# Fellow Profile: Jordan Allen-Flowers

**G-TEAMS Cohort:**2012-13-
**Graduate Program:**Applied Mathematics -
**Teacher Partner:**Matt Reynolds -
**School:**Mountain View High School -
**Grade level:**9-12 -
**Topics:**Honors Algebra II, College Ready Math, Academic Decathlon

"The smartest people in the world are not the ones who can answer the most questions, but the ones who can ask the most."

## Research Interests

My interests are in the theory and application of nonlinear partial differential equations. These types of equations appear in almost every branch of physics, from electricity and magentism to fluid dynamics to astrophysics. Mathematically, these equations rarely yield exact solutions, so some sort of approximation scheme must be employed. I use a combination of asymptotic analysis, perturbation techniques, and numerical methods to gain information about the problem without actually solving it.

One particular application I am interested in is the self-focusing laser. Such lasers can be powerful enough to ionize the air, creating a 'filament' of plasma as the pulse propagates. My current research uses methods from applied mathematics to understand and eventually control the behavior of these filaments.

## Classroom Activities

At Mountain View, I work with Matt Reynolds in his College Ready Math classes and Honors Algebra II class. I wear several hats when I am in the classroom: sometimes I help students one-on-one or in small groups, sometimes I give short presentations that go beyond the normal curriculum, and sometimes I teach full lessons. No matter which role I am filling, I always try to incorporate non-standard approaches to thinking about math problems. In particular, I want students to realize that math is not a collection of formulas, but that the formulas are the product of mathematical thinking. Outside of the classroom, I try to be involved in curriculum development, test writing, and project planning.

I also try to incorporate critical thinking into the Academic Decathlon class. Rather than simply displaying all of the formulas they will need during the competition, I try to motivate them to approach each problem from scratch. This way, they can discover the formulas on their own, and they know how to change the formulas to deal with modified problems.

## Lessons Learned

Perhaps more than anything, I have learned that there is a huge gap between students' computational ability and their conceptual understanding. Most students can memorize the steps of an algorithm and perform it on their own, but virtually none take the time to consider the deeper implications. Somehow, students seem to think that a math class is where critical thinking comes to die; once they have a formula, the problem is solved and requires no more thought, when in reality it is the analysis of the formula that requires the most high-level thinking.

Another surprise for me was just how different high school students are from college students. The College Ready Math class at Mountain View contains almost exactly the same material as the University of Arizona's College Algebra class, and the age difference between a high school senior and a college freshman is not significant, but there are dramatic differences in the learning styles. Lessons and teaching strategies that worked well in the college classroom went over like a lead balloon in high school. With Matt's help, I am learning to tailor my teaching style to a particular audience.

## Teaching Materials

- Introductory Presentation (PDF)
- Class Notes and Lectures
- Graphing Transformations: a worksheet to practice shifting, stretching, and reflecting the graph of a function (PDF)
- Discriminants: A short Powerpoint presentation on the uses of the discriminant (PPT)

- Academic Decathlon homework and quizzes (PDF)