Tina Cardone inspired me to try to articulate my teaching philosophy concisely, without any jargon. Here goes:
They do. Never blame someone for forgetting what they haven’t made use of, and never pretend that a perfect explanation will live in a student’s mind forever. If it’s worth learning, it’s worth practicing, deliberately, over time, and from different perspectives.
It’s all about knowing what they know
Students are not empty vessels. I should spend as much time figuring out what students know as I do trying to fill them with new knowledge. Students do math in my class to show me what they do and don’t understand so I can meet them where they are and decide how to move forward. Without this, I’m flying blind.
Grading hurts as much as it helps
Incentives cause students to worry about performing rather than learning. Grading should send a message about what is important for learning, and then get out of the way as much as possible.
Knowledge for the sake of knowledge
I teach math so that students gain expertise in math — in reasoning, arguing, seeing structure, making generalizations, and constructing models. I don’t teach so that they can get a job someday; I teach to allow students to delve into the discipline of mathematics. That is worth doing in and of itself.
Humans learn more when they are happy
And they are happy when their ideas are valued, they are appropriately challenged, and they have the chance to laugh.