Warning: a lot of this post borrows heavily from education theory. I'm in my student teaching semester right now, so a lot of what I explain is taken from research papers and things like that. So how realistic it all is, I don't know.
I've been thinking a lot recently about different ways of running a secondary mathematics classroom. I've heard some teachers have great success with a flipped model, and some teachers hate it. Here is my current understanding how it all works:
Students are expected to go home and watch a video and do some problems as homework a couple times a week. Then when they get to class, the time is reserved for reviewing the videos and homework, and then spending the rest of the time doing projects and applying the knowledge.
In theory, it sounds great. Less lecturing in the classroom, and more project-based instruction. But I see a few drawbacks as well:
I can see students not wanting to do homework that is "new" to them. Students are used to getting problems in class, and very similar problems for homework. This is a problem in mathematics education, but it is probably the most prevalent model used. Come to class, review homework, see new problems, go home, do problems similar to class for homework, rinse and repeat.
Another issue I see with a flipped classroom model is that it doesn't really allow students to discover the math on their own. Sure, they're learning new material on their own at home via some video and some problems, but it's really not that different from an in-class lecture. In my mind, an ideal mathematics education would have students seeing real problems, and create an atmosphere where the students are asking the questions, and "reinventing" the mathematics required to solve the problem. (This concept is known as RME - Realistic Mathematics Education and/or IBL - Inquiry Based Learning).
It almost seems as if the ideal flipped classroom would be backwards. What I mean is that students begin with projects in class, and then their homework is the lecture which "formalizes" what they discovered in class. This borrows from the idea of something called "The Iceberg Model" or "Progressive Formalization".
I would love to hear what you guys think about this backwards flipped classroom idea, and what you think the ideal classroom would be like. How is class time spent? What is for homework? What does the week look like for a student?