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Evidence suggests that even instructional approaches that produce conceptual gains may leave students reliant and expecting to be reliant on guidance from instructors (Redish et al., 1998). Students do not expect to be able to address situations they have not encountered before or to judge for themselves when an answer makes sense. Instead, students' principal method for assessing their understanding is to check that their answers to exercises align with the published solutions. (National Research Council. 2013. Adapting to a Changing World: Challenges and Opportunities in Undergraduate Physics Education. Washington, DC: The National Academies Press. doi:10.17226/18312.)

My questions are:

  1. Is there any method to avoid the issue highlighted in bold? One approach might be to teach students to check whether their answers make sense (if it is to derive an equation, then check special cases.). But this begs the question of how to teach this technique systematically. Any suggestions?
  2. Would you recommend further reading on this topic? I understand I am coming from a Physics education standpoint, but I believe it is equally applicable to Mathematics as well.

Some might be tempted to just not give answers at all, like in many textbooks (especially Math), but this assumes students have already mastered the aforementioned technique.

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    $\begingroup$ An answer without a solution for any non-trivial problem should not be accepted. $\endgroup$
    – Rusty Core
    Apr 9 at 7:30
  • $\begingroup$ @Rusty Core For the purpose of this question, let's also treat answers as solutions. If my interpretation of the passage is correct, it's distinction is immaterial. $\endgroup$
    – Cheng
    Apr 9 at 8:27
  • $\begingroup$ Even in the late 90's my instructor had the right idea. Assign problems from text, but collect just one problem, hand-written, and grade it with humans. $\endgroup$ Apr 9 at 14:29
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Like you, I'm a physicist. Yes, you teach students this by teaching them to check their own answers. They way you do this is by repeatedly assigning them work in which they're explicitly required to do so. Example.

Would you recommend further reading on this topic? I understand I am coming from a Physics education standpoint, but I believe it is equally applicable to Mathematics as well.

The best review papers I know of on physics education research are:

Sadly, I think research-based reform in physics education has been killed off by a combination of technological factors including MasteringPhysics and Chegg.

Evidence suggests that even instructional approaches that produce conceptual gains may leave students reliant and expecting to be reliant on guidance from instructors (Redish et al., 1998).

This would be a wonderful problem to have, since practices that produce conceptual gains are essentially never implemented.

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  • $\begingroup$ Why would you say that MasteringPhysics and Chegg has killed it off? I mean aren't they the culmination of education research? At least in churning out students who can do quantitative questions well? $\endgroup$
    – Cheng
    Apr 10 at 0:10

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