# Fellow Profile: Matt Lafferty

**G-TEAMS Cohort:**2011-12-
**Graduate Program:**Mathematics -
**Teacher Partner:**David Romero -
**School:**Mountain View High School -
**Grade level:**9-12 -
**Topics:**Intermediate Algebra, Algebra II and College Ready Math

"As a mathematician, I would like to give students a broader perspective and better understanding of what mathematics is, and in doing so, hopefully impart some of my enthusiasm for the subject."

## Research Interests

Matt Lafferty is a graduate student in the Department of Mathematics at the University of Arizona. His research interests are in the area of algebraic number theory, specifically Iwasawa theory, modular forms and *L*-functions.

## Classroom Activities

Matt is working at Mountain View High School with David Romero. The focus of their partnership will be on creating exciting and interesting projects for the algebra and college ready math students that will allow them to utilize what they are learning in the classroom to solve real world problems. In addition, they hope to expose students to the broader world of mathematics, both its diverse areas of research and its history. Besides making lessons more fun and interesting, David and Matt hope this focus will:

- Increase student participation and interest in their math classes.
- Give students a better understanding of how mathematics is used to solve "real world" problems.
- Expose students to possible STEM careers.

## Lessons Learned

In the courses I have taught at the university level, I've had freshman and sophomore students that struggle with the course despite the fact that they did very well in their high school math classes. Being over a decade removed from my own high school math courses, my understanding of why students were having this difficulty and consequently my ability to address it was limited. This year at Mountain View has taught me a great deal about how mathematics is taught at the high school level, and given me some insight into why this transition from high school to college in mathematics can be difficult for some. This insight will be invaluable for my college level teaching in the future, as it will allow me to organize my classes in such a way that I can ease this transition as much as possible. For example, while most of the high school students that I have worked with have memorized the formulas relevant to a given topic, very few of them truly understand the underlying concept, much less where these formulas come from. Because of this they not only see mathematics as an exercise in memorizing arbitrary rules, they have a great deal of difficulty adapting what they've learned to situations not covered in the textbook. To combat this, I would motivate the material by first discussing the types of problems we seek to solve, while tying it to previously covered concepts. Not only will this give students some perspective of where the material fits relative to what they've previously learned, it gives them a context from which they can see why one would want to employ a given formula or technique. In addition, the problems covered in class and in the homework assignments would consider problems from different perspectives and in different contexts. The hope being that this will allow students to better see and understand the underlying mathematical concepts.

## Teaching Materials

- Graphing linear data (pdf) - Students were given several sets of data. They were asked to graph the data in whatever way they liked, and use this graph to write a paragraph summarizing the behavior of the data. In addition, students can find their own line of best fit and use this line to make predictions.
- The Monty Hall problem (keynote) - You are on a game show and are presented with three doors. Behind one of the doors is a pile of money, behind the other two are goats. The host asks you to choose a door. Before opening your chosen your door, the host opens one of the other doors to reveal a goat. The host then give you the choice of sticking with your original door choice or switching to the unopened door. What should you do? This is known as the Monty Hall problem, and the answer is not what most people expect. This is a fun way to introduce experimental versus theoretical probability.
- Quadratic functions (powerpoint) - A lesson introducing quadratic functions.
- Solving quadratic equations by taking square roots (keynote) - A lesson showing students how to solve quadratic equations using square roots.
- Chaos theory (keynote) - A presentation on the Mandelbrot set, which was tied into the section on complex numbers.