Just a quick note to alert you all to the links posted in the comments section of yesterday's post. This forum thread is a classic -- I had seen it before, but I couldn't locate it yesterday (thanks, Shyam!).
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I haven't kept count, but I think some 15+ undergrad students have done an internship in my group, and that experience has been positive enough for (at least some of) them that they stay in touch with me to this day. At least seven of them have gone on to graduate school.
In the 1990s, I used to select the summer interns from the bunch that wrote to me -- and I can recall only one from this group going to grad school (those were also the times when the IT industry was like a super-sponge, absorbing engineers from all disciplines].
In the naughties, students came to my group almost exclusively through references from their teachers (I have also had a couple of them coming in through JNC's Summer Research Fellowship program). And almost all the summer interns who went to grad school are from this group.
In my experience, I have seen two types of students: some are genuinely keen to develop their research skills by spending some time in a research-intensive environment, and some who want to escape from the requirement of "in plant training" at an industry [in metallurgy / materials engineering, most of the industries are in some of the hottest parts of India!]. If there are other motivations, I have not been able to figure them out from my interactions with the students who came to our group.
In any event, I have enjoyed interacting with them, and as I said, the students also seem to have had a positive experience. I still don't know how important this summer internship business is for the students -- other than that they get to see a research group in action, giving them a chance to assess whether a research career will work for them.