Now that I am out from underneath summer teaching, I am preparing my fall classes. I will be teaching two sections of Plane Analytic Geometry and one section of a junior level Linear Algebra class.
I will be doing all these classes in an IBL setting without a book. This is not a big deal for the Plane Analytic Geometry classes because I wrote my own set of problems this summer and have tested them once already. My typical class will start with students presenting selected problems in randomized small groups. I will be collecting students responses for all the problems but I will only be grading selected ones. After discussing presentations and whatever else comes up, I will be handing out the next section of problems and assigning random groups for work during the last part of class. The grading for the geometry classes will have two exams and a final in addition to graded homework and presentations.
I’ve always felt a little uncomfortable with how much students work together outside of class since it can be difficult to really assess how much a student really knows. But I am also a huge proponent of clear and effective communication, so I like student’s discussing ideas with each other. What I have done for the last semester or two is to allow students to discuss as much as they want about the ideas but not at all about their work. I try to give them clear examples of where a line is crossed, like when you see someone else’s work, you will unconsciously (or maybe not so unconsciencely) write your work in a similar fashion and thus represent someone else’s ideas as your own. I would love to have input on how other people allow for students to discuss things without allowing full collaboration.
I taught the junior Linear Algebra class this summer using a textbook and a mostly IBL format. While it was immensely helpful to have a text in helping me organize my ideas and the flow of content, I was really unsatisfied with how much students used the book as a crutch, even when working on problems that I wrote. For this reason, I will be writing my own notes and problems for the fall. I found several resources for other questions and ideas in TJ Hitchman’s notes and David Clark’s Linear Algebra notes and questions from JIBLM. I have what I think is a good outline of where I want to get as far as content and what steps I would want to do to get there. As I need to start writing the notes later today, I am still trying to decide if I want to write the notes and problems similar to how my Plane Analytic Geometry notes work in that I am giving them out section by section with everyone working at roughly the same pace. I am also considering doing something closer to a Moore method setup, where students work at their own pace and problems are presented as they get completed. This second possibility may be too ambitious for me at this point since I am not confident that I could get students without a proofs class to make good progress.
As I write more activities and problems for courses without a text, I am noticing the fine skill of writing problems that illustrate and prod students to discover a new idea versus problems that allow students to practice and apply ideas. It takes me as long to decide what kind of problem comes next as it does to write five problems. In reflection on the activities and problems I wrote this summer, I noticed how much easier it is find the right balance later in the semester. Whether this is because I have practiced writing questions or whether students are more adaptable to new situations, I don’t know.
As always, your thoughts and input on these ideas is appreciated.