I am a new calculus teacher in a high school for gifted students. I am the youngest teacher, I am not in my home country, and this country particularly values age and experience, so I have little room to discuss syllabi and homework assignments.
The level of maths is quite high (senior students deal with vector calculus and Stokes' theorem) and the class requires a large amount of weekly homework (to give an idea: about 15 exercises for each section in Stewart's Calculus, about 3 sections a week). Deadlines for these homework assignments are very strict (new assignment every week, none accepted after the deadline).
I know that practice is important, especially in calculus, but this leads to unintended outcomes:
Grading takes a lot of time, so many teachers don't grade seriously (little feedback; just checking that students did the homework) and instead distribute a solutions printout from the textbook to the students.
Students don't spend a lot of time thinking about or engaged with the problems; they just rephrase the solutions. Good students will try to understand the solutions, but other will not really care.
Even if I don't give them the solutions printout, then they will find the answers online.
Many students don't enjoy calculus and few of them would take an optional class related to calculus (say analysis or differential geometry). Freshmen are really afraid of their future calculus class.
I have seen this with a couple of students: they believe that they will be successful if they copy the solutions for all homework problems (including non-assigned ones) from the textbook (at least 60 per section!). This has led to very poor results.
What can I do? I like teaching in the school, but the general philosophy of education in this country is:
If a student has unsatisfying grades, give him more homework and extra classes.
So far, I have just decided to relax the deadlines, and not to care too much about late homework, but the outcome is still not satisfying. I am also not comfortable with having different rules for homework than other classes.
Is there an efficient way to manage a huge load of homework?
What are the alternatives to the "practice, practice, practice" method to gain good skills in computations?
The ideal solution would be to completely change the homework list in accordance with the philosophy of "less but better," but my colleagues will be hurt if I change the school's habits. How can I discuss this problem with them without hurting their sense of hierarchy?
Thank you in advance, and sorry if my questions are imprecise. To sum up, it could be changed to "What are the most efficient methods to teach Calculus, with respect to the ratio (computation skills)/(homework load)?"