This is an attempt to emulate my betters, which is actually not a bad strategy for improvement.
I want the center of my classroom to be empowerment. As a bad beginning teacher, emulating David Letterman of all people, I realized that I loved teaching math. I'd tell people that there weren't many things you could teach where the student would literally be able to do something at the end of the class that they couldn't do at the beginning. While I still like that, I now think it can happen in many more places than math class, and have a much different idea of what I want the students to be able to do.
On my own I got to realizing that problem solving was what I really wanted to teach, and my friend Sue Feeley introduced me to Polya (figuratively) and the other NCTM process standards. Both helped give me language to describe things I had realized, and both indicated a path to set out on. Vygotsky helped me understand why students responded so differently to the same task.
Mosaic of Thought, Cambourne's Conditions of Learning and other literacy education work helped me start to understand how to teach processes, and I don't know that I would ever have found that were it not for Kathy and Dave Coffey. The conditions are the heart of what I want for my students, and creating or nurturing those conditions is what I see as the main responsibility of my work.
Engagement is first and foremost. Cambourne notes that engagement requires learners to believe:
- they are potential doers of what is being taught. This fits with and explains the idea that the students need to be the ones working in the classroom. (See also expectations)
- what they are doing matters to them. This is why teaching the processes is so important to me. Polynomial division does not matter to 99% of students. Problem solving will make 100% of my students' lives better.
- they are safe to try. This is why classroom community is so important. (See also approximation.)
- Immersion. Learners need to experience real and rich mathematics of all kinds. Still one of my measures of how rich a question is is to consider how many processes it invites learners to engage in.
- Demonstration. Learners need many and authentic demonstrations of what they are learning. This was huge for me. I had become a hardcore discovery-based teacher. I was proud of my students saying things like "Why ask him, you know he won't tell us." (Oh, that is painful to me now.) I took students' feedback about their frustration and decided that it was because they weren't used to this mode of learning. But really, I was asking them to do things they'd never seen. Asking them to learn how to dance when they'd never seen one. Coupled with a lack of good feedback, it's a real testament to those learners that they got as much out of it as they did. Adding demonstration let me back into the discussion. Not to tell the learners how to do it, but to share with them authentically how I think about it. I make space for them first, as I prefer if they're demonstrating to each other, but I watch and assess for when they need demonstration as a support.
- Expectations. This goes hand in hand with the Equity Principle from the NCTM, which is near and dear to me. I believe all people can do significant, important mathematics. I really do. I try hard to communicate this to my learners.
- Responsibility. Learners make their own decisions about when, how and what to learn. THIS IS ANARCHY. I know. It's dangerous, especially when our learners have been trained for dependence and helplessness. Most students are not ready for full freedom immediately, but it is my goal for all of them. It's also my ongoing struggle to get students to understand that I both mean this and it doesn't mean that work is optional.
- Employment. Learners need time to try out their learning in authentic situations. This connects with real life mathematics, with project based learning, with discovery learning and more. The students need to be the ones working if they are to be the ones learning.
- Approximation. Learners need to be able to make mistakes without fear of punishment. If there's one area that math has completely screwed up on in the past, it is this. I do it, now you do it perfectly. This is crazy. We all know that no one learns anything important this way. And that the mistakes people make are crucial for learning in the first place.
- Response. Learners need real and meaningful feedback about what they are interested in working on. I now have my students put stickies on any work they turn in with what questions they have for me. Cambourne: "response must be relevant, appropriate, timely, readily available and nonthreatening." Grades are not feedback in this sense, and can only strive to be timely and readily available. (Although that does make grades better so far as it goes.)