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Constructing Worksheets

Every meeting of an intensive section is oriented around a “worksheet” constructed by you (the TA). The worksheet is a set of calculus problems for the students to work on during the section that day.

An Absolutely Essential Feature of the Worksheets

Worksheets must include problems that are representative of the type and difficulty of problems that students will meet on the mid-terms and final given by the current professor. Students need practice working these kinds of problems, including the most difficult ones, and they need this practice throughout the semester, not just in exam review sessions. This is one of the primary purposes of the workshops. The best way to do this is to find old exams by the current professor and sprinkle some of the problems into every worksheet. If there aren’t enough of these, next best is to get other old exam problems from other professors’ exams. Labeling these problems as such on the worksheet helps gets the attention of students: “Problem #3 from Mid-Term #1, Prof. Hilbert, Fall 1994”

Worksheet Difficulty

It is good to start a worksheet with a few problems that, while not too easy, are not wildly difficult either. This helps build up momentum. But then it is essential that every worksheet get into more difficult problems. How difficult? A good rule of thumb is to make them as difficult as moderate to hard exam problems. (Although PDP sections have always been described as places to work on “harder problems,” this must not be overdone. The above rule of thumb should be the gauge. Really hard problems can be put at the end of worksheets occasionally as extra things to work on for those interested, but these should be labeled as extra.)

Worksheets should be long enough so that, most of the time, most of the students will not be able to finish them during the section. But worksheets should be short enough that students will have time at home before the next section to finish the problems. The worksheets are something in between an assignment that must be completed in class and an open-ended resource of problems. In constructing them you should choose the number and type of problems carefully, and then make it clear to students that they should work all of these problems, either in class or on their own.

Resources for Constructing Worksheets

Each TA is responsible for constructing the worksheets for his/her intensive section. But there are resources to help. First, use each other. Often TA’s with the same professor jointly construct their worksheets. Second, use the PDP old exam files. Third, use the PDP files of worksheets from previous years. Finally, the Dana Center library has a big collection of calculus books of all sorts, and all the publications the MAA has put out on calculus as well. Format

A worksheet generally fits on one side of one page. The worksheets should be done electronically in TeX or Microsoft Word or some other appropriate program. This makes it easy for future TA’s to incorporate your problems.


It would be wonderful if at every section meeting you handed out answers or solutions for the previous meeting’s worksheet. Is the world wonderful? Sometimes, but not always.

The Art of Finding Problems

TA’s typically draw on old worksheets and exams from the PDP archives, and as it becomes available, the Better File Cabinet is a potentially helpful resource. In addition to these, you might consider the following texts for ideas. These books are in the Dana Center and must be checked out properly to borrow them.

(PDP TA Reference Handbook, 8-23-96)