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?
This is where my brain is at right now so remind me to come back to you on this.
ReplyDeleteLooking at what you've listed it seems like you're also recommending a very specific style of teaching. So I guess my question would be if that's your goal or are you looking for more generalized teaching practices that would also be effective should a teacher teach in a different (more prescriptive/traditional) manner? I'm also wondering if it'd be helpful to organize these practices under something like Must Have and Nice to Have. Which of these practices must you get good at now and must you have in each lesson and which would be something you could dabble in and work on as you grow as a teacher.
As you know I've been on a Orchestrating Productive Discussions kick http://www.nctm.org/catalog/product.aspx?id=13953 and one thing I think I'd add is Anticipating. Both anticipating problem areas and also possible pathways. I'm not sure if this is something that's possible for new teachers but having them actually solve the problems being posed using multiple methods would be a good start. Or since your kiddies are in groups, having them share a problem with another teacher and listen to that teacher work through it. In science at least, we have a few very context specific learning progressions that are helpful for this but I don't know that it exists in math.
Something I'd teach under Checking For Understanding is how to respond to an incorrect student response (cue, prompt, rephrase, probe, reteach). New teachers often get stuck in a "repeat it again but slower and with more gesturing" cycle when a student gets something incorrect and really they just don't know what move to make next.
Given the populations your teachers usually teach in and the type of instruction you seem to be aiming for, I think I'd add a language support practice either embedded within each domain or as a separate one.
Also to add, modeling/guided practice. Especially as a new teacher, I defaulted to a lot of talking in front of the class. That was bad. Then it went away entirely. Also bad. There's a specific skill in modeling a thinking or problem solving process that's not lecture in the traditional sense but is incredibly valuable. That whole, "Here's what I'm thinking while I'm doing it" vs. "Here's how you do it."
So to try and not bloat your list, I'd probably add Anticipating and Responding under Checking for Understanding. I'd also consider modeling a more necessary skill than extending (as much as I hate doing that). And perhaps embed language support skills throughout.
Thanks for your input! I think we are prescribing a teaching style... one that we believe, based on research and experience, to be most effective for students (not just in terms of test scores, but in terms of developing their mathematical understanding and developing the skills and habits they'll need to be active participants and advocates for themselves and their communities after they leave the classroom). We'll probably have to do some thinking about how we'll recommend teachers adapt this prescription if they end up hired into more traditional districts, but I'm pretty excited to put a stake in the ground.
DeleteThat said, I would want our list to be all must-haves (although obviously, teacher skill-level will vary with experience), and to be adaptable-- even if you're doing direct instruction, I would hope that you're asking students to share their thinking; the difference would just be that you do so after you've explicitly presented and modeled.
And thanks for the detailed additions as well... I agree that the think-aloud and ability to actually respond to what students are saying (rather than fishing for answers) are critical skills!
Would a Freudenthal style landscape be good here? Organize them by which is more accessible, visually put closer connected ideas, separate out concepts and skills...
ReplyDeleteIn terms of what's here, I'd like to see something about intentional objectives, backward design, gradual release, teacher to teacher collaboration, and teacher reflection.
Thanks for the suggestions! We'll definitely be playing around with organization and concepts v. skills as we refine this list...
DeleteIt sounds like the additions that you've described focus on planning and behind-the-scenes work, and we're hoping to stick to execution skills for this first list because a) we want to get our teachers "up and running" at a level that leads to student learning ASAP, and b) we haven't had much success over the past twenty years when we start with planning and behind-the-scenes work, since teachers tend to find it overwhelming; we're learning, in partnership with UW, that the planning becomes much more meaningful and teachers get better at it faster if they first have some execution experience within which to contextualize and frame it. Is that a fair assessment, or would you argue with either my summary of your comment or with the philosophy of our approach?
I think they come in with a misconception that teaching is all about face time with the students. Becoming more aware of the iceberg below the surface is key to navigating the profession. (Bit high-handed with the metaphor, sorry.) Dave and I ave found the teaching-learning cycle framework very helpful in getting novice teachers to think of the bigger picture. It also helps them move away from the teaching is telling danger that Jason describes. Teaching is supporting learning.
DeleteI also think it will fit in with the why of the practices you describe, which is crucial. "Use manipulatives" would be on many people's lists, or "real life mathematics", but without purpose and understanding of why and how those things can be helpful they can really go awry.
When working with really novice teachers, I have a habit of focusing on assessment and analysis (evaluation) -- the top of the Teaching-Learning Cycle. If they cannot gather and understand data, then I might as well give them a script to follow given the likelihood that they will provide the students with the support they need. Keeping the focus away from instruction also decreases the chance that they will misinterpret students' level of fluency (which often happens when they ask helpful, funneling questions).
ReplyDeleteI also want to instill in these teachers-to-be the question, "I wonder what the students are thinking?" So even if the teacher is doing a think-aloud, it is with the mindset of wondering what the students are making of the experience. At their core, I want the teachers to consider themselves educational researchers. If they take this stance, much of the rest of their practice will sort itself out -- at least that's the view from this ivory tower.
I like your list. I think it's too general for new teachers to follow, however. The difference that experience makes, unfortunately, is how to incorporate all of these elements without it seeming like a FORMULA every time. Each time you elicit multiple strategies, it should feel different to the students, and not just because the topic is different but because you're in the moment and your way of eliciting the strategies is also a response in/to the moment. You can present this theoretical framework to new teachers, but until they've had a couple of years of experience under their belt, it's hard to truly experience the framework beyond theory, I think...
ReplyDeleteThanks for your comments! It sounds like several of you are reacting to the premise of providing a core set of practices rather than the premises themselves; our current thinking is that teaching novice teachers a script/formula/protocol for these practices IS actually going to lead to our teachers getting better, faster, than they currently do, because a) it gives them something to fall back on in those "omg what do I do now" moments, which builds confidence, and b) the baseline automaticity, or muscle memory, developed by these scripts/formulas/protocols frees up the mental space and energy to do things like listen to what their children are saying and consider how to respond.
ReplyDeleteThis has worked really well at the early childhood and elementary levels-- we've seen teachers reach "baseline competence" much more quickly than their peers trained in more conventional ways, seen them build better relationships with students, and seen students learn more. I'm optimistic it'll work in secondary as well, and maybe my mistake here was in calling these "practices" when really, I'm referring to instructional structures activities. Does that change your reaction/feedback at all, or do you still disagree with the premise?
I'd like to chime in on the side of providing a core set of concrete practices that new teachers are meant to attend to in every lesson. For someone brand new to the business, they are going to have the question "okay what the heck do I actually do tomorrow"? Without some specific guidance, they answer that question haphazardly, trying a bunch of things until they develop a sense for what works, which can take years. I don't object to lessons feeling formulaic. If they feel their lessons are becoming formulaic, and want to change it up, I'd rather a new teacher be intentionally deviating from familiar constraints.
ReplyDeleteI also agree with "our current thinking is that teaching novice teachers a script/formula/protocol for these practices IS actually going to lead to our teachers getting better, faster, than they currently do" basically by analogy. If you want to be a great novelist, part of that education is reading great writers. If you want to learn how to code or write proofs, part of the learning is understanding and copying good code or proofs. I don't have a problem with the idea that teaching lessons other people wrote, or adopting practices the profession knows are effective, being part of learning how to be a good teacher.