Teachers’ Work Conditions

Today I was feeling chatty on twitter, so I wished everybody a good morning. It’s nice to hear about what is going on with folks, so it’s a pleasant way to start a day. I got several responses from people I was happy to hear from.

One exchange in particular got me thinking. At an early hour, where I still had one last child to bring to school, Tina Cardone had already attended an intense IEP meeting and faced off with complaining students.

@tchmathculture already had an IEP meeting and some whiny PreCalc kids. Working on recentering during my prep block.

— Tina Cardone (@crstn85) October 26, 2015

@tchmathculture yes, my 9th graders should be thankful I have prep and lunch (brunch-it's at 10:30) before I see them!

— Tina Cardone (@crstn85) October 26, 2015

In just a few tweets, Tina reminded me of some challenges of teaching, ones that are beyond the reach of teacher preparation or most education reforms: teachers’ work conditions. Most of the public debate about the profession skips the work conditions part (although there certainly are many discussions of teacher compensation).

An IEP meeting is usually an add-on to a teachers’ day. Teachers need to attend, both because they are legally beholden to IEPs but also to provide a team feedback on student. However, this time is not typically compensated. The teacher comes early, gives up a preparation period, or stays after school to attend an IEP meeitng.

Aggrieved students can be an emotional drain, as a teacher can find herself defending her professional judgement about something  — a grade, an assignment, a grouping arrangement — to a group of young people who may not see the big picture of her work.

Finally, Tina threw in the bit about her “lunch” time being scheduled for 10:30 AM. It brought me back to my last teaching job, when I was pregnant and hungry at odd times throughout the day. I have talked to other pregnant teachers who commiserate about that physical struggle. The half hour teachers typically get for lunch is seldom enough to eat properly in the best of circumstances. Throw in an early time slot or a physical condition that requires extra nourishment, it becomes difficult to keep the energy and mood up.

I am not singling Tina out here. To be sure, Tina knows how to hit the re-set button better than most folks. She is a frequent tweeter on the #onegoodthing hashtag (some of her #MTBoS pals even have a blog dedicated to this). Even in telling me about what was going on, she took these conditions as a part of the deal, focusing on what she could do: take her preparation time to get her emotions together (“re-centering”) so she can be in a good space for the rest of her classes.

When I think about conversations about teacher turnover, I notice how little we attend to these very basic conditions. Even when talk about making schools welcoming and comfortable places for students, we too often skip the part about making schools welcoming and comfortable places for teachers. We pay attention to school climate for kids so they can do their best work. What would happen if we did the same for teachers?

Here is one idea that could alleviate some of the time intensity of teachers’ work: What if schools staffed one or two adults as permanent in-house substitutes, whose primary job it is to know the students, teachers, and classrooms, so they can step in seamlessly when somebody needs a moment for re-centering after a difficult meeting, to compensate teachers’ time taken for additional meetings, or to allow a pregnant teacher to step out and use the bathroom during class?

In the years since NCLB, I have seen schools find funding for “data managers” so they can generate the tables and spreadsheets needed for evidence-based practice. Why not support teachers in bringing their best selves to each class by giving them an additional resource through by funding the floating support person?

What other ideas do you have for improving teachers’ work conditions?

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The Moral Qualities of Teaching

A few years ago, my colleague Rogers Hall and I looked at how biostatisticians and epidemiologists’ workplace conversations compared with those of instructional coaches and teachers. (We both study how people learn at work.)

As we compared our methods for analyzing workplace learning, we had a few great a-ha! moments. Rogers focuses a lot on epistemic communities in his analysis — that is, how different professions collectively agree about what qualifies as knowledge. The architects, etymologists and epidemiologists he has studied all have different standards for saying that something is “known.” Sharing analytic methods benefited me: the idea of epistemic community helped me describe how different teachers take different tacks on what counts as knowing in teaching.

My work informed his in a different way. In my studies, I examine how teachers justify instructional decisions. Oftentimes, they provide affective reasons for what they do  (“I am skipping this lesson because I don’t like it.” “I am going to do this activity because the kids love it.”)  Sometimes, they ground their choices in technical knowledge (“We need to give kids more time on subtracting integers. Those are hard ideas, and they need to see them lots of different examples.”) In addition, teachers will invoke moral reasons (“I am doing re-takes because every kid needs a chance to learn this. I don’t care who your 8th grade teacher was, you are going to learn in my class.”)

Through the comparison, Rogers saw that morality played in epidemiologists’ decisions too. For instance, in one observation, a scientist and a biostatistician debated how to sample a population to look for relationships between HIV and HPV –– whether to do fewer numbers of a better HPV screening or to get more statistical power by using a less expensive HPV test. If quality data were the only consideration, the need for statistical power would prevail. However, the epidemiologist had a had a strong moral commitment to improving the lives of poor women being recruited in the study and wanted to make sure they got the best screening available. This consideration played into his research design. Even supposedly “objective” scientists have reasons to weigh moral and ethical issues in their research.

Why do I bring up the role of morality in teaching? At the moment, I have intellectual and personal reasons.

Intellectually, I need to push back on how the cognitive revolution impacts how we think about teacher knowledge. Lee Shulman had a critical insight: good teachers have a special kind of content knowledge — what he called “pedagogical content knowledge”:

Pedagogical content knowledge (or PCK) includes: (a) knowledge of how to structure and represent academic content for direct teaching to students; (b) knowledge of the common conceptions, misconceptions, and difficulties that students encounter when learning particular content; and (c) knowledge of the specific teaching strategies that can be used to address students’ learning needs in particular classroom circumstances.

By acknowledging the specialized kinds of understanding that good teaching demands, Shulman did his part to elevate the teaching profession, opening entire programs of research that specify different facets of PCK.

Yet, somewhere in the years that followed, the moral element of teaching has too often been devalued. In our quest to professionalize teaching by defining its specialized knowledge, we have downplayed that teaching, at its best, is a deeply moral act.

For example, the PCK construct says nothing of what Rochelle Gutierréz calls “the political knowledge” teachers need to have truly equitable and inclusive classrooms. For instance, teachers need to understand the often biased structures of schooling and work deliberately against them. Recognizing bias and working against it is inherently moral: it acknowledges the inequities built into schooling, from unequal resources to cultural bias to curricular marginalization.

On the personal level, I have a child who has struggled in school. This child’s school experience has vastly improved when teachers are morally invested, sometimes beyond what would be sensible. I am fortunate because this year, my child’s teacher deeply understands the nature of these struggles.

When we first met, we discussed the history and nature of what has gone on. She shared that she had a child with similar challenges. Then she looked me straight in the eye and said, “So when I say I get your child” –– she tapped her hand to her heart –– “I get your child.”

Since then, she has told me that she finds my kid an “interesting challenge” and a “delight.” I have heard her talk to other parents as well and can attest that this teacher has a strong commitment to find a way to connect with and reach every student in her classroom.

Calling her commitment a form of knowledge does not do justice to the deep place it comes from: from her heart, from her very purpose as a teacher. And I know that has made all the difference.

What I Notice and Wonder about Teaching Like a Champion

Last night, Chris Robinson shared an experience with an administrator who observed his math classroom. He had been doing an activity called Noticing and Wondering with his students, something that Max Ray of the Math Forum has written about extensively. Noticing and wondering is a great discussion starter. You share a mathematical object or situation with children and open up the floor to their curiosity. They can connect the mathematical thing with their own ideas, then a teacher can shape the conversation by building connections to formal math.

Here is the administrator’s feedback:

During post-obs conference, admin tells me he thinks that Wondering was a waste of time because some students wondered "goofy things."

— Chris Robinson (@absvalteaching) April 1, 2015

Now, I am not naive. I understand that our lack of consensus about good teaching leaves a lot of room for interpretation about what is working and what is not. The administrator was obviously perplexed by the wide berth Chris gave to his students to wonder about the math. Kids do say and think goofy things, as do all people. But sometimes our odd ideas need a good airing to connect to what we are learning.

Normally, seeing Chris’s tweet would frustrate me. What do we need to do to drive a wedge between people’s confusion about students being compliant and being engaged? What do we need to do to help educators understand that the path to deep understanding is often not a straight line, and that to connect ideas to our lives, our own thinking –– goofy or not –– needs a chance to come out?

Yesterday, however, the administrator’s problematic response did more than frustrate me. As I told Chris (and the others on the thread):

@reilly1041 @k8nowak @absvalteaching this conversation is giving me the sads. Especially since we watched Doug Lemov's 100% vid today. 😖

— Ilana Horn (@tchmathculture) April 2, 2015

In my class Teaching as a Social Practice, we have been discussing the consequences of our lack of consensus on the nature of good teaching. We often examine what gets put out and circulated as good teaching and hold it against various research on things like  how kids learn or how teachers can teach responsively.

I showed this Doug Lemov video related to his best-selling book, Teach Like a Champion, with the intent to dissect the underlying assumptions about teaching and learning. The 100% technique is a way of managing students’ attention during instruction. Take two minutes to watch it.

What do you notice? What do you wonder?

I notice that these are all White teachers and that the students are nearly all Black.

I wonder why the teacher (above) is signalling this boy to have his hands folded. I wonder if there is any research anywhere showing that folded hands will help with his learning.

I notice that when this teacher reprimands this student for not having the answer to a question (1:11 on the video), she jumps immediately to the assumption that the girl needs to work harder. I wonder why the teacher doesn’t ask her if she has any questions about what was being asked or if everything is okay today.

I notice that this teacher says the following to his class as a motivational speech (1:44):

I can bring it to you but I can’t give it to you. You’ve got to reach for it. If they were free at Toys R Us you would reach. I’m giving you the same kind of gift, just not wrapped up. The gift of knowledge.

I wonder what is going on in this metaphor. I am wondering if I ever have seen wrapped up gifts at Toys R Us. I wonder if other overly analytical kids in this class also got lost down this rabbit hole of wondering.

I wonder if the kids would like the gift of being able to keep their hands unfolded and moving their bodies more freely more than the gift of repeating after the teacher in the name of “knowledge.”

____

What does all this have to do with Chris and his interaction with his administrator?

Teach Like a Champion has been a huge seller, especially in urban schools. It’s highly rated and ranked on Amazon and I have talked to numerous new teachers who report getting handed a copy by administrators. There is even a new edition Champion 2.0.

Activities like noticing and wondering open up classroom discussions and invite kids (goofy ideas and all) to think. Techniques like 100% in Teach Like a Champion limit permissible activity and thinking by students.  Contrasting the two is a productive microcosm on current debates about teaching. The issue is particularly urgent in urban classrooms, where methods like those promoted in Champion emphasize the control of Black and Brown bodies by White teachers instead of the celebration of children’s own ideas. This is especially troubling given what we know about disproportionate discipline of these children.

With this vision of teaching dominating the landscape, it becomes increasingly difficult for teachers like Chris Robinson to invite their children to think with him in the classroom without the risk of being reprimanded.

How Does School Culture Reflect Middle Class Culture?

Class is rarely talked about in the United States; nowhere is there a more intense silence about the reality of class differences than in educational settings.

— bell hooks

One of the things teachers often hear in the course of teacher education is that school culture typically reflects middle class culture. For teachers who grew up middle class, this statement can be perplexing. It’s like trying to alert fishes to the unique presence of water: they are so immersed in it that alternatives cannot be fully imagined.

Yet class shapes everything from interactional styles to the kinds of competencies valued in the home. In her famous ethnography of class and American childhoods, Annette Lareau characterized working class and poor families as tending to promote natural growth in children. These parents tend to let children determine their leisure activities. When they interject authority, they tend to do so with directives.

In contrast, middle-class families tended to practice a form of parenting Lareau calls concerted cultivation. These parents tended to equate good parenting with deliberate development of their children’s talents, especially through organized leisure activities. They also used fewer directives, instead reasoning with their children when seeking to change their behavior.

(There are other contrasts between these approaches to parenting, as summarized in this table.)

Lareau’s point is not that one style is better than the other, but instead to point out that school often assumes middle class parenting, leaving poor and working class families with less of an institutional fit. In fact, as somebody who was raised in this manner, I personally see many strengths that come out of the accomplishment of natural growth. Children have more opportunities to develop autonomy and engage in more social problem solving than children whose leisure activities are organized and led by adults.

How do these middle class assumptions play out in school? Classrooms are crowded places, and teachers frequently need to direct children’s attention and activities. Many teachers tend toward the middle class style of suggesting a transition (“Would you like to join us on the rug?”) rather than directing it (“Please come to the rug now”). If you are used to the latter, the former can be understandably ambiguous and confusing.

What is more, middle class children, through their greater experience with formally organized leisure activities, usually come to school with tacit understandings about how to participate. They have more experience responding to the authority of a non-kin adult with whom they will likely form a superficial and transitory relationship. In contrast, if your early socialization has been primarily with family, taking directions from a stranger may seem like a strange and maybe not entirely wise endeavor.

There are also subject-specific ways that social class makes school more or less a fit with children. Valerie Walkerdine has documented the ways class can interact with mathematics education in particular. She points to the quantitative fictions common to math class, describing, for example, an elementary number game requiring the “purchase” of various items for 1 to 10 pence and then making change. The working class children she observed, whose lives were much more consequentially tied to actual prices of things, found the premise of the game absurd. As I often tell my pre-service teachers, which of your students knows where to find the best price on a gallon of milk, and which simply look to make sure it’s organic? How does that change your job in making sure the cost in your word problem is realistic?

To feel comfortable participating in classrooms, children need to have a reason to be there. They need to see a connection to their lives and experience a sense of belonging. Social class differences are sometimes the source of cultural barriers to feeling like you belong in school, that school is a place that matters, that things make sense. Teachers need to be thoughtful in how they bridge these differences with their students.

First, Do No Harm

I have often wondered if teachers should have some form of a Hippocratic Oath, reminding themselves each day to first, do no harm.

Since the network of relationships in classrooms is so complex, it is often difficult to discern what we may do that causes children harm. Most of us have experienced the uncertainty of teaching, those dilemmas endemic to the classroom. Was it the right decision to stay firm on an assignment deadline for the child who always seems to misplace things, after giving several extensions? Or was there something more going on outside of the classroom that would alter that decision? Why did a student, who is usually amendable to playful teasing, suddenly storm out of the room today in the wake of such an interaction?

What I have arrived at is that there are levels of harm. The harm I describe in the previous examples can be recovered if teachers have relational competence — that is, the lines of communication are open with their students so that children can share and speak up if a teacher missteps.

What I am coming to realize is that mathematics teachers have a particular responsibility when it comes to doing no harm. Mathematics, for better or worse, is our culture’s stand-in subject for being smart. That is, if you are good at math, you must be smart. If you are not good at math, you are not truly smart.

I am not saying I believe that, but it is a popular message. I meet accomplished adults all the time who confess their insecurities stemming from their poor performance in mathematics classes.

Here is an incomplete list of common instructional practices that, in my view, do harm to students’ sense of competence:

1. Timed math tests

Our assessments communicate to students what we value. Jo Boaler recently wrote about the problems with these in terms of mathematical learning. Students who do well on these tend to see connections across the facts, while students who struggle tend not to. But if timed tests are the primary mode of assessment, then the students who struggle do not get many opportunities to develop those connections.

2. Not giving partial credit

Silly mistakes are par for the course in the course of demanding problem solving. Teachers who only use multiple choice tests or auto-grading do not get an opportunity to see students’ thinking. A wrong answer does not always indicate entirely wrong thinking. Students who are prone to getting the big idea and missing the details are regularly demoralized in mathematics classes.

Even worse, however, is …

3. Arbitrary grading that discounts sensemaking

Recently, a student I know had a construction quiz in a geometry class. The teacher marked her construction as “wrong” because she made her arcs below the line instead of above it, as the teacher had demonstrated. This teacher also counts answers as incorrect if the SAS Theorem is written as the SAS Postulate in proofs. Since different textbooks often name triangle congruence properties differently, this is an arbitrary distinction. This practice harms students by valuing imitation over sensemaking.

4. Moving the lesson along the path of “right answers”

Picture the following interaction:

Teacher:    “Can anyone tell me which is the vertical angle here?”

Layla:        “Angle C?”

Teacher:     “No. Robbie?”
Robbie:       “Angle D?”

Teacher: Yes. So now we know that Angle D also equals 38˚…

That type of interaction, called initiation-response-evaluation, is the most common format of mathematical talk in classrooms. Why is it potentially harmful? Let’s think about what Layla learned. She learned that she was wrong and, if she was listening, she learned that Angle D was the correct answer. However, she never got explicit instruction on why Angle C was incorrect. Over time, students like Layla often withdraw their participation from classroom discussions.

On the other hand, teachers who work with Layla’s incorrect answer –– or even better yet, value it as a good “non-example” to develop the class’s understanding of vertical angles –– increase student participation and mathematical confidence. And, they are doing more to grow everybody’s understanding.

What are other kinds of teaching practices that stand to “harm” students?

Beyond Beliefs in Teacher Learning

Every now and then, I try to explain to people on twitter why I recoil a bit from the idea of “teacher beliefs.”

It’s hard to do in 140 characters. The issue isn’t that I don’t think people have beliefs. I am just not sure, from a research perspective, whether “beliefs” get us to the right place.

They are a morass to analyze as well: what is beliefs and what is knowledge? Is saying that “the world is flat” a belief? What if the person saying it lived in 1400?

In other words, there is a lot of context to consider, even when you try to just look inside a person’s head and say what they believe.

Let me give another example.

Think of what it means to be a bike commuter. What beliefs do you think motivate that behavior?

Perhaps you think of personal commitments to the environment, a level of fitness, a desire to leave a small carbon footprint.

But what if I ask you that question in Amsterdam?

Do Dutch people believe more in the environment? Do they believe more in the importance of fitness?

Discussing the ubiquity of bikes in Amsterdam as an outcome of beliefs is acultural. It ignores the impressive infrastructure and cultural practices that support bike commuting.

Bike parking is ample.

Bike lanes are well marked and often separated in heavy traffic areas. People walk single file on a sidewalk rather than impede a bike lane.

Signs and traffic signals help integrate bike and vehicle traffic.

When we ignore these contextual differences, we overplay the role of beliefs in Dutch people’s behavior and underplay the role of culture.

So it is with teaching.

Teachers may believe in the importance of building off of students ideas but may feel impeded from doing so when they have 45 minute periods. Teachers may believe in the importance of building relationships with students but find it challenging to do so with 180 children in their classes.

At what point do we stop looking only to teachers to find more productive beliefs and think about more productive school cultures to foster better practice?

Instructional Activities and Core Practices for Teaching

This past week, I had the great pleasure of spending a few days thinking with some very smart people about issues in teacher education. They included Judith Warren Little, Magdalene Lampert, Elham Kazemi, Nicole Louie, Jessica Charles, Lynsey Gibbons, and Britnie Kane. We had a few other folks interested in teacher education drop in and chat with us too.

From left to right: Nicole Louie, Jessica Charles, Lynsey Gibbons, Elham Kazemi, Magdalene Lampert, Judith Warren Little, me, and Britnie Kane

Right now, debates rage about the value of teacher education. The folks around this particular table take teacher education very seriously. We all aim for what is currently called ambitious teaching — ambitious in the sense that it aims to engage all students in rich and complex forms of content.

To pull a couple of examples from their work, Magdalene currently works with the Boston Teacher Residency. Borrowing the idea of residency from medical education, she and her colleagues work to figure out effective ways to use long-term partnerships with practicing teachers and schools as the grounds for teacher education. Elham has been working with in-service elementary teachers in the Seattle areas, focusing her work with one particular school on mathematics instruction.

Both of these projects have had some impressive successes. BTR has done extremely well in recruiting and retaining teachers, and Elham’s project has dramatically improved math instruction on multiple measures.

Magdalene and Elham are a part of the Core Practices Consortium, a group of scholars from University of Washington, University of Michigan, UCLA, Notre Dame, University of Wisconsin, University of Colorado and the Boston Teacher residency.

If you want to read more details, here is a description of a conference session they did describing their work. Here is a journal article and here is a website cataloging some core practices by content area.

The basic goal of the Consortium is to identify practices that capture specific, routine aspects of teaching that require professional judgment and stand to raise the quality of content-specific instruction in K-12 schools. Because teaching requires thinking and doing, these activities create focal points for the work of teacher education.

Some examples of instructional activities include things like interactive close reading in elementary literacy or pressing students to construct evidence-based explanations in secondary science.

I purposefully used the examples above because I think they are smart choices for this work, but my reservations remain nonetheless.

As we discussed and shared and learned together, I still wonder if it’s possible to adequately capture teaching practice –– in the broad meaning of the word that I know my colleagues intend — through the specification of routine activities.

Let me explain.

I’ll start with a definition of teaching. I’ll extend David Cohen’s formulation slightly and claim that teaching is the deliberate cultivation of learning in others in distinctive teaching situations. The “in others” highlights its relational dependence. The “teaching situation” part points to is context-dependence.

This elaborated definition cuts to the very heart of my concern. While aspects of teaching are undoubtedly routine, their meaning comes out through the particulars of relationships and situations, with all the complexity of that setting and those histories.

My favorite example to illustrate this idea comes from a conversation I had with Peg Cagle. We were talking about whether to put names on publicly displayed student work.

In my working class high school where many of my students’ had histories of struggle in mathematics, I visibly put my students’ names on the work I hung on classroom walls. They needed to have ownership of their mathematical ideas, even in their formative stages.

Peg, on the other hand, taught in a magnet program for gifted students. Many of her students worried about being discovered as an impostor in the gifted track, making them fearful of others’ judgments. She kept her students’ names off of work-in-progress in her room.

Did we have different practices? At a certain level of description, yes. I put names on and she kept them off.

However, on a deeper level, we were attending to the same issue: the social vulnerability of asking students to share what they think. We both wanted to encourage our students to do so in ways that were attentive to their prior histories with mathematics.

So while what we did was different, at a deeper, conceptual level, however, we were alert to the particulars of our teaching situations and modified our practice to meet the goal of students sharing their ideas.

I don’t offer this example to negate the idea of instructional activities. I am convinced that there is value in this approach. I share the example to point out that teaching, because of its contextuality, may not operate like other professions where the meaning does not so depend on the relationships among the people involved.

How do teachers teach responsively?

The idea of responsiveness is one of the biggest challenges of equity-geared teaching approaches.

Responsiveness, by definition, means that lessons cannot entirely be planned without considering the students. What is more, since the students’ input and ideas are actively sought out, it increases the uncertainty of how a lesson will unfold.

This weekend, I have been reading a book by Adam Lefstein and Julia Snell called Better than Best Practice. Like me, these scholars spend a lot of time thinking about good teaching, although their study is in literacy classrooms in the UK, while I spend my time thinking about US mathematics classrooms.

Nonetheless, the premise of their book resonates with me. As the title suggests, they argue against “best practice” language that seeks to “prove” the efficacy of exact teacher moves or curricula. Like me, they are interested in the kind of teaching that seeks out, engages, and responds to students’ ideas.

Lefstein and Snell refer to this as professional teaching, arguing that involves sensitivity, interpretation, judgment and a flexible repertoire of methods. I found this to be a useful framework.

By sensitivity, the authors refer to teachers’ attentiveness and openness to critical moments in the flow of a class. Did a student raise an important issue? Did another student speak up for the first time? Does a conflict seem to be brewing? Classroom dynamics involve numerous people, all with their own feelings and thoughts and challenges, and a teacher must thoughtfully navigate these while moving lessons in a productive direction.

Once teachers are alert to a critical moment, they must then figure out its significance –– what Lefstein and Snell call interpretation. Was a student’s objection to a teacher’s premise simply an attempt to derail a lesson, or is there an important question that needs to be aired?

What will the broader message to the student and the class be if the teacher pursues the question? What if she shuts it down?

In the latter set of questions, sensitivity and interpretation work together as the teacher figures out which part of her repertoire to engage. By repertoire, the authors refer to a teacher’s flexibility and depth in calling upon a range of possible actions and success in implementing them.

Together, these resources come together to constitute judgments about teaching. Teachers make hundreds of decisions a day, and the demand only increases when they seek out student input.

I like this framework because it positions the teacher not as just “doing” things in the class, but actively responding to and making decisions about students. It also broadens the object of professional learning beyond the usual activities or specific teaching moves to increased sensitivity to student and classroom dynamics and their relation to ongoing judgments.

“What do you think and why?”

Today I got to virtually meet up with the amazing math teachers at the Park City Mathematics Institute. In addition to doing beautiful math problems, they have been involved in daily sessions called “Reflections on Practice.”

21st Century PD. I am beamed into the room. Photo: Suzanne Alejandre.

I knew that they had been talking a lot about the 5 Practices, so I decided to spend my time talking about how hard it was for most students to answer the question:

What do you think and why?

Persuading children to answer this question is a big obstacle to getting rich mathematical discourse off the ground in any classroom.

But think about it. That is a really tricky question to answer, both socially and intellectually.

I asked the teachers to spend some time thinking about why students might be reluctant to participate.

They brainstormed a great list:

• Sometimes students are not able to articulate their thoughts.
• Students might fear the judgment of their classmates.
• Students have incomplete thoughts.
• They are not always sure whether a question is a “right or wrong” question or a “share your thinking” question.
• There may be social norms that communicate that being smart is bad.
• They can be in crisis in their outside lives, making the question besides the point.
• They may not see sharing their thinking as a part of their role as students.
• They may have a very individual, internal process that makes “sharing” difficult.
• They may try to share their ideas but find that they are not listened to or valued.
• Sometimes students would rather not risk trying and failing, so it is safer to just not try.
• Language barriers can make it difficult to share.

I have seen all of these things as a teacher and an observer of mathematics classrooms. It is really hard to get kids to share their thinking.

I told the teachers about two concepts that I found to help teachers address these challenges and successfully establish rich classroom discourse with their students.

The first one is classroom norms. The second is addressing social status, which I have written about here and here.

I shared a list of norms that I have found to help encourage participation.

Then I talked a little bit about status problems and how they can get in the way of productive mathematical conversation. First I defined status…

Then I talked about how status problems play out in classroom conversations.

My goal was to help teachers think about the things they can actually do to support productive participation in mathematical discussions. I gave the teachers some more time to think about these ideas and brainstorm ways of developing norms that help alleviate status problems.

Another great list was generated. I am adding my commentary to the teachers’ ideas.

• Frequently vary groupings so people can be exposed to other people. This is important. A lot of times teachers want let students choose groups, which can especially aggravate status problems around social desirability. Other times, teachers use a “high, mid, low” achievement scheme. Students quickly size that up and know where they stand in the pecking order, which reinforces academic status problems.
• Use “round-robins”: everybody gets 1 minute to speak, whether or not you use all of it. This is not one that I have used, but the teacher who introduced this idea talked about how they let the clock roll for the full minute, even when students only spoke for 15 seconds. The quiet time was usually good thinking time for his students.
• Randomly call on kids. The teacher who introduced this one explained that she had playing cards taped on students’ desk, with the number representing their group (“the kings”, “the 12s”) and the suit representing an individual student. She could then pull out a card from her deck and call on “the 2 of diamonds.” I asked her what she did when a student didn’t know. She told me that she would sometimes get others to help them or move on then come back to them later, even if only for a summary statement. I added that I think it is really important to have a clear understanding in the class that partial answers count (see the “right and wrong” answer problem above) to successfully use random calling on kids. Otherwise students might shut down and feel on the spot.
• Making an initiative to make norms school-wide.This was an insight close to my heart. As the teacher who contributed this idea said, it will be much more powerful for students to get the same message about how to participate from more adults in the school.
• Tension: having students value ideas without getting stuck on ideas. This referred to the way kids can get wedded to particular ideas, even when they are wrong. I talked about how important it was to emphasize the value of changing your mind when you are convinced, not based on who is arguing with you. This is the heart of productive mathematical conversations.
• Tension: shifting from right/wrong to reasoning. Need to be transparent. The teacher who talked about this saw that emphasizing reasoning can be a game-changer for students who are good at seeing patterns and memorizing methods. They may know how to do things but have no idea why they do things: they suddenly go from “good at math” to “challenged.” I suggested addressing the concerns of these students from the perspective of advocacy: “I love your enthusiasm for math! I know what happens as you go up the curriculum, and you will really need to understand why things work, so I am giving you a chance to build those skills now.”
• Normalizing conflict through “sentence starters.” Conflict and arguing are usually seen as bad things to students, yet we want to create situations that allow for mathematical disagreements. By using sentence frames  –– and even posting them on the classroom walls –– we can help students learn to civilly disagree. For example, “I disagree because ____” or “How do you know that _____?” This also helps students press each other for justification.
•  “Everyone listening, everyone speaking, everyone responsible for understanding.”
  This was a norm that could really help encourage participation.
• Role playing & discussion as a way of (re)establishing norms. This teacher pointed out that norms sometimes need to be talked about explicitly –– and they often need to be revisited over the course of a school year. I added that I notice that certain curriculum topics (e.g., fractions) can bring up status issues, requiring certain norms to be revisited.
• Celebrating mistakes as opportunities to learn. How is that for normalizing confusion? Normalizing mistakes as a way for everybody to think harder about a topic or idea. I asked for some specific language for this, and the teacher suggested something like, “Thank you for bringing that up. We will all understand this better by discussing this.” (Sorry! This is from memory!)
• High social status kids as “summarizers,” give them math status. Sometimes students with high social status do not have high academic status. By giving them a mathematical role, we can marshal the fact that others listen to them and help build their understanding by giving them a particular role.
• Valuing different ways of contributing. Another one close to my heart! There are many ways to be smart at mathematics, and by valuing different ways kids can contribute, we can increase participation.

Thank you to the teachers of PCMI for the great conversation! Please add anything that I forgot to the comments section, and stay in touch!

How do we build math- and kid-positive department cultures?

I was pleased with the responses to my last post. A number of teachers reached out via twitter and comments, asking how they might build math- and kid-positive cultures in their own schools.

I can’t offer any large scale studies of the answer to this question, even though I am currently engaged in a research project that is trying to work with districts on similar issues. But I can share some of the experiences I had working with teachers in the Pacific Northwest toward this goal.

Gather invested colleagues around a common problem.

I always say, I have yet to meet a teacher who goes into the profession for the glamor or the money. Almost everybody who becomes a teacher wants to help kids. Find the folks whose heart is still in that. Find the ones who are willing and able to invest the time in their professional growth and look for a problem to work on.

That is what we did in the partnership project that went on for 6 years with some urban high schools. We started teachers at a school we called Septima Clark High. To get started on our work together, we used a process called “The 5 Whys” to try to get at the root of a problem that was bothering them. Their burning question was: why are so many kids failing 9th grade math?

First we brainstormed the answers to this question. I listened and recorded the brainstorm non-judgmentally and without conversation. This went on for over an hour, and we only got to a second level of “whys.” The result came to be known among us as “The Wall” because, as I wrote all the reasons on giant post it notes, they filled an entire wall. Seeing all the answers to this question was rather overwhelming.

The next step in the process was to look at this vast list and identify the things we could actually do something about. I underlined these. A small fraction of the reasons were actionable, but they gave us a way in to make a plan and set goals.

We sorted the actionable reasons into categories. From this, the teachers arrived at two conclusions:

• that their curriculum wasn’t engaging all students, and
• they needed to update their teaching practices.

The process was vital to teachers’ sense of ownership over our subsequent work.

Work together on a productive framing of that problem, linked back to math teaching and learning.

It’s one thing to identify a problem, like a high failure rate in 9th grade math. It’s altogether another thing to come up with a productive framing of that problem. Problem framings are how we define the parameters of something.

All too commonly, it is easy to point fingers and play the blame game: prior teachers did not do their job; the promotion policies that pass kids along; a lack of academic role models in kids’ lives. These reasons made the teachers’ brainstormed list. But none of them supported anything actionable on the part of the teachers. On the other hand, things like “kids aren’t engaged in the mathematics” did provide inroads for the teachers. By pressing teachers on what they can do, the framing that came out of this observation was that classroom activities and structures needed to encourage more participation. That was something teachers could work on.

Get support to have the time and space to meet to work on that problem regularly.

The hardest part about this process is that there is no way around how time-intensive it is. We all know teachers’ days are already overly full, despite the myth of teaching as an “easy, kid-friendly schedule.” Time diary studies of teachers’ work show that they work long hours, fitting a lot in on schooldays, weekends, and summers.

This is where administrative support can help. If there is already professional development time designated for your school, see if you can repurpose it for your goals. Even one hour after school weekly can make a difference. The best situation is to have common planning time with your collaborators, but this is a tricky and even expensive investment for schools.

Set short term and long term goals for your work, and find resources.

Too often, educational reform is treated like an appliance that can be brought anywhere and work the same way every time. We expect schools and teachers to “try” something, as if it’s just a matter of flipping a switch and saying yea or nay.

Education, however, is a human endeavor. The specifics of any setting and situation matter a lot for what works and how to get it working. Change takes time, especially ones that press on teachers to examine their core assumptions about teaching, learning, and mathematics.

One of my former doctoral students, Nicole Bannister, studied the Septima Clark teachers for her dissertation. She writes about their learning process and how they found ways to see and support their struggling students in their classrooms.

Celebrate the small victories, because there will always be setbacks and challenges.

School was originally designed on the factory model. Knowledge was thought of as a product that teachers could give to students efficiently on a set schedule. We now know that learning does not work that way — deeper understandings that support retention and fluency with mathematics cannot simply be delivered.

Re-culturing teaching –– reimagining the relations among students, mathematics, and teachers, as well as the activities that happen in the classroom –– to support more effective learning  is challenging work. Fundamentally, it involves working against the institutional grain of schooling, so there will be setbacks and challenges. For this reason, the small triumphs cannot go unnoticed: the student who makes sense of an idea for the first time, the one who participates after a long period of silence, the eagerness students have for a certain problem or project. All of these moments matter and need to be shared with the team. Otherwise, a team risks discouragement and burnout.

Share your work to help build critical mass.

Even before any results came in, the Clark teachers worked hard to communicate what they were doing with colleagues and parents. They held a meeting in the school library one evening to explain their understanding of the failure rate problem and the work they were invested in addressing it. Having the community support mattered. Even skeptical parents were heard saying, “If the teachers are this excited about what they are doing, I won’t stand in their way.”

Eventually, the kind of results administrators care about came in too. In the 2004-05 school year, before the team’s work began, less than half of the students who entered ninth grade at or below grade level were promoted to 10th-grade math. The following academic year, 83%
of those students were promoted.

This was not about dummying down content. In fact, the mathematical depth of classroom activities increased, as did student participation.

During the next state testing cycle, the student gains at the school caught the attention of the district. As the above chart shows, we saw higher achievement among Black* students and low income students, two groups that were of concern in the school and district. Soon, other schools wanted to learn about their work. Clark became a place that administrators visited, as did other teams of teachers.

*   *   *

The ongoing challenge for departments that reculture is how to sustain that work over time. In the last post, I told you about Railside, a place where I studied and taught. They managed to sustain their work for over two decades before policy pressures undid significant aspects of their work. Maybe if we can get critical mass at a national level, we can convince more people that organizing teaching so kids can learn is a worthwhile investment.

 

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* I use the term “Black” because some students were African and some were African American, but they generally referred to themselves as black.