One of the many great ideas that I use from the University of Colorado Physics department is to start my 3rd-year Quantum Mechanics course off with a review assignment. On the first day I gave them an assignment which was due on the second day and had questions addressing the major relevant things that they should know coming into this course based on their prerequisites.
It consisted of some fairly straight-forward review questions on topics such as complex numbers, matrix multiplication, dirac delta functions, the relationship between energy and frequency for light, orthogonal functions, the deBroglie wavelength and basic discrete probability.
But what really makes this work is that you ask them to include, along with their solutions, a rating for each question on the following scale (credit goes completely to the University of Colorado folks that put the original assignment of this type together for these ratings):
- I knew this material, it was fairly trivial for me.
- I knew this material, and didn’t need to look up anything or get help, but it was not what I would call “trivial” for me.
- I knew this material, but still need to look something up in a book/notes or on the internet.
- I knew this material, but still need to get help from a person.
- I did not know this, and had to learn it for this homework.
I really like this system for multiple reasons. It communicates to them that there are some things that they should know from their previous courses and we are not going to use class time to review it. And if for some reason they have completely forgotten that material or never learned it in the first place, that they are in a position to go out and use the resources at their disposal to learn it. It is also a bit of a reflection exercise in that there are students that probably don’t realize how much help they ask for with their assignments and having to rate how much help they got might be a bit enlightening to them. And, of course, their rating of each question gives me a much better understanding of where everybody in the class stands coming in compared to if I just gave them the review assignment without asking them to rate the questions. This is related to the common issue of never knowing how much a student’s written homework represents their true level of understanding.
As for the idea of the review assignment in general. It won’t work that great if every single class they are taking has one, but since they typically have very little homework in the first week, asking them to do this first assignment in two days was very reasonable. It also saves me some class time and sets us up to immediately challenge more difficult things in class instead of always having to go through some review first.
Note: The University of Colorado shares all their course materials for their intermediate and upper-division reformed courses (Classical Mechanics, Quantum, E&M), including the review homework assignment that I adapted slightly based on my students’ prerequisites coming in.