The Native American Summer Institute is a joint endeavor of the Pascua Yaqui Tribe, the Wa:k O'odham Community, the Carl Hayden Bee Research Center (USDA-ARS), and The University of Arizona. A description of the summer activities can be seen at the Institute's website http://www.math.arizona.edu/~jwatkins/institute.html

The Institute conducted a three week program at the University of Arizona for the summer of 2000. In previous years, the Department of English through the Southern Arizona Writing Project conducted a two or three week program in writing and culture. This year, due to financial difficulties, the English Department chose to take a hiatus from these activities.

The math/science portion of the activities was funded by RAIRE. The faculty at the Summer Institute would like to express our appreciation to Randy Richardson and to the RAIRE committee for its support. The funds were used as follows:

Native American students also participated on campus in a program financed by the Pascua Yaqui Tribe. This program succeeded in some degree as a substitute to the English Department's program.

The math and science portion of the program were administered by the Department of Mathematics. The Institute began with 21 participants from the Tohono O'odham Nation and the Pascua Yaqui Tribe.

The National Science Foundation through the Recognition Award for the Integration of Research and Education (RAIRE) provided financial support for the program for the summer of 2000. We would like to thank the funding agencies, and RAIRE Program Coordinator, Dr. Randall Richardson, Vice President for Undergraduate Education, for their support of the Institute.

The site of the math/science program was the Mathematics Department on the University of Arizona campus. By emphasizing the university as a learning environment and by having a university become a familiar place, the student participants can become comfortable in a university environment during their time as Institute fellows and when the time comes for their university education.

At present, two Tohono O'odham or Pascua Yaqui students are studying math, science or engineering at the University of Arizona. Three former participants in the Institute - Joaquin Muñoz, Damon Corella, and Elena Cordova - have internships at the Bee Center. They will all be enrolled at Pima Community College with plans to continue their education at the University of Arizona. Joaquin is leaning towards a political science major. Damon is interested in computer science, and Elena is planning on a degree in engineering.

The short term goal of the proposed project is to give Native American students who plan to pursue higher education a set of ideas in mathematics and biology that relate to their personal life experience. The Institute also works to show how education can be integrated into research project that contribute to the communities that are represented by the participants.

Recognizing that many American Indian students are behind in their mathematics and science education, the Summer Institute strives to assist the students in making up lost ground and prepare students for their math and science classes in the fall.

In addition, for those Native American students who do not plan to pursue higher education, the project is designed to position them to work for an enterprise that allows them to continue to live on tribal lands and maintain contact with their traditional culture.

Leesa Johnson coordinated the morning activities at the Institute. Leesa, a former and returning high school teacher on the Navajo Reservation, has recently completed a Masters' Degree in the American Indian Studies Program. She designed a program of mathematics education for the participants to improve their algebra and problem solving skills. The students also learned how to use a spreadsheet.

Leesa plans to take her experience here to create a similar structure in northern Arizona.

For the first week, the afternoons were devoted to BeePop: The Population Dynamics of Honey Bees in the Hive and in the Wild. These class notes take an in-depth view of the nature of mathematical modeling. These notes, an educational perspective of the original research at the Bee Research Center, are found at the website

BeePop is a set of hands-on exercises and projects designed so that the participants will use mathematics to learn about the biology of honeybees, the dynamics of the hive, and the mechanisms for colony migration. Joe Watkins, one of the authors of BeePop, coordinated these activities.

During the second week, the afternoons will be devoted to the Economics of Beekeeping. The Economics of Beekeeping activities have the students using their spreadsheet skills to learn basic principles of economics and to use these principles to design a business strategy for a beekeeping operation. The students also use BK-Economics, a software package, designed by a team of scientists at the Carl Hayden Bee Research Center to assist commercial beekeepers in streamlining their business practices. This software allows the students to simulate years of business, taking into account factors like equipment purchases, labor force, transportation, marketing strategies, loans, honey flow, and other hive products without taking the usual risks.

Even though the model system is a beekeeping business, these skills, particularly during these activities, will be valuable for any participant considering a career in business, especially in a small business for themselves.

Mark Muktoyuk coordinated the Economics of Beekeeping.

Joe Watkins is an associate professor and Mark Muktoyuk is a recent Masters' Degree recipient in the Mathematics Department. Mark is Inupiac Eskimo.

Our tutors this summer were Marietta Brady and Elena Cordova. Marietta is Navajo. She is a recent graduate of Fort Lewis College in Durango, Colorado. Her major is Southwest Studies. Elena is a recent graduate of Cholla High School in Tucson, Arizona. Elena finished first among Native American Students at Cholla and is the first Native American student in a decade to take calculus at Cholla. Elena also coordinates the math tutoring program at New Pascua Pueblo.

The Institute operates Wa:k Apiary on land generously provided to us by the San Xavier Farming Cooperative. This apiary, the only apiary on tribal land run by tribal people, is one-half mile southeast of San Xavier del Bac Mission in the San Xavier District of the Tohono O'odham Reservation. Clifford Pablo is the president and Julie Ramon Pearson is the vice-president of the Farm Coop. Eric Erickson, the director and Gloria DeGrandi-Hoffman, the senior entomologist at the Bee Center, have been training students at the Wa:k Apiary throughout the year in beekeeping.

We had two visits to the apiary postponed due to the early monsoons. The high humidity agitates the honey bees to the point that they are not suitable for training of novice beekeepers. Consequently, the annual honey havest was postponed until July.

On the third week, the participants continued to work with Leesa on their math skills. In addition, the Institute conducted a series of special events and field trips. The students made a visit to Native Seeds/ SEARCH and received a visit from ethnobotanist, Suzanne Fish. Erin Peckol let an afternoon in the Koffler Building in which the students isolated honey bee DNA.

The students also made a visit to the Bee center, and to the Tree Ring Lab. They also had the opportunity to learn about New Start, a summer program to prepare students entering their freshmen year at The University of Arizona, and to visit the Native American Student Affairs Office.

Continued life and funding for this Institute has been a challenge. The receipt of a RAIRE Grant in March allowed me to work on a more stable existence for the Institute. In this regard, I describe the program to Mary Jo Tippeconic Fox, the University of Arizona's Ambassador to the Native American People. Mary Jo was very receptive and helpful. She suggested that the Institute form an advisory council guide the students and to represent the Institute. Specifically, if other tribal groups would like to consider such a summer program, this advisory council would be in a position to share our successes and to advise them on which pitfalls to avoid.

Such a committee is nearly formed:

The Institute has made tremendous strides in its lifetime. On the other hand, it still has tremendous unrealized potential. Commitment to education come through commitment to community. Students will be more disciplined and more focused when this relationship becomes more clear in their eyes. Therefore, before we can take some of the next steps, for example, moving to a residential summer program or having regular visits by elders, we need to become more well integrated into the activities of both The University of Arizona, the Wa:k O'odham Community, and the Pascua Yaqui Tribe.

Joseph C. Watkins

Director, Math-Science Program