This video represents my greatest drive for my own classroom. It delves into a full understanding of mathematical processes so that students understand the WHY as well as the HOW. They're taught the process and the reasoning behind it using examples, manipulatives, charts, and other visual aids. Building from this, the students are challenged to design their own presentation and defend their ideas in front of the class.
This approach significantly expands the impact of learning. By understanding the reasoning behind a theorem (or process or equation) to the point that they can teach it to someone else and explain their reasoning, they are strengthening their knowledge of math principles and the entire system of mathematical reasoning. By doing so, they are more able to approach greater challenges and high order processes.
An interesting video about Visible Thinking. I especially like this one as it shows VT in practice without the typical TED Talk stage, audience, and projector. Ideas in action!