Here are the reports for the Fall 2008 UTAs.
Joshua Davis-Salsbury
Sponsor: Ed Alexander
Course: Math 129
With the semester coming to an end, I'm disappointed that my experience as a UTA for math 223 is over. Throughout the fall, I assisted in the learning process of many students and actually gained a better understanding of all my previous math courses. Most importantly though, at the end of it all I improved the way I present and teach mathematics. As Ed. Alexander's TA, I led review sessions prior to exams. Of course, my first session went horrible. While I arrived with a plan of attack and understood what I wanted to do, I came to understand that 30 faces terrified me. While I improvised and managed to keep composure, this experience showed that I may not have been the best guy for the job. However, based on my performance at the future sessions it was clear that I was getting something out of this experience. My very last session revealed a confident UTA with a style that was remarkably different than the one who lost control of the first. I was able to answer questions I was unprepared to answer and did so more effectively than ever. Instead of just preparing to know the answers to questions I may have been asked, I prepared the best way to teach the answer. This revelation was most pronounced when I was asked to teach the introduction to divergence. Once again, I made a few mistakes, as most usually do when presented with a new task, but I was also given the chance to fix them by giving a quiz and going over the common errors. At the end of all of it, I guess I can say that I found my confidence and became a bit enlightened. Unfortunately, now I find myself preoccupied with whether or not my professors are considering the numerical aspect of teaching as opposed to what may be on the test tomorrow.
For my presentation, I will be showing how math is involved with game theory; more specifically, how it is involved with texas hold'em. Although it may be surprising to math majors, few people are aware of the more complex math problems of poker, and I would like to illuminate the possibilities of the game should a person be aware of the math.
Rebecca Strautman
Sponsor: Paul Dostert
Course: Math 215
Being a UTA for the math department was a great experience in a number of ways. It helped me improve and maintain my math skills, as I had to review the material taught in the courses I tutored and understand the material well enough to explain it to someone else. More importantly, it gave me a glimpse into the world of math education. While this was a field I had considered going into, I had no real experience, and the UTA programs was a great place to start.
As one of my responsibilities, I tutored students in calculus, and also held office hours for Math 215. During office hours, I would usually end up helping a few students with their homework. I also held one office hour per week in the computer lab with Dr. Dostert to help students with MATLAB.
While I had some previous experience tutoring students and grading their work, I had no experience in actually writing tests or projects. As a UTA, I would go through the exams before they were given and give my feedback on them. It was interesting to have to take into account things such as the length of the tests and difficulty of the problems. We also wrote a project for the students on applications of linear algebra to problems in other fields, and I wrote a few of the project options. This was a good experience not only because I got to design a project that the students would actually complete, but because I learned more about the applications of linear algebra myself as well.
For my final presentation, I researched the Comprehensive School of Mathematics Program, a K-6 program implemented in the 70s and 80s. It had some similarities to the “new math” programs, emphasizing elementary sets and relations in order to promote good problem-solving skills rather than memorization of algorithms. I looked at some of the problems used to teach new concepts, such as fractions, multiplying with decimals, parallel lines, and geometric shapes. One method of teaching that stood out was the use of a mini-computer: a board with squares representing 1, 2, 4, and 8, that students would place checkers on to represent different values. This was used to help students think of operations on numbers and numbers themselves in different ways so that they wouldn’t just rely on memorization. It was very interesting to read through lesson plans and see what kinds of methods were used to encourage creative mathematical thinking, as well as interest young students in math. This was another good opportunity to expand my knowledge of methods in math education.
Ryan Wong
Sponsor: David Glickenstein
Course: Math 223
I had always been a go to friend for math help – how bad could it be as a teaching assistant? It seems from that statement like I was asking for trouble. The first day of tutoring, I walked in and approached a group of students. Of course, they were in vector calculus. I thought, vector properties, okay, I can do these. Little did I know, the first question I would ever get in the tutor room was prove that a dot (b x c) = (a x b) dot c. For a moment, nerves took over and everything about vectors escaped my head. It took me a moment to recover and then I realized: okay, bring it back to the basics and vectors began to return to me. From the first day, I discovered a useful strategy I could use: bring everything back to simple terms- the basics- and then build from there.
The tutor room was a great environment. It brought back concepts and theories that had become virtually automatic to me. For the first few weeks, it bothered me that I was unable to answer every question. As the semester continued, I realized that most of the students were appreciative of a different view of approaching problems. Although there were days were I felt I could not answer any question, it made the days that I could answer them all that much more rewarding. It was gratifying hearing “thank you” as the student walked out the door with a lightened disposition.
This semester, I was quite lucky to be placed with an honors calculus II section taught by Dr. David Glickenstein. My main responsibilities were to run discussion sections, grade papers, and create review sheets. The first discussion section I lead was quite intimidating. I had never been in front of a group of people. The night before, I prepared all sorts of sample problems and tried to gain as complete of an understanding as possible. Running through potential questions students may have and how I would answer them. Arriving to the first discussion, I was expecting the worst- a student asking me a question I had no idea how to answer. To my relief, it was nothing like that and never was. The students were extremely knowledgeable about the subject but interestingly enough lacked the knowledge of some key concepts that would make their adventure through calculus that much easier. It was actually the most fun when there was a problem that I could not do off the top of my head. It forced the students and of course me to think. The additive knowledge was able to synthesize a pathway and method to arrive at an answer.
It was interesting to see mathematics from another perspective. Dr. Glickenstein was an extremely helpful mentor. He provided many of the helpful techniques for preparing for reviews and discussion that both saved time and were most effective. I was also grateful that he gave me some freedom to take the problem sessions in my own direction. I found it most useful if I asked for questions instead of just doing problem after problem. This allowed me to interaction with the students the most. I felt that this was the best part of this experience. Helping students find a new appreciation for mathematics is what mathematics education is about.
Mathematics is important in many subject areas. I chose to focus my presentation on the importance of mathematics in regards to an ecological perspective. An ecologist’s ability to create models and interpret models from data in the field is indispensible. Many equations are given in terms of rates. An individual’s ability to use simple differential equations to derive a population vs. time plot is useful in determining population number. In the rate equation for logistic equation, dP/dt=rP(1-P/K), it is important to recognize the effect of altering variables. For example, when carrying capacity K approaches P, we know that the equation will approach an exponential growth equation. Understanding and interpretation of graphs in ecology can be cultured by and learned from the four method approach to mathematics which is the understanding of graphical, algebraic, numerical, and verbal interpretation of math.