As I was thinking about Sue's list, my list quickly turned into a mini version of my teaching philosophy. I realized that my list of issues was really just a list of ways we go away from what we know about how people learn, which is obviously related to how people learn math. A lot of this I have learned through discussions and teaching with Dave and Kathy Coffey ( I wish they would write about teaching) and Esther Billings, and previously Jan Shroyer and Georgi Klein and, and, and...
My list from there:
- Learning starts with engagement. Engagement is more likely when learners are safe, the content furthers their purposes, and they see themselves as potential doers of the content. (Cambourne)
- Humans learn best and retain longest when new learning is connected to prior learning. (Piaget)
- Reflection is essential for consolidation and extension of new learning. (Piaget/Vygotsky)
- Learners build and consolidate understanding through discussion and communication. (Vygotsky)
- Learners build abstract understanding by generalization of concrete experiences. (Piaget)
- Teaching furthers learning when it is starts with what students can already do, has planned worthwhile and reachable objectives, supports students in their diversity of learning styles and preparation, and assesses the effectiveness of instruction by measuring student learning. (Teaching-Learning Cycle)
- Comprehension is best taught with a process focus. (Mosaic of Thought)
- Math should make sense and be about making sense of ...something. The something depends on how you define math. My current try at this is making sense of quantifiable or describable objects and their operations and properties. Jo Boaler (and others) describe this as pattern finding activity. (Don't know how to source this. Seems obvious, though it took me forever to understand it.)
- All students are capable of significant and important mathematics. (NCTM Equity Principle)
- The mathematical processes are at least as important as the content. Problem Solving is central to these processes. (NCTM, Polya)
One thing Kate points out about the article is that it posits that teaching is not just an innate gift, that we can get better at it through work. I agree wholeheartedly - it is no better to say some are teachers and some are not than it is to say some can do math and some can not. The main attributes needed to both are desire and willingness to learn.
Several of my student teacher assistants are in struggling schools this semester as student teachers. They are very frustrated. It is clear that what is being done is not working, but teachers and administration are afraid to change anything as that might make it worse. The student teachers are forbidden to change anything, and that leads to the frustration as the problems continue and grow.
Jim Knight is an expert at Kansas on instructional coaching. (Knight has a blog covering coaching and various sundry topics.) His big questions for coaching are: (my paraphrases)
1. Is classroom behavior under control?
2. Are you comfortable with all the content? The pedagogy of the content?
3. Do all students master the necessary content?
4. Do you know and how do you know if students are mastering the content?
He starts with classroom management. I, unfortunately I think, have traditionally left this issue to the College of Education. I have seen my role in covering 2-4. But everything continues to point to first things first. The push to make teacher education more clinical, supports this - IF we support novice teachers in the same ways we know all novice learners need support. It is a whole cloth.
I do believe that engagement is key to real classroom management, and for math to be engaging it has to be authentic, and that means teachers need to have experienced it authentically... these things cannot be separated. But first, the class needs to be open to teaching and learning. And there are places where that's counter-cultural. Especially in math class. It has been proven to students that it is not a safe place to learn, that they are not potential doers and it is irrelevant to their purposes. It is natural and even wise in a way that they have closed it off.
Then classroom management is justifiably number one, except even the name is misleading. Environment construction, conditions setting... hosting? Whatever it's called, it's got to be part of the process of teaching as we teach it. I think placing student teachers in groups or pairs in classrooms is part of this, too. Students learn best when they can discuss and dialogue. Most of this stuff has been known since Dewey... why is it so difficult?
So I'll give Lemov's book a try, and pass it on to preservice teachers if there's even a hope of it helping.