Linear algebra first

Now that I’ve decided to start converting my classes to the flipped classroom approach, the next question was which class to start with for the spring 2021 semester. This should be a course that is in high demand so that many students all over the world can benefit from the free content I will create. On the other hand, this should be a course that I can teach regularly, and for which I already have some digital assets. Additionally, having free content in mind, the students should be able to complement my lessons with an open-source textbook.

These criteria narrowed down my options to one clear winner: linear algebra!

This is a core course that many students have to take for their majors, and it is a prerequisite for the trending fields of machine learning and AI. There are several excellent open-source texts on linear algebra, and I’ve been using one of them for several years to teach linear algebra. I created slide presentations for all my lectures because I realized I was spending too much time during lectures to write on the board the linear systems, matrices, etc. I could instead devote this time to conceptual explanations. Additionally, students receive printable PDF documents with lecture slides, and they don’t have to take extensive notes during class. They can concentrate on my explanations instead and occasionally add some remarks to the printed notes. Students seemed to like this approach, and I received consistently positive student evaluations.

Even though I revised my content and approach every time I taught linear algebra, converting all content to the flipped classroom approach will give me an opportunity for a more substantial revision. My current approach focuses on conceptual understanding and proofs, and I would like to bring more applications and numerical computations into the course.

In the next post, I will outline my approach to the linear algebra course redesign. It will build on the current strengths, but it should also provide students with a more complete view of the subject.

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