When I first went back to school for tech stuff (ultimately a master's in EE), my instructor for the entire calculus sequence -- and later on for linear algebra -- struck what I found to be the ideal balance. Something like:
0. Homework is never collected or graded, but don't be fooled into thinking it's not required -- that is, if you don't do the homework, you are extremely unlikely to pass the exams/course. Essentially, this is not knowledge we were learning -- it is skills that require practice. Homework is an opportunity to practice and hone skills.
1. Each lecture introduces a concept and/or technique, and works through a few demonstrative problems to show what it means or how it is done. Homework is assigned from textbook problems that involve the same techniques with progressive difficulty or complexity. The textbook used that pattern where odd-numbered problems included solutions, and assignments usually involved the ones with solutions.
2. The last one-quarter to one-third of every class period was dedicated to review and questions about the homework assigned for the previous class. Because we had the correct solutions in the text, we knew what to ask about (i.e. the ones we couldn't get to come out right). This particular instructor was fantastic at thinking on his feet and working problems on the fly, correctly and without preparation, so usually he'd just work the problem on the board and we could stop him to ask for a more detailed explanation if necessary.
Granted, this model didn't work as well for his linear algebra class. Since many of those problems involve long slogs through tedious and error-prone matrix operations before/while you were really dealing with the concept or technique being introduced, he couldn't as easily demo entire solutions during the question/review periods. I suppose that difficulty would apply to several other higher-math topics, as well, but even so, later in my education I often found myself wishing this or that professor would follow the pattern of my humble calculus teacher.
0. Homework is never collected or graded, but don't be fooled into thinking it's not required -- that is, if you don't do the homework, you are extremely unlikely to pass the exams/course. Essentially, this is not knowledge we were learning -- it is skills that require practice. Homework is an opportunity to practice and hone skills.
1. Each lecture introduces a concept and/or technique, and works through a few demonstrative problems to show what it means or how it is done. Homework is assigned from textbook problems that involve the same techniques with progressive difficulty or complexity. The textbook used that pattern where odd-numbered problems included solutions, and assignments usually involved the ones with solutions.
2. The last one-quarter to one-third of every class period was dedicated to review and questions about the homework assigned for the previous class. Because we had the correct solutions in the text, we knew what to ask about (i.e. the ones we couldn't get to come out right). This particular instructor was fantastic at thinking on his feet and working problems on the fly, correctly and without preparation, so usually he'd just work the problem on the board and we could stop him to ask for a more detailed explanation if necessary.
Granted, this model didn't work as well for his linear algebra class. Since many of those problems involve long slogs through tedious and error-prone matrix operations before/while you were really dealing with the concept or technique being introduced, he couldn't as easily demo entire solutions during the question/review periods. I suppose that difficulty would apply to several other higher-math topics, as well, but even so, later in my education I often found myself wishing this or that professor would follow the pattern of my humble calculus teacher.