepared to tackle new challenges in industry and education. Our new curriculum gives graduate students a broad introduction to three areas: statistics, operations research (optimal decision-making), and classical applied mathematics. In addition, courses in modeling and simulation introduce students to the craft of quantifying and analyzing real-life problems, and to using a state- of-the-art computer simulation language.

Most classes are offered late afternoons and evenings, making the program convenient for non-traditional students. Class sizes are small and students receive individual attention. The program provides opportunity for practical experience.

Recent graduates have attained interesting positions at firms including Biocontrol Technology, Mellon Bank, Orthstar Enterprises, Price Waterhouse, and Butler County Community College. If you are interested in more information about the Applied Mathematics program, email us at math-grad@grove.iup.edu

or check our internet homepage http://www.ma.iup.edu/programs/grad.

**Changes in the Study of Change**

by Jim Reber

Calculus is sometimes described as the study of change and there are several changes occurring in the way students study Calculus at IUP.

The one change is in the organization of the Calculus sections. We now require majors to take the two semester sequence: Calculus for Chemistry, Physics, and Mathematics (rather than a three semester sequence). Students who complete the two semester Calculus sequence will follow that up with a two semester sequence: Introduction to Mathematical Proof (rather than the one semester Introduction to Mathematical Structures).

The other change is in the changing technology used. In recent years the Calculus classes required the use of the TI-85, which is a graphing calculator that computes derivatives and integrals numerically. We now require the TI-92 which does algebra and also calculates derivatives and integrals algebraically.

Using a hand held computer that solves equations and computes derivatives and integrals at the push of a button obviously changes the emphasis of the Calculus course. Less time is spent on manipulation that can be done by computers and the major emphases become the definitions and concepts related to derivatives and integrals and **word problems**. Those word problems you might remember from Calculus have not changed.

**New Hires 1992 - 1998**

Dr. John Baker 1996

Dr. Janet Scholz 1996

Dr. Frederick Adkins 1996

Dr. Dale Peterson 1996

Dr. John Zhang 1995

Dr. Mary Enderson 1994

Dr. Gary Stoudt 1992

Dr. Daniel Burkett 1992

Dr. Francisco Alarcon 1992

**News about Statistics at IUP**

by Maher Shawer

We have two new professors teaching Statistics in the Mathematics Department this year.

John Zhang joined the department in 1995. Even though he joined the department as a statistician, he is interested in a variety of topics related to mathematics. John received M.S. degrees in mathematics, computer science, and statistics, and a Ph. D. in mathematics. Currently, John's research interests include ranking and selection, time series, and statistics education. John is active in different professional organizations and is the second vice-chair of the Allegheny Mountain Section of the MAA. He also administers actuary exams at IUP for the SOA and is the coordinator of the IUP Graduate School Applied Research Lab.

Les Oakshott comes to us from England in an exchange program with Charles Bertness. Les graduated in 1969 from the University of Hull, England with an honors degrees in Physics. Later Les graduated with an M. Sc. in Operations Research and then worked for British Rail as an Operations Research Analyst. In 1981 Les returned to college for postgraduate work in teaching and spent the next two years as a secondary school teacher of mathematics. In 1984, Les became a senior lecturer at an Institute of Higher Education and later moved to the University of West England (UWE) at Bristol. Les teaches operations research and statistics at UWE and has written several textbooks.

We would like to congratulate one of our graduates, Vivek Ajmani, on receiving his Ph. D. in statistics at the University of Florida in May 1998. Dr. Ajmani is now working for 3M in Austin, Texas.

**Glimpses of Math Ed Graduates**

by Ann Massey

When a questionnaire was sent out to the 1992-1996 IUP Math Ed graduates three years ago, we asked for addresses and places of employment. Those who replied were sent a print-out titled "Where are we?" Now it seems only fitting to comment on what some of those graduates are doing, especially in professional development.

For many years, IUP graduates have been wonderful teachers as well as leaders in mathematics education. In the next newsletter, we will report on some of the achievements of past graduates, but, in this issue, I would like to concentrate on some activities in which our recent graduates have participated. We are reaching a point when many teachers are retiring and young teachers will be taking their places. We can be proud that our recent graduates are actively involved in professional development and assuming leadership roles. What follows are glimpses of where they have been seen and what they have been doing.

Among the 18,000 people who attended the annual meeting of the NCTM in Washington, D.C. last spring were Amy Anderson ('94), Wayne Biernesser ('95), Kate Bigham ('96), Todd Myers ('94), and Dana Nichols ('94). Believe it or not, we all found each other! It is wonderful to see graduates of our IUP Mathematics Education program attending conferences.

The methods class of Spring 1992 takes the prize for participation. Caren Glowa, Jennifer Hagyar, Mark Karpinski, Greg Kaylor, Jim Preston, and Jeff Schmook have all been seen at conferences or regional meetings for mathematics educators. Jeff has been on the PCTM Executive Board, edits the Mathematics Council of Western Pennsylvania (MCWP) newsletter, and has presented at local and state conferences. Jim is a teaching associate for IUP's SEQual (Statistics Education through Quantitative Literacy) program. Jen and Jeff are chairpersons of mathematics departments. Marlena Herman, who was also in that methods class, is pursuing her Ph.D. in Mathematics Education at Ohio State. I hereby challenge other classes to get as involved as that class has.

Others seen at meetings have been Lisa Ceraso ('95), Lynnann Peluso Charnego ('93), John Diehl ('93), Nicole DeCroo Fello ('93), Rhonda Fedyk ('95), Loretta Fouse ('93), Susie Geist Krause ('96), Becki Keagle ('96) and Michelle Lepionka ('95). Please forgive me if I have omitted anyone and send me a note so that I may include the information in our next newsletter.

(Continued on page 6)

Glimpses of Math Ed Graduates, continued from page 5)

Rhonda, Jim, and Jeff have all helped mentor pre-student or student teachers. We are always in need of more cooperating teachers; if you teach within 60-70 miles of IUP and would like to assist, please let us know. Many of you have sent letters or materials that we have put to use in methods classes. Eric Reid ('94) sent an inspirational videotape. Chris Konkus ('97) and Susie have written letters detailing their experiences and offering advice to future teachers. All these contributions help strengthen our mathematics education program.

From October 13 to 15, 1999, The Northeastern Regional Meeting of NCTM will be held in Pittsburgh. The IUP Mathematics Department will sponsor a "reunion" for its graduates. We'll aim for late afternoon of the 14th and we hope you will be able to attend. You do not have to be teaching to come to the reunion. Some of you have found jobs in fields other than education or have chosen not to teach. You are all graduates of our program and we are always delighted to hear from you.

**Write to Us**

Send us your comments and suggestions on the newsletter or let us know what you are doing. You can write us at:

Department of Mathematics

Indiana University of Pennsylvania

233 Stright Hall

Indiana, PA 15705-1072

You cansend email to us at:

jburiok@grove.iup.edu

or