## Initial Impressions

Since this was my first semester as a TA for the Professional Development Program, I had no idea what the students would be like. I expected that they would be highly motivated since they signed up for the extra time, and that with the extra work they would easily outperform a regular section. I assumed that these highly motivated students would read the book, go to lecture, and understand the basics through homework and lecture. So the best use of the worksheets would be to stress the more difficult problems and some of the implications of the basics they had teamed. With this approach, I thought that my students should not only learn the mechanics of calculus, but also the ideas of how to use it and why it works.

## First Worksheets Too Hard

At the first class meeting, it was clear that many of the students already knew each other, and that there would be no problem getting them to work together. They were animated, and it appeared that they were excited to be involved in PDP. In their introductions to the class, many said that they had received a C in 1A, and their goal was to earn a better grade in 1B. The motivation that I expected was there for many of the students. At first, I carried out my plan to put more difficult problems on the worksheets. Unfortunately, I believe that I did this to an extreme. There is a need for easier problems on the worksheets because the students do not all go to the lecture, and few actually read the book. Prof. Ole Hald told me that my worksheets were too hard, but I didnâ€™t believe him. it was my belief that because the problems were done in groups, and with my help and that of the UGAs, it was necessary for the problems to be more difficult.

The results of the first midterm shocked me. It was almost purely a computational exam, and the students performed poorly as a section. Although many students were hampered by poor algebra skills, there were many who were not able to recognize how to approach a given problem. This was a signal to me that I needed to stress the basics more than I had.

## Suggested Worksheet Structure

From that point on, I tried to structure my worksheets in roughly the following manner:

- Use of Terms. Terms from the section that the students should understand and be able to define.
- True or False Problems. To help the students define the limits of the techniques that they are learning.
- Introductory Problems. Like on the homework.
- Slightly more difficult problems. Problems of the same type, but perhaps using some techniques of previous sections as well, e.g. an integration problem that requires a substitution and integration by parts.
- Difficult problems. These are really for the better students. The average students did not usually get to these. I tried to write the problems in several parts, so that the students could see how the techniques they were learning were useful in other contexts without having to think of something very clever.

This is a structure (more in line with the recommendations of Prof. Hald, and I think it lends itself to helping a wider range of students). However, I was not always able to construct such a worksheet. Making these worksheets is very time-consuming since the TA must think each problem through completely and anticipate the difficulties the students will have.

## Two Suggestions

Among the many useful suggestions by Prof. Monte Boisen, I used the following two:

- Allow the students a certain limited amount of time to work on each problem.
- On a detailed answer sheet for the UGAs, include hints to give to the students when they are stuck at certain points in the solution to the problem. I found that the first kept the energy of the students focused more on the math at hand. The second suggestion takes time and effort to implement, but it increased the effectiveness of my UGAs tremendously. I wish I had been able to do this on a more regular basis.

## Challenging the Students

After the second midterm, when the scores were still low, I came down pretty hard on the class. I told them that I could work very hard, but their grades depended on how hard they worked. After depressing them a bit, I stressed that a good showing on the final would be 70% of their final grade, so that all was not lost. After the second midterm, there were nine students on track for a D+ or below. I think that putting the responsibility on them personally made them work harder, so that only three got a D+ or lower. (PDP TA Reference Handbook, 8-23-96)