Here are the reports for the Spring 2003 UTAs.

Han Gao

During freshman year in high school, there was an unforgettable quote on the wall of my class — “A mediocre teacher tells, a descent teacher explains, a good teacher demonstrates, and finally a great teacher inspires.” In math, it is easy to tell, to explain, to even demonstrate, but out of the numerous classes I have taken, and all the teachers I.ve come to know over the years, there have been very few math teachers that can inspire math. Coming into this UTA program, I tried to be one of those tutors who not only can explain a concept, do all the problems, but one that can get students interested in mathematics.

I worked with Dr. Valerie Watts in her Vector Calculus class (Math223). Weekly, my time was broken down as follows: Three hours of tutoring the Math223 students; Three hours were spent in the math tutoring labs, where I taught from college algebra, to trig, to some beginning calculus; Three hours were spent grading papers; and the tutors met once a week for an hour to discuss individual progress.

I'll start with Math223. Out of all the math courses I have taken, this class is by far the hardest one for students to master in my opinion. The class starts off easy — basic operations on vectors, drawing contour curves, then gets exponentially harder towards the end of the semester — flux, divergence, etc. During my office hours, students mostly come in seeking homework help. One major flaw is that most students care more about the percentage on their homework than understanding of the material. During orientation, we were taught not to do the problems on the board, instead, give hints, pointers, and “teach with hands behind our backs” This was exceedingly hard to do in practice. Secondly, many students did not learn the prerequisites of this class very well, for example, basic calculus, trig, graphing conic sections, etc which many of them did not master. During the exams, a lot of them do poorly not because of any misconceptions of Math223, instead simple mistakes or a missing link from a previous class. Finally, not all students that need help show up for my office hours. I end up with the same 7–8 people every time during office hours and from grading homework, I know lots of them need help besides those few individuals. I try to apply many problems to real life situations when possible and try to keep a big smile to show how much I enjoy triple integrating strange functions.

In the math tutoring labs, there are great gaps between students. Some of them need simple homework help; others are clueless and need complex concepts explained. Either way, the tutoring lab experience was very fun. There are lots of tutors there, business math tutors, graduate students, and even teachers. You can never get bored, even when no students need help. Dr. Hartman said that attitude is very important, which is very true. From my experience, by keeping a clear, and seemingly excited voice, it will draw the student's interest. Many times I have to encourage them, keep them interested, challenge them, or make up problems off the top of my head to make sure they understand a concept. Basically, use every possible way to make them understand and remember the material. I've heard complaints, where us tutors teach a concept differently, the student end up getting points off on the homework or test. During orientation, we were taught, “not to be friends with our students”. However, that was also extremely difficult. From my experience, I teach someone and they understand it well, they will come back and look for me, and over time, you become familiar with each other. Also, when approached by a business math student, I simply said, “I'm not sure” and directed them to a business math tutor. Personally, I've spent a lot more time in the tutoring lab than 3 hours a week, but to me, it's extremely fun.

Grading was not really time consuming for me. Students divided homework into two stacks and I only graded one stack. Most of the time it is only two problems, Dr. Watts gives me a very specific rubric for grading, no problem ever came up. I am an easy grader; I give pity points and half points and round up etc, which does not really matter, as long as all the homework is graded fairly. Fairness is key. I also try to write the correct solutions on students. papers and point out what they did wrong. Afterwards, if I find a concept on the homework that many people did not understand, I leave Dr. Watts a note.

The first week of the semester, couple students claimed I explained a homework problem incorrectly. Dr. Watts spoke to me later, turned out to be a problem I have never seen in my life. She gave points back to all the students. At first, I was furious! I asked many students in that section what really happened and received vague answers. From then, I made a list of all the students that come to my office hours, and I looked over every single homework problem assigned beforehand. However afterwards, I've come to realize that my job, as a UTA is to better serve the students and my teacher, not to show people what an awesome mathematician I am. If my teacher by giving back points can avoid a trial and students get their grades raised, I should be happy.

This was a great semester overall, I really enjoyed working with Dr. Watts and Dr. Hartman. They are both very nice and capable mathematicians. I've really had fun being an UTA and I recommend this position to any student on campus.

Matthew Green

During the spring semester of 2003 I was a UTA for Edward Alexander, Math 129. I worked 10 hours a week. For 3 of those hours, I tutored in the algebra tutoring room. I spent another three holding office hours in the calculus tutoring room. I also spent 3 hours grading papers. The final hour was for group meetings.

My time in the algebra tutoring room has been both instructive and frustrating. I have learned a lot about my abilities to communicate mathematical ideas. It is easy to underestimate the difficulty of teaching someone mathematics when the mathematics is simple. I learned that I am not always the most understandable person, and I have had to work hard to find effective ways to relate ideas. While some students will understand a topic presented in one way, that same student may have difficulty understanding the topic presented a different way. As a tutor, I have had to develop my ability to quickly determine how the student thinks about things and what the most beneficial presentation of the material will be. Although my time in this room has a some points been very tedious, I think the overall experience has been very positive for me, and has developed skills I was lacking.

I spent my office hours in the calculus tutoring room on the suggestion of Professor Alexander. He had told me that from previous experience, very few people would show up for my office hours and that I would be using my time more effectively in the tutoring room. While in the calculus tutoring room I not only had to tutor for 129, but also multivariabble calculus and differential equations. This provided me with a rather shocking review of my lower division mathematics. I was not always able to help people, particularily in differentail equations, towards the end of the semester when things got a little more complicated. Sometimes I had to sit and think about a problem too long and offended the patience of the student I was trying to help. For the majority of the 129 students, I think that I provided reasonably good help. I was able to be more effective with the 129 students since I was grading their papers as well and knew exaclty what they were learning ahead of time.

Grading papers provided me with an in-depth review of the calculus 129 material. Having never graded before, I started out very slow and sometimes had to spend more than 3 hours on a stack of papers. I tried to grade fairly and consistently but also provide detailed commentary. When students made a honest effort to solve the problem but made a mistake I tried to explain what had gone wrong a much as possible, and offer suggestions on how to correct the error. Grading papers has improved my ability to quickly evaluate and solve calculus problems and has trained my eye to catch common mistakes. This helped me in the tutoring room because I was able to identify the student's errors more rapidly and save the student some time.

My experience overall as a UTA has been a times tedious and frustrating, due to my lack of certain skills, I think it has had a very positive effect on me and has forced me to develop those skills in which I was lacking. If I were to participate in the UTA program again, I would like to spend more time in direct contact with the students, and possibly come up with ways to improve my communication.

Bob Jenkins

It seems to me that my UTA experience was a lot different than that of the other UTAs this year. Math 254 is a BIG lecture, on an average day we had roughly 250 students in class, which make things a lot crazier than in most other math classes. For one thing the class practically has a staff of student help. Besides myself there were 3 graduate TAs who ran recitation sections and my favorite, paid graders, 10-15 student preceptors, and of course Dr. Bayly. All this help meant that I escaped the worst duty of most of the UTAs, grading lots of homework.

The change in class size altered my day-to-day duties as well. My most important duties were writing up solutions to the weekly homework assignments and running a 3 hour tutoring room Tuesday mornings that served as a weekly homework marathon for several of the students in the class. I found that writing the homework solutions to be the hardest and most fun part of the job. I found there's a big difference between solving the problem, and explaining your solutions. Showing the students how the solutions connect to other problems we tackled this year and others they had probably seen in other classes.

My only other duties had to do with the exams. One of the toughest things I did all year was holding review sessions on my own for the entire class. I'm not the most comfortable person you'll meet in front of a crowd, and the first time I stood there in front of nearly 300 students I was really nervous. Luckily, I got over it fairly well and I hope the next review session — tomorrow night as I write this — goes just as well as the last. Dr. Bayly put me through the grinder with my other exam duty; I had to take the tests myself with the students. This served two purposes. I was used as a guinea pig to see how long the test were and also that test solutions could be posted as soon as the test was over. This meant that not only did I have to take the test, but also I had to be sure I didn't make any mistakes! I actually did make a mistake on the first test and was more than a little embarrassed when a student pointed out my error in class. Luckily things have gone better since, or at least no one has caught any errors yet.

All things considered I thought that being a UTA was a worthwhile experience. The work duties are never too daunting and the pay is decent though not spectacular. For me this was a good prequel to the teaching I'll be doing as a graduate student in the next few years. I would recommend this job or one like it to anyone who wants a little teaching-like experience before getting stuck teaching as a graduate student.

Anita Lee

My experiences this semester as in Undergraduate Teaching Assistant have been very rewarding. I have learned a lot and have has the opportunity to help a lot of people learn as well. Math has always been a strong subject me for me and math class has always been my favorite class. However, like with many things that you do not use often, I easily forget many of the obscure topics, concepts, and rules that I have learned. This semester working as a Teaching Assistant for a second semester calculus class has given me the opportunity to solidify my knowledge in some of the areas of calculus that I had glossed over when I took the class. This experienced has really helped me understand the concept of infinite series and convergences and all the tests that go along with each, as well as with the purpose and usage of Taylor polynomials. I have also been able to review concepts that I already know. Knowing how to do a problem is one thing, but being able to explain how to do it to another person and why is a completely different level of knowledge. During review sessions, having to answer questions as to why I did something that why to solve a problem, really challenged my knowledge of the situation.

The Undergraduate Teaching Assistantship has also provided me the opportunity to help others as well. Between tutoring in the tutoring room and holding weekly review sessions for my class, I was given numerous opportunities to help many students. When a student comes to you not understanding what they are doing and you are able to help them understand math in a way they never thought possible and you are able to see them leave with confidence in what they are doing, it creates a rewarding feeling that validates your purpose for being there. Service to others has always been an important part of my life. Being able to incorporate service with something that I enjoy has been a great experience this semester.

This program is definitely something I would consider doing again as well as recommend to another student. However, I would definitely inform them about the large time commitment involved. It takes a lot of time to grade homework and to fully understand what you are teaching. If I were to do it again I would defiantly do it during a semester that I knew I did not have a lot going on.

Kenneth Porter

When I first entered the UTA program, I expected my years of teaching swim lessons to be helpful in teaching mathematics. As I first stepped into the tutoring room, however, it was a completely different experience. Rather than directing a whole class's learning, I had to enrich one pupil's (and oftentimes, many pupils working on completely different subjects) knowledge. While my previous teaching experience did not directly help me in tutoring, it likely made for a short learning curve.

Tutoring was the most fulfilling part of my experience. Review sessions and grading cannot compare to helping a lost student find his way. Tutoring was often difficult when the students had problems in areas that very scarcely or never used in the higher level math classes. Also, some of the advice that was received prior to tutoring was rather specious. It was encouraged that the tutors act less as a guide but rather as a follower while letting the student find his way. This works very well when the student knows how to solve the problem, but those understanding the problem do not come into the tutoring room. When tutoring, it is rarely a matter of connecting the dots, rather, it is introducing a concept to them that he missed in class. The students who seek assistance in the tutoring room are always capable of doing the work, but are not mathematicians and cannot derive the concepts themselves. The tutor, acting only in letting the student work his way through the problem only frustrates himself and the student. For the student to understand, it is often called upon the tutor to teach, not to act as a simple flotation device in the sea of mathematics.

Tutoring is not all I did as a UTA. I also graded papers. It's a tedious task that needs to be done. I had no trouble with it. In Math 215, however, proof problems often appear. These problems were hard to grade. All in all, grading is good experience in the behind the scenes teacher work.

For the first month or so, I was working on a review sheet in LaTeX. I enjoyed working with the language, and creating things. However, it is very complicated, even in working at it for a long time, the subject matter and a new and complex medium are not easily synthesized. And thus, I had little work to show for my hours of toil in the realm of LaTeX.

Actual teaching was the highlight of my experience. I hosted two sparsely attended review sessions, but that was much like tutoring. I gave a presentation in Dr. Hartman's linear algebra class introducing eigenvalues and eigenvectors. I captivated the class for an hour with the information from the book and an example about Fibonacci numbers. I spent a lot of time in preparation and in rehearsing in front of the class's true teacher. It was worth it when my true teaching experience went very well. I would have liked to teach again, but time dictated that it was not to be.

All in all, I enjoyed the UTA experience very much. The ten, varied hours of work a week is an excellent amount for the student-worker. I plan on returning in the program next semester and I would (and have) recommend it to my friends.

Matt Rounds

The experience as an Undergraduate Teaching Assistant (UTA) has been better than I could have hoped. I worked with a great professor and didn.t have much difficulty communicating with the students. This position has reaffirmed my desire to possibly teach at a university after graduation.

The class that I aided with was MATH 124, first semester Calculus. This was a great choice because I had taken the course only a year earlier and it was not difficult for me to recall the material. My duties required me to hold four hours a week of office hours, exam review sessions, and be in the classroom twice a week. While in the classroom I assisted the professor by helping students with in class problems to be solved in teams. I could walk around the room to discuss the problem with a student or check their solution. Being in the classroom also helped me to determine the ways in which the professor would explain a concept or the types of questions she liked to ask. Being in the classroom is an extremely important part of being an effective UTA.

At times holding office hours can be the worst part of the job. My office hours were four days a week, but unless it was close to an exam or homework due date, hardly any students show. Even at the end of the semester students were still asking where my office is and what times I would be there. At first it was very difficult for me to help students during my office hours. This was due to the fact that most of the questions I were asked were not conceptual and instead homework problems. In the beginning of the semester I had the idea that there wasn.t a homework problem I couldn.t answer. That couldn.t have been farther from the truth. My advice is to at least look over the homework and better yet to actually do the homework so you can know where problems might exist before you hold office hours. Another great way to help students with homework is to post the solutions on the Internet after the assignment is turned in.

Being a UTA is a rewording experience and is worthwhile for anyone interested in teaching because there are many people gifted with Math talent but it takes a special person to be able to effectively relate Math to others.

Curtis Rosenow

Everyone always seems to have a favorite teacher or mentor. That is, we all see and experience a personification of our individual concept of learning and knowledge. Through that teacher, we can then reap the rewards of our academic and personal endeavors more readily and with greater satisfaction. I asked myself a question at the beginning of my UTA term relating to these ideas. How can I benefit the most people like the favorite teacher that we all have?

In a nutshell, I figured out through the semester that easiest way to benefit everyone is to figure out how to show them the satisfaction that I get in teaching them. In the review sessions that I held, I would have several students stay beyond my expected ending time. I believe those students benefited the most because they showed me that they still wanted to learn. I could then reciprocate the favor in teaching them with greater enthusiasm and vigor. Those times were ultimately the best in the UTA experience, and it was then I could put an extra effort to help them learn.

Often times, it was more difficult to sustain an interest and enthusiasm in the work. This mainly came when a stack of papers landed in my mailbox or during the lonely office hours. The key to successfully navigating these difficult times was to jump to my feet and sell myself the idea these behind the scene jobs were just a part of teaching. They are the little things that add up, but when a student is confused on homework and needs the correct comments or my undivided attention, those little things become the big things that make the job worthwhile.

Encountering countless questions from many students with varying degrees of mathematical strength, I tried to keep focused on one thing. I keep trying to ask the right questions. Intelligence doesn.t lie in having the correct answers. Instead, it is asking the right questions. With those right questions, I could extend the thought process of a problem to the student allowing them to answer the question themselves. Good experiences came when working with a student and witnessing the epiphany of coming to the correct conclusion. At that time, I can leave the student with the better skills to approach other questions, and I can leave the job knowing everything was worth it.

Dave Schumann

The undergraduate teaching assistant program I would describe as one of the more valuable and enjoyable programs I have participated in during my time at the University of Arizona. For me, the program consisted of five main parts: grading papers, tutoring in the algebra tutoring lab, holding review sessions for my class, attending weekly UTA meetings and holding weekly office hours. I enjoyed some aspects more than others . but all aspects were equally beneficial to me.

I spent approximately 2–3 hours a week grading papers and this was generally boring and time consuming, but as the semester progressed it became more enjoyable as I became quicker and developed an interest in how each of the students performed. Although largely boring, the grading allowed me to refresh lots of math weekly because I preferred to solve some of the homework myself so I could better understand where students erred.

The tutoring lab I worked in for 3 hours a week and this was very enjoyable. The time always flew and I always enjoyed working there. My math skills also increased a good deal because of the pure variety of people and subjects. A certain method of explaining a problem would work with some of the students and other students required me to explain the problem in a different light. It was this diversity of students that helped my math so much and had me realizing things that I had never seen before. Another great aspect of the tutoring lab was that I worked with some graduate students and teachers here at the University who I could listen to explain problems to students and this helped me with my understanding and how I taught it as well.

I held a number of review sessions. They allowed me to practice my classroom teaching skills and helped my math tremendously because I had to understand the sections completely so I was ready to answer any question. I.m in 100% agreement with the statement that you don.t understand something until you have to teach it.

I had office hours for about 2 hours every week and this was a rewarding part of the program for me. When I did have students attend, I enjoyed helping them.

The weekly UTA meetings were for one hour a week (closer to 40 minutes) and I enjoyed them. We watched some teaching videos, talked about our experiences with the program, and all taught a lecture.

Overall I would say the program is a wonderful opportunity and recommend it to anyone who thinks they would enjoy teaching. I met some great people, solidified some math skills, and had a good time in the process. It is a shame there is a two semester limit.

Daryl Wieneke

Working as an Undergraduate Teaching Assistant this semester was great! I got the opportunity to broaden my horizons, and at the same time I was able to help other students learn math.

My ten hours each week varied a little and were spread out between the weekly UTA meeting, three hours a week in the tutoring lab, attending math 110 class, review sessions, and, of course, some grading.

The UTA meetings were helpful and interesting. We looked at different aspects of teaching, and we each did a small presentation on some interesting math idea or concept of our own choosing. I thought the “How was your week?” opening question from Dr. Hartman was a great way to share our experiences, problems, and questions.

I really liked the tutoring lab, although I have to admit I was always a little nervous that someone was going to ask me something I didn't know. That did happen a few times but there was always someone else to ask for help. And a couple of times I even answered some business math questions (I always liked probability.)

Listening to Dr. Laetsch explain math concepts in class, sometimes in new ways, really reinforced my math abilities, which I got to use during group workbook activities helping other students.

The night before each test day I would hold a review session (probably my favorite part). I really felt like I was helping the students to understand the material and consequently earn a better grade.

Grading papers usually took about four hours a week. Sometimes grading was a little tedious, but I found it to be very useful. Grading was great at making me practice my skills and it gave me a lot of insight into how and what the students were thinking about the material. I was able to use those insights to improve my review sessions.

I recommend the Undergraduate Teaching Assistant program to anyone who likes to help people learn and grow. It is an excellent opportunity to do some of your own learning and growing at the same time. Thank you, Dr. Laetsch and Dr. Hartman.

Megan Wilson

The Undergraduate Teaching Assistant position changes you into a teacher for several hours every week through tutoring and grading. It brings a whole new perspective to learning math.

Tutoring lower division math students is a challenge in itself. Many a times I would think I knew everything about algebra, and then the first question I was asked of the day I would be unable to help them. It may not be that you do not know the technique or type of problem they are working on, but that you are unable to explain clearly enough so that they understand. At the same time it is also very satisfying. If the student does not understand immediately you can try another approach to the problem. Or another. Eventually the cloud lifts and understanding dawns. The expression on the student's face and relief radiating from them is an addicting reward.

Grading gives insight to the student's understanding, but it can also be very frustrating. After grading a whole pile of papers that every one did poorly on, there is very little desire ever to pick up a red pen again. Yet sometimes it is interesting to watch people's logic unfold on paper. Personalities develop on paper. I personally did not have much interaction with the students I graded for, but that may have been a good thing overall as it gave me complete objectivity when it came to grading.

The UTA position has put me, temporarily, in the teachers seat. It is a very different view of the world from up there. It has been an educational experience for me and hopefully for my students as well.