The Great Divide

An April post on Research in Practice caught my interest, and made it very clear what's been going on for me the last year and especially since I started daily reading all the great math teaching blogs out there: 

There is a growing divide between my students' and mine perception of what good math teaching and learning looks like. 

Simply put, I'm breaking the math-class contract. 

Some examples of what I do, or try to do, that many students find weird and somehow wrong: 

• Rarely use the textbook in class 
• Give them open-ended questions
• Ask them to explain concept and rules - not just apply them
• Almost never give answers to problems, or if I do - don't give the solution
• Encourage the students to discuss solutions and convince each other
• Give them problems that require hours of work
• Give them problems they cannot solve

Now, to be fair, my higher level kids are enjoying themselves plenty. Dissent is negatively correlated with achievement levels, which is kinda obvious really but also ironic considering how many of the lower level kids  wouldn't even be so weak if only they had learned that math is about independent and creative thinking.
Weaker students need more structure and safety, but it traps them in a vicious cycle of low interest, low effort, and low results. What can be done, during the senior year of high school?