Breedeen Murray writes about the importance of having an image of the kind of teaching we are striving to be:
[…]I had seen video of this problem being taught at PCMI the summer before. And this was a HUGE thing for me. I had a template for how this lesson should be taught. I didn’t have to imagine how to transform it from the book to something better all on my own. I didn’t have to create something from scratch. I just did what the teacher did in the video. Which is exactly what I did with the exception that I had a document camera, so I had students come up and put their work under it, instead of writing on an overhead. And this too was amazing. I had students who had been giving me grief all year long produce such beautiful explanations that it hurt my heart. How could I have waited so long to let them be this awesome?
The models of teaching we carry around in our heads are so very, very powerful. Here are some resources for independent study: