Activity: Applied Math Activity
Submitted by Sarah Lams, Applied Math
- To enable students to effectively formulate and communicate mathematical ideas, and to engage with challenging mathematical concepts in a supportive classroom environment.
- To gain confidence as mathematical thinkers through practicing math problems in class
Class: AM147 – Applied Math, Nonlinear Dynamical Systems
Introduction/Background: This in-class activity is designed to challenge students to work through problem sets during the entire class period. Using a topic in class, the instructor formulates an activity sheet based on the topic.
Before Class Preparation:
- Have students watch the videos linked from the course website and fill out the pre-class reading quiz on Canvas. The videos for each class are available at http://scholar.harvard.edu/siams/am-147-nonlinear-dynamical-systems and introduce students to the concepts of each class meeting.
- Prepare activity sheet for in-class activity. Problems are to be designed appropriately in order to reduce calculation time in class and for students to engage with multiple topics during a single class period. The sheet should include graphs or intermediate results that would allow the students to move faster through the problem than if they were working out every detail themselves.
In Class Activity:
- The first week of the semester, the instructor divides students into pairs or groups of three to four to discuss the ideas from the video lectures. Later on students select their own groups for the rest of the class.
- Per the activity sheet instructions, students go to the blackboard to work on the activity at hand
- Students take turns writing at the board while discussing and explaining their idea to the other group members. A TF or instructor walks around and talks through the problem with those that are struggling.
- The instructor moves through the class and periodically pauses for a whole class discussion of a particular problem
Follow up: The end product is the work students write on the boards as they work through the problems. The concepts that are learned in class are sometimes used for homework. The board work is at times photographed for future reference.
Comments from Instructor: The instructor reports that having students do a lot of thinking during class time, while working in groups feels like a valuable use of time. Creating activities designed to take up part of the course time with active work on simplified problems requires substantial pre-class work for the instructor. Carefully simplifying the problems is very important to giving students an opportunity to engage with a cross-section of math ideas.