Our intent with these practices is to simplify the incredible complexity of learning to teach by giving our brand new teachers a small set of things to focus on and get really good at so that a) the children they're teaching actually have a meaningful learning experience despite teachers' inexperience, b) they develop some automaticity and fluency in being a teacher and in being the adult in the classroom so they've got legs to stand on, and c) their mental capacity and energy is being used in the most productive, high-impact ways-- while the jury is still out on what these ways are, I'm fairly certain that it's not what we currently ask our brand new teachers to do: sit in really complicated sessions on backwards design and lesson planning, and then spend hours upon hours writing not-so-good lesson plans that they then struggle to execute.
As I've briefly described, once we have these practices, we'll try to codify them into protocols and provide illustrative examples. Then, we'll engage our new teachers in practical learning cycles where they experience these practices (as led by a skillful teacher), analyze them for their value and nuances, rehearse them, receive feedback on their execution, implement them in a classroom with real children, and then reflect on the experience.
As you review these instructional practices, I'd particularly appreciate your feedback on whether they meet the following criteria:
- Are these practices routine? Could they (and should they) happen every single day? While exceptions are certainly possible, we want these practices to be common enough that new teachers can rely on this as an initial repertoire. Teachers can innovate and be more flexible once they have the fundamentals down.
- Are these practices effective? Individually and taken together, are they likely to lead students to develop the type of mathematical understanding, thinking, and agency that we aspire to for our children?
- Are these practices comprehensive? If these practices are executed skillfully and nothing else happens in a lesson (pedagogically- I'm sure there will be management and relationship-building and procedures), do they comprise a holistic, thorough lesson that allows children to walk away having learned something worth learning?
- Are these practices generic enough? Can they be applied to just about any objective or standard or mathematical topic?
- Are these practices specific enough? Can they be codified into protocols that new teachers could rely on to know exactly what should be happening during each portion of the lesson?
- Activating prior knowledge: how do you meaningfully activate prior knowledge beyond simply giving students a problem and then pointing to it and saying “look, see!”? What about the prior knowledge should you elicit; what are some good questions to ask or statements to make at this point?
- Posing a problem: how do you present a new problem to students (beyond just reading it out loud and then having a student read it out loud)? What questions should you ask them about the problem (e.g. does anyone have an estimate, what do you already know, what information are you missing)?
- Eliciting multiple solutions/approaches: how do you ensure that students share their ideas and hear the ideas of others without immediately judging any idea as right or wrong? How do you revoice effectively without simply repeating what students have said (as Brian so elegantly described here)? Sub-categories of this, or strategies, could include:
- Whiteboarding (as used by @fnoschese and many other spectacular teacher bloggers)
- Gallery walk (as described here)
- Math Congress (see article above)
- Generalizing or formalizing an idea: After an exploration or conversation has taken place, how do you help students “officially” formalize or generalize or synthesize what they’ve learned? What structures (notes, tables, etc.) should you implement? How do you ensure you’re not just shutting everyone down with the “right” answer but meaningfully integrating the ideas that have been aired? Sub-categories could include:
- Some of the synthesis activities described in this post
- Think-pair-share (or any of the million variations that make this such an instructional coach darling)
- Checking for understanding: How do you know where ALL of your students are at any given point in the lesson? Sub-categories or concrete strategies could include:
- Whiteboards (as more commonly used- for students to hold up an answer)
- Conceptests (as pioneered by Eric Mazur)
- Extending student thinking: After students have reached an apparent consensus, how do you push them to take the next step? What are some common extension questions to ask (e.g. is this always true? what if we used negative numbers? can you come up with a counterexample? why else is that true?)? What should students be thinking about?