Thing about it is the students should be given an explanations about why each topic is important for them to learn to be able to learn more advanced topics.
Maybe briefly show how that adavanced topic will be taught and let them realize they can not possible even start to understand advanced topic because they are missing the more elementary pieces.
Similarly why they can't got further without doing their homework. How mastering the homework exercises let's you solve more problems.
I know that is not easy, the teacher may not quite understand how topics relate, why each of them is needed in a specific order, if they have not thought about that much.
One of my favorite teachers that I ever had was my Calc 2 teacher in high school.
He always made a very special point to explain the "why" of everything. Not just "how is this used?", but he would also derive a lot of the formulas for us instead of having us just memorize forms. I think it makes you better at math in general; the whole point if mathematics education, in my mind, is to teach you the how and the why of things, not just to get to an answer.
I already loved math by the time I got into that class, but I attribute him as the reason that I love formal math so much.
Yes, to all of this.
The pedagogical term for the concept in your final paragraph is "scaffolding", and it's critical. Teachers have to know how to break their subject down into digestible pieces, and then find the proper order in which to build it up again. Advanced mode: be able to break it down and build it up again in different ways, for students with different backgrounds or learning styles.
(This is why many teachers - I was among them - aren't immediately good at teaching concepts or subjects that come easily to them as they may be at teaching things they struggled a bit to learn. If you've had to break something down for yourself then you're ahead of the game when it comes to breaking it down for others.)
For a while I taught an "Improv For Teachers" workshop (I have a theatre background), which was really about listening to your class and being ready to adapt your lesson plan to where they are in their course of work, or even to their mood on the day. It was mostly elementary school teachers, and some of them really resisted that idea. I'm convinced, though, that that's an important skill: the most memorable and successful classes I've taught have happened when I've been able to take advantage of a student question or a student interest and run with it - sometimes not even knowing where it'll go - with the confidence that I'll somehow be able to pivot back to the curriculum. You have to be willing to be a bit vulnerable, and embrace a bit of fear, and risk a bit of failure to do it, hence why the Improv experience is so helpful.
Do you have teaching experience?