# Fellow Profile: Christopher MacGahan

**G-TEAMS Cohort:**2011-12-
**Graduate Program:**Optical Sciences -
**Teacher Partner:**Jeanne Deloria -
**School:**Tucson Magnet High School -
**Grade level:**9-12 -
**Topics:**Honors Geometry, Pre-calc, AP Statistics

"Students think of math as some sort of separate entity from their other studies, a list of equations and algorithms that can be memorized and spit back out on a test. But there is a hidden beauty in math – while its most direct usage may be in number crunching, it is so much more than this. Math can be used to explain everything from the physical world around us to the nature of our economic system. By using these real life examples and stressing how important math is to everyday thought and analysis, we can change students perceptions of the subject."

## Research Interests

I am a Ph. D student in the College of Optical Sciences. I work in the Image Quality group, led by Dr. Matthew Kupinski. Many imaging groups around the country work on reconstructing some sort of a scene given image data, whether that scene be a city block or the human body. The IQ group focuses on task based imaging – developing mathematical algorithms to best execute a certain task, such as malignant tumor detection. My research focuses on applying this to nuclear imaging for military applications – when detecting a bomb, it is unnecessary to reconstruct the whole city, just to determine the location of the signal with the greatest magnitude.

## Classroom Activities

I am working at Tucson High Magnet School with Jeanne Deloria with her Honors Geometry, Pre-calculus and AP Statistics classes. I am trying to bring my background in physics into the classroom. We have done a couple of optics problems in Jeanne’s geometry classes, for example looking at beam deviation when a laser is incident upon a hinged mirror. In her pre-calculus class, I’ve tried to bring in physics problems into the class. One example was manipulating the equation for the height of a thrown ball as a function of time and looking at how changes in initial height and velocity affect the plot.

## Lessons Learned

This experience has been an eye opener. Going into the year, I was hoping to run experiments and teach the students about real world uses for the math they see. While I’ve tried to do that as much as possible, a good amount of time has been spent reviewing and connecting basic ideas. We are using a new, project based curriculum in Jeanne’s Geometry classes, and while I love the idea in theory, it introduces conflicts not present in a normal curriculum. First and foremost is that students are just uncomfortable with word problems, and a few of them have significant language barriers. I guess the lesson here is that there are just so many different things an educator must keep in their mind before deciding on a lesson plan

One thing that always amazes me is how students have been taught to memorize certain equations. The clearest example of this is the concept of the slope of a line. If Jeanne talks about slope, a different subset of the class will understand her if she describes slope as “rise over run” as opposed to the equation for the slope between two points on a line. Only a portion of the students see the two as equal and just a different description of the same idea. Ultimately, that is the key to understanding math and thinking like a mathematician. Those that can’t make the connection between the two seemed to struggle later in the semester with concepts like the fact that two lines with the same slope are parallel.

Teaching statistics has been an interesting experience. Probability and statistical thinking are not something taught heavily in schools, and at the start of the semester, the students struggled with the idea that statistics could be used to analyze a claim, whether it be through a simulation or experiment. As the semester has gone on, it has been fun to see the students improve as they slowly begin to understand the concepts.

## Teaching Materials

- Pendulum Activity
- Fiber Optics Activity
- Law of Reflection and Mirrors