Acknowledgement: The University of Arizona Mathematics
Department thanks the Southwest Regional Institute in the Mathematical
Sciences for the production and use of this manual.
Welcome to the Southwest Regional Institute in the Mathematical Sciences! The Southwest RIMS, established in 1994, is currently sponsoring projects at Northern Arizona University, the University of Arizona, and Utah State University. Together, the mathematics departments at these universities share a common belief that the distance that has developed between teaching and research is artificial, and with the right leadership this great distance can be successfully closed.
Historically, the great diversity in teaching and research responsibilities of the mathematics community has led to fragmentation and poor communication among the many ongoing activities. The glaring separation between research and teaching is evident at institutions worldwide, where traditional "publish or perish" philosophies have greatly exacerbated the divide. This separation is a major roadblock to the desire to communicate the beauty and utility of mathematics to the entire community. The Southwest RIMS plans to consolidate and significantly enhance existing structures, support a new initiative towards the integration of research and teaching in the mathematical sciences, and facilitate the expansion of established core activities into a full scale regional institute in the mathematical sciences with many more universities involved.
The goal of the Southwest RIMS is to expose students of all ages to mathematics as practiced by professionals and to empower them with a feeling that useful information can be gleaned from the simplest of models. Interacting with these professionals, seeing their lifestyles and work habits, becoming involved with the same problems, will yield a much more accurate picture of careers in the mathematical sciences and the rewards, both intellectual and financial, that they bring. It is also necessary to involve instructors of the mathematical sciences in this adventure because it is they who will transmit the excitement and importance of mathematics and science on a day-to-day basis. They, too, must feel comfortable in using quantitative analysis to address real world challenges.
The infrastructure for supporting these educational experiences is already in place at all levels of teaching and research at the universities that are a part of the Southwest RIMS. The many educational activities spawned by dedicated individuals or small groups within the mathematics departments over the years is testimony to our awareness of the seriousness of the educational problem nationwide and exemplify our dedication and our experience in addressing this challenge. The Southwest RIMS and The University of Arizona Department of Mathematics have written this catalog (this catalog represents the first installment of our efforts to describe the outreach activities throughout the region) listing educational activities sponsored by the University of Arizona which encourage students, minorities and native peoples, women, parents, mathematics teachers of all levels, and professionals in the community to recognize the importance of mathematics in society.
Communication is the key to education. The Southwest RIMS hopes that by reaching out to the community and working together we will teach all of our children to become mathematically literate. This is a task that requires not only a rethinking of what it is that we teach, but also how it is that we present the material. With this last thought in mind, I am reminded of a saying that my mother was fond of: "Hablando se entiende la gente" - By speaking, we make ourselves understood.
We, in the mathematics community, study the most fascinating of subjects. It is we who should take a leadership role in communicating this fascination to the community. We can. Listen to my mother.
This catalog, A Tour of Outreach Activities in the Department of Mathematics at the University of Arizona, has been written and compiled for mathematics teachers of all levels who are interested in programs designed to improve the communication of mathematics to students of all ages. This catalog represents the current activities that are being sponsored by the University of Arizona Department of Mathematics. In looking over these activities, the reader will be struck by the fact that these efforts are being addressed to students at many educational levels.
The entries are arranged alphabetically with the program sponsors'/administrators' names and phone numbers at the beginning of each entry. In addition to the description of each program, we have tried to include information about how to start a similar program. These descriptions entail what to do, who to contact, program expenses, and budget details. If you have any questions about any of the programs please contact the person(s) listed. Two appendices have also been provided detailing the mathematical software the University of Arizona Department of Mathematics has written and how to obtain it.
Please note that on March 19, 1995 the Tucson area code will be changed from 602 to 520. The 520 area code has been listed in the catalog for your convenience.
The Coalition to Increase Minority Degrees
Undergraduate Peer Study Groups (1987 - 1994)
Faculty-Directed Individual and Group Research Projects
(1992 - 1994)
David Lomen, professor, (520) 621-6868,
lomen@math.arizona.edu
William Yslas Velez, professor, (520) 621-2259,
velez@math.arizona.edu
The Coalition to Increase Minority Degrees (The CIMD) is an alliance of over 75 institutions of higher education, corporations, government laboratories, educational organizations, and foundations throughout Arizona, New Mexico and Western Texas, Colorado, and Utah. The CIMD has received a $5 million five year cooperative agreement from the National Science Foundation (NSF) to increase the number of underrepresented minority students who receive baccalaureate and doctorate degrees in mathematics, the sciences, and engineering. A significant amount of the NSF funding will be distributed to faculty members, other appropriate professionals, and their students to lead and participate in:
All faculty members at The CIMD institutions in fields under NSF's jurisdiction or other appropriate scientists, administrators or research staff at The CIMD institutions or organizations are eligible to apply for funding of a project satisfying the goals of The CIMD. Funding may be sought to start a new project, or to expand an existing one. There is no limit, per se, on how many applications any one institution or individual can submit during a semester.
For more information on CIMD contact:
CIMD has provided Dr. Velez with the funds to be able to hire student help to aid him in his efforts to bring in more minority students to the study of mathematics based careers. He began his program of advising around 1987. He contacted all of the minority students who were enrolled in first semester calculus. There were fewer than twenty such students at the time. Since there were so few students, Dr. Velez was able to interact with them on a weekly basis. Over the years the number of minority students has increased and it has become impossible to spend a weekly hour with each student advisee. With the number of minority students enrolled in the three semester course in calculus numbering about 200 students, Dr. Velez has had to change his tactics.
The contact Dr. Velez has with the students he advises has now become very focused. He attempts to contact minority students early in the semester, preferably before the semester begins. He uses CIMD funds to hire a student to do the phone contacts for him. After appointments have been made, Dr. Velez spends approximately 15 minutes with each student advisee. During this short period of time, he goes over the student's schedule, asks about their career plans, talks to them about the importance of calculus, and encourages them to join minority student scientific organizations. If the student has not declared a major yet, Dr.Velez suggests that she/he become a mathematics major. This is done for several reasons. Students without an advisor can get lost. Because records of mathematics majors are forwarded to the academic advisors, Dr. Velez as the students' advisor will make every effort to open up career opportunities for them. Part of this process is having the students explore their interests. Although many of these undecided students change their major after a semester or two, at least they have taken more mathematics than the average student.
At present, Dr. Velez is the advisor of about 30 minority mathematics majors. Six of his advisees graduated with baccalaureate degrees during the 1993-1994 academic year and eight more plan to graduate in 1994-1995.
CIMD has provided Dr. Lomen with funds so that he may conduct Faculty- Directed Individual and Group Research Projects. He has worked with fourteen minority undergraduate students on various research projects ranging from developing laboratory experiments to enhance calculus courses to creating a mathematical model concerning blood and oxygen transport in the circulation system.
Dr. Lomen's goal when supervising CIMD Faculty-Directed Individual and Group Research Projects is to join with the students in the excitement and satisfaction that comes from making new discoveries. He believes that the crucial thing in directing student research projects is to find a research topic of interest to the student, and then provide the proper mix of additional mathematical background, guidance, and encouragement so each student is able to progress on his or her own. It is as a student discovers new insights or mathematical properties that they obtain some insight into graduate school. If a creative student gets a taste of the thrill and satisfaction of discovery, there is a better chance of that student taking his or her mathematical education beyond a bachelor's degree.
One such research project involved working with three students on developing explanations for several experiments using the IBM Personal Science Laboratory. These students conducted their own experiments (involving motion, temperature, light intensity, and pH), collected data using the IBM Personal Science Laboratory equipment, and analyzed their data using the University of Arizona Department of Mathematics "electronic classroom." By the end of the semester, the students developed (for each specific experiment) a "Fact Sheet" containing: what mathematical idea is illustrated by the experiment, at what point in the syllabus the experiment is appropriate, what equipment is needed to perform the experiment, a step by step list of how to perform the experiment, a handout containing specific mathematical questions for students to answer concerning this experiment. These "Fact Sheets" were later distributed to other faculty members interested in integrating technology into the classroom.
Dr. Lomen has served as an advisor and a mentor to the students he works with. Having students work on mathematical research projects under the direction of a faculty member is an enormous help in encouraging them to continue their education in graduate school. In accordance with the CIMD's philosophy, Dr.Lomen made arrangements for the students to meet with the University of Arizona Department of Mathematics Graduate Committee Chairman so that they could learn and ask questions about what graduate school in mathematics entails, how to fill out applications, what information to include in a personal statement, and when to apply.
Carnaval Matemático
(summers of 1992 and 1993)
Marta Civil, professor, (520) 621-6873,
civil@math.arizona.edu
Carnaval Matemático took place in the summers of 1992 and 1993.
There were four sessions each summer, each a week long, with about
32 participants per session. The first summer, the sessions took place
at the Tucson Children's Museum.
The following summer, they took place at the Tucson Public Library.
Carnaval Matemático was a program for ethnic minority middle school
students that has as primary goal to engage the participants in
hands-on mathematics activities in geometry, probability, logic,
measurement, statistics, computers, and problem solving. The program
emphasized group work and areas of mathematics that are often neglected
in the regular school year.
This program was directed by Marta
Civil, David Gay, and David Lovelock, from the Mathematics Department
at The University of Arizona. The carnivals were in cooperation with
Tucson Unified School District (TUSD) and Sunnyside School District.
Funds for this program were provided by a grant under the Eisenhower
Mathematics and Science Education Act (administered by the Arizona Board of
Regents in cooperation with the Arizona Minority Education Access and
Achievement Cooperative).
David O. Lomen, professor, (520) 621-6868,
lomen@math.arizona.edu
The University of Arizona Department of Mathematics offers a National
Science Foundation sponsored faculty enhancement program directed at
the thoughtful introduction of modern technology into the
undergraduate mathematics classroom using the University of Arizona's
free software (for a complete listing see Appendix A). The program
deals primarily with college algebra, trigonometry, calculus, vector
calculus, ordinary differential equations, linear algebra, graph
theory, and finite mathematics.
Over the past few years, with the aid of other faculty
members and students, Drs. Lomen and Lovelock have been creating
commercial level educational software for use in and out of the
classroom. This software has been designed and tested to have a
specific educational impact. It can be used by instructors for
classroom demonstrations as well as by students for the exploration
of and the solving of mathematical problems.
Rather than create one massive comprehensive package, it was
decided to write "small packages." Each package is designed to do
one thing very well, and to be used with little or minimal training.
In general, these programs require 640K and a CGA graphics card.
They are all self-documenting, have "pull down" menus and context
sensitive help. One of the software packages is an English to
Spanish mathematics dictionary that was created jointly with Pima
Community College, Tucson, AZ.
All the software created can be freely copied without fear of
legal reprisals. Each package contains the following statement:
"This program may be freely distributed by any means, including
bulletin boards, provided that there is no fee or charge or
consideration of any kind which is in excess of $8. However, we
retain all the rights to this program." We encourage anyone to make
copies of the software via the World Wide Web, the NSFnet, or by
writing to:
"Enhancing Mathematics Education Using Technology" workshops
were developed in view of the fact that it takes planning and
practice to use the software effectively. Approximately eight
workshops are offered each year which are aimed at teachers (college
and high school) that are using or are planning to use the
mathematical software in their classes. These workshops are held at
national mathematics meetings, the University of Arizona, and other
universities in the United States and Mexico.
These workshops consist of two components:
The University of Arizona Mathematical Software and the
Enhancing Mathematics Education Using Technology workshops are
on-going projects that have received funding from:
Making Everybody Count (1992 - 1996)
Transforming the Middle School Mathematics Curriculum
"Making Everybody Count" is a current program designed to
enable well- prepared middle school mathematics teachers from the
state of Arizona to develop new pedagogical competence and leadership
abilities. The main focus of Making Everybody Count: Transforming
the Middle School Mathematics Classroom is reflected in its title.
This venture involves University of Arizona faculty helping middle
school teachers with innovative ideas of how to use problem solving
and technology in their teaching; the teachers' principals also
become involved and provide support for the participants; the
teachers encourage students and parents to become actively involved
in learning mathematics; and the community supports the idea that
mathematics and other science fields should be open to all groups,
including women and minorities. Making Everybody Count is a sequel
program to Making Math Count.
Making Everybody Count has funding for three years from NSF.
For each of the three years, a different group of thirty middle
school mathematics teachers from throughout Arizona will spend four
weeks one year, and two weeks the next year, at a summer institute
learning methods for getting their students to become actively
involved in solving problems, using computers in doing mathematics,
and connecting mathematics with its uses and with success in future
careers. Participants receive a total of six graduate credits for
their work. The institute is designed to provide the participants
with an array of tools to improve their students' competence,
confidence, and interest in mathematics. An emphasis is placed on
how to encourage minorities and women in developing their mathematics
skills as these are traditionally underrepresented groups in the
sciences and engineering. The Making Everybody Count institute makes
extensive use of materials developed by the EQUALS project of the
Lawrence Hall of Science, University of California at Berkeley.
A year long series of activities follows the first summer
Institute in order to support the implementation of Institute
techniques and materials in the classroom and broaden the impact of
the program in participants' schools and districts. During the
academic year, each participant will attend regional meetings with
project staff, visit other participants' classrooms, make inservice
presentations, and write articles for the project newsletter.
The project will also involve participants' principals in the
Institute. This will help to maximize the impact of the project not
only by providing additional support to participants during the
implementation year but also by creating a mechanism which will
amplify the momentum for change begun by the project.
In administering these programs, the University of Arizona
Department of Mathematics teamed up with the University of Arizona
Women's Studies Program. Women's Studies has been active in the
projects through their interest in increasing the participation of
women in mathematics and science related fields. Everyone involved
in the administration of the programs felt that equity issues should
be addressed in the programs as teachers needed to pass this
important message of equity to their students so that they would
understand that an active learning of mathematics is worthwhile.
Making Everybody Count is a successful, replicable program.
Reasonable start- up funds would be $10,000 for release time, to
travel, and to write proposals. An appropriate bare-bones pilot
project (30 teachers, one summer) would require at least $40,000.
Making Math Count (1989 - 1992)
David Gay, professor, (520) 621-6876,
dgay@math.arizona.edu
"Making Math Count" was a three-year National Science
Foundation (NSF) funded project to assist middle school teachers
throughout the state to use problem solving and technology in their
teaching. The three-week program had an equity component whose goal
was to encourage more minorities and girls to pursue mathematics
related fields. Three groups of thirty middle school mathematics
teachers from throughout Arizona spent three weeks at a summer
residential institute developing new approaches to mathematics
education, including exploring the connections between mathematics
and real world situations. Participants later returned to campus for
a two-day workshop to discuss successes and failures after a year of
implementation.
David Gay, professor, (520) 621-6876,
dgay@math.arizona.edu
Math Movies, sponsored by the University of Arizona chapter
of Pi Mu Epsilon mathematics honorary and the University of Arizona
Math Center, are films/videos that deal with interesting mathematical
topics and are designed to pique the interest of students as well as
provide a diversion from the usual class lecture and study routine.
A series of four hour-long programs is shown each semester.
When choosing which films/videos are to be shown, the
abilities, ambitions and interests of the undergraduate and graduate
students and faculty are kept in mind. Thus a wide variety of
films/videos is presented each year - filmed lectures, computer
animated films, NOVA videos about mathematical topics, film
biographies of mathematicians, etc. A typical audience is 20 -30
people.
Expenses only involve film/video rental or purchase and
copying of flyers/publicity. The average cost of a video is $20 -
$40. Recommended videos are published by MAA, AMS and NOVA.
Listings of some films are available in American Mathematical
Monthly, January 1983 and in an 1980 MAA publication, Films and
Videotapes for College Math by David Schneider. For a good rental
catalog, contact:
Mathematics Instruction Colloquium (1987 - 1994)
David Gay, professor, (520) 621-6876,
dgay@math.arizona.edu
The goal of the Mathematics Instruction Colloquium (MIC) is
to encourage more interaction between the University of Arizona
Department of Mathematics faculty, Department of Teaching and Teacher
Education faculty and students, local school teachers and principals,
and others interested in mathematics instruction.
The MIC holds weekly hour-long meetings to discuss issues in
mathematics instruction from kindergarten through graduate school.
These discussions are led by a different designated person each week.
Occasionally a guest speaker is invited to attend the meetings and
address a particular issue. Past speakers have included Peter Hilton
who spoke on mathematicians as teachers, Hassler Whitney on how
children learn and Bruce Meserve on MAA initiatives in mathematics
education.
Participants include local school teachers, students and
faculty from the College of Education, the Department of Mathematics,
and other departments of the University of Arizona. At the beginning
of each academic year, notices about the MIC are sent to local
schools, University faculty in the Department of Mathematics and in
the College of Education who are asked to pass on this information to
their students and other interested people who ask to be on the
mailing list. Occasionally, people who attended the MIC as students
continue to attend the MIC as local school teachers.
The University of Arizona Mathematics Instruction Colloquium
began with a few people willing to come together to talk about math
education, and has grown to a regular meeting size of about 20
people. The MIC was started and ran for two years without funds as
no start-up funding was available or needed. The Department of
Mathematics now funds the MIC with approximately $1000 annually for
publicity and guest speakers.
John L. Leonard, lecturer, (520) 621-6874,
jleonard@math.arizona.edu
The University of Arizona chapter of Pi Mu Epsilon, the
national mathematics honorary, recognizes interest and achievement in
mathematics. Current activities are limited to sponsorship of the
Math Movies series.
All students who have completed at least 12 units of
university-level mathematics (including linear algebra or
differential equations) with a mathematics grade point average of at
least 2.5 are invited to become members of the society. An
initiation fee of $14 is required. Essentially, there are no costs
involved in running the honorary.
To start a new chapter of Pi Mu Epsilon, contact:
PRIME - Promoting Reform in Mathematics Education
(1993 - 1998)
Marta Civil, assistant professor, (520) 621-6873,
civil@math.arizona.edu
"Promoting Reform in Mathematics Education" (PRIME) is a five
year training program to enhance the mathematical knowledge and
leadership skills of teachers of grades 3-8. The goal is to select,
when possible, teams of teachers from the middle school and feeder
elementary schools. The program adopts an integrated approach to the
teaching of mathematics - to blend the teaching of subject matter
with the use of problem solving and technology.
Each year thirty selected teachers from the Tucson area
attend a total of six weeks of summer courses at the University of
Arizona, Tucson, over the training period of three years. The
participants attend courses [These course deal with geometry,
probability and statistics, the number system, how students learn,
and reform in the schools.]
for three weeks the first summer, two
weeks the second summer, and one week the third summer for a total of
14 graduate units. During the summers the participants are on campus
for seven hours daily, which includes a two hour block to pursue
workshop activities of their choice. Participating teachers receive
graduate units of course credit, free tuition, and a $300 stipend per
week. The teams of teachers work together during the duration of the
program. All participants also attend two to four one-day inservices
each academic year during their three year training period.
Teachers participating in PRIME are provided with various
support activities during the academic year including team meetings,
inservices, and classroom visits by PRIME faculty and support
teachers, peer teachers, and evaluation team members. During the
academic year, the support teachers have a unique role as the key
link between the University of Arizona Department of Mathematics and
the participating schools. The support teachers are "on call" for
any needs that the participants may have. They may help PRIME
participants teach a lesson they are not quite comfortable with yet,
or help model a different approach to teaching a particular lesson,
or demonstrate how to integrate technology in the classroom. The
support teachers also help plan new lessons, inservices for non-PRIME
participants, and Family Math Workshops.
PRIME participants are expected to work with their team
members to develop a plan to implement change in their schools, share
information with colleagues, participate in an academic year Family
Math Workshop, and assist with the evaluation of the project. To
facilitate the implementation of the goals of the program, the
participating school districts equip the classroom of each
participating teacher with a set of calculators, a microcomputer with
overhead and LCD panel, selected manipulatives and software.
To start a program similar to PRISM or PRIME the interest of
local school districts, administrators, and teachers is needed.
PRIME funding is a combination of private grants, university sources,
state funds, and federal grants. The school districts have obtained
private grants for equipment, University and State sources have
contributed matching funds, other funding has come from the National
Science Foundation. Although it depends on how the program is
structured, i.e. stipends, salaries, etc., the University of Arizona
Mathematics Department recommends running a similar program on
approximately $250,000 per year.
PRISM - Promoting Reasoning in School Mathematics
(1989 - 1992)
Marta Civil, assistant professor, (520) 621-6873,
civil@math.arizona.edu
"Promoting Reasoning in School Mathematics" (PRISM) was a
three-year NSF-funded teacher enhancement project for middle and
high school teachers in the Tucson area. Seventy-five selected
participants spent four weeks at the summer institute taking morning
courses on how to use problem solving, calculator and computer
technology in their teaching. In the afternoons, the teachers worked
on curriculum units for their classroom. The success with the NSF
funded PRISM program for teachers of grades 7-12 suggested extending
the interaction to lower grades.
Professional Internship Program for High School
Students (1972 - 1994)
David Lomen, professor, (520) 621-6868,
lomen@math.arizona.edu
For many years, faculty of the University of Arizona
Department of Mathematics have been involved in the Professional
Internship Program for High School Students sponsored by Tucson
Unified School District (TUSD). This program currently operates at
ten high schools in TUSD and serves 200-250 students per year. These
students are placed throughout the Tucson area in hospitals, computer
companies, newspaper offices, professional businesses, and University
departments. These students work with a professional who is
currently active in a field which interests the student. The student
gains knowledge about experience in a particular field that interests
them, aiding the student in such decisions as whether to attend
college now or perhaps later, which colleges they should attend, and
what to major in at college.
High school seniors who have at least a "B" average are
eligible to participate in the Professional Internship Program. The
supervisors of the program help match up the students with the
professionals. Once the contact has been made, the student then
spends about five hours each week during the school year working on
site or at home on various projects. The student maintains a journal
about his/her experiences related to the program. She/he meets once
every two weeks with other student interns and the program's
supervisors. The student receives high school credit for the
internship.
The University of Arizona Department of Mathematics has had
over twenty students participate in the program. These students meet
weekly with their mathematics mentor to discuss calculus, computers,
mathematics software, mathematical problems, various mathematical
projects, and university life. For example, one student recently
visited the University of Arizona Mirror Laboratory. She wrote a
summary of the visit, created and solved a problem involving the
parabolic shape of a mirror and its reflection properties. The
students learn different applications of mathematics, how mathematics
is used in science, and ways in which a mathematics degree may be
used in different careers.
The students' favorite part about the program is that they
can meet and interact with a mathematics faculty member and that they
get hands-on experience with activities involving mathematics. The
University of Arizona Department of Mathematics faculty especially
like the Professional Internship Program because they enjoy working
with motivated young people and because it gets students learning
mathematics on their own.
Research Experiences for Undergraduates
(1993 - 1996)
J. M. Cushing, professor, (520) 621-6863,
cushing@math.arizona.edu
The University of Arizona Department of Mathematics has
recently placed emphasis on providing undergraduates with the
opportunity to experience first- hand the various research projects a
mathematician works on. The students work on a part of a professor's
research project, and are exposed to the importance, the usefulness,
and the applications of mathematics to the world around them.
Several faculty have participated in these activities, two advisors
of such projects are Dr. J.M. Cushing and Dr. Carl L. Devito.
Dr. Cushing currently has funding from the National Science
Foundation (NSF) for three undergraduate students to work with his
research team on an interdisciplinary research project. This project
involves mathematical modeling exercises and both numerical and
analytical studies of the new models. Currently the three students
are writing computer software for the biological modeling project.
The minimum qualifications for working on this type of research
include completion of course work in differential equations and
linear algebra. Some experience with computers is useful but not
required.
NSF provides stipends for students to work with university
faculty members on some research projects. Any recipient of a
currently funded NSF grant can request additional funds to work with
an undergraduate on a research project by applying to the NSF
Research Experiences for Undergraduates program.
Dr. DeVito works with undergraduate students on an ongoing
space research problem dealing with communication. This research is
funded annually by the University of Arizona/National Aeronautics and
Space Administration (NASA) Space Grant College Program. Students
have worked on how to develop a language based on mathematics,
chemistry, and physics. At first it is very much like a computer
language, but it goes far beyond such languages by using science in
its foundation. A knowledge of calculus, chemistry, and physics is
helpful, hence primarily junior and senior science majors work on
these projects, although interested non-science majors could also
become involved. At the end of the academic year, the students
working with Dr. DeVito attend the statewide Arizona /NASA Space
Grant Undergraduate Research Internship Symposium and give a short
presentation about their project and findings.
The NASA Space Grant College Program for Land Grant
Universities was proposed by former senator Lloyd Bentsen and was
passed by Congress in 1987 as part of the National Space Grant
College and Fellowship Act. Under the Space Grant program a national
network of public and private colleges and universities with varying
degrees of aeronautics and space-related resources and capabilities
are joined by space-related industry, state and local governments and
nonprofit organizations. Space Grant Consortia have been established
in every state, the District of Columbia, and Puerto Rico. Each
consortium receives NASA funds to be used in implementing a balanced
program of research, education and public service.
An important component of this three-pronged approach is the
establishment of Space Grant fellowships. Fellowship programs are
administered by each consortium and are targeted to both
undergraduate and graduate students with emphasis on reaching women,
underrepresented minorities and individuals with disabilities. To
find the nearest Space Grant Consortium, contact:
Students enjoy working on this communication project with Dr.
DeVito as they are given the opportunity to incorporate their
knowledge of many subjects. They like working on an unusual problem
with many intriguing facets. It is often the case that one solution
leads to another question. Many people take language for granted or
seem to feel that language is "trivial." Students are fascinated by
the fact that this is not so -- languages are highly non-trivial and
have a rich structure! After working on this research project the
students realize not to take so much for granted when trying to
communicate their ideas. Being sensitive to who the audience is and
their understanding of the topic is one of the fundamental lessons
taught by this research experience.
The University of Arizona Department of Mathematics has found
that research opportunities and qualifications have helped inspire
undergraduates to do well in their courses and better understand
"where is this mathematics stuff used."
Undergraduate Mathematics Colloquia
(1991 - 1994)
William McCallum, assoc. professor, (520) 621-6872,
wmc@math.arizona.edu
The Undergraduate Mathematics Colloquia at the University of
Arizona were developed to enrich the experience of undergraduate
mathematics majors and to expose them to mathematical ideas they
might nor encounter in their courses. Approximately six hour-long
colloquia are presented per year by different faculty members. The
colloquia are held in a comfortable lounge with a blackboard and
where a portable computer with projection system is available. The
colloquia are well attended by undergraduate students, graduate
students and department faculty.
The colloquia at the University of Arizona started with local
faculty members who were asked to give talks on subjects that
interested them. The response was very encouraging. The speaker is
asked that the lectures/demonstrations not be too technical as the
colloquium is aimed at an undergraduate audience. Often a short
demonstration and visual aids are included in the speaker's
presentation, thus making an effective and successful lecture for all
attending.
Currently, the Department of Mathematics Chairperson provides
funding for the Undergraduate Mathematics Colloquia from the
department budget for refreshments and inviting outside speakers from
other universities and industries. The University of Arizona Math
Center sponsors the colloquia and does the advertising. However a
similar program could be started without any funding if the speakers
were solely local faculty who wanted to share their mathematical
enthusiasm with the students. Recommended start-up funds are $0 -
$500.
U. of Arizona - Pima Community
College Co-op Program (1995 - 1994)
Elias Toubassi, professor, (520) 621-6881,
elias@math.arizona.edu
The University of Arizona and Pima Community College Co-op
Program promotes a regular exchange of ideas between the mathematics
faculties at the University and the Community College. Participants
in the program are mathematics faculty members from Pima Community
College (PCC) who remain employees of PCC with full salary and
benefits, but perform their duties at the University of Arizona (UA),
and adjunct faculty under contract to the University of Arizona who
perform their duties at PCC.
The success of the University-School Cooperative Program
provided the spark to increase dialogues with the local community
college thus the University of Arizona and Pima Community College
Co-op Program was created. During the program, the PCC faculty teach
three lower division mathematics courses per semester at the
University of Arizona, take two or more courses, and work on
pedagogic projects of their choice. The UA adjunct faculty teach four
mathematics courses at PCC and perform other duties required of
full-time PCC faculty.
The program lasts for one year after which the participants
must return to their respective campuses to teach for a minimum of
one year. The University of Arizona selects the participants based
upon their educational goals and commitment to teaching. The program
benefits all: UA and PCC departments of mathematics and the students
taking the mathematics courses. Because many of the Community College
students transfer to the University, having equivalent mathematics
standards will make the transition easier for the students and the
mathematics faculty will not have different expectations of the
students.
To start a similar co-op program one needs to lay the
groundwork with the faculty in the local community colleges and
determine if the interest is there. Next, one needs to develop a
plan so that the co-op participants will be a productive addition to
the participating schools, start-up funding should then be obtained.
The University of Arizona and Pima Community College Co-op Program
runs on approximately $25,000 per faculty member per year and is
supported by University sources and State funds.
William McCallum, director, (520) 621-6872,
wmc@math.arizona.edu
The University of Arizona Math Center was created in response
to the need to centralize advising and other services for
undergraduate mathematics majors and improve undergraduate
record-keeping for the Department of Mathematics. The center's main
purpose is to assist and support the interaction between the students
and faculty of the department, and to take care of the administrative
details of advising. The Math Center keeps accurate, up-to-date
records, summarizes information about undergraduate mathematics
majors, and provides reports on a regular basis to department
administrators and faculty committees.
The Math Center provides support, general academic advising,
scholarship and summer internship information, and career advising
for undergraduates who either are considering becoming, or are
already mathematics majors.
Each undergraduate mathematics major is
assigned a faculty advisor when she/he has successfully completed the
second semester of calculus. Math majors vary greatly in ability and
ambitions, thus it's important that advisors represent a good cross
section of the faculty so that a suitable advisor can be found for
everyone. The Math Center's aim is to match the ambitions of the
students with an advisor who could be a mentor, and who is also
active and has up to date information on the student's area of
interest. Faculty advisors are therefore allowed to concentrate on
the mathematical aspects of advising.
The Math Center also organizes events where mathematics
students and faculty can meet. These events include open houses,
math movies, undergraduate math colloquia, career advising sessions,
and meetings of women and minority math majors. The Math Center
provides support for student organizations such as the University of
Arizona Student Actuary Club and the mathematics honorary, Pi Mu
Epsilon. A newsletter for undergraduate mathematics majors is also
prepared each semester that includes department information and a
calendar of events.
A suite of four rooms including an office for the coordinator
and assistant, a small library, and a commons room are dedicated to
the Math Center. The undergraduate mathematics library is stocked
with good mathematics books and periodicals, as well as information
about graduate programs and careers. The commons room is a place for
undergraduate math majors to socialize and study. Upper division
tutoring for undergraduate students by faculty is also available in
the commons room for an average of eight hours per week.
Staff of the Math Center can supply information about careers
in mathematics, graduate programs in mathematics, applying to
graduate schools, and graduate fellowships to interested
undergraduate students. Each year the Math Center schedules at least
one talk about preparing for, applying to, and choosing graduate
schools, given by a faculty member involved in the admission of
University of Arizona graduate students. Qualified students are
contacted and encouraged to consider continuing their mathematical
studies. The names of these qualified students are provided to other
institutions upon request, who then contact these students and
provide them with information about the graduate programs offered at
their universities.
Starting a facility /service such as the Math Center requires
a commitment of space and funds for staffing the center. The amount
of staff time needed is determined by the kinds of services to be
provided and the number of students to be served. The Math Center is
staffed by a part-time faculty director, a full-time coordinator, and
a part-time student assistant (10 hours per week).
The coordinator
position has evolved over a six-year period from a quarter-time
position to full- time. Funding for the University of Arizona Math
Center comes from the Department of Mathematics budget. Expenses
include: space for the center, staff salaries, computer resources,
copying, postage, publicity, refreshments for events, and guest
speakers.
Student Actuary Club (1993 - 1994)
Donald Myers, professor, (520) 621-6859,
myers@math.arizona.edu
Information about the University of Arizona Student Acutary Club.
Summer Mathematics Camp II (1986 - 1994)
Daniel Madden, assoc. professor, (520) 621-4665,
madden@math.arizona.edu
The University of Arizona Summer Mathematics Camp was created
so that mathematically talented middle school students could have the
chance to directly experience research mathematics. This is done
through the use of "exploratory problems", problems that allow for
the freedom to explore and create mathematics without the threat of
an immediate answer. (Refer to the book, Exploratory Problems in
Mathematics, [Stevenson, Frederick W.. Exploratory Problems
in Mathematics. NCTM -- National Council of Teachers of
Mathematics. 1992.]
for examples of mathematical exploration.) The annual
two-week camp is held in mid-July. After a short course with
computers the students are introduced to several exploratory problems
and asked to team up into groups and work on a problem of their
choice. They work for seven days, write up their findings, and give
an oral presentation to their colleagues, interested parents,
teachers, and guests from the Department of Mathematics. On the last
day, each student receives a booklet containing the results of their
colleague's research activities.
Students who apply to the University of Arizona Summer
Mathematics Camp must be recent graduates of the eighth grade. They
are selected on the basis of a seven question test and a teacher
recommendation. Sixteen students are selected from dozens of
applicants from throughout the country. The students stay in a
campus dormitory and do their work in the Department of Mathematics
at the University. Each student has access to IBM compatible
computers, hands-on equipment from the University of Arizona
mathematics education laboratory, and other equipment from the
Department of Mathematics. Two faculty members and two graduate
student chaperons are in charge of the students. Participants are
charged $250 which approximates the room and board cost to the
program.
Primary funding for University of Arizona Summer Mathematics
Camp comes from local foundations through the University of Arizona
Foundation, a funding arm of the University. Program expenses
include student room and board, instructor and counselor salaries,
computer resources, publicity, supplies, and accommodating students
needing financial aid.
David Lomen, professor, (520) 621-6868,
lomen@math.arizona.edu
In 1987, the National Science Foundation (NSF) decided to
encourage initiatives to reform the calculus curriculum. One of the
projects it funded involved the formation of the Calculus Consortium
Based at Harvard (CCH), a consortium of eight diverse schools
(including a high school and a community college), with Harvard
University as the base. Its mission was to completely redesign the
calculus curriculum. The result is a book
[Hughes-Hallett, Deborah, et al. Calculus. John Wiley & Sons,
Inc. 1994.]
and an approach to
calculus that are very different in spirit from the traditional ones
that had become standard since the 1960's. The approach places heavy
emphasis on graphical analysis, numerical estimation and the concepts
underlying calculus, with less time spent on algebraic manipulations,
formalisms, and rote calculations. Use of technology is incorporated
into the course, but it is not tied to a particular technology. The
CCH text and approach have been used at over 500 institutions in the
last four years and have been judged by teachers and students alike
to be a success and an exciting and refreshing experience.
The University of Arizona is one of the original consortium
members. Informational Seminars about Reform Calculus were held at
various universities that introduced the calculus curriculum to
teachers, administrators, parents, and other interested parties at
the college and secondary education levels. As college and
university personnel and secondary personnel had different concerns
on the implementation of the reform calculus separate sessions were
held for each level.
As an increasing number of schools adopted the CCH textbook,
some of the difficulties that instructors had teaching from the new
calculus material was brought to the authors' attention. The authors
were interested in helping the instructors overcome these
difficulties and they wanted to make sure the reform calculus was
taught in a manner that would take advantage of its content. Thus,
the University of Arizona Workshops on Teaching Reform Calculus were
developed.
The three-day Workshops on Teaching Reform Calculus are
hands-on workshops for individuals who will be using the CCH textbook
in their calculus classes (in the coming academic year).
Approximately twenty workshops are given each year and
are held at national meetings, at the
University of Arizona, and on other university campuses. Workshop
topics include: discussion of the philosophy of reform calculus,
summaries of the topics and concepts of the course, problem solving
(this forms the basis of the course and of the workshop), lesson
preparation, use of technology, classroom dynamics, homework and
tests, and any other issues of concern to participants.
Primary funding for these activities comes from the NSF
Calculus Initiative. Program expenses include stipends for workshop
participants, travel costs, computer resources, publicity, and
workshop supplies.
For more information, contact:
The University - School Cooperative Teachers Program
(1987 - 1994)
Elias Toubassi, professor, (520) 621-6881,
elias@math.arizona.edu
The University-School Cooperative Program enhances the
involvement between the University of Arizona and local school
districts. Participants in the program are middle school and high
school teachers on paid leave from their district. During the
program, the participants teach three courses per semester in the
entry level mathematics program
[The entry level mathematics courses range from introduction to
college algebra to first semester calculus.]
at the University of Arizona, take
two or more courses, and work on pedagogic projects of their choice.
The teachers are given fee waivers for the courses they take.
The program lasts for one year after which the participants
must return to their respective school districts to teach for a
minimum of one year. The University of Arizona selects the
participants based upon their educational goals and commitment to
teaching.
The University-School Cooperative Program is an excellent way
to improve the bridge between higher education and secondary
education for everyone involved. It keeps the University faculty
aware of what the students are learning in high school, it makes
middle and high school teachers aware of what universities expect
their students to know and lets these teachers develop their own
creative teaching methods, thus helping the students by making
mathematics interesting.
To start such a program, one needs to develop contacts with
local school districts and teachers to determine if the interest is
there, and if they could be a productive addition to the University's
Department of Mathematics. The key to the success of this program is
that both the University and local middle and high schools benefit.
A minimum of two local teachers at approximately $24,000 per teacher
is needed. The University-School Cooperative Program at the
University of Arizona is supported by University sources and State
funds.
Whiteriver Junior High School Summer Math Camp
(1989 - 1994)
Daniel Madden, assoc. professor, (520) 621-4665,
madden@math.arizona.edu
The purpose of the Whiteriver Junior High School Summer Camp
is threefold: i) to enhance the participants' problem solving skills,
ii) to acquaint the participants with computers and the latest hand
calculators, iii) to enhance written and verbal communication skills.
This camp was created to give the Apache students the same
opportunities the brightest students in the city have to explore and
create mathematics.
The Whiteriver Junior High School Summer Camp evolved from
the University of Arizona Summer Mathematics Camp. Each summer
twelve eighth graders from Whiteriver Junior High School on the White
Mountain Apache Reservation spend a week at an intensive summer
residential program dealing with problem solving and technology.
The format of the two-week University of Arizona Summer
Mathematics Camp was adapted to a one-week camp for the Apache
students. The students arrive on a Sunday afternoon after a 200 mile
trip to Tucson. On Monday, they are introduced to the computer they
will be using throughout the week and how to use it. Tuesday, the
students are introduced to several exploratory problems,
[For examples of exploratory problems refer to: Stevenson,
Frederick W.. Exploratory Problems in Mathematics. NCTM (National
Council of Teachers of Mathematics). 1992.]
students team up, choose a problem and work on it the remainder of
the day and all day Wednesday. On Thursday the students write up
their findings in the morning and in the afternoon give oral
presentations to their colleagues, their school principal and
teacher, interested parents,
and guests from the University of Arizona Department of Mathematics.
On Friday morning there is a "graduation" ceremony where each student
is presented with a booklet containing the results of their
colleague's research activities.
Participants are selected by their mathematics teacher based
on their abilities and interests in mathematics. The Whiteriver
Junior High School eighth graders have various fundraisers throughout
the school year so they can have some spending money when they attend
the summer camp.
Primary funding for the Whiteriver Junior High School Summer
Camp comes from the Apache Nation and local foundations through the
University of Arizona Foundation, a funding arm of the University.
Program expenses include student room and board, travel costs,
instructor and counselor salaries, computer resources, publicity, and
supplies. Future plans include developing similar programs for the
high school on the White Mountain Apache Reservation, and for other
local reservations such as the San Carlos Apache, Navajo, Hopi, and
Tohono O'odham.
Women In Mathematics (1990 - 1994)
William McCallum, assoc. professor, (520) 621-6872,
wmc@math.arizona.edu
Women in Mathematics meetings are sponsored by the University
of Arizona Math Center. They are semi-annual meetings that are
well attended by female undergraduate mathematics majors and graduate
students, and female and male faculty members. These meetings serve
many purposes, as they bring women in mathematics together in an
informal setting to discuss their experiences and issues they are
concerned about, for example, gender equity in and out of the
classroom, employment issues, and lack of role models in the
mathematics profession. A guest speaker is usually invited to speak
at the beginning of each meeting with a follow up discussion by the
participants. Women in Mathematics brings together all participants
in the mathematics educational process and provides role models and
extra encouragement for the students, both graduate and
undergraduate. It also helps the faculty who attend the meetings
become more sensitive to the issues women face in today's society.
Women In Mathematics meetings came about when someone in the
Department of Mathematics took the initiative to schedule the first
meetings. Women in the department were notified and many came to say
these meetings were long overdue. The direction of the meetings
changes from year to year depending on the needs and interests of the
people who attend. Future plans include becoming more involved with
mentoring.
The budget for running the Women in Mathematics meetings is
relatively small, approximately $200. Funds are needed for the guest
speaker, mailing, copying fliers, refreshments, etc. Since the
University of Arizona Math Center sponsors the meetings, all funding
comes through the same University sources that fund the University of
Arizona Math Center.
Home Page (Mathematics Department, University of Arizona)
Last modified on 10/15/95 by webmaster@math.arizona.edu
David Lovelock, professor, (520) 621-6855
To start a similar program that helps
incorporate technology into the classroom, contact a local department
of mathematics chairperson, dean of science, university provost, the
National Science Foundation, or other agencies of support. Request
start-up funds for computers, computer time, and travel costs.
Deborah Yoklic, research associate, Women's Studies, (520) 621-7338
John L. Leonard, lecturer, (520) 621-6874,
jleonard@math.arizona.edu
Fred Stevenson, professor, (520) 621-6880,
frstv@math.arizona.edu
Stephen Willoughby, professor, (520) 621-6866,
ssw@math.arizona.edu
Fred Stevenson, professor, (520) 621-6880,
frstv@math.arizona.edu
Elias Toubassi, professor, (520) 621-6881,
elias@math.arizona.edu
Fred Stevenson, professor, (520) 621-6880,
frstv@math.arizona.edu
Elias Toubassi, professor, (520) 621-6881,
elias@math.arizona.edu
William McCallum, assoc. professor, (520) 621-6872,
wmc@math.arizona.edu
Judy Turner, adjunct lecturer
Carl L. DeVito, assoc. professor, (520) 621-2891,
devito@math.arizona.edu
Chris Mikel, coordinator, (520) 621-2056,
mikel@math.arizona.edu
Fred Stevenson, professor, (520) 621-6880,
frstv@math.arizona.edu
David Lovelock, professor, (520) 621-6855
William McCallum, assoc. professor, (520) 621-6872,
wmc@math.arizona.edu
Fred Stevenson, professor, (520) 621-6880,
frstv@math.arizona.edu
Christine Mikel, adjunct lecturer, (520) 621-2056,
mikel@math.arizona.edu