More musing on the coaching relationship… I thought it might be worthwhile to imagine how I would assess myself and how I’d want observers to assess my classroom. Here’s what I’ve got so far. I hope that observers would see:

  • Classroom Culture:
    • Students looking to themselves, their text, and other resources as much as they look to me for mathematical expertise.
    • Students checking to see if any mathematical claim made (by me, themselves, each other, a text, etc.) makes sense & is reasonable.
    • Students having a routine for checking if things make sense: looking for accuracy, reasonableness, connecting to concepts they already know, etc.
    • Students having multiple routines for “getting unstuck” or facing novel problems: they notice and wonder, they try strategies, they check for reasonableness and sense-making.
    • Students are “learning to learn”: they know what math content we’re exploring, and can say what their learning goals are for this activity.
  • Planning the Lesson
    • That I can articulate what role this lesson plays in the larger curriculum: what came before, what’s coming after, how the big concepts in math that run through many lessons are represented in this one.
    • That I can articulate what the concept is behind this lesson, anticipate methods that students who understand the concept and have good mathematical problem-solving skills could come up with to solve problems in this lesson, and that I am aware of the efficient mathematical procedures associated with this lesson and how they connect to the concept and students’ anticipated methods.
    • That I know what difficulties students might face, and ways to use multiple representations, simpler problems, practice, journaling, and other problem-solving and learning to learn strategies to address those difficulties.
    • That I’ve thought of my particular students and ways that I might need to adjust the ways students interact with the lesson to meet their needs (e.g. extensions of problems, identifying the basic ideas everyone must understand, supports for reading and writing, etc.)
    • That the activity structures I planned make sense with the kinds of reasoning and communicating I want students to do, and my students are ready for.
  • Working with small groups of students, individual students
    • That I hear my students’ mathematical ideas, never interrupt students, and rarely interpret their work (but instead ask a follow-up question to help them interpret their work).
    • That I listen to what students are understanding about concepts, and what methods they’re heading towards, before moving them towards efficiency.
  • Leading a whole-class conversation
    • That I pick appropriate moments to bring the group back together, for brief check-ins
    • That I choose students to hear from that will model multiple ways of thinking, and reflect the diversity of my classroom
    • That I model and enforce accountability to community, knowledge, and content.
    • That students ask questions of themselves, me, and one another that are accountable to community, knowledge, and content; that they have questions in the back of their head that they use appropriately.
  • Connecting across lessons
    • That students and I step back frequently to ask and answer, “what are we studying? what are we trying to figure out? what do we already know?”
    • That I make connections explicit, by both asking students to make connections, and reminding them of work we have done before.
    • That both “what is this problem/type of problem about?” and “what is the math we are learning to solve this type of problem?” both are asked frequently, by teacher and students.
  • Teaching Students to be Learners
    • That strategies and learning habits are explicit and are picked up by the students over the course of the year.

OK, that’s all I’ve got so far… I’d love to see how others would make their own assessment protocol thingies.