Under what situations is it more productive for math students to stop attending lectures and learn the material alternatively? What are some remedies?
I originally posed this as an Example Question.
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Class time is a designated time for students to sit and focus on the material of the course. From experience advising college students, here are the most valid rationalizations I've heard for skipping all classes:
These are all complaints about how class time is being used -- not objections about spending time itself.
However, most students who use one of these reasons stop attending class but then do not replace it with anything similar. Students who stop attending class still must have some minimum amount of time spent sitting and focusing on the material of the course if they hope to succeed.
I can imagine replacing all lectures with a weekly session in a college's tutoring center -- a weekly study group that meets in reach of a tutor who is familiar with the material. This feels to me like the easiest way to replace lecture time in a constructive way.
In summary, I would say that a necessary but not sufficient criterion for an answer to this question is: the solution must involve multiple hours per week of focused struggle with the material, in addition to any assigned homework.
There are a variety of lecture styles that often result in students, for either valid or totally invalid reasons, stopping coming to lecture. Here's a quick outline of a few:
1) Many lectures consist of worked examples from the book. These can be helpful for students who are confused, but, often times, students convince themselves that they can just read the book. For some of them, this works out, but for others, they are completely unable to recover. A nice, easy way of dealing with this is to survey the class on how they feel about this type of lecture. If they all say "they don't find it useful", that doesn't mean you shouldn't do it---just that you might consider mixing it up more.
2) Another type of lecture in a proofs-based class is to just write up solutions to proofs. This can be really tedious for the students--and worse, it can make them feel like they're learning when they're actually just mechanically writing down what's on the board. Since they believe the "value" of these lectures is the notes, students will often ask their friends to write notes for them and just copy them (or not!) later. This can be even worse when instructors give out typeset notes to the students. One way of mitigating this is to intersperse the proofs themselves with other content--like explanations of how and why things are the way they are. I've also found that giving students notes that they can follow through the lecture and explicitly downplaying the importance of the content of the proof itself helps students realize that just copying someone else's notes isn't particularly helpful.
The students are legally adults, they are entitled to make their own mistakes...