Here are the reports for the Spring 2005 UTAs.

**Sponsor:** Sacha Swenson

**Course:** Math 120R

I had done my research. I knew the topic thoroughly. Yet, the first time I stood in front of my Pre-Calculus class, I could feel my heart pounding. Outside of brief presentations, it was to be my first time speaking in front of class. Not only that, but my words would be affecting someone else's understanding. What if I led them down the wrong path? What if my explanations only confused their thinking further? What if (God forbid!) I could not answer a question that was posed to me? Or worst of all, what if one of the students pointed out something wrong in my presentation?

It was a scary moment, but I was able to make it through my presentation. Afterwards, when several students complimented me on my lecture, I felt confident that I had been an agent of comprehension. The next week, when I made a presentation in another class, it was surprising how little my nerves affected me.

I had spoken on the history of sine (a subject rather difficult to make interesting), and I felt like I learned more then the students. This seemed to be a theme running throughout my time as an undergraduate teaching assistant. Leading review sessions required me to know more about the subject then every student who came. It was encouraging to see attendance grow after each one.

Although the tutoring was occasionally slow during my hours (11-12 on Friday), those who came were eager to learn and ready to explore. Although I did not have an answer for every question, it was satisfying to embark on an exciting journey with each student who walked through that door. I especially liked a certain student, who I will call Brint. Brint was a bright guy, but had a very weak background in math. It seemed like every time I tutored he was there, trying to figure out a new concept. What a reward it was to lead him towards a broader understanding of what he was studying.

Here is the abstract from a presentation that I was able to put
together through this program:

Education in the United States is often negatively compared to education in
many other countries. To investigate this, we drew comparisons, both from
our experiences and from documentation, between the mathematics education
in Vietnam and in Arizona. Both countries feature graduation tests. We
found that Vietnamese education is more intensive and in general more
effective for a variety of reasons. In Arizona, we found that the emphasis
on group education and application prepares its students better for both
higher education and real-world uses of mathematics. However, the gap
between the stated goals and the actual performance of students remains
wide.

**Sponsor:** Bruce Bayly

**Course:** MATH 254

Sometimes I feel like being an Undergraduate Teaching Assistant is like sticking a needle in my eye. Just kidding. Having been a UTA for a semester, I can safely say that it is far more comparable to a Swedish massage than a shot to the eye. I end a semester of working with Professor Bruce Bayly teaching Differential Equations (Math 254) on a very positive note. The experience was worthwhile and I am fortunate to have had the opportunity.

To begin, Professor Bayly was an outstanding instructor to work for. Attending class regularly, I experienced one of the department.s premier mathematicians in action. I tried to attend class as often as possible to be available to the students and to refresh my memory about the subject I had learned many semesters before. Although I held office hours outside of lecture, few students chose to attend. My primary role as a UTA was to make up solutions to the homework assignments each week. These solutions were posted online (D2L) and the students could check and grade their work. In addition, I assisted in grading a page of each exam given. These two roles suited me nicely.

I have always heard that starting homework assignments early is invaluable to doing well in a class. Working under Dr. Bayly, I was expected to complete each homework assignment in a timely manner. Unlike my coursework, I could not procrastinate as I typically do. I saw first hand how convenient it is to finish assignments early. When I did have a question on the homework, I had plenty of time to confer with the instructor. I hope to carry this habit to future classes. My other responsibility as a UTA was also very beneficial.

In addition to making solutions, I also graded one page of each of the exams. I enjoyed the esteem and responsibility of the position, although grading is time intensive and a tedious task at times. Entering this program I was a bit interested in teaching as a possible option for the future. Teaching in the most classic sense is a small aspect of the position, however. Tutoring in the tutoring room for three hours a week was an interesting look at the teacher student relationship. Other than tutoring though, grading gave me a glimpse at one of the major jobs of an instructor. Grading exams opened my eyes to the importance and difficulty of test writing. I have a newfound respect for the time and effort it takes to be an instructor. In fact, participating in this program has interested me in teaching rather unexpectedly. I have become very interested in teaching in some manner in the future. Although my major will continue to be optical engineering, upon graduation I may apply for Teach for America. Teach for America sends college graduates to teach in some of our country.s worst schools in hopes of closing the education gap in our secondary schools. I contribute my newfound interest and respect for teaching to the UTA program and to Professor Bayly. I feel fortunate to have participated in such an outstanding program.

**Sponsor:** Kirti Joshi

**Course:** MATH 125

Being an Undergraduate Teaching Assistant has been fun, challenging, rewarding, and stimulating, as well as very beneficial. I gained valuable experience in tutoring, mentoring, and, most important, interacting with other people. Not only did I work a lot with the students, but I also worked closely with a professor and the other UTA's. I learned skills that will be valuable both in school, and out.

Some of my duties were grading weekly quizzes, holding regular office hours, giving review sessions, and tutoring. By grading, I learned how other students think in test-like situations, and it helped me to see how much they were actually understanding the material. As a grader I was able to specifically see what areas students were having trouble with and put a higher emphasis on these concepts in my teaching. Holding office hours was another beneficial experience gained from this program. It allowed me to work one-on-one with students and make a direct impression on them. The review sessions were also important, as they gave me a feel for teaching in front of a group of people. It's interesting to see how much harder math gets when you are doing it at the front of a classroom. Finally, working in the tutor room was one of the most important aspects of being a UTA. It allowed me to interact with students, and teachers, from several different math classes, not just the one I was involved with.

Overall, I feel that the UTA program was a very good experience. Although there were many times it proved to be quite challenging, there were many times it was very rewarding as well. It will have a definite impact that will affect me both as a student in my future classes, and as a teacher when helping friends and classmates. I hope that the UTA program will be available again in the future, and that those UTA's will get as much out of it as I did.

**Sponsor:** Nick Rogers

**Course:** MATH 223

I had the wonderful opportunity of working with Dr. Rogers for his Vector Calculus class last semester. During the semester I held office hours, wrote quizzes and graded homework every week and even had the opportunity of writing a fraction of one midterm test on top of spending a couple of hours in the calculus tutoring room every week. Before this appointment, I did not have any prior experience working as a tutor, so initially I was very nervous about tutoring others. However, as the semester slowly progressed, I started enjoying my position as a tutor and it really helped me gain confidence in what I do. Even though not a lot of people showed up for my office hours during the semester, those who showed up made me feel like I was making a difference in somebody's life. It also showed me the importance of interaction and communication with others for the working field. After this experience I also developed a lot of respect for professors and the amount of time they devote to teaching because it took me a couple of hours just to write a few problems for a weekly quiz and I spent an even longer time just to write a few problems for a midterm. Overall I really enjoyed my time as an undergraduate teaching assistant, it really helped me experience a different part of the college life.

**Sponsor:** Elias Toubassi

**Course:** MATH 113

I really enjoyed being a UTA this semester. I had the nicest (and probably the best, in my opinion) sponsor teacher, Elias Toubassi. He taught Math 113, which is Topics in Calculus. We got along extremely well and communicated frequently either through email or in person. From the classes I did see him teach, he was very communicative with the students and explained everything in thorough detail. That made grading papers much easier for me.

I liked this good immensely. The most satisfying part of the job was working in the lower level tutoring room. Although I only saw a few of my students from Professor Toubassi's class, I really liked helping other students, ranging from low level algebra to pre-algebra. On several occasions I had students ask me what my schedule was just so they could come back to see me! That was the most rewarding part of the job.

Another part of the job I liked was the review sessions. Although I will have only done four, I feel that the experience has benefited me greatly. Students who were hard working came to the review session obviously wanted to learn the material and came prepared with questions. I was nervous for the first session, as I had never done a review for an exam before and didn't know what to expect. But after the first, the next ones were a breeze. Before I knew it, the hour was up. Professor Toubassi even told me the students had wished it lasted longer! I am happy to know that I helped the students and made a difference.

Now for the parts I didn't like about being a UTA. My biggest gripe is office hours. I didn't mind holding office hours, but not once this semester did I have a student. At first I was doing two hours a week, but since no one had been coming, I had it cut to one hour. The only student that came was someone who was in another section. I felt that holding the office hours were a waste of my time. The majority of the time I either graded papers or studying, which is not a bad way to spend my time, but it was irritating to know I had to be there in case someone showed up.

Another aspect of being a UTA that I didn't like was grading papers. I found it really tedious after a while as well as boring. It often took me roughly two hours to grade, depending on the complexity of the assignment. I was always second guessing my grading. Was I being too nice? Too mean? I didn't like being the decision maker of someone's grade. But I did get to see where students made common mistakes and hopefully I fixed those mistakes. If everyone made a problem, I left a note with Professor Toubassi for him to fix.

Overall, I really liked being a UTA. If I could do it again, I would. Since I am going to be a math teacher, I felt this job was great experience in what it would be like to help with a math class. I highly recommend this job to anyone who likes to help people, whether they are a math major or not!

**Sponsor:** Hideo Nagahashi

**Course:** MATH 124

I applied for the UTA program because I am interested in becoming a math teacher and this seemed like the perfect opportunity for me to gain some experience working with students. I spent the semester working with Professor Nagahashi and his Calculus I class. The class was not very big, only about 15 students, but this was a perfect opportunity for me to be able to get to know the students further than just by name. Aside from the three hours per week spent in the Math Tutor room, I was responsible for writing and grading a weekly quiz for the class. The students would take the quiz each Tuesday and I would grade and return them by Thursday each week. On Thursdays I would answer questions about the quizzes and do some of the problems on the board for the class. I also had an office hour right before class on Tuesdays, which was perfect for the students to be able to ask questions before they took their quiz that day. I usually had between three and six students come to my office hour each week. During my office hour on Tuesdays was the most valuable time for me because I was able to talk with the students and find out what concepts they were struggling with and how they felt about the class in general. During the semester I also had the great opportunity to lead the class in a review before an exam. I prepared practice problems for the students and we went through the material together. The students were very understanding about my limited experience and they were very active in the activities that I had planned. I had a great time working with the students and especially Professor Nagahashi this semester and am grateful to have been given this opportunity.

For the final presentation I decided to focus on different types of assessment. I had spent the entire semester writing quizzes and had to deal with all of the complexities that go along with writing assessments for the students. Things like difficulty of the problem, type of question to ask and expectations of the students were all challenges at the beginning but by the end of the semester I had written ten quizzes and had gotten positive feedback from most of the students. The presentation covered the pros and cons of different question types such as multiple choice, true/false, and essay questions. I was honored when Professor Nagahashi decided to include an essay question on the last class exam after watching my presentation.

**Sponsor:** Steve Foster

**Course;** MATH 124

I found out about the Undergraduate Teaching Assistant Program in December 2004. I was just done with my paperwork for transfering to the University of Arizona and I was searching for a job on the campus that would involve assisting people in learning math. Although I do not plan on becoming a teacher, I do think I'll wind up being a TA for a couple of classes when I attend graduate school, so I thought it would be good to have some early experience with standing in front of a class, grading papers, and developing lectures and review sessions. I was able to practice all these tasks in my UTA position, and I had an outstanding time in the various activities directly relating to my course as well as the weekly UTA meetings.

I helped Steve Foster with MATH 124, Calculus I. The reason I chose Calculus 1 is that I've always felt it to be a new level of math compared to trigonometry and college algebra. When I studied calculus in 11th grade I was initially very confused about the new concepts that were thrown at me, but after a while I noticed that this was the point where math really was beginning to be fun. I had always been pretty good at lower level math but I never really felt that there was anything special about it in particular. Calculus was the first step towards my full appreciation of how math is more than just a bunch of numbers and symbols. I made it my mission to help people seeing the underlying beauty that math carries, to understand that math is nothing else but common sense, cloaked in the economical language of symbols, and backed by the rules of logic.

As to my actual experience, I was a little disappointed that close to nobody came to my office hours, which shows that people did not use every resource available to them to succeed in the class. Based on the grades of some homeworks that I graded, they were in dire need of using these. I think what lead people to not use all the ressources was a lack of curiosity. One can look at the subject matter of calculus and just see the theorems without perceiving them, and come to the conclusion that they have no connection to reality, or that they serve no purpose other than to let the teacher torture his students with the drudgery of memorizing them. In actuality, the study of calculus can be seen differently, and one can ask after reading a theorem: Why does this have to exist? What would happen if this theorem wouldn't exist? Isn't much of our modern technology - that paradoxically, as in the case of the TV or computer, might distract us from studying calculus - not possible to construct without the knowledge of calculus?

I presented one in-class lecture, on theory and application of optimization and regression, to instill more of an awareness that calculus does play a major role in many applications. In retrospect, I wish I would have talked about the history of calculus instead and talked about why people came up with these methods, and how long it took humanity to actually come to the point of even thinking of the questions whose answers were hidden in calculus. This would have led people to think about calculus not as a mere technical matter, but to see that people actually invented this in years of hard work. This is my advice to anyone who is teaching a mathematics course, or any science course: Remind your students that the subject matter was not always there, that it's not static, that people actually developed it and that it mostly arose from a real-life problem that needed a solution.

I thank Steve Foster for giving me the opportunity to help with his class, Feryal Alayont for help with my current math classes and a good time in the meetings, and of course all the cookies she brought, and all the other UTAs for interesting and thought-provoking conversations. I would recommend anyone to apply for this program if they have a passion for helping other people in math.

**Sponsor:** Ted Laetsch

**Course:** MATH 323

This past semester I had the pleasure to work as a undergraduate teaching assistant in mathematics working for Feryal Alayont and Dr. Theodore W Laetsch. During the program I held office hours twice a week, ran review sessions, made reviews for tests, and spent three hours a week in the calculus tutoring room. Prior to the program to entering the program I had no notion of going into teaching mathematics, or any other subject, but I found the entire experience extremely rewarding and now I am interested in pursuing teaching as a career. I can't think of any higher praise for this program. The supportive leadership and unique rewarding opportunity make this program an unparalleled and extremely important portion of our institution, and it is a sign of the poorly guided attitude our society has towards education that there will not be enough funding for this program to run next fall. If this is an outcome that is at all avoidable I would recommend it in the strongest.

**Sponsor:** Larry Grove

**Course:** MATH 215

I enjoy teaching. I have never had trouble giving a speech or being in front of a class. But here's why I really liked my semester as an undergraduate teaching assistant: I was able to interact with a class (16 students) and get an idea of what it is like to be a math teacher, while only taking on a small portion of the responsibility that a teacher normally has.

Every week, I spent three hours in the math department's upper-division tutoring room (for Math 124-299); I held two office hours specifically for Dr. Grove's 215 students, and I graded the daily(Monday, Wednesday, Friday) homework assignments for that class. Even I will tell you that forty homework assignments times 16 students is a whole lot of work for everyone involved. But I think that 215 is the first math class where students are introduced to entirely unfamiliar concepts, like vector space, linear map, and isomorphism. The frequent homework assignments forced (hopefully) the students to keep up with the material, and it also allowed the students to get plenty of feedback from me (whether they wanted it or not). I also had a great opportunity to see how some undergraduates think about mathematics. In general, I think that the hardest homework problems for the students were the ones that asked them to prove something. Usually writing down the definitions of the math vocabulary found in these proof problems would constitute at least half the work involved in coming up with a solution. I hope I was able to prepare these students for the greater importance that definitions (and theorems that establish relations and equivalences between definitions) will continue to play as they continue to take higher level math classes.

I also gave one regular lecture during the semester. The time went by so fast I felt like I was barely able to cover any material. I definitely have more respect for teachers, now that I have found out how hard it is to stick to a schedule and do a good job of conveying the material. It was much easier for me to help students in the tutoring room, where I could work with just one or two students at a time. In case you are wondering, most of the students who came to the upper-division tutoring room were taking 124 or 129 (Calculus I and II). And it also seemed like these students were doing fairly well in their classes. Almost everybody that came in for tutoring was asking about details and specific situations, not looking for a quick fix to avoid bombing a quiz/test/whole class. In other words, it was easy to work with these students because they were motivated.

I would recommend the UTA program to anyone who is interested in teaching math, working with students, or anyone who has about ten free hours a week and wants to answer a bunch of math questions.

**Sponsor:** Kathleen Marrero

**Course:** MATH 124

When I was first exposed to the UTA program, I felt very interested but worried at the same time. I am excited about the program and worried if I could be a good UTA if I was offered the position. I even felt more nervous when I knew that I was offered the position.

I soon found out that it was not hard to be a UTA. I even had fun and enjoyed working. It was a great opportunity for me to get to know other students and their learning styles. I always enjoyed tutoring in the tutoring room. I felt grateful after helping other students. I was especially happy when the students understood the problems and the concepts. However, it was not always the case. There were a few students who came in just to get the answers. I had never liked their attitude.

When I conducted review session before tests, I wished there were more students showed up. Usually, only about 3-4 students attend. I would feel happier if there were more students than that because I helped a lot of people.

Overall, this has been a great experience I had. It helped me become more professional and understand more about different learning styles. In addition, the presentations in each meeting helped me a lot in becoming a better person. I am more mature than I was last semester.

Abstract of presentation:

I and my partner, Steven Crawford, presented a topic on the difference between Arizona Math Education and Vietnam Math Education. We explored the positive and negative things present in both education systems based on our own experience as well as documentations. We found out that Arizona school focus on application of mathematics while Vietnam focus mostly on theory and less application. Another big difference is the expectation of the knowledge. Everybody in Vietnam is required to be at the same level while Arizona schools allow students to be in different levels.

**Sponsor:** Fred Stevenson

**Course:** MATH 129

Before being an Undergraduate Teaching Assistant, I planned on teaching math at a High School. But after being a UTA for Dr. Stevenson's Calculus II class and tutoring higher level math classes, I decided that I want to teach math at a college or a university level. As a UTA, I tutored in the math tutor room, held office hours, attended class some of the time, and I was even able to teach the class when Dr. Stevenson was out of town.

Because I tutored for Calculus II, I often had to explain the applications and the theories of the techniques that the students used in class. I enjoyed tutoring at this higher level of thinking because it was new to me. I have tutored high school students in Geometry and Algebra, but the applications of those subjects is mostly memorizing and applying formulas. This UTA experience gave me the desire to teach higher levels of math where concepts, not formulas, is the main focus of the material.

I had the opportunity to teach the Calculus II class one class period. This was one of the best experiences that I have ever had. I had to prepare to review past material, and be ready to present new information. This was the first time that I got up in front of a class and taught. By the end of the class, I was very comfortable standing in front of the students and lecturing. It made me have more respect for my teachers, and encouraged me to be a better student.

Tutoring in the higher level math tutor room was the constantly the most beneficial experience that I had. In the tutor room, I was asked a wide variety of questions from a wide variety of class?s everyday. The variety of questions kept me on my toes. Helping students in different classes reinforced my Calculus and Algebra skills, which helped me in my other math classes.

Being a UTA was a great experience and it even changed my career goals. I would encourage anyone who is interested in mathematics and especially teaching mathematics to be in a program like the UTA program.