*In this section, Dr. Snowden shares strategies he used for helping students learn to present mathematics.*

One goal of undergraduate math seminars is to help students develop their mathematical communication skills. A key aspect of this is presenting mathematics.

Many students entered this class without any experience presenting mathematics in a lecture setting. Below are several approaches used in this class to help students develop their presentation skills.

I think the key to learning how to give a good math talk is practice. It's all about just doing it.

— Dr. Snowden

## Ample Practice in a Realistic Setting

I think the key to learning how to give a good math talk is practice. It's all about just doing it. Over the course of the semester, each student gave six 25-minute lectures.

To maintain a realistic classroom atmosphere, it was important that the whole class attend each class session. There were roughly 10 students in the class, so if 3 people didn't show up, then the lecturer would feel like he/she was talking to a small group instead of a class.

I also wanted there to be a lot of interaction between the audience and the student lecturer, with questions and discussion, and you need people there for that to happen. Most students were a bit shy about that, so that didn't actually work out so well, but it was still good to have more people there.

## Helping Students Prepare Their Lectures

For the first few lectures each student gave, I met with the students individually beforehand. I also did this throughout the semester with students who wanted to continue meeting. During each meeting, we went over what should be in the lecture and how to present things.

For each lecture, I gave the student a section of the textbook to lecture on, and there would be maybe two general topics in that section. There would always be a lot more content in the book than the student could cover in the lecture, and so the student had to decide what to include and what not to include in the lecture. When I met with each student, I'd try to get the student thinking about what would add to the lecture and what wouldn't, and to get the student to make decisions that would make the lecture better.

## Providing Feedback on Practice Lectures

Before each student's first lecture, the student would give a practice lecture with just me and the writing instructor for the class as the audience. Some of the students had never given a lecture before, and we wanted to give them some initial comments and help them get over any anxieties.

Some of the students seemed pretty nervous about presenting. A few of them got over that with practice and a few of them didn't. I don't think we found a good way to help students to overcome their nervousness other than practice.

## Providing Instructor and Peer Feedback After Student Lectures

One thing we did that I think helped improve the lectures was that for the first two rounds of lectures, everyone in the audience had a notecard and would anonymously write down criticisms or compliments of the lecture. I took everyone's note cards and then sent the student lecturer an e-mail with what I thought were the relevant comments. I gave each of the students comments afterwards as well, via e-mail.

Via these comments, we saw that some of the things the lecturers did would be unanimously reported as bad, and then they would know that, which tended to fix things.

I talked to the writing instructor for the class about coming up with a rubric for grading the lectures. After each lecture, I wrote down some comments and assigned the student a numeric score using the rubric. Then, I weighted all those grades at the end of the semester.

Initially, I graded more on perceived effort. How hard did they try? Later in the semester, if they had been told that something they were doing wasn't good and they didn't do anything to correct that, I would grade them negatively.

Although I assigned numeric scores during the semester, I didn't share these scores with the students. I didn't want them to feel like they were being judged constantly, even though they kind of were; I thought that would be bad psychologically.