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I am teaching a linear algebra class for math majors and non-majors out of the first 4 chapters of Lay's book. My plan is to have the students read a section prior to each class, have them answer a few questions about the reading (submitted online before class), and discuss their answers during class. (There will be a group work component too, but that's not why I am here.)

I am trying to think of questions that would help them engage thoughtfully with the material. I feel good about asking some questions like "find the row echelon form of the following matrix," but I think there are some more foundational questions that I might ask, like "What new results/definitions are introduced in this section" or "how does this section relate to the previous section," or "what new problem is introduced in this section" etc. The kinds of question that experts ask themselves all the time (possibly without thinking about it).

Can you suggest any such questions?

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    $\begingroup$ Is this the kind of linear algebra class where it is also serving as an intro to proofs course? $\endgroup$
    – Chris Cunningham
    Commented Jan 3, 2022 at 15:44
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    $\begingroup$ No, we have a separate course for that (although this is an interesting idea) $\endgroup$
    – David Steinberg
    Commented Jan 3, 2022 at 20:00

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Lay is the textbook I use. (And I love it.) I wonder if you'd find the true-false questions valuable. There are usually 8 of them (2 problems near #23 and 24, usually with 4 parts each). Those seem like questions you could ask after the reading but before lecturing.

[I don't do what you're doing. I do have them take notes on each section, but they turn those in with the homework, after lecture.]

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