I decided to group the courses by instruction techniques I used.
Student teams
Here are the courses that I taught using the student teams approach. My experience has been that teamwork is an increasingly familiar way for the students to study. Technology (Zoom, cloud drives, services like Overleaf and CoCalc) make collaboration easier. On the other hand, technology makes it harder to ensure that tasks are equitably split between the students.
Some of the techniques that I find help minimize problems are: keeping teams as non-homogeneous as possible (this means in particular that the instructor picks the teams, not the students); change the teams twice during the semester (this helps students who are struggling with their team get a “fresh start” and prevents students from being “boxed into” specific roles in the teams).
- Introduction to Abstract Mathematics. Elements of peer-instruction are perfect for students mastering problem-solving techniques and dealing, perhaps for the first time, with things like equivalence relations, partitions, and connections between them.
- Mathematical Structures II. This is the second in the series of three mathematics courses for the students who are on their way to become elementary school teachers. I found that these students study much better in teams than individually: even the weaker students who actively participated in teams have done very well on (individual) assessments.
- Introduction to Abstract Algebra. High level of abstraction calls for a combination of individual study time and group discussions.
- Introduction to Cryptography. The class is taken mostly by Computer Science majors with interest in cybersecurity. Productive work in teams will be a feature of their work
Technology
Here is a list of courses that were taught with additional technology (WeBWorK, Mathematica, Sage, etc.).
I used WeBWorK in
- Precalculus
- Calculus for Applications
- Linear Algebra
For more information on the online homework, please visit the WeBWorK page on this site. I used both WeBWorK as well as Mathematica, and Sage labs written by my colleagues in
- Calculus I and II
- Calculus III (only Mathematica in this course)
Research component
These are the courses in which I included a research component. Additional information about the undergraduate student research projects that were completed as the result of the courses is on the Student research page on my website.
- Applied Mathematics Laboratory.
- Senior Seminar. After some initial hesitation, the majority of students welcomed the student-taught style of lectures. The evaluation criteria for oral presentations worked out quite well. It was important to give (private) nearly immediate feedback on the presentations at the start of the semester.
- Applied Combinatorics. I taught this class only a few times, but I directed several independent study courses using essentially the course syllabus. One of these independent study courses has resulted in a nice research project by the student.