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Trivial is, I suspect, best expressed in terms of inferential distance that the student has to cover. Education naturally works on the borders of what people know: too far and showing people something is incomprehensible to them, too close and they're learning nothing they couldn't have found themselves simply by looking at your powerpoint stack.
I suppose, to develop that line of reasoning, it might go something like this:
Given that you're operating on the edge of people's concept space to be teaching them something worthwhile, if you're saying that something's trivial (i.e. that they should find it trivial) a lot, you're either:
A) Wasting people's time, (it's too close to their known concepts)
or
B) Confusing people, (it's too far from their known concepts)
If you're in the goldilocks zone for learning, it shouldn't be trivial. Might it rely on things that are trivial to them? Sure. But I don't see any value in mentioning that they're such, and if you're dealing with varying ability it's worth keeping in mind that some of the things you think are trivial aren't going to be to everyone.
Basically, my question to you, would be: What value is added by calling something trivial to justify the harm to those who don't find it such?
You could after all just not mention that the thing is trivial, perhaps more students would have the courage to ask you about it if they don't understand it that way.
I also don't think a university course has to hold every students hand. For example if you offer Advanced Calculus or whatever, it is fair to expect students to know that 2+2=4. If some step is too far from a students known concepts, they can either invest extra time trying to catch up (Google is your friend), or they can switch courses.
You could also debate which approach is better for learning maths. In my time, there were comparatively thin books about calculus and comparatively thick books about calculus. The latter spelled everything out. I hated them - too many words really made it hard to focus. I personally much preferred the dense books that left more thinking to the reader.
Maybe for some students the thick books are better, but I don't think a teacher has to please everybody. Students should have the opportunity to switch to another teacher or subject if they can't cope with the current teacher.
Just stop when you've got as deep as you care to go. I don't see the necessity to say anything there. If it is trivial, then it's not going to be challenged because everyone will know that they'd lose, and if it's not trivial and it is challenged, then you've identified that at least one of you's going to learn something in the exchange.
> I also don't think a university course has to hold every students hand. For example if you offer Advanced Calculus or whatever, it is fair to expect students to know that 2+2=4. If some step is too far from a students known concepts, they can either invest extra time trying to catch up (Google is your friend), or they can switch courses.
There's failure on both sides if students are being entered for a course that's significantly beyond their ability in that sense.
On the one hand, the student needs to try if they expect to get anything out of it, and persistent focused effort should have equipped them for most of what they can reasonably expect to run up against. On the other hand, the college shouldn't be taking people on who are manifestly unsuited to the subject they're being admitted to.
Perhaps in first year, that's understandable. Testing what people know for admittance, especially given the pitiful standard of secondary education and testing, is a non-trivial task. However, by the time you're getting into second year, if the university has passed them, and they're under-equipped for the second year... well, why the ever loving spaghetti monster did you pass them from first year?
I think we'd probably both agree that both parties in education need to make reasonable effort. If the student isn't willing to try, then there's nothing that can be done. If the college isn't putting its best foot forwards, then the student may as well just be paying for the right to sit the exam for all the value the college is providing.
Really, I don't think saying "it's trivial" is such a big ordeal for students. In maths at least, they'll quickly learn to get over it. I think in the beginning I was surprised a couple of times. Then I thought about it, and then after a while I realized it is trivial. It is also a pointer for the students so they can see "I should know this".
As for passing students from first term to second term - I am not sure if I care. Why not let students enter any course they wish?
