There has been a shift at several universities to teaching calculus courses in large lectures of 100 students or more. In interview surveys conducted by the university officials at our institution, one of the most common issues brought up by students of large lecture classes was the lack of connection they felt with the instructor (in class and outside of it). In order to tackle this problem in our first-year calculus courses, we are using a fairly new idea in conjunction with the regular lecture. The students’ response to this practice has been extremely positive and encouraging; therefore, we want to share the details of what we do and how we do it so others can use this approach in their own classes.
We are using what we call ’Micro-videos’. These are short instructor-prepared videos that complement the in-class instruction. The videos are posted online and can be viewed by students at a time most convenient for them. To increase the students’ interest in using this tool, the videos have an average length of 10 minutes. Our main goals for each Micro-video are to help clarify students’ common difficulties on a key concept and to encourage student-instructor discussions.
There are two important issues to consider before using Micro-videos in a course:
1. What to present in each video?
2. What does it take to make a video?
The answer to the first question depends on the course where you plan to use the videos. You should have a good understanding of the key concepts or problems that students struggle with the most; and understand why. This will guide the careful selection of a problem(s) or example(s) to present in the video. Since the video should be short (10 min.), you will be forced to choose the example(s) that best address the students’ difficulty and help advance their level of understanding.
For example, one of the videos we use focuses on the concept of Chain Rule. Students have had difficulty with this particular topic on previous semesters. In particular, they seemed to be confused with the idea of finding the derivative of a composite function (function of a function). In the Micro-video the instructor presents the following examples in details:
1. f (x) = sin(3x)
2. f (x) = sin(ex^2)
3. a) f (x) = sin(ex), b) g(x) = esin(x)
The first example, which takes one minute, reviews the Chain Rule on a simple case. The second example significantly increases the complexity of the problem involving use of the chain-rule multiple times. This example is worked out in detail and takes five minutes. The third example is three minutes long. It illustrates the difference between similar composite functions pointing out the importance of identifying the “outside” and the “inside” functions while providing more practice for the Chain Rule.
Once the material to be presented in the video is chosen, the second question has to be addressed. It is not necessary to use state of the art technology to prepare these videos. You will need a quiet place with good lighting, a board, a digital camcorder, and a movie editor (more details on technological issues).
You should observe the same teaching practices you use in the classroom. That is, do not speak to the board, do not cover the writing with your body, present the material in an organized way, and so on. You should also provide opportunities for students to actively participate as they watch the video. This can be achieved, for example, by asking students to pause the video and work on a certain problem by themselves before they watch how you solve it. In our experience, once the initial challenge of choosing the appropriate content is taken care of, the making of the videos is a smooth process. It is also important to recognize that the better prepared you are to tape the video (just like you would be for a class), the smoother and faster the process will be. For further details on this question follow this link.
This method has proven very effective not only for clarifying students’ difficulties, but also for improving the student-teacher interactions. As a result of watching the videos, students have felt encouraged to approach us with questions regarding the material presented. They have also commented on the convenience of watching the video at their own pace and multiple times if necessary. Additionally, one short video can help multiple students and be re-used semester after semester. The only inconvenience of this approach is the time spent pre/post processing the video but this is far outweighed by the advantages.
Fabiana Cardetti is Assistant Professor of Mathematics at the University of Connecticut. She is also a Teacher for a New Era Fellow at the university. She earned her Ph.D in control theory at Louisiana State University where she was awarded certificates of teaching excellence. Her current research interests include undergraduate mathematics education and teacher preparation. She can be contacted via e-mail at firstname.lastname@example.org.
Amit Savkar is a Lecturer at the Department of Mathematics at the University of Connecticut. He is a coordinator for undergraduate calculus courses. He earned his Ph.D in Applied Mechanics in the department of Mechanical Engineering at the University of Connecticut. His research interests include pedagogy of mathematics in large lecture classes and understanding student learning of mathematics at the college level. He is also involved in projects looking at different issues in K-12 education in the U.S. He can be contacted via e-mail at email@example.com.