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Nowadays, a student should be able to learn the course material at home through reading the textbook or follow one of the many free online courses. Some universities record video or audio of lectures so students can watch them at a time convenient for them.

So as mathematics educators, how should we justify that students should still come to classes? Is there any research about the correlation between attending classes and learning outcomes?

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A student-attended class does not have to be a one way flow of information. Even if there are 200 in the lecture theatre, the lecturer can set a problem, break off from teaching, ask the students in pairs to come up with a solution (hopefully productive chaos ensues for a few minutes) , then the lecturer rings a loud bell bringing the class to order, takes a vote between various solutions (some of which contain pernicious errors), then presents a solution or leaves the solution unfinished for an assignment. This encourages students to engage with the material and debate it with someone else.

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    $\begingroup$ There is considerable evidence that active learning simply produces better results than lecturing, across all STEM fields: pnas.org/content/early/2014/05/08/1319030111 . There are many active learning techniques, some adapted to large class sizes (like your example) and others to smaller ones. Another technique that works with large class sizes is Eric Mazur's Peer Instruction method. $\endgroup$ – Ben Crowell May 21 at 2:17
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"Nowadays, a student should be able to learn the course material at home through reading the textbook or follow one of the many free online courses. Some universities record video or audio of lectures so students can watch them at a time convenient for them."

I have to disagree with your premise - especially in the case of technical education. It quite often isn't enough just to "read the textbook" or "watch the video". In fact, many undergraduates aren't at the level where they can do that.

Have you actually tried this with a class? I can see how it would work with graduate students or even upper division undergrads but, other than that, I'm having a hard time imagining a scenario where this ends well.

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    $\begingroup$ No, I haven't tried this. But students could not understand something by watching a lecture video, perhaps they would also have trouble to understand when they come to the lecture. $\endgroup$ – ablmf May 19 at 15:00
  • $\begingroup$ And they also might not understand when they go to the tutoring center for help. Does that mean we should do away with tutoring? The lecture should be the place where most issues get cleared up since that's the point where they can actually interact with a professional who fully understands the material being studied/taught. I don't see this as a step that can be edited out of the process. $\endgroup$ – G. Allen May 20 at 22:24

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