Ed Dubinsky, Georgia State University

Title:  Meaning and Formalism in Mathematics

A question that is important in the philosophy of mathematics and mathematics education is, What is the source of mathematical ideas, of meaning, in the mind of an individual?   It is surely the case that this question does not have a single answer applicable to all mathematics and all people, so it is unsurprising and appropriate that many answers have been proposed.  One possible source that may not have been given sufficient attention is formalism in the sense of expressing mathematical concepts in a formal language.

In this talk, after discussing briefly some sources of mathematical ideas that have been considered in mathematics education such as direct physical experiences, metaphors, analogies, and intuition, I will consider two ways in which formalism can relate to mathematical meaning.  One way is to capture an idea, perhaps held vaguely and intuitively and then use formal analyses to make it more precise and to investigate its properties.  An even less considered use of formalism is to begin the development of an idea from its formal expression and to use the syntax to construct  meaning for the concept.

Both of these uses of formalism are skills that mathematicians generally possess and students need to learn.  Although this is a major responsibility of mathematics education, it is not one which we are very successful at for more than a very small percentage of students.  A major point of the talk is to describe some pedagogical approaches that can help students develop these skills so as to incorporate formalism as a powerful tool in understanding difficult mathematical concepts.
 
Biographical Information:

Ed Dubinsky received his B.S. from Temple University, his M.A. from the University of Pennsylvania, and his Ph.D. from the University of Michigan.  He was an Associate Professor at Tulane University and a Professor at Clarkson University and Purdue University before becoming a Professor at Georgia State University.  He was a Visiting Professor at the Polish Academy of Sciences in Warsaw, the University of Bonn in West Germany, the University of California at Berkeley, and the University of New Hampshire.  In addition, he was a Research Associate at McMaster University and a Visiting Scientist at the Education Development Center.  Dr. Dubinsky received the award as Outstanding Undergraduate Teacher and the Charles B. Murphy Award for Outstanding Teaching from Purdue University.  He has published numerous articles in Mathematics, Mathematics Education, and Computer Science journals.  He has written eight books and given more than 120 invited lectures and conference presentations since 1984.  His current professional interests include development of instructional materials for Post-Secondary Mathematics courses and development of new approaches for teaching Calculus and Abstract Algebra.

Robert Case and Carla Oblas, Northeastern University

Title: "Interactive Learning"

This session is intended to explore the issues of student-active mathematics learning which  arise from using group problem-solving as the principal strategy.

Biographical Information:

Bob Case was chairmen of the Department of Mathematics at St. Anselm College from 1967 to 1970.  In the seventies, he developed and taught graduate courses in logic at Northeastern University where he is an Associate Professor of Mathematics.  In the eighties, he was involved in Calculus reform and in the nineties, he is working with high school teachers in Boston where state-of-the-art Calculus courses have begun in five schools which previously offered no Calculus whatsoever.  Dr. Case is the 1998 Distinguished Teaching Award winner for the Northeastern Section and the winner of the 1998 National Distinguished Teaching Award  for the MAA.

Carla Oblas is Assistant Professor of Mathematical Practices at Northeastern University, and a coordinator of the Interactive Mathematics Program for New England.
 

Kathy Bavelas, Manchester Community Technical College (CT) 
 
Title:  How I (Almost) Became a Multimillionaire or Why Didn’t I Really Learn Those Elementary Functions

This workshop will ask participants to play the role of students in a pre-calculus course or a calculus I course ( the review of elementary functions at the beginning of the course).  Students (in a group setting) will try to outfox the crotchety old lady and take her for her millions.  The little old lady, however, was a mathematics teacher before retiring, so getting her millions won't be easy.  Please bring your graphing calculators. After role playing the activity, we will discuss various possible extensions and how, if students had applied of the Rule of Four as well as good problem-solving strategies, all groups could have become millionaires.

Biographical Information:
 
Kathy Bavelas received her BA from University of Connecticut, her MS from Central Connecticut State University, and her M.A.L.S. from Wesleyan University.  Her recent honors include  Who's Who In American Education, Who's Who Among of America's Teachers (1998), Distinguished Professor in Residence at the CT Academy for Education in Mathematics, Science, and Technology, CT Academy for Education Fellow, MCTC Teaching Excellence and Distinguished Service Award, PIMMS (Project to Increase Mastery in Mathematics and Science) Fellow and the 1995 MCTC Women's Leadership Award.  She has served as secretary, vice-president, president, and past president for the Mathematics Association of Two Year Colleges in Connecticut.  She is active in the NES-MAA, serving as the two year college representative, being a member of the program committee for the Fall 1997 Section meeting and the Spring  1998 Section meeting.  For the past 6 years, she has spent her summers writing and providing professional development for the field test teachers for Math Connections, A Secondary Core Curriculum Project which is now being published by Its About Time.

Robert L.  Devaney, Boston University

Title:  Chaos, Fractals, and the Internet
 

We will describe some of the "chaos games" and "fractal movies" that we use with students from sixth grade through graduate school.  The  goal of the games and movies is to help students understand the geometry of affine transformations.  We will also describe some of the related tools available over the Internet.
 

Biographical Information:

Professor Robert L. Devaney received his BA from Holy Cross College and his PhD from the University of California, Berkeley.  He taught at Northwestern, Tufts, and the University of Maryland before coming to Boston University in 1980.  His research area is Dynamical Systems.  He is also director of the NSF sponsored Dynamical Systems and Technology Project at BU.

Jerry Johnson, University of Nevada, Reno
 
Title:   Mathematics Across the Curriculum

Mathematics Across the Curriculum is an NSF-funded program  (DUE 9354652) whose aim is to improve the quantitative literacy of students and promote their appreciation of mathematics by integrating quantitative components into a variety of courses in the university curriculum. It was conceived at the University of Nevada, Reno along the lines of a successful "Writing Across the Curriculum" model.

Our goal is to enhance the quantitative content of courses where it exists and introduce it where it does not, thereby increasing students' exposure to applications of mathematics in a variety of courses and making quantitative learning a shared responsibility across campus.

In particular we will describe quantitative components we have implemented in political science, humanities, anthropology, psychology, and art, among others. We will also discuss a mathematics competency testing program for economics, nursing, and the natural sciences. We are currently moving some of this testing to a web-based format.

A Math Across the Curriculum web site has been established that allows users to get detailed information and to download documents and resources. The URL is http://www.math.unr.edu/MAC
 
Biographical Information:

Jerry Johnson received his B.S. from Oklahoma State University and his M.S. and Ph.D. from the University of Illinois, Urbana.  He was an Full Professor at Oklahoma State University and a Visiting Professor at Penn State University before joining the faculty at the University of Nevada, Reno as a Professor and the Director of the Mathematics Center in 1993. He has been Chair of the Department of Mathematics and Director of the Mathematics Center since 1995.  He has presented numerous conference papers and colloquium talks.  Dr Johnson has published more than seventeen papers in refereed Mathematics journals, and he has more than twenty-four publications related to Mathematics Education.
 

 Murray Eisenberg, University of Massachusetts, Amherst

Title:  Active Learning---High-Tech and Low, in-class and out
 

"Active learning" connotes a variety of instructional strategies and techniques that may be used in place of, or in addition to, conventional lectures. We present a number of examples of active learning approaches and activities from freshman and sophomore calculus, linear algebra, and differential equations. These range from out-of-class multi-week projects that involve computer programming to brief individual or shared problem-solving exercises during class that use nothing other than paper and pencil.  The discussion will touch upon rationales for such activities as well as related issues of educational goals, consonance of active learning with instructor's attitudes and experience, and the ideal classroom/lab physical environment. Our evaluation of these activities' effectiveness has been largely informal, owing primarily to small class sizes, and so the presentation will include anecdotal evidence of the impact the activities have had on students and instructor alike. There will be opportunity for interchange with the audience.

Biographical Information:

Murray Eisenberg is Professor of Mathematics and Statistics at the University of Massachusetts, Amherst, where he has taught since 1965.  His principal mathematical interest is the topology of dynamical systems. He has published articles on topological dynamics, topology, the APL and J programming languages, and the use of computing in teaching math. He has made conference presentations about and conducted workshops on the Mathematica software package. He is the author of three undergraduate texts: "Axiomatic Theory of Sets and Classes", "Topology", and "The Mathematical Method".  Murray has been using computers to teach mathematics for over twenty years. He has been an implementer of Wattenberg's "Calculus in a Real and Complex World" reform curriculum and its sophomore sequel on multivariate calculus, linear algebra, and differential equations. Recently he has been a participant in a multi-institution project to bring active learning to introductory college science and math courses.

Sandy Rhoades, Keene State College

Title: Waking Them Up: Three Tried and True Ways to Spice Up a Lecture

 In this interactive session, participants will be introduced to three techniques commonly used to get students involved during a lecture.  Participants will leave the session prepared to test out these techniques in their own classrooms.

Biographical Information:

In addition to a Ph.D. in mathematics from the University of Massachusetts at Amherst, Sandy Rhoades has an M.Ed. in counseling and human development from St. Lawrence University. Her way of melding these seemingly disparate interests in mathematics and learning and growth is to create ways to draw people into learning mathematics. Sandy spent three years teaching at Smith College in Massachusetts before beginning a position at Keene State College in New Hampshire in the fall of 1996. She has facilitated a variety of workshops and special  sessions on active learning.

 George Markowsky, University of Maine

Title:   The Not-So Golden Ratio

The golden ratio, also called the golden section or the golden number, has captured the popular imagination and is discussed in many books and articles. Generally, its mathematical properties are correctly stated, but much of what is presented about it in art, architecture, literature, and  esthetics is false or seriously misleading. Unfortunately, these statements about the golden ratio have achieved the status of common knowledge and are widely repeated. Even current high school geometry textbooks make many incorrect statements about the golden ratio. This talk discusses some of the most commonly repeated misconceptions and sets the record straight.

Biographical Information:

George Markowsky received his BA in mathematics from Columbia University and his MA and Ph.D. in mathematics from Harvard University. From 1974 to 1984 he worked at IBM's Thomas J. Watson Research Center. Since 1984 he has been at the University of Maine and is currently the Chair of the Computer Science Department. His primary mathematical interests are lattice theory, discrete mathematics and the applications of computers to mathematical problems. He became interested in the golden ratio as a result of preparing a talk on the subject for the  Classics Club at the University of Maine.
 

STUDENT POSTER SESSION AT THE SPRING 1999 MAA/NES MEETING
 

The Northeastern Section is sponsoring a poster session for students at its Spring Meeting at Colby College, June 11-12, 1999.  Students will display their solutions to the problems of the 1999 Mathematical Contest in Modeling (MCM), sponsored by COMAP. In the MCM format, all of the student work takes place over a four-day weekend in February; this year's competition was February 5-8, 1999.   During that time, each team of three students chooses one of two problems, develops a mathematical model for the problem, and produces a solution paper which is submitted for judging. This year Problem A involved assessing the effects of an asteroid hitting the Earth, and Problem B involved establishing the maximum/lawful capacity for various kinds of rooms and facilities.  In addition, this year a new Interdisciplinary Problem in Mathematics, Chemistry, Environmental Science, and Environmental Engineering  (Problem C) was introduced.  In this year's  problem on ground pollution, teams accessed through the web a data base for an actual pollution problem and then developed an appropriate model. Teams had to choose the Problem C option ahead of time.

The poster session is designed as a presentation, not a competition. For those students who participated in this year's MCM competition, this session will provide the opportunity to see solutions from other teams and to discuss their solutions with other participants and perhaps some judges or practitioners. Students from schools that do not participate in the competition are also welcome to submit posters.

For a more detailed announcement of the poster session, including guidelines for submission of a poster and registering, click here.

To register for the poster session or to ask questions about the session, please contact Ross Gingrich at 203-392-5581, or at gingrich@scsu.ctstateu.edu, or at Mathematics Department, Southern Connecticut State University, New Haven CT 06515.