A very important supplement to my textbook, Mathematical Reasoning: Writing and Proof, is an extensive collection of screencasts developed by Robert Talbert, a colleague of mine at Grand Valley State University. Although these screencasts are structured around this book, they can be used in conjunction with any introduction to proofs course. Please review these screencasts and see if they are suitable for use in your course. Most of the screencasts deal with one topic or example and are approximately 10 minutes long. They are a great supplement to a course and give the students a chance to have examples done outside of the classroom. You can find the complete collection of screencasts in the MTH 210 Playlist in the GVSU Math YouTube Channel.
These screencasts are very valuable if you want to design your course using an inverted classroom model. I did that last winter semester and I was very pleased with the results. Students were more engaged with the material than in a more traditional classroom model, and we had some very interesting discussions during class. This is because students have access to me while they are doing some of the most difficult work for the course. I am no expert on the inverted classroom, but I will continue to use this model in MTH 210 – Communicating in Mathematics.
If you would like to learn more about the inverted classroom, you should read the series on the inverted classroom by Robert Talbert in his blog Casting Out Nines. Although it is not in this series, the post on “Inverting the transitions-to-proof class” is very informative.
Robert and I and some other colleagues at Grand Valley have now used the inverted classroom model for our transitions-to-proof course, and I am pleased at how well my text, Mathematical Reasoning: Writing and Proof works with this model. It was not specifically written for an inverted classroom, but in reality, that term was not being used when I started writing it over 12 years ago. However, I did design the book to be studied by students and have incorporated active learning strategies into the book. The most evident of these are the preview activities that begin each section. The book also has several progress checks for students in each section, and these seem to help the students quite a bit. For me, the combination of the book and the screencasts are about as good of a combination for an inverted classroom as there is.