**
Master Teachers: Reaching Students and Teaching Faculty**

**Thomas Banchoff**

**Brown
University**

**Reaching Students in the Digital Age **

**Abstract:** Reaching students has always been a mark of teaching
effectiveness. How have things changed over the years and how does the Internet
make it possible to rise to new levels.

**Bio:** Dr. Thomas Banchoff received his BA from the
University of Notre Dame in 1960 and his Ph.D. in 1964 from the University of
California at Berkeley under the direction of Shiing-Shen Chern. He was a
Benjamin Peirce Instructor at Harvard from 1964 - 1966 and a Fulbright
post-doctorate fellow at the University of Amsterdam 1966 -1967 before his
appointment to the faculty at Brown University in 1967.

Dr. Banchoff’s numerous awards for teaching, include the 1995 NES/MAA Award for Distinguished College or University Teaching of Mathematics, the 1996 Deborah and Franklin Tepper Haimo Award for Distinguished College or University of Mathematics, and the 1998 RI Professor of the Year from the Carnegie Foundation for the Advancement of Teaching. Most recently, Dr. Banchoff received the 2004 Director’s Award for Distinguished Scholars from the National Science Foundation – he is one of eight to receive this award, the NSF’s highest honor for excellence in teaching and research.

Known for his pioneering research on the geometry of the fourth and higher dimensions, Dr. Banchoff is the author of more than eighty research articles and three books, Beyond the Third Dimension, Linear Algebra Through Geometry, and Cusps of Gauss Mappings, as well as a new introduction to Flatland. His 1978 film, "The Hypercube," won the Prix de la Recherche Fondementale at the Brussels Festival of Scientific and Technical Films. He is the founding editor of the electronic journal Communications in Visual Mathematics and past President of the Mathematical Association of America.

**Ezra Brown**

**Virginia
Polytechnic Institute and State University **

**The Many Names of (7,3,1)**

**Abstract:** (7,3,1) is a magical mathematical
object with connections to finite geometry, combinatorial designs, graph theory,
matrix algebra, number theory, abstract algebra, map coloring on the torus,
error-correcting codes, the octonion units, Klein's Quartic Curve, and the Seven
Hats Problem. The speaker promises not to talk about all of them. There will be
audience participation.

**Bio:** Ezra (Bud) Brown has degrees from Rice and
Louisiana State, and has been at Virginia Tech since 1969, where he is currently
Alumni Distinguished Professor of Mathematics. His research interests include
number theory and combinatorics, and he particularly enjoys discovering
connections between apparently unrelated areas of mathematics. He received
Virginia Tech's W. E. Wine Teaching Excellence Award in 1998 and his MAA MD-DC-VA
section's award for outstanding university teaching in 1999. He has received the
MAA's Polya (in 2000, 2001 and 2006) and Allendoerfer (in 2003) Awards for
noteworthy expository papers. He enjoys singing (everything from grand opera to
rock'n'roll), playing jazz piano, and working with students who are engaged in
research. He occasionally bakes biscuits for his students.

**Robert
Case
Northeastern University**

**Engines of Access: Toward a New Era of
Mathematics Achievement in Urban High Schools**

**Abstract:** The study of
advanced mathematics in high school is the central predictor of college success
(Adelman; 1999, 2006). Yet urban high school students have historically been
unable to access advanced mathematics. These schools have a high percentage of
minority, new immigrant, and low-income students. Fortunately, urban
schools are now poised for reform and renewal around this reality. But central
to the restructuring is the collaboration of colleges and universities. To do
this, colleges need to re-configure themselves as authentic agents of outreach.
This outreach includes the areas of curriculum, teacher preparation,
professional development, campus programming for high school students, AP
support, and building the bridge to college.

**Bio:** Robert Case is Professor
of Mathematics Education at Northeastern University. He received a PhD in
mathematics from Yeshiva University, where his doctoral dissertation in logic
was mentored by Martin Davis.

For the past twenty years he has been involved with equity in mathematics
education in the cities. He has had a SUMMA grant from the MAA, an NSF grant for
calculus reform outreach to the schools, and, most recently, a five-year Nellie
Mae Foundation grant to promote AP calculus success among minority students at
John O’Bryant High School in Boston. He has written about secondary school
mathematics in the United States, in India and in the Netherlands.

Robert Case has received the 2001 Northeastern University Outstanding Teacher of First Year Engineering Students Award, the 1986 Northeastern University Excellence in Teaching Award, the 1998 Northeastern Section of the 1999 MAA Distinguished Teaching Award, and the Haimo Award of the MAA.

**Carl Cowen **

**Indiana
University - Purdue University at Indianapolis **

**Challenging Your Students to Do Their Best **

**Abstract:** We all want our students to learn as much as
possible in our courses, and we're willing to help them do so. But how can we
help them? This presentation will address several of the pertinent issues
related to the question, including meeting the students where they are, raising
expectations, challenging yourself, and teaching for your students' futures.
Some of the ideas will be illustrated by mentioning some techniques that I've
used in my own teaching, especially teaching linear algebra.

**Bio:** Carl Cowen, a member of the IUPUI mathematics
faculty, is a native of Indiana, was educated at Hanover College, Indiana
University, Bloomington, University of Warwick (England), and received his PhD
in theoretical mathematics from the University of California, Berkeley. After
holding teaching positions in junior high school, small colleges, and a post
doctoral position at the University of Illinois at Urbana-Champaign, he was a
member of the mathematics faculty at Purdue University, West Lafayette, from
1978 to 2004. Cowen was Director of Purdue's Actuarial Science Program from 1992
to 1997 and was Head of Purdue's Mathematics Department from 1997 to 2002. He
served as Dean of the IUPUI School of Science from 2004 to 2006. Cowen was
honored for his success in teaching by the Purdue University School of Science,
the Indiana Section of the MAA in 1995, and received the MAA's Haimo Award for
Distinguished Teaching in 1997.

Professor Cowen's primary pedagogical interests have been in linear algebra, in the use of technology, and in the preparation of high school mathematics teachers. He has directed more than 30 undergraduate students in research, mostly on topics in linear algebra. In addition, he has supervised eleven PhD students and several post doctoral faculty. For many years, Cowen's primary research interests have been in operator theory and complex analysis, but in the past few years he has devoted some of his research and pedagogical attention to applications of mathematics to biology, especially to neuroscience. In addition to his academic work, Cowen has been involved in the governance of each of MAA, AMS, and SIAM, and is currently finishing his terms as Past President of the Mathematical Association of America and Past President of the recently organized SIGMAA on Mathematical and Computational Biology.

**Robert L. Devaney **

**Boston University
**

**Chaos in the Classroom **

**Abstract: **In this talk we will describe various ways that we bring
contemporary topics in mathematics (usually involving chaos or fractals) into
the introductory level calculus, differential equations, and even lower level
courses. The idea is to show students that mathematics is an alive and exciting
discipline. As a subtheme, all of the ideas will be presented using
spreadsheets. The advantage of this is that all of my students know how to use
spreadsheets already, so no time is wasted getting them up to speed to do their
labs on these subjects. Furthermore, spreadsheets are an ideal tool to animate
various graphical objects.

**Bio:** Robert L. Devaney is Professor of Mathematics at
Boston University. He received his BA from Holy Cross College in Worcester, MA
in 1969 and his PhD from the University of California at Berkeley in 1973 under
the direction of Stephen Smale. He taught at Northwestern University and Tufts
University before coming to Boston University in 1980.

Dr. Devaney is renown for his teaching and his research, and he has won numerous awards for his teaching and for his innovations in teaching mathematics. In 1994, he received the Award for Distinguished College/University Teaching of Mathematics from the Northeastern Section of the Mathematical Association of America. In 1995, he was the recipient of the Deborah and Franklin Tepper Haimo Award for Distinguished College/University Teaching. In 1996, he was awarded the Boston University Scholar/Teacher of the Year Award. In 2002, he received the National Science Foundation Director's Award for Distinguished Teaching Scholars. In 2002, he received the ICTCM Award for Excellence and Innovation with the Use of Technology in Collegiate Mathematics. In 2003, he was the recipient of Boston University's Metcalf Award for Teaching Excellence. In 2004, he was named the Carnegie/CASE Massachusetts Professor of the Year.

He is the author or co-author of several books on various aspects of dynamical systems theory. These include “An Introduction to Chaotic Dynamical Systems”, a text for advanced college students in mathematics, as well as researchers in this field. He has also produced the Mandelbrot Set Explorer, an online, interactive series of explorations designed to teach students at all levels about the mathematics behind the interesting images known as the Mandelbrot and Julia sets.

**Joseph
Gallian
University of Minnesota Duluth**

**Section NExT:** Communicating
Mathematics

In this presentation I will offer my advice on how to present your mathematics orally and in writing. Topics pertaining to oral presentations include preparation, content and delivery. Topics pertaining to writing include the title, an abstract, the introduction, the body, joint authorship, acknowledgements, and where to submit your work.

**Workshop: **Research by
Undergraduates is Hot!

**Abstract:** Although involving
undergraduates in research has been a long standing practice in the experimental
sciences, it has only been recently that undergraduates have been involved in
research in mathematics in significant numbers. In this talk I will discuss in
general terms such things as the reasons for this dramatic growth, how to get
started in involving undergraduates in research, the benefits of undergraduate
research to faculty and students, and how to find suitable research problems.

**Bio:** Joe Gallian received a
Ph. D. from Notre Dame in 1971. He has been at the University of Minnesota
Duluth since 1972 where he is a Morse Alumni Distinguished University Professor
of Teaching. Among his honors are the MAA's Haimo Award for distinguished
teaching, the MAA Allendoerfer and Evans awards for exposition, an MAA Polya
Lecturer, a term as MAA Second Vice President, co-director of the MAA's Project
NExT, associate editor of the American Mathematical Monthly and the Mathematics
Magazine, advisory board member for Math Horizons, and the Carnegie Foundation
for the Advancement of Teaching Minnesota Professor of the Year in 2003.

Since 1977 over 130 research papers written under his supervision by undergraduates in his summer research program have been published in mainstream journals. He has given more than 250 invited lectures at conferences and colleges and universities and is the author of more than 100 articles, the book "Contemporary Abstract Algebra" (6th edition) and coauthor of the book "For All Practical Purposes" (7th edition). His research interests include groups, graphs and combinatorics.

Besides the usual math courses, he has taught a Humanities course called the "The Lives and Music of the Beatles" for more than 25 years and a liberal arts course on math and sports. In 2000 a Duluth newspaper cited him as one of the "100 Great Duluthians of the 20th Century."

**Thomas Garrity **

**Williams
College**

*Christie Lecture: *Using Mathematical Maturity to Shape Our
Courses, Our Curriculums and Our Careers

**Abstract:** For the last years, I've been in charge of
mentoring new Williams faculty, from in all departments. I've been surprised to
learn that no other discipline that I know of has a term analogous to our
"mathematical maturity". This talk will discuss how we can build on the rhetoric
of mathematical maturity to shape not only our teaching and research careers but
also the workings of our departments.

**Bio**: Thomas Garrity was an undergraduate at the
University of Texas in Austin, a graduate student at Brown and a post-doc at
Rice. He then joined the faculty of Williams in 1989, where his has been ever
since, save for sabbaticals spent at the University of Washington in Seattle and
the University of Michigan in Ann Arbor. Currently at Williams, he is the
William R. Kenan Jr. Professor of Mathematics, department chair and the director
of the Williams College Project for Effective Teaching (Project PET). His
research has been in algebraic geometry, differential geometry and, more
recently, number theory. He is the author of *All the Mathematics You Missed
[But Need to Know for Graduate School]* and appears, against Colin Adams, in
the MAA DVD *The Great Debate: Which is the Better Number?*, moderated by
Edward Burger. Among his honors is the 2004 Deborah and Franklin Tepper Haimo
Award for Distinguished College or University of Mathematics.

**Kenneth I. Gross
University of Vermont**

**Symmetry -
Some Personal Reflections**

**Abstract: **We will explore the concepts of symmetry
and invariance in an expository style suitable for undergraduates, K-12
teachers, college and university mathematics faculty, and even
non-mathematicians who are willing to practice inner tranquility when a formula
comes up now and then. Starting with a potpourri of examples of symmetry in
nature, art, architecture, poetry, and science, we will discuss rotational
symmetry from its historical ori-gins in astronomy to the modern mathematical
point of view, and the way in which symmetry considerations enter into present
day cosmological speculation.

**Workshop**:
Elementary School Teachers as Mathematicians

** Question**: Why should college
or university mathematics faculty care about the teaching and learning of
mathematics in the elementary grades?

* Commentary*: There is nothing
“elementary” about the mathematics taught in the elementary grades. Fluency in
arithmetic is the gatekeeper for success in higher mathematics. In essence, the
elementary teacher has as much, or more, to do with the student’s success in
college or university mathematics courses as the instructors in those courses.

* Question*: Why might a
mathematician consider becoming involved in the teaching and learning of
mathematics in the elementary grades?

* Commentary*: The principle
“one can not teach what one does not know” is nearly as secure as a law of
nature. Yet, since the appearance of the NCTM “Standards” in 1989, we have
required elementary teachers to teach mathematics that they do not know at a
level of depth to which they had never been exposed in their own education.
Mathematicians, in collaboration with educators, can help close the gap between
the insufficient mathematics training of elementary teachers and the demands of
the contemporary K-6 mathematics classroom. The content of this workshop is
based on a program, the Vermont Mathematics Initiative (VMI) that has succeeded
in doing so.

* About the mini-workshop:* The
VMI, established in 1999, is founded on the belief that mathematics knowledge is
prerequisite to enhanced pedagogy and higher student achievement. In this
workshop we will first review the VMI design, curriculum, and outcomes. Then, in
a participatory fashion, we will explore strategies for transforming elementary
teachers – many of whom are ill-prepared in and fearful of mathematics, and do
not find teaching mathematics a pleasant experience – into mathematicians who
are enthusiastic about teaching mathematics. Along the way, we will discuss
implications for teaching mathematics to college students in general.

**Bio**: Kenneth I. Gross is a
distinguished mathematician who has had a profound impact on mathematics,
education, and the lives of his students. Ken’s teaching and mentoring have been
inspirational for all levels of students, from high school students, to entry
level college students, undergraduate mathematics majors and graduate students
who are now accomplished mathematicians, elementary and middle school teachers,
and adult learners who desire to further their education. Ken is the 2007
recipient of the NES/MAA Award for Distinguished College or University Teaching
of Mathematics. He has also received the Chauvenet Prize and the Lester R. Ford
Prize from the MAA.

As a mathematician, Ken’s research in the areas of Lie groups, representation theory, and harmonic analysis was supported by the National Science Foundation for over three decades before his interests turned to the mathematics training of teachers. In 1993, Ken and a high school teacher co-founded a residential summer enrichment program for talented Vermont high school students that is still thriving today as the Vermont “Governor’s Institute in the Mathematical Sciences.” In 1999, Ken founded the Vermont Mathematics Initiative (VMI), is a statewide master’s degree granting program that trains K-8 teachers across the state of Vermont to serve as mathematics leaders in their schools and districts. Other programs modeled on VMI and utilizing VMI designed materials have been introduced in Arkansas, Massachusetts, Nebraska, and New Mexico.

Ken is currently Professor of Mathematics and Education at the University of Vermont, where he has received the university’s highest awards in both research and teaching.

**P. Joseph
McKenna**

**University of
Connecticut**

**Workshop: **Out of The Mouths Of
Babes And Sucklings: What We Learned From Third Semester Calculus Students

**Abstract:** For the last several
years, Fabiana Cardetti and I have been teaching a quasi-experimental writing
course at University of Connecticut, in which a small self-selected group or
third-semester calculus students write a weekly journal reflecting on their
experiences in their respective sections. The topics of the week vary and can
range from simple things like preparing for exams to more mathematical thought
problems. I will discuss some of what we learned over several semesters. At the
end, we can brainstorm for other suitable weekly topics.

**Bio:** Joe McKenna was born in
Dublin in 1948 and did his undergraduate work in University College, Dublin. He
then completed his Ph.D. under Lamberto Cesari at the University of Michigan.
His research is mainly in nonlinear partial and ordinary differential equations
and especially their periodic solutions. Much of his recent work concerns large
nonlinear oscillations in suspension bridges. This has been covered in many
science magazines such as Discover, Science News, Inventions and Technology as
well as several undergraduate textbooks on differential equations. He described
some of this in a Monthly article in 1999, for which he received the Lester Ford
Prize at Mathfest 2000. Having previously worked in the Universities of Wyoming
and Florida and University College, Cork, he is currently Professor of
Mathematics at the University of Connecticut. He is the winner of the 2004 NES/MAA
Award for Distinguished College or University Teaching of Mathematics. He
is identified by the Science Citation Index as a highly cited researcher in
mathematics, at www.isihighlycited.com.
He was also quoted in William Safire's weekly column on language in the New York
Times magazine.

**Frank Morgan**

**
Williams College **

**Workshop:** The Soap Bubble Geometry Contest

**Abstract:** In response to the concern that teaching
often provides the answers before students have the questions, I decided to
prepare a talk in the form of a guessing contest in which students had to face
the questions before seeing the demonstrations and explanations. Each question
about soap bubbles was designed to get at some important geometric idea, and the
soap bubble demonstrations add to the fun. But I won't just talk about it: I'll
do it for you today. The show starts with some math news, including some
advances by undergraduates.

**
Bio:** Frank Morgan
studies optimal shapes and minimal surfaces. He has published over 100 articles
and six books, including "Calculus Lite" and "The
Math Chat Book," based on his live, call-in TV show and column. His teaching
awards include the Baker Award at MIT, the 1992 MAA Northeastern Section Award
Distinguished College or University Teaching of Mathematics, and the 1993
Deborah and Franklin Tepper Haimo Award for Distinguished College or University
of Mathematics. Founder of the NSF "SMALL" Undergraduate Research Project, he is
Atwell Professor of Mathematics at Williams College.

**Student Panel Discussion:**
What
Can I Do With A Mathematics Major?

**Abstract:** Mathematics is
fun and intellectually stimulating to study. Studying mathematics helps one
to develop skills that will be beneficial in the workplace. Join area college
graduates and college students for a panel discussion of the benefits of a mathematics
major workplace.

**Student Panel Discussion:**
I am the Teacher Now: Advice to Future Teachers

**Abstract:** Are you
planning to be a teacher? Are there any courses beyond those required for
your degree that you should consider taking? Are there things that you can
do now to help you to feel more prepared and more confident when you begin
teaching? Join area teachers as they share their advice to future
teachers. Find out what it is like to be the teacher from those who are teaching for the first time as well benefit from lessons
learned by those who have been teaching for several years.

NES/MAA Fall 2007 Meeting Page| Northeastern Section NeXT | NES/MAA Home Page | MAA Home Page | S. L. Mabrouk's Home Page

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This page was last modified on Sunday, September 23, 2007. |