1) All students are sense-makers. All students have ways of thinking (mathematically).
2) There is little to no value in a teacher demonstrating a procedure and a student then practicing it, no matter how creatively the teacher demonstrates the procedure nor how important we think the procedure is.
3) We learn the most when we think deeply and then communicate our thinking. We all learn more when we have the opportunity to receive feedback on our thinking and to revise.
I think this covers it. It’s funny, despite having spent upwards of 7 years thinking about math education specifically, I haven’t ever written down my first principles. These might be controversial. What thoughts do you have about them?