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I and my colleague will teach an elementary linear algebra next few weeks, but the way our course is planned mostly is by turn teaching. By that I mean, my partner will teach the first 8 weeks of the semester, and I will teach the last 8 weeks. That's how it works here. Tradition you may say. However, we both agree that this should not be the only way. The course itself is scheduled at 2 hours on each Monday and 2 hours on each Friday.

My Q is: Are there other possible suggestions about better teaching method that we can use? The aim is that we want to distribute our teaching load a bit more even, not like this which eventhough seems even in total, but separated in distribution. We also want better result for student.

What we think can be the solution: 1. We follow the planned responsibility but with a small difference. My partner teaches first 8 Mondays, and I serves as tutor in first 8 Fridays. This means I help student focus more on problem solving, applications, etc each Friday related to the material/basic concept given last Monday by my partner, and then we swap roles last 8 weeks. We think about this option often but wonder a lot abour whether all materials will be covered. 2. We simply teach the planned course but my partner teaches on Monday and I teach on Friday. This way, it seems pretty confusing to be honest for the student. 3. ...?

What we think CANNOT be the solution: 1. CoTeaching in class. This actually just means that my partner does not really like being observed by someone else who is not the student. I wonder why but we will talk about this too.

Eventhough we do turn teaching a lot here, we still communicate very often between lecturers. Even some pairs of lecturers do co-teaching already, including me with another partner, and help breaking the tradition for the sake of our students.

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    $\begingroup$ Split the course. The first lecturer teaches "theory" (matrices, determinants, vector spaces, proper vectors...) and the second one teaches the "applications" (system of eqs, polynomials, identifying second degree equations, ...). $\endgroup$ – llllllllllllllllllllllllllllll Aug 13 '18 at 15:47
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    $\begingroup$ I've done a lot of coteaching, and this sounds like a situation where you will have a very bad experience. $\endgroup$ – Brian Borchers Aug 14 '18 at 2:32
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    $\begingroup$ Personally, I'd much rather have the last half and just take it from wherever the partner teacher gets. The idea of keeping track of what has and hasn't been said (as it very mission critical in linear) on a weekly basis does not sound like fun for you. $\endgroup$ – James S. Cook Aug 15 '18 at 0:28
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This doesn't address co-teaching per se, but I strongly suggest you check out:

http://bentilly.blogspot.com/2009/09/teaching-linear-algebra.html

This link covers how you can incorporate effective learning methods into homework policy and Q&A. It seems to have worked incredibly well in a very important course that many students struggle with.

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This is a student perspective.

In Moscow (during my third year) I took an algebraic topology course which was split between class lecture and a problem-solving session. These roles were not strictly adhered to, and indeed some easier proofs were deferred to the problem solving session and likewise instrumental examples were solved by the class in lecture (things like homotopy invariance for pairs via the five lemma.)

Pros

  1. Deferring some proofs had the advantage of not interrupting the flow of lecture with technical points, and gave students the feeling of "doing" some algebraic topology in the problem session.

  2. A diversity of opinion on what points were central in the lecture. The second teacher supplied the problems for the class and also assigned homework.

Cons

  1. There were days where the problem-solving session assumed knowledge not covered in lecture. This sometimes led to unreasonable homework assignment, but this may have had something to do with an attitude of "just go learn it."
  2. The difference in approach between two professors was sometimes baffling. One would hand-wave away certain issues, and the other could be pedantic about similar problems and vice versa.

Altogether, I think I liked the approach, and I think doing something like this would require some collaboration on the problem set (especially if one wants to cover some central/personally important material in the second half.) I also think the tutoring approach requires some extra attention to what is going on in class/ where confusion is, so it seems like a lot of communication is needed.

Sorry this is not new advice (not that I am equipped to give it) but it was too long for a comment. Maybe also what I've said is obvious.

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split it half way as the traditional solution. Better for the students and better for the teachers. Allows focus.

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