# Fellow Profile: Amy Veprauskas

**G-TEAMS Cohort:**2012-13-
**Graduate Program:**Applied Mathematics -
**Teacher Partners:**Chuck Taylor -
**School:**Flowing Wells High School -
**Grade level:**9-12 -
**Topics:**Pre AP Algebra, Pre-Calculus, AP Statistics

"I am a great believer in luck, and I find the harder I work, the more I have of it." -Thomas Jefferson

## Research Interests

Amy is a graduate student in the Program in Applied Mathematics at the University of Arizona. Her research interests are in ecological mathematics. By combining mathematics and ecology, it possible to understand and answer some important questions in ecological theory. For instance, this theory can be used to examine how the introduction of an invasive species will affect the native species and whether or not the species can coexist. It can also be applied determine if a species will become endangered given present or new conditions or verify that an endangered population has reached a stable population level.

Amy's current research focus is on Darwinian models. These combine a population model which describes the growth of the population based on life history parameters such as birth and death rates with an evolving trait that affects these parameters. Since organisms are evolving with changing environments, these types of models can help us better understand the long-term behavior of a population.

## Classroom Activities

Amy has been working at Flowing Wells High School with Chuck Taylor. Her role in the classroom varies with the day's schedule but it ranges from assisting students with problems to teaching the classes and designing activities. Amy's goal for this year is to try to improve the students’ mathematical understanding by changing the way they think about math. Mathematics has a lot of rules and these can seem a little overwhelming. However, if you can shift the students’ focus away from what a rule says to why the rule is true, then they can get a more intuitive understanding of the material and mathematics becomes more about critical thinking than memorization.

In addition, Amy is trying to incorporate activities into the classroom that demonstrate that mathematics is actually useful. She hopes that by the end of the year, she will have convinced at least some of the students that mathematics is valuable both in their daily lives and in solving real-world problems.

## Lessons Learned

I have learned a lot both from observing Chuck in the classroom and from the students. When I first started, I realized that I had no idea how to teach basic arithmetic. It had become so second nature to me that I had to really think about how to explain certain concepts. Chuck has some great explanations and he breaks the problems down into very clear steps that are easy for the students to remember. He also has various mottos and phrases that are both catchy and address some problems that come up time and again. The two that come first to mind are "make zero your hero" and "factor first or fail".

Another lesson I have learned is that I am a lot more comfortable with representations of mathematical concepts like function notation and graphs than my students. When a student is lost on something, I like to go back to the rules; if the problem is to evaluate something, then I'll write down a string of equations until I get to the answer. However, I have realized that sometimes the notation is confusing for the students and the real problem is that they don’t have an intuitive understanding of what all the symbols and equations mean. Instead, I have been learning how to think of other ways to present and explain problems that make the problems less abstract and have more meaning the students.

## Teaching Materials

- Introductory Presentation
- Class Notes and Lectures
- Applications of Quadratics: Catapults
- More FUN with FUNctions: a worksheet aimed at getting students to better understand function notation.
- More FUN with Inverse FUNctions: a worksheet like the previous but including inverse functions.