How does a former student respectfully submit suggestions on how to teach a class better to a professor after graduating?

Question

How does a former student respectfully submit course suggestions about how a professor should teach and examine students after graduating? I always think class-feedback given by students who just took XYZ class is useless because the students don't have enough outside knowledge to accurately judge whether the professor did a good job. Maybe they think the only perpsective on a topic is what the professor said and they don't have the chance to compare viewpoints. Maybe instead of course feedback from students, professors should ask other professors to look at their syllabuses in detail and ask whether they're teaching the right things.

So, I took XYZ captsone class at a school, and after graduating and learning more about the theory in graduate school, I realized there are details not covered in the XYZ class that should be emphasized that do not requiring some esoteric backrgound knowledge only taught in graduate school. I am not even a PhD yet, and I know how to revise a PhD's class. Now I should re-learn everything from a more rigorous perspective myself.

There were practical projects that weren't done, and we didn't have a project to apply everything we learned or challenge ourselves to connect the information. There were topics discussed without connection to the things they were related to, and undiscussed applications. There were approximations used that were asymptotically correct, that we were told to use in non-asymptotic scenarios where they are inadmissible.

I think if we had been asked to do things more rigoursly, I might have had a higher score, but the professor made the class focused on more elementary things such as regurgitating a textbook explanation or a competition on arithmetic calculations. The person who had the highest score didn't necessarily understand the theory better. Their weaknesses weren't tested because some things weren't tested at all in class.

Answer 1

I'm going to suggest that unless you have a long term relationship with them that is friendly and productive, that you don't even attempt this. It is too easy to go "off the rails" and become contentious.

And, some of the things you say might actually be justifiable in an undergraduate teaching context. Some things are difficult to get across to large groups in undergraduate education so sometimes shortcuts are suggested. It can be a judgement call and such things work for some students but not for all.

But if you do have such a long term relationship you can sit down and have a discussion about the theory of teaching (and learning) and share ideas back and forth.

But a note "out of the blue" that seems to be criticism is unlikely to be well received.