Here are the reports for the Spring 2002 UTAs.
My experience as an Undergraduate Teaching Assistant was marked by three significant characteristics: learning, service, and experience. Primarily, being an UTA is a learning experience. As an undergraduate, I had never truly led any discussion or classroom lesson before; as an UTA, I was exposed to the learning experience that is teaching. Teaching is like learning — it requires mastery over a topic and inspires questions that one must answer. Teaching a mathematical concept taught me a great deal about not only the concept, but my process of conceptual understanding. Moreover, the UTA program is marked by service: I was able to help others with their problems and discover my unique method of explanation. This, in turn, gave me a deep sense of satisfaction as the people I assisted conquered problems or gained mathematical insights. Finally, the Undergraduate Teaching Assistantship gave me a breadth of experience to draw upon in the future. My professor allowed me to present quiz solutions in front of the class every week and gave me a class period to show examples pertaining to the lesson he had previously motivated; furthermore, he met with me weekly to go over my presentations and give me constructive criticism. His encouragement and training have better prepared me for my graduate school plans.
In sum, I had a wonderful UTA experience, particularly due to Dr. David Lovelock, and I thank those who were responsible for my acceptance as an UTA. I would recommend the Undergraduate Teaching Assistantship to anyone who wants to more fully master mathematical concepts or desires to gain experience for their future.
My experience as a UTA has really allowed me to experience life as a teacher. The grading, the review sessions, the one-on-one tutoring really opened my eyes to how hard it really is to teach a subject like math.
So what have I learned from being a UTA? I have learned that explaining a math concept in just one way usually doesn't suffice. Having a plethora of examples doesn't hurt either. I have also learned that too much explanation can be confusing and actually harmful. I have learned that knowing a concept is different from understanding a concept. Some students know how to use math without ever understanding why it works.
I have learned that the best way to understand a subject is to teach it. Tutoring has been the best review of math overall that I have ever had. The little things that you learn in algebra, trigonometry, and calculus that are basic and really the building blocks of higher math become very clear through explaining them over and over to other people.
Overall working as a UTA has been one of the best jobs I have had so far. Getting to know students and actually helping other people learn and better themselves through education is a powerful thing. It has been a very rewarding semester thanks to the VIGRE program.
My experience as an Undergraduate Teaching Assistant has been beneficial in every way. The program required me to achieve a better understanding of the subject matter (First Semester Calculus) as well as to develop techniques in explaining concepts and ideas. In addition, I had the opportunity to work with a mentor, Mirayama Varghese. Her instruction and knowledge proved to be a valuable resource throughout the semester.
As a UTA, I was responsible for a multitude of tasks, including grading, tutoring, holding review sessions, and providing individual instruction. As a grader, I selected problems from the assigned problem set and graded them, then gave the students answer keys and rubric. The tutoring sessions were held in conjunction with the Math Tutoring Center, and were offered to all students in algebra through calculus, requiring me to learn these subjects in a far deeper manner than I had done previously. My review sessions proved to be the most challenging of my duties. They required me to reformat the course material and present it in a variety of manners to facilitate the different learning styles of the students.
During the last few months of the Fall 2001, I found out about the UTA positions available in the spring. Initially, the most difficult part was deciding which math course to UTA for and for which professor. Finally, I chose to work with Kathy Lackow, a co-op professor, who was teaching Math 124 (Calculus I.) I really enjoyed working with Kathy throughout the semester. However, there were some responsibilities and tasks that were not so enjoyable.
First, I will state what I liked most about being a UTA. I enjoyed helping out in the classroom with answering homework and review questions. In addition, the “hands-on” projects were fun too, including the Lollipop activity. Also, grading for both of Kathy's calculus classes was beneficial in knowing what to advise students about what needed to be reviewed or improved and what was done well. In addition, holding office hours with Kathy was fun and definitely a learning experience for myself. The orientation, which consisted of training and collaboration with others UTAs, was fun, but could have been better. The weekly UTA meetings were fun with completing disparate math related projects, like teaching other UTAs math related lessons that they might not have already known how to do before and the “Different Ways of Thinking” exercise.
Second, I will mention what I disliked about being a UTA. I did not enjoy working in the tutoring lab, because I was not always treated with respect and courtesy from the students in the lab. In addition, the tutoring lab's location was in an inconvenient place, even prior to the construction south of the Mathematics Department Building. Also, the tutoring lab's supplies were limited with no stapler, no pencil sharpener, a few pieces of scratch paper, no air conditioning, and a few writing utensils that were not in satisfactory usage conditions. Also, it was difficult to walk around the room with too many chairs in a small room. In addition, the office was sometimes locked and it was frustrating at times. And, I thought it was unfair how some UTAs “chose” not to show up for the UTA meetings even though the hour was included in our ten hours for each week. In addition, some UTAs did not spend ten hours a week doing work while others spent over ten hours. Finally, it was inconvenient not being able to contact other UTAs directly throughout the semester.
Overall, I think the UTA position was enjoyable, beneficial, and not completely satisfactory. I think the VIGRE Committee should consider making several changes for improvement. First, make the orientation better in terms of training, demonstrating, and advising the UTAs in conducting review sessions, teaching students, tutoring, and preparing lesson plans. Second, the UTA meetings should be mandatory unless prior arrangements are made with the UTA Coordinator. Finally, the tutoring lab needs a lot of improvement including more supplies, a larger room with air conditioning, and more accessible on campus. If these changes are made, maybe being a UTA might be a more attractive position.
As a UTA for Edward Alexander's math 129 class, I graded all the homework, gave a lecture, lead a problem session, made and graded my own quiz, pointed out the common errors on the quiz to the class, held office hours three hours per week, proctored during the class's group work a few times, and tutored at the math learning center three hours per week. I also attended a one hour per week teacher training session, lead by Russel Carlson, with the other UTAs. I like helping the students so much that at the end of the semester I held two review sessions for the class's final, even though I was not required to. They totaled five hours and attracted as many as eight students.
Every part of the UTA experience was positive for me. I enjoyed grading because it gave me an excellent review, taught me topics I did not learn when I took the class, allowed me to see many ways to solve the same problem, taught me to recognize most common errors, and was a fast, easy way for me to correct students mistakes by writing notes on their homework. Towards the end, though, I think many students were using the solutions manual, so I stopped writing comments and just started speed grading. Very few students came to my office hours, whereas many came to my final review sessions. I think grading should be done in a place where students can come for office hours, and that the official office hour time should be concentrated into review sessions before each test or quiz. The teacher training with Russel Carlson was a laid back, small group, easy yet educational session that gave me food for thought about teaching. Since everyone there was going into math, engineering, or teaching, I could ask each of them questions and get a better idea of what I wanted to do with my life. The proctoring was where I helped the most students. Some just wanted to know if they were doing a problem right, some were so lost that I had to send them a different tutor to explain it in different words, and there was everything in between. I tried to answer questions with questions, but explained concepts to people I thought might not figure it out otherwise. I even got stumped a few times. Overall, I think I helped the vast majority of the students. It was fun watching students go from clueless to doing several problems correctly without any clues from me. Then there was the actual teaching, in front of the class:
Edward Alexander's approach to UTA mentoring is, in addition to the other responsibilities, to take the UTA through one cycle of “the teaching cycle”. He believes that teachers should teach a topic and then quiz the students to see if they got the message. If everyone misses something different, that means the teacher did a good job, and the students made the mistakes. If everyone misses the same exact problem, then perhaps the teacher did not explain the problem in a way compatible with the students. background, in which case the teacher briefly covers the missed topic again in different words. He had me do exactly that. I got to make my own quiz for them and grade it myself.
My first attempt at a lecture on sequences and series had many mistakes. I started the lecture by trying to review the definition of a limit. In my outline notes, all I had was the word “limit”, and my head went blank as I tried to give a concise, precise definition. Lost for words, I told the class I would skip the theory and go straight to the examples. I failed to title any of the rules I was teaching. I tried to come up with examples on the spot, which I discovered I could not do. I did not label my graphs because I assumed everyone would recognize them, but many did not and were lost. I used many pronouns when referring to concepts and graphs, which lost anyone not looking at the board right then. I also had a few of my rules wrong and at first forgot to use sigma notation when naming series. I rarely looked at my audience to see if they understood. When I put graphs up to make a point, I took them down before people could copy them. The only good thing I did do was using every part of the board to give maximum visibility. I could tell the students were not happy because of all the yawns I heard. At the time, I interpreted the yawns to mean they were bored with the slow pace.
I prepared for my second attempt, this time a separation of variables problem session, so that I would not repeat those mistakes. First, I wrote out everything I would say, underlined what I would put on the board, starred the verbal questions I would ask, and drew a picture of an eyeball and a watch everywhere I would face the class to ask if they had any questions. The picture of a watch was to remind me to give the class at least 10 clocked seconds to look at the example and decide if they had any questions. I stapled my pages together, wrote neatly, separated and numbered each example, worked the problems out before hand, and wrote on only one side of the page. To avoid stuttering, I read my notes to myself several times and then performed the lecture in front of just Dr. Alexander, and edited it were he saw necessary.
When I did the actual problem session, I did much better than my first lecture. I faced the class often, but I failed to give them enough time to answer my question because I called on the first hand to come up, and sometimes started answering the question before I got an answer. That is a mistake I see many teachers make all the time. I made excellent use of the board, but talked into it a few times. I remained calm and composed throughout the review, and did not stutter much, unlike my last performance. I had to improvise three times when I was asked questions I had not planned for. For one of the questions the students asked me, I had to answer, “I think so”. I got off schedule from my notes part way into it, but because I had so many examples worked out, I just moved on to the next rather than trying to fit the missed example back in. When explaining some algebra to one of the students, I made a side example and left it up there so everyone could look at it. Afterwards Dr. Alexander said I left it up too long, which was distracting to the students. When I graded the quiz, I noted that most the people who failed it were absent the day of the problem session. Most students got at least a C, but the fact that so many people make mistakes on topics I thought I taught shows that I did not teach it as well as I thought. I then took five minutes the day after the quiz to point out the common error to the class.
The main point I learned from the lecture experiences is that a lecture is a time for audio learners to learn. Giving a preplanned, non-adaptive speech, no matter how good of an explanation, is pointless because its mission can be accomplished by passing out a handout of the written speech and drawings. Moreover, it must not be the same explanation the book gives, unless it is worded much differently. The point of the lecture is for students to learn at the lime of the lecture the material in a way different from their other resources. If they don't understand the book's wording, the lecture will fill the gap. The teacher must make sure the students understand before building to the next step. While following the pre-made list of examples and watching the clock for general structure, the teacher must be able to improvise within each example and interpret the expressions on each student's face. This requires good people skills, as well as speaking, organizational, and time management skills.
I have thought about being a professor, at least a fall back job if my career in industry or research does not work out. Definitely would like to teach my own class as soon as I get enough experience from being a UTA, but I will probably have to be a grad student before I can do that. I think teaching is fun, and is a skill I want to work on, and one that will help me in other areas of life.
Until this past semester, I never realized that there was a difference between understand something and knowing it. I always thought of the two as synonyms, and assumed that if I could do something, I understood it. I learned how incorrect this was when I spent the last semester working as an Undergraduate Teaching Assistant for Professor Eugene Smith and his MATH 129 class. Going into the semester, I figured the job could be cake. I mean, I had taken the class less than a year ago, and had gotten an A without too much difficulty. I thought I completely understood the material, but it turns out I didn't know it as well as I thought I did.
It didn't take long for the difference to hit me. I made it the first couple weeks without any trouble. The work in the tutoring room wasn't too challenging material-wise, it was just a matter of trying to find the words to explain mathematical concepts that are clear to some but more difficult to others. Grading homework took some time to get used to, but when you have the solutions manual sitting right in front of you, it can't be too challenging. For the first couple of weeks, I handled these tasks without much difficulty. The hard part came when I started getting visitors to my office hour. Suddenly, I was being forced to explain the trickiest and most confusing parts of the text book; the parts that I had skimmed over thinking “I'm never going to need this” when I took the class myself. Some of the times, I didn't remember the subject at all, while other times I remembered the formulas, but was at a loss when asked where they came from or why they were a given way. This is when the distinction between knowing and understanding finally hit me. I knew this stuff: I could solve the problems in the textbook, because I had memorized the formulas. However, I didn't really understand it.
The questions I got during my office hour forced me to work harder as a UTA, but I noticed the advantages immediately. Suddenly, I was able to take the lessons that I previously had been able to apply only to book problems and use them to help me in my other classes. I'd heard before that you never really understand anything well until you have to explain it. My work as a UTA showed me how true this was.
Commissioner Carlson emailed me in an emergency. The UA Math department was short one UTA. I must rush over there immediately to alleviate the critical situation. My mission was to help the poor victims of vector calculus survive the semester. Seemed a small mission for a super powered UTA, but nothing prepared me for what was in store...
Armed with my knowledge, their book, and the golden answer key book, I charged into the class prepared for the worst. Sure enough, the students were already losing their breath climbing the mountain before them: the Contour and Cross Section Mountain. I was too late to save them from that turmoil. I did my best, but for most, the mountain won the battle.
My next task was office hours. I envisioned spending many hours helping my trusting students with their homework. However, things did not work as I thought. Super hero UTA ran off thinking, “People need me... must hurry! People need me... must hurry!” But when I get there, the office was empty. “People need me... they do... must be held up,” but the people still didn't come... Someone walked in. Excited, I rush over, “You need me! How can I help you noble student?!”
“Who are you?”
“I am the fabulous super powered vector calculus UTA!”
“Oh! I'm not in vector calculus, sorry.”
My day of saving students was foiled again!
I did finally reach a point of accomplishment in the fearful Tutor Room. In this room students from all over campus came to correct their numerous life threatening, or at least grade threatening, problems. I rushed from victim to victim tired and fearing that even my great speed would not be adequate for the task. Occasionally, confronted with the math forgotten in the back of my mind, I had to resort to relying on my UTA sidekicks to solve the ails of the poor student. In the three hours that ensued I saved at least 99% of the homework grades. The small victory gave me courage for what was to come next.
Finally the day came for my first review session. I was scared and a little excited. I stood in front of the class of about 10 students determined to help them and to answer their questions despite my shaky knees. I asked for questions... silence. I asked again... silence. I asked again...
“I have a question.”
“Yes! What may I help you with? I am at your service!”
“How old are you?”
“Huh?... uh... well... 19...”
Suddenly, as I uttered those words I shrank into a small child, helpless. How could I have expected to help these fine students when I myself was too young? I was about to succumb to this defeat when a student managed to think of an antidote, “I have a question on the review, problem number 17.” Magically, I was back to my original self and attacking the problem. I had it defeated shortly and felt proud of saving one of my students.
Despite the small set back, my first review session went smoothly. It proved to be the turning point in my adventures. My office hours began to fill with regulars and my following review sessions went smoothly. Both of these things led me into my new enemy: CHALK. Yes, the evil chalk monster was after my hands to add to its wall of hand trophies. I needed to subject myself to the deadly chalk for the sake of my pupils. Day after day it ate away more of my hands. None of my weapons, water, soap, pant legs, seemed to be working. All hope was almost lost until I found my new weapon, waterproof extra strength moisturizer! With a good coat of it on my hands the chalk monster ran in fear and disgust. I had conquered my last monster. Clear skies seemed to be before me.
With all the monsters destroyed I concentrated on saving my students. I worked hard, but even a super hero has her limitations. I was able to help some with my review packets, office hours, and review sessions, but some were too far away to reach. It was painful to see them struggling and not being able to do more than cheer for them and hope for the best. Despite not achieving complete success, I left as a winner. I started with students and colleagues and left with friends. I came with small weapons and tools and left with not only a strong sense of vector calculus, but also improved skills in college algebra through calculus 2. With my new strength I brace for my new adventures as a tutor in New Start this summer.
To all the students out there... good luck and know there is a super powered UTA nearby for your grade safety.