Wednesday, January 21, 2015

equity, the sequel

Given all the reading and thinking I've been doing, I'm wondering if what I need is a more fundamental definition of equity: what if I were to conceptualize equity as a state in which all people in a group (society, writ large; a classroom, writ small) are valued-- in which they're seen for who they are, heard and understood as stakeholders but even more so as contributors, supported in their goals, given dignity, etc.? If so, then I think our work as teachers is twofold:

1. Create classrooms in which that is true (and serve as a microcosm of this vision of an equitable broader society): in which students (and the teacher) see each other, understand each other, support each other, and learn from each other, both in terms of what they bring into the classroom and in terms of what they create/do once they're there.
  • To do this, teachers must create what Esmonde (2009) writes about as intersubjectivity: a shared meaning of a situation, or a meaning that's as shared as possible. Through classroom culture, through structures, through relationships, teachers develop a space in which students actively seek to understand one another (even if they disagree with one another), and engage in related behaviors such as asking clarifying questions, building on ideas, inviting one another to speak, etc. It's Staples' idea of creating common ground, and central to the model of a participatory democracy in which well-informed citizens are able to create the world they aspire to live in, rather than just being acted upon by those with more power.
  • For intersubjectivity to exist, teachers must pay attention to the intersection of identity and ideas, because they so deeply influence each other. 
    • Our identities (both the more macro identity markers such as race, class, language, gender, ability, etc. and the more transient identities that we negotiate in the moment depending on our context) influence the experiences we have, because of how people respond to us and what they expect from us-- whether they expect us to have good ideas in an academic environment or not (Nasir and Shah write about how African-American boys interpret racialized narratives about who is good at math, particularly in comparison to Asian-Americans)-- and they also directly influence our ideas because these experiences shape how we understand the world and how we think and reason. While several of the pieces I've read about identity and status in math classrooms focus on ideas of smartness and competence, we must also be explicitly conscious of race and other social identity markers. Two primary reasons occur to me: 1) we cannot create equitable environments without being sensitive and responsive to the ways in which our identities-- particularly visible and marginalized ones-- have shaped our life experiences and therefore the beliefs and behaviors we bring into a classroom, and 2) because our socially marked identities are a rich, important, fundamental part of who we are and ignoring them means seeing only part of us, shortchanging what makes us who we are. In the article cited above, Esmonde summarizes this as saying "identity-related processes are just as central to mathematical development as content learning."
    • When we have good ideas, which we gauge through signals from others about whether they value our ideas, we develop identities as people who have good ideas; people who are smart, people who are competent, people who are valued. And it's particularly important for students from traditionally marginalized backgrounds to develop those identities to counteract the messages they're receiving from the broader society on a regular basis.
Esmonde cites a number of interactions that are "more likely than others to lead to meaningful mathematical learning," the types of things you'd aspire to in a student-centered, inquiry-driven classroom: discussion (not just show-and-tell), productive group work, etc. But, students' positioning (which is based in part on their identities) expands or limits their ability to participate in and access these activities, which in turn expands or limits their ability to negotiate their identities as successful learners and thinkers.

2. Use such classrooms and the affirming space they create to explicitly discuss and address why this is so hard to do as a society more broadly, given what has happened in history, given our psychological and cognitive biases, given power structures that are difficult to change, etc.
  • To do that, teachers must be aware of and create connections between what happens in a classroom and what happens outside it; for example, a breach of classroom norms could be an opportunity to discuss what happens when societal expectations are thwarted, using any number of examples, depending on students' interests and on current events: when someone doesn't follow gender norms and is shamed or bullied; when a relationship doesn't fit mainstream images of "normal" and the partners are harassed; when people and institutions we're supposed to trust-- who are supposed to protect and serve us-- instead become the ones who we fear most. Where does the norm come from? Why do people respond the way they do when they sense a breach, and how does that compare to the way they should respond? Does it matter who's breaching the norm? How egregious the breach is? Where or when the breach happens? Consider the ways in which we've addressed the breach in our classroom; could that process work outside of our classroom? 
What do you think? What's my definition of equity missing, and what else can/should teachers do in its service?

Tuesday, January 20, 2015

bridging children's knowledge bases

For a related but slightly different take on (what I'm calling, because this is my mini-research project) culturally competent teaching, I read Turner et al.'s 2012 paper, which uses a framework that I find very similar to Lefstein and Snell's (described in this post): attending to particular aspects of students' thinking or knowledge, developing a particular awareness-- or interpretation-- of what students think or know, and then eliciting that thinking or knowledge. They apply this framework to two types of thinking/knowledge in particular: students' mathematical thinking and reasoning, and students' cultural/home/community-based knowledge and understanding.

My first question is whether the two are necessarily distinct-- my sense is no, and implying that they are necessarily distinct implies that students' cultures/homes/communities are not mathematical, and mathematics doesn't exist in their cultures/homes/communities. I don't think that's what Turner et al. are trying to imply. However, it does raise a question for me of where you draw the line-- is it that the two exist in a blurry Venn diagram, such that some types of thinking or knowledge are just mathematical, some are clearly not mathematical, and there's some overlap?

Regardless, the literature (and common sense, one would hope) suggests that bringing students' cultural/home/community knowledge (also known as "funds of knowledge") into the classroom is a good idea for two reasons in particular: 1) affirming and leveraging students' funds of knowledge makes them feel valued/welcomed/included in a classroom and 2) it helps them make sense of school mathematics that otherwise can seem foreign or intimidating by providing a schematic hook, so to speak.

Turner et al. also write about how school mathematics (or formal mathematical thinking) and cultural, home, and community-based knowledge and reasoning (or "informal" mathematical thinking) can be bridged in superficial ways-- like I wrote about here; they call these emergent connections-- or in more substantive ways-- which they call meaningful connections. Meaningful connections are grounded in understanding students' non-school lives rather than assumptions (emergent connections might be too, but meaningful ones have to be), exist in contexts that are familiar and common, AND use mathematics in an authentic way (remember: no student takes a given dollar amount and tries to determine the total number of combinations of three separate snacks that can be purchased with that exact dollar amount).

This brings me to a hypothesis: can we say that the thing that makes "good teaching" (as implied over the past several posts-- instruction that attends to and values and is designed around student thinking in such a way that makes students feel competent, affirmed, and at the center of the classroom) culturally competent, in addition to just being "good teaching," is this explicit leveraging of students' funds of knowledge? After all, it requires the type of deep relationships and deep understanding of students' individual and collective identities and interests that are a hallmark of culturally competent teaching.

And it brings me to a question: when we're talking about bridging school mathematics with students' funds of knowledge by selecting or creating tasks that are locally contextualized and authentic, we're talking about curriculum: the things they know. That seems fairly straightforward to me. But what would it look like to make a pedagogical bridge: to bring in students' ways of thinking, communicating, and interacting (how they know and learn), too? I can think of some ways in which this makes sense: outside of school, children tend to talk and laugh and ask questions, so they should be able to do that in school too. But I also know that in many homes, particularly for children of color and children whose parents may have had limited formal education or are working class rather than professional class, children are expected to unquestioningly obey authority-- in fact, that may be how they're taught to survive a world where even doing exactly as a police officer asks could still result in your untimely death if your skin is dark enough.

The type of pedagogy we've been describing as desirable is the exact opposite: where students think for themselves, ask questions, and don't unquestioningly internalize what the teacher says, and where the teacher's authority is limited. And I'll stand up for this type of pedagogy, because I think it's ultimately more affirming (even though I recognize as I say that that I may be implying that authoritarian parenting styles are not affirming), and because I think it's what students from traditionally marginalized backgrounds need and deserve for education to be liberatory. But then, aren't we contributing even further to the wedge that some students feel education places between them and their families? How do we talk with them about that?

Friday, January 16, 2015

so, is culturally responsive teaching just good teaching?

I asked this question a few posts ago, so it seems worth sharing how I'm thinking about it so that you can push my thinking; is culturally relevant/responsive teaching-- or equitable teaching for students of color-- simply good teaching (as Gloria Ladson-Billings herself writes in her seminal 1995 article, although you should also check out her more recent "remix" on culturally sustaining pedagogy)? @elizabethaself, in her comment on that post, reminds us that "good teaching" is ill-defined and what is considered "good teaching" often differs for different groups of students. My read of Hand's paper (from two posts ago) suggests, in an argument I've heard and made often, that yes; good teaching is just especially important for students from traditionally marginalized backgrounds.

A recent conversation with a colleague, however-- who's been thinking and studying this since I was a toddler in snowpants-- leads me to add a few more layers. "Good teaching," construed in this way-- I realize I'm not defining it either, except to reference what I've been writing about over the past few posts specifically and past few months/years more broadly-- is especially important for students from traditionally marginalized backgrounds if they're to have the learning opportunities that they deserve simply because they're human children, yes. AND, it's revolutionary because not only have they been denied this type of education for so long, they've also been subject to denigrating and destructive modes of education (rote, silent, focused on control and social reproduction) that tear at the fabric of who they are. AND, it's necessary for revolution because education for such students needs to be about liberation rather than assimilation if our society is to ever have any hope of becoming more just and equitable.

Would you add more layers or different layers?

Thursday, January 15, 2015

"student-centered," teacher-directed

I tweeted this yesterday, and got a few questions, so I'm going to pause the post I had planned and try to explain myself-- because I think this is deeply tied to conversations about equity and about what it looks like to affirm and value the students in our classrooms:


A few colleagues and I will be co-facilitating a conference session about what it means for a classroom to be truly "student-centered," and our hope is to push the conversation beyond what I'm going to call superficial-- even though they're not insignificant or worthless and in fact can represent a meaningful starting point as long as they're not the end goal-- representations. Often, when I ask what it means for a classroom to be "student-centered," I hear things like "the texts/tasks are relevant to students' interests" and "students are talking instead of being talked at." Sure. That's step one, because in and of themselves, they're not enough.

Imagine, for example, this classroom:
The teacher has decided that today, students are going to work on systems of equations. She decides to frame an example problem in the context of football, because many of the students in the classroom play football and there's a big game coming up. She opens the lesson by asking them to raise their hands if they like football, and to guess who they think will win the big game and why. She tells them they're going to use football to continue learning about systems of equations, and lists a few applications of systems. Then, she presents a word problem: a team has scored 31 points in a football game; if they have only scored 7-pt touchdowns (including PAT) and 3-pt field goals, and scored a total of five times, how many of each did they score? She walks them through the steps: first, they should write an equation representing the number of scores. Then, they should write an equation representing the points. Then, they should solve the system. Students dutifully copy down the steps from the board whenever she pauses for them to do so. She occasionally stops to ask questions like "and how many points did we say a touchdown was? So what should be the coefficient of our x term?" and "what were the three ways to solve systems of equations we've talked about so far? which one should we try first?" When she does, students raise their hands and volunteer answers. After she's walked them through the first example problem, she walks through two more, this time adding questions like "so what was the second step?" and "what should I write next?"
Then, she assigns students to groups of four and gives them each a worksheet with problems to the examples they've just completed, with the instruction that if they have questions, they should ask their group members before they ask her. Students mostly work in parallel (see the animation in this post), pausing occasionally to check their answers with their group members, or asking questions like "can I see how you did #7?" As they do, the teacher walks around monitoring progress, giving suggestions like "make sure you write two different equations" and "try using substitution instead of elimination for that one." She tells one student he can't go to the bathroom until he finishes two more problems because he's been talking off task, and gives another a warning for getting out of her seat to borrow a pencil from a classmate across the room. After about 20 minutes, the teacher brings the class back together and chooses a handful of problems she selected for the worksheet purposely because they were tricky; a student puts each of those problems on the board and talks through the steps s/he used to solve it. The teacher asks if anyone has any questions. When the teacher later watches a video of this clsas period, she notes that her lesson took about 15 minutes, and students worked in groups for about 30 minutes, so students did more talking than she did.
The surface elements of "student-centeredness" are nominally present: the teacher uses a relevant example, describes applications, asks questions, lets students work in groups, spends more of her class period with students working than with her talking. And let's say that students are generally agreeable, cooperative, and like their teacher. But when we think about the space this teacher takes up (see yesterday), it's just about all of it. She has dictated what mathematics the students are going to be thinking about, which procedures they should use (via the steps she introduces; even though she later lets them choose which method of solving systems they want to use, she has-- and offers-- strong feelings about which method is most efficient or easy for each problem), and when they should be writing, listening, thinking and about what. Students are not figuring out for themselves how to approach a task or applying what they've learned to novel contexts; they're not sharing their observations, hypotheses, predictions, conjectures, or reasoning. What matters most is that they complete a worksheet, not whether they develop deeper understanding, or make connections between new knowledge and existing knowledge. And that they follow the rules about where their bodies belong during which portions of the class period. The purpose of sitting in groups appears to be primarily social, or about efficiency, and the purpose of the whole-group discussion at the end seems to be a show-and-tell (Takahashi, 2008; I can't find a link for the life of me, but it's a paper called "Beyond Show and Tell" and it's about neriage) about how students followed steps rather than ongoing development, consideration, or reinforcement of mathematical reasoning.

see also this Nellie Mae report on student-centered instruction which includes vignettes of classrooms at several places along a spectrum from "teacher guided with some student participation" to "exploration with strong student contribution;" personally, I think it could go even farther, but the descriptions are helpful clarification along this part of the spectrum

This probably isn't news to anyone. All I'm saying is that "student-centered" is used to mean many things, and simply because a classroom or a lesson has some characteristics of being "student-centered," that doesn't necessarily mean it's not teacher-directed, teacher-controlled. The teacher has simply chosen to direct and control students to do things like talk, instead of directing and controlling them to do things like sit passively (an elementary analogue might look like giving students manipulatives and then dictating how they use the manipulatives). I name this because if we call this type of instruction student-centered, we distract ourselves from continuing to develop the type of classroom environment/space that truly center students' experiences, perspectives, and ideas.

So how do we continue to develop that kind of classroom environment/space? I asked this question on twitter, and here's a synthesis of the responses I received (I was quite glad to see the full range of starting points, at least in my mind: curriculum, pedagogy, and relationships/knowing students):
  • @datadiva recommended using tools such as this one to support teachers in analyzing their units and assessments
  • @shevtech suggested have teachers put themselves in students' shoes and map out life priorities to see how school is only one element of students' lives
  • Similarly, @edifiedlistener thought teachers might benefit from recreating a day from a student's perspective, which reminded me of schools I know where teachers have had to shadow a student for a day
  • Both @SciEdHenry and @MathMinds suggested having teachers experience a lesson as if they were students, and then debriefing/reflecting on what made it student-centered and the role of the facilitator; @MathMinds would follow it up with a lesson of students experiencing the same lesson
  • @maxmathforum chose readings: Staples' "Supporting Whole Class Collaborative Inquiry" (linked in the post linked above), material about sharing strategies vs. inquiry (I suspect the aforementioned Takahashi piece would be a good one, as would Smith and Stein's 5 Practices), and Talking Points as an exploratory talk strategy (from @cheesemonkeysf)
  • @mpershan wouldn't just read about Talking Points; he would use them to problematize the idea that "student-centered" = "good teaching"
I started this post by mentioning that my colleagues and I are co-facilitating a session around this very question in a few weeks. We plan to start with Talking Points about the idea of "student-centeredness," and then engage small groups in conversations about the idea of taking up space. The (hopeful) magic will happen through skillful facilitation within these small groups, debriefing the way in which our time together was structured, and then reflecting on a recent classroom experience through this now-deepened-or-sharpened-or-refined lens of what it means to be student-centered. I'll let you know how it goes.

Wednesday, January 14, 2015

"equitable" teaching = taking up space?

I work in a world where teachers and instructional staff alike routinely assert their commitment to equity and to classrooms that dismantle inequity or promote equity; when pressed to elaborate, they can often cite social justice aspirations, quotable inspirations, and evidence of extensive perspiration in the service of beliefs and dispositions. But if asked to define "equitable teaching" or "a classroom that promotes equity," very few could articulate an answer. Myself included: I'd probably look at you as if you'd asked me to explain why water is wet, and realize that this idea is so inherent and self-evident to me that I actually don't understand it very well.

Rochelle Gutierrez, here, says that addressing equity requires considering four dimensions: in preparing students to participate in society as it currently exists, students must gain from their math classes 1) access to resources and 2) tangible academic achievement by the metrics that dominant society cares about, and in preparing students to then critique and change society such that it becomes more equitable for all, students must also develop 3) a strong sense of identity and 4) power.

Vicki Hand, in this paper, offers four criteria for classrooms that are equitable for students from traditionally marginalized backgrounds: 1) rigorous mathematical inquiry, 2) academic success, 3) a sense of "competence, ownership, and belonging" for students, with 4) rare student opposition. What I particularly love about the model she presents is that it can be conceptualized more simply as a classroom in which students "take up space."

(see also NCTM's fairly recent research brief on classroom practices that support equity-based mathematics teaching, and this recent Joshua Block post on building an anti-racist classroom, h/t @chrislehmann)

I'd never thought about classrooms in terms of taking up space before, even though we regularly talk/read about taking up space more broadly. There are physical manifestations (wrt gender, see manspreading on the subway and the MTA's recent initiative to combat it and manslamming on the sidewalk; and wrt race consider representation in boardrooms and police departments) and conversational manifestations (my former advisor recently wrote a NYTimes piece about "speaking while female;" and so many of the people of color I know would agree that the same goes-- and multiplied and exacerbated-- for "speaking while not white"), and in sum, whoever controls the physical-or-metaphysical space has the power.

In a typical classroom, the teacher tends to own most of the space. Physically, even though there is one teacher body and thirty student bodies, the teacher is the one with the freedom to walk around, to choose when to sit and stand and where, to hover over others, and even to dictate how others occupy space (where they sit, when, whether they're allowed to get up, etc.). Conversationally, the teacher decides who speaks and when and what about. Intellectually, the teacher often does his/her best to determine what students are thinking about and how-- arbitrating which questions are worth asking, which ideas are worth discussing, which methods are worth examining, which solutions are worth sharing, which tangents are worth indulging, and when it is time to move on.

It makes sense to me that the teacher takes up more space in a classroom than students-- after all, there's a reason (hopefully more than one) s/he is the teacher, and from a pragmatic perspective, the teacher is also the one mediating between students and whatever accountability systems are in place from parents, administrators, districts, states, etc. But I do think it's worth considering how much more space the teacher takes up (ratio, math teachers), and what space the teacher takes up. I could expound further, but I'm afraid I'd be both speculating/pontificating and rehashing some of the concrete examples from yesterday's post. Let me try this instead: if you're a classroom teacher or have been one, I would love to hear: what's an example of a place in your practice where you think you could take up less space?