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Working at the Institute

Mathematical and Theoretical Biology Institute/Strengthening the Understanding of Mathematics and Science (MTBI/SUMS)

Research Mentor: Carlos Castillo-Chavez

Graduate Research Associate: Edgar Diaz

Participants: Matt Davenport, Eric Heim, Stephanie Huckins


The Mathematical and Theoretical Biology Institute/Institute for Strengthening the Understanding of Mathematics and Science (MTBI/SUMS) supports the development of students through educational, research and mentorship activities from high school to the postdoctoral level. The program offers an intensive eight week summer research experience for those that are interested in working in the mathematical, statistical and the natural and social sciences fields. Within this program, the students receive intensive research training, research opportunities, and long-term support from its mentors. Students also take away the experience of collaborating with highly experienced faculty, graduate student mentors, and national/international visitors.

MSTF Participants
As part of the MSTF program, we have been introduced as active participants in the MTBI/SUMS program. During our five week program, we will be participants in research training, attending conferences, and conducting a research project of our own.

Week 1
In the beginning of the week, we spent time with our research mentor and graduate research associate learning about the research that is currently being done in regards to the H1N1 influenza virus. With the recent outbreak of the "swine flu", this is a hot topic for many researchers.
For the remainder of the week, we spent our time attending a four-day conference that was headed/sponsored by our research mentor. The conference included presentations from researchers, mathematicians, and health officials from Mexico, Canada, and the United States. Some of these presenters included individuals from within the MTBI/SUMS program as well.
Throughout the duration of the conference, several different speakers presented information about their most current research findings and the mathematical models used to reach these conclusions. There were also presentations that included how past outbreaks of very similar viruses could be applied to predict the emergence and spread of current viruses. Many presenters also stressed the importance of how mathematical modeling could be actively used in the planning of control programs and vaccination strategies.

Week 2
Throughout the week, many different mathematical models were presented to us by our graduate research associate and visiting professors within the MTBI/SUMS program. A large part of the presentations covered material that included S-I-R models, discrete growth models, predator-prey models, population models, and difference equations.

Weeks 3-5
Taking the information we have learned over the past two weeks, we will now be conducting our own research over the next couple of weeks. The emphasis of this project is to learn how to effectively create a mathematical model that can be applied to our specific research topic.

Our research project:
For our research, we have chosen to study the effects of teacher qualifications on student success.

Non-Highly Qualified Vs. Highly Qualified Teachers: Does This Effect Student Success?

Abstract
The main goal of this study is to quantify the impact of teacher qualifications on student achievement. For this study, we utilized a multiple regression model that examines the effects of teacher qualifications on high school students’ success. The model focuses on the impact of teacher qualification, teacher education, and teacher experience on high school student’s AIMS scores in Arizona. The study also takes a look at the implications of student-teacher ratio and student population. The model indicates that schools with a larger percentage of non-highly qualified teachers will have lower scores, while schools with more educated teachers will do better. The model also predicts that a higher student teacher ratio will result in better scores. The model can be used to make predictions of how adjust the variables to produce a desired reasonable increase in student scores. It predicts for some schools it is practical to increase student success by reducing the percent of teachers who are non-highly qualified to zero, while increasing the average educational level to 7 years, corresponding to a Masters degree for many teachers. At the very least, this model will make it possible for policy makers to make informed decisions and avoid “common sense” conclusions that may be incorrect.

We have created a poster that describes our project here.

We would like to say a special thanks to the following for helping us with our research:
Christopher Kribs-Zaleta, Fred Brauer, Jose Flores, and Nala Brewer.

Also, a very special thank you to Edgar Diaz, for helping us out with everything we could possibly think of during our five weeks in the program.