# Fellow Profile: Sarah Mann

**G-TEAMS Cohort:**2010-11-
**Graduate Program:**Applied Mathematics -
**Teacher Partner:**Michael Herzog -
**School:**St. Gregory College Preparatory School -
**Grade level:**8-12 -
**Topics:**Geometry, Algebra II, and Quantitative Analysis

"Go down deep enough into anything and you will find mathematics."

## Research Interests

Sarah Mann is a graduate student in the Program in Applied Mathematics at the University of Arizona. Her research interests are at the intersection of mathematics and computing. She is interested in information theory, the study of how information is represented, compressed, stored, and communicated. Recently Sarah has been studying the reliability of RAID-like systems for data storage, as well as the error correcting codes that are at the heart of RAID technology.

## Classroom Activities

St. Gregory is offering a new fourth year math class for students who have completed Algebra II but who do not wish to continue into a Pre-Calculus class. The development of this course, missnamed "Quanitative Analysis", has been the primary focus of Sarah and Michael's partnership.

During the first semester, the class has followed the text "Problem Solving Strategies: Crossing the River with Dogs and Other Mathematical Adventures" by Ken Johnson and Ted Herr. Each chapter of this text presents a new strategy for problem solving and example problems that may be solved using that strategy. In class, students work in group to solve problems, present their solutions to eachother, and discuss their solutions. Regular problem sets are assigned in which students are assesed primarily on how completely, succintly, and effictively the student presented her solution, and secondarily on the correctness of the solution. Sarah and Michael serve as fascillitator and organizer in the class room, only occasionally lecturing on new material. They encourage students to think creatively about problems, fully explore how each strategy may be implemented and justify their solutions.

## Lessons Learned

It has been interesting to watch students encounter various mathematical concepts for the first time, in particular in the Geometry and Algebra II classes. It has given me a new appreciation for how much students struggly with these concepts at first, and how non-inuitive they can be. Things that seem obvious to me, are totally non-obvious to them, and it is an art to figure out exactly where the students are getting lost.

Many of the issues teachers have to address in a high-school class room are not subject related, but behavioral. Much time and energy is spent keeping students on task, making sure they are doing their homework and showing up where they are supposed to be. Designing a course in which students really learn the material is as much an exercise in teenage psychology as a reflection of the material being covered.

## Teaching Materials

- Research Talk
- Algebra II lessons:
- Python programming: