Many freshman-sophomore mathematics courses at NIU are taught using the lecture/recitation method. A faculty member gives lectures to a class of 100-300 students three times each week. The class is divided into smaller recitation sections (about 30 students each) for which the teaching assistant is responsible. During the recitations, questions are taken and answered, detailed solutions to problems are presented, homework may be collected, quizzes administered, and homework and quizzes returned to the students. As a teaching assistant, you play a vital role in this program, because you are in a position to address the needs of each student individually. Moreover, since you are both a student and a teacher, you can bring a perspective to your teaching role and an appreciation of the students' difficulties that many professors cannot.
In most cases your duties will require an average of 14 hours per week. You will attend the class lectures given by your faculty supervisor (3 hours per week) and will conduct scheduled recitation sections (3 or 4 hours per week). The remainder of your time is split between office hours, preparation, writing quizzes, and grading papers. The time distribution depends on the course and will be explained by the course coordinator.
Your attendance at lectures serves two purposes. First, you are able to follow the methods and point of view of your faculty supervisor. This allows recitation sections to run more smoothly and greatly increases the amount of material that can be covered. It also avoids any confusion that would arise if you approached a problem differently than the lecturer did. Second, your ability to provide reliable feedback is enhanced by your attendance at lectures. If a student has a question on something the lecturer said, you will know what the student is referring to, since you were also present at the lecture. It is your responsibility not only to assist the students with their difficulties, but also to point out to the lecturer if there is widespread misunderstanding of a problem or technique among the students. Since substantial feedback from the students is generally not possible in the large lectures--it is your responsibility to receive this feedback, organize it, and pass the information back to the lecturer.
If you are unable to perform one of your regularly scheduled duties, due to illness or other unforeseeable reason, notify your faculty supervisor as early as possible. If you are unable to reach your supervisor, contact the Assistant Chair or the Director of Graduate Studies.
Each TA will be evaluated by their faculty supervisor. Your performance as a student naturally is of primary importance; this is your reason for being here. Nevertheless, in questions of reappointment, your performance as a teacher does play a role. In fairness to our undergraduate students, we cannot reappoint TAs whose teaching is unsatisfactory. Moreover, TAs are always expected to carry out their duties reliably and responsibly.
The Mathematics Assistance Center is located in DuSable 326. TAs who are assisting in 110, 155, 210, and 211 will be assigned two office hours per week in the MAC. You are responsible for helping all students who come to the MAC, not just the ones in your own recitation sections. You will be also select a third office hour in the MAC each week for the benefit of students in your own recitation sections.
In any situation where a student must use some thought and ingenuity to solve a problem it is not enough to simply present a solution. The students' understanding is greatly increased if someone can look at their work, indicate the point where they started to go wrong, and propose an alternative direction. It is very difficult to provide this service in the recitation sections. For this reason the Department maintains the Mathematics Assistance Center. The Center also permits students to meet and work together, getting help when they need it. This aspect should be actively encouraged. It gives the students a chance to meet others in the same course and with the same difficulties.
The technique for handling the sessions will vary with the number of students present. The emphasis should be on individual help and hence recitation session techniques will not apply. The following are a few suggestions. Work individually or with small groups of students. Keep moving; don't permit one student to monopolize all your time. An amazing number of students are too timid to ask for help. They will attend the session and sit quietly at a table, waiting for you to approach them. Keep an eye out for these people. They frequently need the most help.
The two basic challenges you will encounter during these help sessions are to encourage substantial student participation and to provide a sufficiently high quality help to all students that attend. Both the faculty and the teaching assistants must continually remind their classes and individual students of the availability of these sessions. A schedule of the TAs assigned times which lists the course to which the TA is assigned will be provided for all students. The second difficulty hinges more than anything else on the sincerity and enthusiasm of the TAs. If students are not satisfied with their treatment at just one session, they are not likely to be back. This is (unfortunately) the nature of a voluntary program.
Be sure to announce your MAC office hours to your class and to encourage your students to come to the MAC if they desire assistance. Suggest that your students try to go to the assistance center when there is an assistant there who is assigned to their course. Stress that all questions concerning requirements, examinations, grading, etc. should be directed to their own teaching assistant or professor.
Perhaps the most important thing to keep in mind is that most courses in which you assist will be largely populated by freshmen who have not yet adjusted to college life or to this university. They may be somewhat bewildered and intimidated by the academic life at NIU. The following suggestions can help to develop a positive relationship with your students through which effective learning can take place.
Knowing and using students' names helps establish a comfortable atmosphere in class and demonstrates an interest in your students as individuals. You can quickly learn names by making a seating chart (let them choose their own seats if you like) and then memorizing names from it. Returning quizzes to your students individually also helps to quickly learn their names. Another helpful device is taking attendance several times early in the semester. When a student complains of difficulty in the class, a record of attendance at the recitations can provide a useful gauge of the student's attitude and sincerity.
Clearly state your name, location of Math Assistance Center (DU 326), and office hours. In order to convince students that you are willing to help, it is necessary to repeatedly invite them to make use of your office hours; many TAs announce their office hours at the beginning of each recitation session. Also make it clear that you are available by appointment if your hours are inconvenient for the students.
Early in the semester, identify people who do poorly on quizzes or indicate lack of preparation. Ask them to talk with you and try to discover the difficulty. Sometimes a little encouragement or a suggestion for studying will help immensely. Also, compliment students for good work.
Questions are never stupid; no one intentionally asks a ridiculous question . Questions can indicate a lack of understanding (at times an incredible lack of understanding), but the successful teacher develops the ability to use a student's question to isolate their underlying difficulty. It is acceptable to delay a question and speak to the student after class, especially when the question appears to be too superficial or too time-consuming. However, never criticize a student in front of the class, or you will have alienated a non-negligible portion of the class for the rest of the semester.
Don't be embarrassed about mistakes you make. Admit the mistake, correct the mistake, and continue. If a student catches the mistake, make the correction and thank them. Try to maintain an attitude of working together instead of trying to find mistakes in each other's work. If you can't answer a question, admit it and promise to answer the question at the next session. Don't waste class time Be sincere. Be honest in your interactions with your students and supportive of their efforts, regardless of their proficiency in the class.
Some useful phrases:
Follow the lead of your faculty supervisor. Try to present the material from the same point of view. Solve problems or present material using techniques familiar to your students. You may occasionally introduce alternative methods so long as you are sure they don't undermine the purpose of the lecture. Never present material or make comments that appear to be a criticism of your faculty supervisor or your supervisor's techniques. This confuses the students and undermines the morale of the class. If you need further convincing on this point, consider what effect such criticism would have when your faculty supervisor learns of it.
Begin each class by spending several minutes reminding students what has been covered in lecture and how this relates to previous work. Solid contact with new concepts grows out of an association with older and more familiar material.
A large amount of material must be covered, particularly in those courses for which a student has only one recitation per week. The content of the three previous lectures should be covered. You will develop your own techniques for handling this challenge. One possibility is to choose several (three or four) of the most important problems from each assignment to receive first priority in the recitation session. You could have solutions and complete explanations for these problems prepared in advance. Instead of asking generally, ``Are there any questions?", ask for questions on each of these problems individually. After covering these key problems for the entire week, the discussion could then be opened to other questions. The key problems could be chosen by the instructor, the TA or the two working together. In order to focus attention on these problems, they might be announced to the students in advance.
Be well prepared beginning with the first class period. If you're unprepared, you'll look like you don't know what you're doing and you'll lose important credibility with your students. You're also wasting your students' time. The ability to gradually ``beat a problem to death" without previous preparation is not good teaching (nor are the students seeing a ``keen mathematical mind at work"-as the standard excuse for lack of preparation goes). By knowing in advance how a problem is worked, you will naturally point out the key to the solution, rather than leaving the students to hunt for it in a jumbled mess containing the solution as a (proper) subset. Prepare for each recitation by working out at least one problem of each type before class. Some time should also be spent in second guessing; try to determine before class what questions will be asked. (This is easy with a little practice.) If you prepare questions about the material before your recitation, you can encourage student participation.
Encourage participation. One method, without taking the time to have students go to the board, is to ask them for suggestions on how to proceed and then do the work yourself at the board. This allows the student to do some work, but you can save time by correcting errors immediately. If you can establish a helpful attitude from the beginning, participation should follow. If all else fails, have students do two problems (easy and moderate) to be handed in, graded, and returned. But remember that recitation sessions are help sessions, not punishment.
You will spend most of the recitation time working problems. Begin by writing the problem number, its page in the text, and (except in the case of lengthy word problems) the full statement of the problem. Make the notes self-contained. For example, when assigning letters to quantities in application problems write out clearly what each letter means. A more complicated problem can be broken into a sequence of steps; begin each step by a written statement of what you are trying to accomplish.
Omitting details. It is important not to spend an entire class on just a few problems, unless they are really important and illustrate all the techniques of the past week's lecture. If a question does not appear to be of general interest or promises to take too much time, ask the student to stop after class. If you get stuck on a problem postpone it until the next class, but do not forget about it in the meantime. Be sure you can solve it the next time around. It is also permissible to omit routine computation-but be sure that it truly is routine computation and clearly indicate where you are making omissions. Time is frequently saved by ``setting a problem up" and leaving the rest to the student. This should never be done on key problems. It is permissible if a similar problem has already been solved in the same period.
Duplicated solutions to quizzes might help save time. Hand out the solutions first; then the students can look at them while you pass back the quizzes. This is not a good technique to use on the key problem described above. Students gain something from actually seeing the problem worked.
Vary the type of students you call on. Continually calling on good students discourages the rest; while continually calling on poor students bores the good and gives the average a false sense of security.
Recitations are extensions of the lecture, not merely problem sessions. When appropriate, or in difficult sections, devote some time to a summary of the material covered in the lecture. Outline the most important techniques and results. If a lack of understanding of a basic concept becomes evident, several minutes reviewing essential theory is well spent.
Most students' notes are an exact copy of what you write on the chalkboard. When you do a problem at the board, students not only see the solution, but how to organize a solution. Effective board work provides a model for writing and doing mathematics problems. The following tips should help you structure your board work.
Some faculty supervisors will give regular quizzes during their large lectures while others will prefer to use the recitation sessions. In either case, you will probably be involved in writing these quizzes. Writing good questions requires practice. Perhaps the following will give you a point from which to start.
Quizzes should be used primarily as a teaching mechanism; evaluation is a secondary purpose. When writing a question, write out a detailed solution. This will help you avoid giving questions which are mechanically more complicated than you desire, and will also give you an idea of how long it will take students to write a solution once they know how to proceed.
GTAs are assigned proctoring duties at several mass examination time periods during finals week. It is a good idea to check that these do not conflict with your own final exams.
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