# Fellow Profile: Andrew Leach

**G-TEAMS Cohort:**2013-14-
**Graduate Program:**Applied Mathematics -
**Teacher Partner:**Charles Taylor -
**School:**Flowing Wells High -
**Grade level:**11-12 -
**Topics:**Precalculus, AP Statistics

"...if one is accustomed to easy success, one may not develop the patience necessary to deal with truly difficult problems."

- Terence Tao

## Research Interests

Andrew's research interests are primarily oriented towards computational probability. This entails Monte Carlo methods and their implementation to estimate solutions to problems that arise in areas as diverse as Neuroscience and Statistical Mechanics. Included in these efforts is the work to extend some classical numerical procedures from the deterministic to the stochastic setting.

## Classroom Activities

Andrew works with Chuck Taylor at Flowing Wells High School, and primarily teaches pre-calculus. Goals for teaching include bringing students to a point of engagement in the material where they feel comfortable thinking critically. One way this is accomplished is through in class laboratory experiments where the course material must be taken out of its original context. The intention is to mimic the mathematical modeling process of determining which methods are appropriate, a scenario that does not arise when students are given a purely mathematical problem and the method to solve it.

Additionally, the philosophy is upheld that the active participation of students is imperative to their learning. Open questions are asked in class, and students are called on directly to provide their insights. The students are encouraged to assist neighbors with their questions, as the students learn quite a bit in doing so. Group discussions also serve as a forum to assess the level of understanding that the classroom is at.

## Lessons Learned

As a teacher in the college class setting, it is easy to press forward to achieve an agenda of the material. Teaching in the high school setting has brought into perspective how important it is to allow the class dictate the pace. It is more important that the students learn a little of something than a lot of nothing. That is not to obscure the differential in student ability, which is more pronounced in high school. It is very challenging to achieve a balance that satisfies both the quick and slow learning students.

Also learned is the philosophy of "never ask a question a student can answer". Each question that arises in class is a learning opportunity for the students. If it is something that they are able to reason out themselves, they should be left to do so rather than have the answer handed to them. Determining what the students should be able to answer themselves though always proves to be a challenging task.

## Teaching Materials

- Introductory Presentation (PDF)
- Pre-Calculus
- Pendulum lab (PDF)
- Cylinder lab (PDF)

- AP Statistics
- Tree diagram problems (PDF)