Linear Algebra: In previous semesters, students who put forth a good and legitimate effort were not just able to pass the course, but make great progress in how they were working. I had three students who were really trying to do well, and while they made progress, they did not pass the class. I am trying to figure out what more I could have done, but I think there was too significant of a gap in their ability to get work done in timely manner. After I let students know that I want them to come talk to me about how they did in the class (individual feedback other than their grade), I had a lot of students recognize how far they came in terms of problem solving and understanding the importance of sense making. I think I will keep sending out that email at the end of the semester because it really reinforces the idea that this is about more than a grad
Geometry: This semester has been a struggle for many different reasons. I feel like I need to find a better way to get students going at the beginning of the semester. As part of this I am going to be evaluating how I do Buy-in in my 100 level classes. I will probably be bothering some of you about ideas.
In reexamining the activities I used this semester, I found that I was just covering topics with some of the problems in my notes. But this, I mean that I talked about a topic just to talk about it, rather than building towards something. Stan’s post about ways to get students to learn what your really care about is something that I am trying to take to heart as I rewrite a good bit of my materials this summer.
Another difficulty I had was that I was not able to build persistence in my students this semester. The final stretch of problems includes many that can not be done (even by the best students) in 15 minutes. Students were able to do these in small groups but it took a long time. Even after congratulating them, they just saw it as a bunch of algebra they did rather than they had a great new tool to solve the next set of problems.
Differential Equations: About half the class was able to make great progress in understanding the whys of the class but I don’t feel like I made much of a difference in the students who were either ill prepared or unmotivated. This was a difficult class to teach because I only had about 50% attendance in many class meetings. Since I did not have time to prepare much active learning for this class, I would usually introduce a new topic and then start students working on problems. I would usually try to pull things back together after most students were able to finish the first few problems. This really seemed to work well since homework scores and exam scores significantly improved over the course of the semester.
I will also be preparing to teach a freshman level trigonometry course and a multi-variable calculus course in the fall. I have decided to use a traditional text for each and to supplement with my own problems and projects. I am hoping that this will mitigate some of the complaints that I need to do more example problems for students in the future.
And finally, I will be heading to Mathfest this summer (my first one), so come out and see my talks in sessions on building a problem solving culture and teaching tips for early career faculty.