Tuesday, August 26, 2014

Support the Ferguson Public Library

I've heard a lot of folks wondering how they can show their support for the Ferguson community, and a few lists of ways and places to donate and/or volunteer. Like this one, from the Organization for Black Struggle. If you're a teacher and haven't seen the resource lists yet, check out #FergusonSyllabus (or this Atlantic post from @DrMChatelain), this set of resources from @chrislehmann and #educolor, and these five tips from @chrisemdin.

Of the many moving ways people have been supporting Mike Brown's family and the Ferguson community lately, this resource drive for the Ferguson Public Library (@billfitzgerald) speaks to me both as a human and as a professional. I can't overstate how much public libraries have shaped who I am; given that my formative language-learning years were spent in a non-English speaking household that couldn't afford AC south of the Mason-Dixon line, my mom took me to our local library 4-6 times a week, and we spent hours soaking up free storytimes and methodically reading each and every book in the children's section (I was a hungry and indiscriminate reader). In elementary school, I joined a team that traveled to other libraries for children's fiction trivia competitions (In this book, Winnie chooses not to drink the water-- Tuck Everlasting, Natalie Babbitt). In middle school, the library was the after-school retreat of choice for me and my friends (where we'd read teen magazines and listen to CDs until our parents came to pick us up for dinner), and in high school, it's where I tutored, attended club meetings, and wrote my college application essays. A library card is still the first thing I get when I move to a new city-- even if I'm only going to be there for a few months-- because it's the only way I can afford to sustain my 5-book a month habit (or, let's be honest, 5-book a week binges during vacations). The only exception? When I moved to the town where I taught, where even before I could make it to the only public library within 20 miles, I made an offhand comment to a student about looking something up at the library and was quickly informed that at this library, she could barely get in the door without being followed around and glared at.

In the past week, the Ferguson Public Library has hosted local teachers who set up classes when the city decided to delay the opening of its public schools, and its staff has provided space, resources, outreach, and partnership so that nearly 200 students, by the end of the week, could learn and talk and think (and so that their parents had child care during working hours). You can see some of the photographs and tweets at #TeachForFerguson (and many more under the general #Ferguson hashtag, particularly from last Thursday and Friday).

There are so many public and private ways to show support; I suspect we all feel drawn to different forms for reasons tied deeply to our values, our beliefs, and our stories. Here's to public libraries as safe spaces, community partners, and resources: donate over on the Ferguson Public Library homepage or purchase a book from their wishlist.

Thursday, August 14, 2014

notice-and-wonder: when it works, when it doesn't

One of the strategies/routines/techniques/activities/moves/whatever you call these things we taught our novices this summer was the Math Forum's notice-and-wonder. If you're not already familiar with it, it's simple: prior to engaging students with a problem (which could be a scenario, a graph, an image, a video, etc.), first ask what they notice about it, and faithfully record everything they say (no matter how silly; in fact, it's often helpful to throw out a silly example as a starter, like "I notice the graph is blue," to demonstrate that all responses are welcome). Then, ask what they wonder, and faithfully record every question they ask (again, consider prompting with something like "I wonder why we're doing this," especially if your students are new to this exercise). If desired, have students stop-and-jot for a moment first to list out their own noticings and/or wonderings, so that everyone has time to think and everyone will have something to share, and/or have them turn-and-talk to their neighbor before sharing with the class. There are plenty of variations available on the Math Forum website, but we kept it simple: pure noticings and wonderings (as opposed to targeted ones, like "what do you notice that is similar about these two [representations]" or "what relationships could you find," and as opposed to predictions, like "make a guess that you know is too high/low").

Why notice-and-wonder? It lowers the barrier to entry-- everyone can notice or wonder something-- and gets students thinking and talking early in the lesson, which means they're more likely to participate later. It gives teachers a low-stakes opportunity to position students as competent and affirm their ideas (because really, no response is wrong here). It directs students' attention to the things that are mathematically important in the representation, particularly as they become more practiced with the notice-and-wonder. It gives them time to make sense of the problem without any pressure to solve it or even start trying. It allows teachers to build on what students have shared-- often borrowing their exact language-- to ease into the next part of the lesson, especially when students make an observation or pose a wondering that can be leveraged as a direct transition ("[student] asked what the next image in the pattern would look like; that's exactly what we're going to figure out next!" or "[student] noticed that the last part of the graph looks like a hill, and that's what we're going to focus on together today-- we're going to look at graphs that look like hills, and think about why they might look that way"). Basically, it's a lovely way to launch a mathematical task.

How did it go? Our novices loved it. So much so, in fact, that they used it almost every day, and sometimes multiple times a day (they taught 2-hour blocks). Too much? As a raw number, I don't think so-- for the most part, their students knew what was being asked of them, appreciated the consistency, and offered interesting noticings and wonderings. A few cautions though:
  • Sometimes the notice-and-wonder dragged on for a bit, and there were two primary causes: a) because some teachers wanted more students to participate, they had a hard time moving on when there were still hands in the air, even when additional observations or questions became a bit redundant, or b) because they hadn't yet heard the exact noticing/wondering they were hoping for, they continued to ask "any more?" and wait even though no additional hands went up. Gradually, however, novices refined their sense of how long the notice-and-wonder should take, and it helped when they both knew exactly what information would be most important to elicit in order to prepare students for what was next, and also knew that it was okay to throw in their own noticing or wondering ("one thing I noticed was that time was on the x-axis...") as a nudge for students to shift their observations and questions in a particular direction as long as it didn't become all about them or have the tone of "by the way, here's the answer I was looking for."
  • Not surprisingly, this didn't go as well in classrooms where students didn't yet have strong relationships with their teachers; they still participated, but languidly, just enough to move the lesson along. In classrooms like this I generally think about what role the pedagogy is actually playing in students' disinvestment because it often is, but I don't think the notice-and-wonder actually did any harm.
  • After the first day, we rarely saw any irreverent responses, and the ones that did pop up popped up in good humor, were enjoyed by both students and teacher, and the class was able to move on quickly. I did see, however, a few instances where responses seemed to fall a bit flat.
And that brings me to my biggest caution. In the form of a question, when is it appropriate to use a notice-and-wonder, and when is it not? Given our novices' experience this summer, I'd say that it's especially appropriate as a precursor to representation-heavy lessons (particularly when students are about to be asked to match representations or find/extend a pattern) because it draws students' attention to key features. I'd say it becomes more risky-- and in fact, probably is not the best way to launch a task-- when:
  • It's likely to surface some meaty conversation. In one lesson, a teacher used a notice-and-wonder after students read a scenario about charter school growth in their city (it was about to be a linear regression and extrapolation task). Students surfaced observations and questions like "I notice that charters are taking over the city" and "I wonder why people support charter schools when it sucks to go to one," which was followed by "I wonder why charter school teachers act like police." Given that all of our summer school students attend charters during the year, these statements would certainly be worth talking about further-- or at the very very very least, acknowledging that the humans in the classroom have some mixed feelings about charter schools. For the teacher to simply write the question on the board and move on felt awkward, at best, and minimizing, at worst, even though the teacher's reasoning was undoubtedly more along the lines of a) I'm trying to stick to my plan and b) I don't know how to have the conversation.
  • It's insufficient preparation for the lesson. This was the most common challenge we saw, and I'll describe it in the context of the same lesson as above: in order to successfully tackle the regression task (they hadn't attempted regression before, although they had constructed scatterplots and studied linear functions more generally) and engage with the analysis questions in it, students would have benefited from spending some time thinking about the data presented in a table: what it said, what the units were, what the numbers indicated was happening over time, and hypotheses about how the data might be used to make a prediction. They would have benefited from thinking about the language in the scenario: what's meant by "enrollment," what's being asked by "predict," and what "trend" means. They would have benefited from thinking about the context: what the total enrollment in the district was, why more students might be attending charter schools, what factors might limit or bolster charter school growth, etc. I didn't make up this list: check out Jackson et al's article on Launching Complex Tasks to see which four things are most critical for preparing students for novel, problem-solving tasks. Simply noticing and wondering wasn't enough.
In sum? The notice-and-wonder is powerful, but, like everything else, not a magic wand. Use it liberally, but use it wisely, and prepare a few other tools for launching mathematical tasks. Have you found that it's more/less effective under conditions different from the ones I've described?

Tuesday, August 12, 2014

small things: increasing participation in classroom discussions

There are a number of big things going on right now: I encourage you to pop over to twitter to follow #MikeBrown and #NMOS14, and keep an eye on the flooding in Detroit (see this photo). I'm writing about small things because doing so helps me maintain hope.

In my understanding, the approach to new teacher training is often to start with simple easy things (direct instruction, I do-we do-you do), and allow novices to work their way up to more complex and harder ideas (constructivism, productive classroom discussions)-- at least, this seems to be the assumption I've seen in many alternative certification programs (with notable exceptions, like the Boston and Seattle Teacher Residencies). Given that novices generally have more support up front than they will 2-3 years in (or even 6-8 months in), however, I believe teacher education should start by preparing teachers for meaningful instruction (the cynic in me has been known to say to my colleagues, "if first-year teachers are going to fail anyway, why not at least have them fail in the right direction rather than fail a little less at something that doesn't matter?"). And that's the approach my team took this summer: we spent last year partnering closely with the University of Washington school of education and one of our regional teams to redesign our pre-service training from scratch so that a) our teacher education pedagogies were practice-based (McDonald, Kazemi, Kavanaugh, 2013) and maintained the complexity of ambitious teaching (Lampert et al., 2013), b) the curriculum our teachers taught was task-based and deliberately provided opportunities for students to engage collaboratively in the CCSMP and with problem-solving contexts relevant to the urban district in which they live, c) our teachers engaged daily in social justice and equity seminars designed to establish culturally responsive dispositions and community orientations as the center of their work.

(aside: I'm really proud of what we did, and it totally burned me out: seven 85-100 hour weeks preceded by many more weeks of prep in the 70+ range meant that I came home last week with a feeble short-term memory, weak emotional regulation, poor human interaction skills, and terrible skin.)

There's much I really appreciated about this model (and of course, because it was a pilot, much that needs to be improved on), but I'll start in the weeds: one of the ones on my mind right now is how it allowed us-- through targeted rehearsals and video clubs-- to focus on small things that have an outsize impact on how students experience their math classrooms, but in a way that didn't get entangled in technical, non-transferable tips (this is always such a tricky balance-- the things that help for tomorrow vs. the things that help for the long-term vs. the things that help for BOTH tomorrow and the long-term). For example, when teachers felt they weren't getting sufficient participation in their class discussions, we could have gone to popsicle sticks and cold calls-- which can increase student anxiety by creating "gotcha" moments (even though that certainly isn't the intention)-- or worse, back to direct instruction, but rather, we targeted the ways in which a teacher subtly signals his/her expectations and values, trying to "sweeten the deal," so to speak, for students to volunteer:

  • Asking students for their "ideas" or "hypotheses" or "predictions" or to "share their thinking" rather than asking "what do you think the answer is" or "what did you get" or "who knows how to do this?" minimizes the risk that students have to take in order to make their thinking public and respond; students who may not feel confident that they have an "answer," which implies that they may be wrong, are often still willing to share thoughts or ideas, especially when they know from experience that the teacher will affirm something about their offering and then encourage others to build on it. This simple change-- although it was hard for many of our novices to make this shift, because we're not always used to hearing this language in math classrooms-- increased student participation in whole-group discussions and in one-on-one check-ins as well.
  • Asking direct questions, rather than "who can tell me" or "does anyone want to share" or "someone tell us" or "can anybody explain" reduces the temptation for students opt out (those stems can all be responded to with "no thanks," unlike "why might that work?" or "what would that look like?" or "what did you and your partner talk about?" or "how did you begin this problem?"), and increases perceptions that the teacher is both confident in what s/he is asking and trusts that students will have something worthwhile to say. These questions are tricky to catch, but easy to fix: most of the time, there's a perfectly good direct question already being asked right behind the pleading language, so just cut the pleading language. Bonus round: consider Lemov's "no opt out" strategy; compare the two approaches in the implicit messages they send around compliance, power, and who ultimately controls whether or not-- and why-- students speak.
  • Providing clear instructions for how others should engage when their peers are talking, beyond simply "tracking" or "listening" or "following along," such as "listen for whether you used a similar method or did something different" or "as you listen, think about how you would say this in your own words" or "listen for how [student] used a pattern to find a solution" gives students a reason for listening-- not just because the teacher wants to "hear from everyone" as a well-intentioned but not particularly purposeful principle, or because "respect is the expectation in this classroom," but rather because there is concrete mathematical and pedagogical value in their peers' ideas-- and can cue them as to where the discussion is going to go next so that they're prepared to contribute. These participation instructions can be particularly effective when followed by a signal of what was most valuable in what was shared, either through teacher revoicing, direct cues like "that was really important; can you repeat that?" or "[student] talked about using the graph as a tool; raise your hand if you also used the graph," a turn-and-talk/stop-and-jot processing moment, etc., but our novices were surprised by how much impact (both on students' ability to follow key mathematical ideas in the conversation and on their attentiveness during discussions) participation instructions had on their own.
Of course, there's a lot more a teacher needs to do for a successful classroom discussion (if you haven't read Stein & Smith's 5 Practices yet, what are you waiting for? and it should go without saying that a meaningful discussion can't happen without a meaningful problem and proper preparation for students to engage), and a successful classroom discussion is only a slice of what we worked on with our teachers this summer. It's an important slice though, and one that is notoriously tricky, and not just for novices. By focusing on these small things, we were able to coach teachers on improving their classroom discussions in rehearsals, in the moment, and in reflection, and also connect more broadly to several of our focal core practices for the summer: eliciting and responding to student ideas, creating and maintaining a learning environment, and positioning students as competent.

Do you do these small things when you facilitate discussions? How do they work for you?

Tuesday, May 27, 2014

mis-education of a negro, part 2, and power

I also finished reading Carter Godwin Woodson’s The Mis-education of the Negro (here’s part one), and I’ve probably got two big takeaways: (1) I’m constantly struck by how little seems to have changed in the past 80 years, both in terms of the ways in which individual, structural, and institutional racism all persist, and in terms of the arguments and ways in which people talk about race relations; and (2) I’m wondering about where the burden of change really lies.

Woodson presents the argument, for example, that talking/teaching about race will only make things worse; this sounds to me an awful lot like the colorblind or post-racial perspectives that plague the liberal (maybe mainstream is a better word, because I see this on both sides, but it strikes me as particularly pervasive and particularly unwise on the liberal side) media. Woodson deconstructs this argument using a critique I’ve also read more recently (and more recently grounded in “science,” such as with the Bronsons’ reporting): even babies and very young children learn about race through their daily lives, regardless of whether we as adults talk about it or not. I do wonder, though, why we (well, nobody I’ve read, although I’m sure this perspective exists and is written about) aren’t as outraged by the absence of race teaching/conversations in predominantly white schools as we are in schools with predominantly students of color—it seems they need it just as much, if not more, although perhaps for slightly different reasons, no?

Perhaps my broader question is about where the responsibility lies to change the societal, structural, systemic, and sometimes individual issues that Woodson raises. There's a refrain, throughout the book, urging people of color (Blacks, specifically) to rise above the trifling, and Woodson even lays it out bluntly: "the exploiters of the race are not so much at fault as the race itself... the matter is one which rests largely with the Negroes themselves. The race will free itself from exploiters just as soon as it decides to do so. No one else can accomplish this task for the race. It must plan and do for itself."

On the one hand, Paulo Freire, Pedagogy of the Oppressed, "this, then, is the great humanistic and historical task of the oppressed: to liberate themselves and their oppressors as well. The oppressors... cannot find in this power the strength to liberate either the oppressed or themselves. only power that springs from the weakness of the oppressed will be sufficiently strong to free both... Freedom is acquired by conquest, not by gift." On the other, what the two are talking about feel a bit different to me-- Woodson's language throughout the book calls to mind a bit more bootstrapping than I can agree with (although I haven't read anything else of his yet, so please let me know if I'm misinterpreting), and Freire seems to be talking more about moral right/strength than tactical strategy. Woodson seems to clearly acknowledge that individuals have not risen above because they've been miseducated through no fault of their own, but then, is the burden of responsibility really theirs?

I'm thinking of a recent email conversation I had with colleagues about designing a learning experience around power, and whether (after an analysis of ways in which people with/without power engage to create power dynamics) it's fair to ask those who identify as being in target groups to take an action step similar to the action step requested of those who identify as being powerful. One colleague suggested that if not, then we're essentially continuing to marginalize the marginalized by telling them there's nothing they can do. Here's what I had to say about that:
...It strikes me that we might be talking about two different things: agency vs. power. Both parties absolutely have the agency to disrupt the pattern or to change the situation; the person in a position of power has the agency to acknowledge his behavior, recognize that his preferred patterns are damaging, and change the way he is operating. The “powerless” or marginalized person has the agency to acknowledge her behavior, ways in which he may be triggering her to act in ways she doesn’t want to act, or ways in which she may be triggering him to act in ways that are unproductive, and to change her own behavior. She even has the agency to call him out on what he’s doing and demand that he act differently. She may not always feel safe doing so, however—because she’s not the one with power in the dyad—or she may simply not have the energy to do so in a particular situation given that she fights this battle every day. And it shouldn’t be her responsibility or burden to fight it in every single situation. In terms of agency, both people have it, and both can exercise it to create change. 
I don’t think, however, we can say or imply that both parties have the same amount of power to change things. If both parties had the same amount of power, there wouldn’t be a power dynamic, and one party wouldn’t be dominant and the other marginalized; that’s the nature of power. The person from the dominant group has the power in that pair, and it is his responsibility and his moral obligation to notice his behavior and change it. There is no responsibility or moral obligation on the part of the marginalized person, even though she has the agency to act if she chooses to. The dominant person MUST be willing to change, which was the language [originally suggested in the action step]; the marginalized person CAN, but doesn’t HAVE to. 
The reason this distinction matters to me is because I worry that if we frame up a situation where marginalized people have to act—to disrupt the pattern, shift the dynamic, whatever—to live up to their empowerment, we a) nudge ourselves towards the philosophical territory where it becomes okay to blame the marginalized for their marginalization—after all, you were empowered to do something, and nothing’s changed, so it must be in some way your fault that you’re still marginalized—and b) ignore the fact that resistance happens in many other ways—not always in directly confronting the oppressor and not in every single situation.
This feels tricky; by and large, I don't think people with power (whether we're talking societally, big picture, or just micro, daily interactions within an office or relationship) are particularly apt to voluntarily give up power just because, and even if they do, I'm not sure that cessation out of charity is actually going to level the playing field. So, people without can't simply sit around and wait (nor are they particularly inclined to, I think), but without power there are limits to what they can (and should have to) take personal responsibility for. Right? 

Monday, May 26, 2014

teachers' beliefs and conceptions, part 2

In the past 30 days, I’ve been in 7 cities and on 12 flights (+ 4 Amtrak trains), which has been an emotional roller coaster of work stress and joyful college graduations. It unfortunately explains why my #MTBoS30 attempt was abandoned partway through (heck—if I had made it, I would have written more posts in a month than I did all of last year), but fortunately, two of those flights gave me the opportunity to finally finish reading two pieces I started writing about.

Here’s my summary of Thompsons’ Teacher Beliefs and Conceptions: A Synthesis of the Research, which I started reading here, and because of which I’ve been kind of obsessed with the Rene Thom quote “all mathematical pedagogy, even if scarcely coherent, rests on a philosophy of mathematics.”

Preface: We take our beliefs as knowledge (Thompson says that teachers do this, but I suspect all humans do this); they’re often deeply rooted but not always consistent or conscious enough to be vocalized.

What we believe about the nature of mathematics drives the way we teach (read the paper for a plethora of frameworks for organizing what we believe about the nature of mathematics, including Skemp’s classic instrumental vs. relational, but also a whole bunch I’d never heard of). Often, teachers’ practice is aligned to their beliefs. When it’s not, there’s generally what I would consider a “downward” shift—teachers who believe in dynamic, student-constructed mathematics teaching in rote, fact-driven ways due to social/contextual pressure or lack of skill.

The more teachers process, reflect, etc., the more consistent their beliefs and their practice become, through three cognitive exercises: identifying their assumptions, constructing rationale, and becoming aware of viable alternatives. Sometimes, their beliefs and practice become more consistent by modifying their practice, and other times, by adjusting their beliefs (Piaget).

What helps teachers change their understanding of and beliefs about math? Doubt. Confusion. Controversy. Especially the doubt, confusion, and controversy created by doing problem-solving tasks collaboratively and acquiring information about the complexity of student thinking.

So what? Through the lens of my job, my so what is twofold, both grounded in a strengthened conviction that math teachers need to profoundly understand the nature of mathematics as a way of knowing that is problem-driven, uncertain, relative, fallibilist, etc.:
  1. Content work should be central to teacher training and professional development—not just because teachers need content knowledge with which to exercise pedagogical skill, but because doing content work collaboratively and with a facilitator is a mechanism by which to create controversy and conversation about the nature of mathematics. This may sound obvious, but I don’t think it is—especially in the alternative certification world, where we often assume that teachers get their content knowledge by having an undergraduate degree in the subject (as opposed to in subject-specific education), or that content knowledge matters but not as much as a whole host of other (instructional, pedagogical, planning, management, class culture, relationship-building, etc.) skills. It’s not just the alt cert world; Thompson cites Madeline Hunter (the progenitor of the infamous 5-step lesson plan) as an example of a school of thought where content takes a backseat to general “good teaching.”
  2. Training and professional development should create opportunities for teachers to reflect, collectively construct rationale, and revise their thinking about the nature of math—we can build skill through more concrete instructional strategies (instructional activities, in the pilot my team is working on this year with UW), and if teachers take up these strategies and become more skillful, they’ll be able to execute instruction aligned with their and our vision of math teaching and learning. And if they don’t? I’ve long been a believer in “failing in the right direction,” operating under the premise that all novice teachers will fail, more or less, and I’d rather have them fail attempting more sophisticated, meaningful instruction than fail attempting “safer,” boring, less good-for-students methods.