You Are More than Your Achievements

Last night, I was invited to address the new members of the National Honors Society at my daughter Naomi’s high school. I am sharing the text of my speech here.

Good evening. First, let me congratulate you on all the hard work and talent that is reflected by your being here tonight. Your presence in this auditorium means that have worked hard. You have earned good grades. You have demonstrated a commitment to your community.

No doubt, you deserve to be congratulated –– to be honored ––  for all of these things.

I too am honored to be here this evening, to share in your accomplishment, to beam alongside your parents.

As Naomi mentioned, in addition to being a parent here, I am a professor. My research is in the field of math education — secondary math education, in fact. So I have spent a lot of the last 25 years in public schools, especially urban high schools. In that capacity,  get to work with and talk to kids and teachers about their experiences.

I do my research anthropologically: that is, I study schools as cultural systems and try to understand what makes them work, what values they convey through their customs and rituals, with an eye toward helping them become places that serve our country’s democratic ideals. When U.S. public education was founded in the 1800s, one of its central purposes was to  build citizens who can make good lives for themselves and contribute to our society.

After 25 years of working and living in schools all across the U.S. (and even a few of them abroad), I can say: schools are wonderful and terrible.

Sometimes even one school is both at the same time.

At their best, schools serve the democratic ideals I just described. The open up opportunities, promote social mobility, and develop informed and thoughtful citizens.

When schools operate in this way, they fill me with hope and optimism. I see young people discovering what is possible, preparing themselves as the next generation of leaders.

At their worst, schools work against democratic ideals. They operate in ways that preserve opportunities for some while shutting others out. They contribute to social reproduction. They fall short of their mission to develop informed and thoughtful citizens.

When schools operate in that way, I imagine them as heartless machines, pumping kids through, sorting them on a conveyor belt toward paths of success or failure.

My observations about the dual possibilities of schooling are not meant to denigrate your important accomplishment tonight. Your induction into NHS means that you have been  sorted into the academic successes.

To the contrary, my observation only increases my accolades and admiration, because it means that, in addition to having talent and working hard, many of you have very likely managed to advocate for yourselves, size up a system that is not always kind, and maintain a strong academic record in spite of various blows to your humanity along the way.

Every one of you has a story. Every one of you can tell me about how you got here tonight. And if your stories are like the stories of other high achieving students I have met over the years, along with your talent and hard work, your presence here tonight very likely also shows resilience and savvy. This deserves its own congratulations and it will also no doubt serve you well in your future.

Becoming a member of NHS marks you as an achiever. The culture of achievement to which you are being formally inducted here is a wonderful thing. It gives your families cause for pride and celebration. It will open doors to jobs and colleges for you.

Spending time in schools and studying adolescents in education, I know that (perhaps for some of you more than others), there are also personal costs for joining the culture of achievement. I want to take a moment to consider those, out of a sense of care and concern for you and your long term wellbeing.

May is Mental Health Awareness month, and we know right now that young people are facing greater rates of anxiety and depression than they have previously. The last statistic I saw reported about 1 out of 5 college students experiencing these things. That’s about a 33% increase over previous rates.

People my age like to think this is, in part, because of social media — you put your social lives online. On Snapchat and Instagram, you are constantly comparing yourselves to others. We even have a word –– FoMO –– to describe the special angst of missing out on things you see others doing that, in my generation, we most likely would have never known were happening.

I think there is more going on than that. I think there are vulnerabilities here in this room that are not often enough addressed.

I am bringing up mental health because it matters for your long term happiness. I teach in a university. I see students, just like you, who have successfully navigated the perils of schooling, who got sorted in the right ways. They, like you, are creative, inquisitive, driven. Sometimes, they end up in my office, and I offer tissues as they share their concerns and their worries. I see that too often they are led to believe that their value as a person is directly tied to their achievement.

So much emphasis in high school is on getting into the best college. And what happens if you manage to get there? We all hear of the benefits: Great education, valuable social network, important internship opportunities, a “brand name” university on your resume.

What we hear about a lot less are the risks to you, as a person and a human being.

Jamie O’Keeffe, an educational researcher at Stanford University, studied high achieving undergraduates at a top-tier university and how they contend with the pressures to achieve. She describes that when students “make it” to a selective university, they feel pressure to maintain the image of a “total winner”: the ideal self-made individual who excels without effort, confidently demonstrating genuine intellectual passion and desire to make a difference in the world, while effectively realizing increasingly greater achievements.

Paradoxically, this pressure makes it harder to maintain a sense of wellbeing. They experience stress, insecurity, and self-criticism, as any sense of struggle or failure feels like it is evidence against their legitimacy there. We have a name for that feeling. It’s called impostor syndrome. These feelings are amplified for first generation college students or students from historically marginalized groups.

So what is my message? Do I recommend slacking off? Bailing on NHS and aiming for the middle?

No. Absolutely not. As I started out saying, what you have done is commendable, maybe more so than many even realize. It is worthy of the honor you are receiving.

All of you sitting here belong here.

I suggest you follow Albert Einstein’s advice: “Try not to become a person of success, but rather try to become a person of value.”

I just want you to remember that you are more than your achievements. You are more than what you can list on the Common App next Fall. In fact, much of what is so precious about you won’t ever make it into that form.

I also am asking you to remember this. Aim to be honorable, not only in the ways that got you here tonight, but honorable to your friend who needs you to listen. Be honorable as children to your parents who have cared for you all these years. Be honorable as members of your communities –– your churches, synagogues, mosques, or whatever you consider your community. Be honorable to strangers in need. Be honorable to the students who struggle more than you do, the ones who are not here today.

Being honorable means doing what is right. And doing what is right is not always easy. It is not always obvious. Part of being honorable involves really knowing what you stand for and what you care about. It means knowing who you are. That should, ideally, be a part of your education too.

What does this have to do with mental health? In my experience, people who know who they are tend to hit those challenges, those setbacks, those inevitable and often unexpected bumps in the road with, if not grace,  with inner strength. They get knocked down, but they see a bigger picture, a larger purpose. They have people they can lean on, a sense of their own value beyond whatever went wrong. In this way, they maintain their perspective, even when they are shown to be less than a “total winner.”

From honor –– true honor –– comes strength in the face of adversity.

So congratulations on this honor. Be sure to cultivate it, and I wish you all a good life.



Public Education Matters for Democracy

I have struggled to find my place in my online communities as the political ground has so dramatically shifted in the past few months. The US Presidential election fostered a climate that counters so much of what I stand for as an educator and a citizen. My twitter feed has been taken over by politics as I watch so many institutions struggle to uphold our democracy, institutions designed to safeguard cherished ideals like free speech, the right to assemble, and the pursuit of happiness.

I am grateful to have spent the week between Martin Luther King, Jr. Day and the Inauguration with a group of like-minded scholars at a Spencer-sponsored conference at UCLA. We share a commitment to preparing asset- and equity-oriented educators, so it was a great moment to figure out what that might mean in the years ahead.


Left to right: Manka Varghese, Matt Diemer, me, Lauren Anderson, Mariana Souto-Manning, Dorinda Carter Andrews, Thomas Philip, Jamy Stillman


Clockwise from left: Gloria Ladson-Billings, Mariana Souto-Manning, Lauren Anderson, Elizabeth Self, Thomas Philip, Matt Diemer, me, Alfredo Artiles, Marilyn Cochran-Smith, Sharon Feiman-Nemser, Jamy Stillman, Josephine Pham, Dorinda Carter Andrews

It was a productive week for clarifying my values and commitments. We even wrote an editorial together arguing against Betsy DeVos’s appointment as Secretary of Education.

I think I will need to return to these commitments a lot over the coming years. For this reason, I am going to go back to basics and sharing those commitments with you.

To be sure, I have no illusions that the prior administration upheld my educational values. Market-based reforms have been a centerpiece of educational policy for the past several administrations. President Bush’s landmark legislation No Child Left Behind certainly advanced this agenda, but President Obama’s Race to the Top put it on steroids. By tying teaching and learning to narrow metrics, discourses of desirable educational outcomes became less about children’s growth, their humanity, and their potential as future citizens. On the whole, national goals for children’s learning slid to the bottom of Bloom’s Taxonomy.

I believe in education as a public good. We live in a time and place where the ethos of individualism prevails. In this logic, if my kids are okay, everything is fine. In contrast, if we see education as a public good, our concerns must extend beyond our own children into our communities, states, and country. Whether we realize it or not, we have a vested interest in the solid education of all our citizens. To take an example that begins with  individual needs, I want the nurse administering my chemo to know the difference between .5 L and .05 L when pulling the dose. Beyond that basic skill, I also want him to be an empathetic person who can talk my family and I through our fear. There are countless situations where our personal interests depend on others’ competence and humanity.

Market-based reforms emphasize competition between institutions. This corrodes the ideal of schools as places that should be serving children and communities, contributing to their development and well-being. In a market-based framework, there are winners and losers, successes and failures. Despite meritocratic ideas, these winners and losers are not determined by raw talent but rather the status and resources of children and their families. I recognize that education has always been an unevenly distributed resource, especially in the U.S. I felt I could do my work as an advocate, because there were enough shared commitments to democratic ideals of opportunity. I am not so sure at this moment.

I believe that meaningful learning engages the whole person. It is not just knowing but also becoming. In my work, I study what it means to teach in ways that allow children become mathematicians. I also study what it means for teachers to become humanistic educators who engage with children’s experiences, build learning communities, and respond thoughtfully to children’s ideas.

Some children, however, are given more opportunities to become themselves than others. This starts with issues of language and culture, with some children’s home language and culture fitting into the social patterns of school, providing an important resource for their success there. Aside from such cultural capital, parents actual capital allows them to navigate the system in radically different ways. I have noticed a pattern in middle class parents’ rationale for sending their children to private schools. Most of the time, they are working to preserve their child’s competence. A child’s anxiety increases untenably in a test-prep focused school. A child’s difficulties with memorization lead to failing grades in a narrow curriculum. A child’s artistic strengths are not given adequate play in the school day. A child is inadequately challenged by a constantly changing cast of temp-work teachers.

I believe that strong community schools can anchor families and bring neighborhoods together around common concerns. Community schools, at their best, provide gathering places. They allow neighborhoods to feel like neighborhoods, with children getting to know the people around them. When there is a shared concern, community schools provide a space for people to come together around that concern. Dissolving community schools feels like another part of the effort to weaken the collective impact of people with shared interests.

In short, I believe that public education is central to meeting the ideals of our democracy. I know that a lot of work needs to be done to have it meet these ideals, but if we gut it completely, we will only be further behind on meeting the potential and promise of America.

Auditing Your Classrooms for Competence and Status

This past weekend, I had the great pleasure of giving a keynote address at the Mathematics Council of Alberta Teachers (MCATA) Conference.

First things first: @minaclark did sketch notes of my talk!  I am delighted because I have always wanted somebody to do that. She did a fantastic job too.

During the breakout session afterwards, I talked about how we can audit our classrooms to support better interactions. In particular, we need to pay attention to issues of mathematical competence and student status. (I have written a lot on these topics since they are critical to fostering positive relationships between students and the subject. You can read earlier posts here, here, and here.)

Here are my audit questions.

Competence audit:

  • What kinds of competencies are valued in your classroom? Where do students have a chance to show them?
  • Consider the last few activities you have done in your class. Did they provide multiple entry points toward a rich mathematical idea? If not, can you use the table below to adapt them to become a low ceiling/high floor question?
  • When you look at your class roster, can you identify at least one way that every student is mathematically smart?
  • When you think of students who struggle, do they have competencies that you might better support by redesigning some of your class activities?
  • When you think of students who have a history of high achievement, do they value other ways to be smart aside from quick and accurate calculation? Do they value other competencies in themselves? In others?

Some low floor-high ceiling question types. (Adapted from Will Stafford’s “Create Debate” Handout)

Status audit:

  • When you think of the students you worry about, how much of their challenge stems from lack of confidence?
  • How much do students recognize the value and contributions of their peers?
  • What small changes could you make to address status problems and support more students in experiencing a sense of competence?

Please feel free to add others or offer your thoughts in the comment section.

Renegotiating Classroom Treaties

Many classrooms are governed by tacitly negotiated treaties. That is, students trade in their compliance and cooperation –– student behaviors that alleviate the challenges of crowded classrooms ––  for minimal demands for engagement by the teacher. When I have worked with teachers trying out open-ended tasks for the first time, I will often hear about “pushback” or “resistance” from the students: “I tried using this activity but the kids balked. They complained the whole time and refused to engage.”

These student responses indicate that teachers are violating their part of the treaty by going beyond minimal demands for engagement and increasing intellectual press. Put differently, by using an open-ended task, teachers raise the social risk, leaving students open to judgment since they can not rely on the usual rituals of math class to hide their uncertainty. Treaties may, as their name suggests, keep the peace, but they reflect norms of minimal engagement that interfere with deeper learning.

In my own observations, I see teachers struggle to move students past their initial reluctance to participate and make it clear that active involvement is required in their classrooms. Renegotiating classroom treaties requires a clear vision for what student participation can look like, structures to support that vision, along with the determination to see it through. The teachers I interviewed for my forthcoming book all emphasize how critical the first days are for setting these expectations for their students, particularly since their expectations may differ from what students are used to in math class. “It’s entirely intentional that I begin setting norms and structures on the first day of school,” Fawn explains. By launching the new school year by showing students what it means to do math in her class, Fawn renegotiates the classroom treaty through norms and structures, introducing the Visual Pattern and other discourse routines from the start. She says, “I need to provide students with ample opportunities to experience the culture that we have set up. We need to establish and maintain a culture that’s safe for sharing and discussing mathematics, safe for making mistakes, and a culture that honors each person’s right to contribute. There needs to be a firm belief among everyone that mathematics is a vital social endeavor. Building this culture takes time.”
Starting the school year with clear expectations is important, but guiding individual students’ participation is an ongoing project. The teachers I interviewed have numerous strategies for monitoring and building positive participation throughout the year. Students students who hide or students who dominate make for uneven participation. The teachers describe how they contend with these inevitable situations.
When figuring out how to respond to quiet students, the teachers try to understand the nature of students’ limited participation. Not all quiet students are quiet for the same reasons. At times, quietness is rooted in temperament: some students inclined to hang back until they feel confident about what is going on, but they are tracking everything in class. These students do not contribute frequently, but, when they do, their contributions add a lot to conversations. This kind of quiet is less of a concern and can even be acknowledged: “Raymond, you don’t talk a lot, but when you do, I always love hearing what you have to say.”
Other times, quietness signals students’ lack confidence. That is, students indicate some understanding in their work or small group conversations, but they do not have the confidence to participate in public conversations. With these students, the teachers seek out individual conversations. Chris calls these doorway talks, while Peg calls them sidebars. (“Trying to deal with calculators and rulers at the end of class, I couldn’t make it to the doorway!” Peg tells me when I note the different names.) “I might say to a kid, ‘You know, you had really good ideas today, and I would have loved to have heard more of them in the conversation we had a the end. I think you have a lot more to contribute than you give yourself credit for.’” Sometimes, there are ways of encouraging good ideas to become public that do not directly address the student. Chris explains that he might say something like, “I haven’t heard from this corner of the room.” He then asks other students to hold their ideas while waiting for a contribution from the quiet group.

Of course, some students are quiet because they really do not know what is going on. This could be due to a language issue, in which case, the teacher needs to modify instruction to give them more access to the ideas. If there are other learning issues going on, this might suggest the need to check in with colleagues about the students performance in previous years or in other subjects.

Talkative students pose another kind of challenge to the expectation that everyone participates.  On the one hand, they can provide wonderful models of sharing their thinking. They can be the “brave volunteers” who explore their thinking publicly, and teachers can lean on them to get conversations started. On the other hand, they can be domineering, making it difficult for other students to get a word in. The quiet students who temperamentally need to think before they speak have their counterparts in some talkative students: these are the students who think by talking. Asking for their silence sometimes gets heard as asking them not to think. When I have had students like that in my own classes, I make sure to assure them that I value their engagement but that I need them to find other strategies for processing so that other students can be heard. Sometimes, students with impaired executive functioning, like those with ADD, have a hard time with the turn-taking aspect of classroom dialogue, so not only do they talk a lot sometimes, they struggle to take turns. Again, teachers can respond by valuing students’ ideas while helping them participate more effectively: “I know you get excited, but we need to take turns so that we can hear each other.” Finally, domineering behavior can get expressed through a lot of talking: students who are highly confident in their understanding and want to explain to others. Teachers need to judge the extent to which this is altruistic, a sense of trying to share knowledge, and the extent to which it shuts conversations down. In the first case, students can be coached towards asking questions of their classmates, channeling their impulse to talk into something constructive. In the second case, the dominance can be corrosive to the classroom culture and the students might need stronger redirection. For all of this feedback, similar strategies of direct address (via sidebars or doorway talks) and indirect address (“Let’s hear from somebody else”) can help teachers manage participation.

Structure Can Change Agency

One great privilege of the work I do are the many opportunities I get to share the things I care about with different groups of people. If you do it enough, you get a chance to clarify your own ideas, learn from others, and notice connections.

This past weekend, I had the honor to give a keynote talk at the Carnegie Math Pathways Forum. If you don’t know about their work, it is worth checking out. Briefly, their work addresses the enormous blockage in the math pipeline as students transition from secondary to post-secondary. A staggering number of students get placed in developmental math classes, and often, these courses become a holding bin students cannot get out of. The Carnegie folks have worked primarily with community college instructors to re-think developmental math curricularly and pedagogically. It’s fascinating and important work.

My talk was about the relationship between structure and agency, how both contribute to inequalities in mathematics education. When we are teaching in a classroom, it is easy to see problems of inequality as they look locally: high enrollments in developmental math, over-representation of students coming from poverty and students of color, a sense of student apathy. To make progress, however, instructors can learn by linking the local to broader social processes: the maldistribution of qualified math teachers, STEM classrooms that are hostile environments to minoritized students, a K-12 curriculum that often reflects the institution of schooling more than what it means to do meaningful mathematics. I argued that if we frame these problems through what we see locally, we give ourselves, as teachers, less leverage to make progress on them. I shared two key concepts for linking these social processes to what we see in our classrooms: social risk and status. I have written about both of these (click the links if you are curious), but briefly, social risk refers to the threats people feel are posed to their status in a community while status describes the perception of students’ academic capability and social desirability. Both of these ideas link the social process explanations for inequality to what teachers see in their classrooms locally.

Teachers can then work to design classrooms that reduce social risk by, in part, attending to status dynamics. In other words, to connect structure and agency, we need ways to think across scale and look at the social origins of problems too often narrated as individual issues. Instead of, for example, blaming students for being apathetic about mathematics learning, we need to recognize what their history has likely been in our current system and accept their apparent apathy as a reasonable response. Our task shifts from finger pointing (“My students just aren’t motivated!“) to having the productive challenge of honoring their experience while trying to change their ideas about math and learning.

In the end, then, structure can help us change agency in two ways. First, by recognizing that it is there, along with the social processes it holds in place, we can arrive at more productive framings of the problems we face locally. Second, we can leverage the structural designs in our classroom to invite students’ agency.

I have written about designing structures to promote agency before. If you don’t feel like reading that (I realize it’s summer!), maybe watch this video instead. It is quite a joy.

And don’t we all need more of that right now?


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.

lareau cover

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.

“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!

The Tweet Heard ‘Round the Edu World

Recently, my twitter world has been on fire in response to comedian Louis C.K.’s anti-Common Core rant.

It started with this tweet:

A lot has been said already — check out Audrey Watters’ storify on the subject for one example.

I agree that, as a parent, C.K. is a stakeholder in public education and therefore should have a voice. But I would like to attempt to push back a bit to put the Common Core Standards in a little bit of context in the hopes that C.K. and other middle class parents can sharpen their advocacy.

As I have said previously, we need to distinguish among the standards, their implementation, and the accountability system they have been stuck into. Otherwise, we will repeat our American tendency to simply throw out babies with the bathwater.

In the spirit of nuance, I have two responses to Louis C.K.’s tweet and those who endorse it:

(1) The Common Core is not the same as No Child Left Behind. The Common Core State Standards (CCSS) have been implemented hastily and without any modification of the NCLB accountability system in many places. This has resulted in middle-class public schools feeling the heat that has been around for some time in schools in lower-income communities, as teachers worry about evaluations that are based on assessments and standards that are unfamiliar, and perhaps in their hurried, underfinanced implementation, unreasonable.

The kind of overkill test prep has been going on for a long time in schools who don’t rate well under the NCLB regime. These schools are put on probationary status, as they have to demonstrate making “adequate yearly progress” (AYP). Researchers (including myself) have reported that test prep has taken over other more humanistic educational goals like so much kudzu. I predicted that if rapid implementation led to this form of schooling for the middle class, there would be a larger outcry.

(2) The goal of standards is to provide more equal learning opportunities.

Do you remember Williams vs. California? Students from high poverty communities sued the state because state agencies failed to provide public school students with equal access to instructional materials, safe and decent school facilities, and qualified teachers.

This is a serious problem. I had the opportunity to visit schools across the country in the mid-1990s. To deform Gertrude Stein, algebra wasn’t algebra wasn’t algebra. The content of courses could too easily be predicted by the community’s SES. Even the best students in high poverty schools were not given the same level of content as mediocre students in wealthy schools.
Standards are not a perfect solution, but they are a tool to set a bar that is public and transparent for teachers, students, and communities. They say, “This is what algebra needs to include. Students, you have a right to learn this. Educators, you need to work out how to get students there.”

Of course, this last part of the mandate is where we find the rub. Educators are expected to know how to successfully work with the standards NOW — often with minimal support and training, and certainly with very little time.

As I have listened to some of the push back on the actual content of the CCSS, the most troubling to me is along the lines of “our kids can’t do that.”

Let me just say right out: I am quite certain that almost all of them can. How many Bob Moseses and Megan Bangs do we need showing us the unrecognized competence in kids of color or kids in poverty? Something needs to be done to bring high quality content to all students. Standards should not be the only tool, but they could be one of several that would include full funding of education and improving teachers’ working conditions to attract and retain our best people.
I  know firsthand that figuring out new ways of teaching to engage that different kinds of mathematical competence are hard and take huge investments on the part of schools.

The question remains: what are we going to let prevail? The status quo in which the kids whose parents have the ears of the world can have a quality education while others remain on the margins? Education is a key to a democratic society. The standards may not be perfect but they can be one tool of rectifying our history of unequal education.

Recognizing Smartness and Addressing Status in the Classroom

When status plays out in the complex world of the classroom, it takes many shapes. Although blatant dominance, insults, or non-participation are easy to spot, the more subtle manifestations take skill to identify and remedy. Effectively intervening with status problems first requires analysis of the situation. Figuring out the best strategy is often a trial-and-error process. Teachers get better at managing status in their classrooms over time, but even accomplished teachers run into challenges that force them to further sharpen their intervention tools.

The following strategies outline a starting point for status interventions. Unfortunately, this is not a recipe that will make status problems magically disappear. Status will always be part of our social world. The trick is to manage it such that students begin to reimagine themselves and their peers in the context of their competence and not their deficits. Every class you teach will have different personalities and dynamics, so these will play out differently in each circumstance. Nonetheless, here are some tested status interventions that can be adapted to any classroom.

Establishing and Maintaining Norms

Effective classroom norms support equal-status interactions. In the previous discussion of status problems, I suggested some structures teachers can use, such as “no hands, just minds,” that help curb status problems. These all communicate norms for participating and interacting. For our purposes, I will use the following definition of norms:

Classroom norms are agreed-upon ways of behaving.

Establishing norms requires a conversation with students. Some teachers do this interactively, asking students to contribute their answers to the question, “What makes you comfortable in a classroom?” Other teachers let students know that they have found certain behaviors helpful in making a positive classroom environment where students feel comfortable to learn. However they are arrived at, posting a list of norms on the wall as a reminder can help keep these at the forefront.

Norms can help curb status problems. For example, establishing the norm of no put-downs can minimize negative talk about oneself or others.  Examples of other norms that help support equal status interactions include the following:

  • Take turns.
  • Listen to others’ ideas.
  • Disagree with ideas, not people.
  • Be respectful.
  • Helping is not the same as giving answers.
  • Confusion is part of learning.
  • Say your “becauses.”

Since norms are associated with classroom behavior, they are often thought of as a classroom management tool. In a sense, they are, but they go beyond that. Classroom management is often understood as serving the important goal of managing the crowd in the classroom. Students may or may not value that goal. The use of norms as I describe them helps students learn.

To make norms more relevant to students, always link norms to your learning goals. For example, helping is not the same as giving answers values explanations and learning over the completion of work. Similarly, say your “becauses” values the mathematical work of justification over assertions of correct answers that may be based in status. This norm also helps alleviate the problem of nonmathematical assertion of an argument by helping a lower-status student demand that a higher-status student better explain an assertion. In classrooms where this norm is in use, I hear students say to one another, “Yeah, but why? You didn’t say your ‘because.’”

Telling students expectations for acceptable behavior does not, of course, ensure that they will always meet them. Norms require maintenance. New situations might create a need to reestablish them. Even new content—particularly content that highlights differences in prior achievement—can heighten status issues and therefore require a strong reminder about classroom norms.

Addressing Status through Norms

Over time, teachers get better at analyzing which norms might help shift negative status dynamics in their classrooms. Teachers pick one or two norms for a particular activity and tell students, “While you are working on this, I am going to watch how you do on these norms.” The teacher then reminds students of the expectation for acceptable behavior.

Sometimes the choice of norms comes from a teacher’s reading of the dynamics in prior class sessions. For example, if student conversations are coming too close to personal attacks, a teacher might highlight the norms be respectful and disagree with ideas, not people. If the teacher then circulates around the room and reminds students of these norms, he is not picking on problem students; rather, the teacher is stating a classroom goal that everybody is trying to work on.

Likewise, teachers can predict mathematical activities that might lead to status problems and use norms to head these off. Any topic that is confusing may make students vulnerable to status concerns. Reminding students that confusion is a part of learning can help. I have heard teachers say, “Now, I don’t expect you to get this problem quickly. It’s really hard and you will need each other’s help. If you get confused, that’s great because it means you are learning.”

Sometimes, specific topics expose students’ status concerns. Calculations with fractions commonly bring out insecurity in previously low-achieving students and impatience in students who are already fluent in these calculations: a recipe for a status collision. Anticipating this, a teacher can let the class know that she will be watching for the norms helping is not the same as giving answers and say your “becauses.” The first norm will send a clear message that students who can calculate quickly need to do more than show the other students their answers. The second norm offers less confident students a means to demand explanations from their peers (“Okay, but you didn’t say the ‘because’”).

Multiple-Ability Treatment

So far, this discussion of status has acknowledged the different status levels of students in any classroom and how it can undermine productive mathematical conversations. No doubt, addressing status through norms is crucial to creating equal-status interactions. By helping students interact more productively—listening respectfully, justifying their thinking—we help support meaningful mathematical conversations.

Norms, however, will take us only so far. Unless we address underlying conceptions of smartness, we risk reverting to the commonly held belief that group work benefits struggling students because smart students help them. As long as we have a simplistic view of some students as smart and others as struggling, we will have status problems in our classrooms. (Please see my previous post on different kinds of mathematical smartness.)  Students quickly pick up on assessments of their ability. For example, when teachers arrange collaborative groups to evenly distribute strong, weak, and average students, children will figure out that scheme and rapidly learn which slot they fill. No doubt, learners benefit from seeing more expert performance and should have opportunities to do so. But if we value only certain kinds of expertise, the same students will always play the role of experts. The question then becomes, What kinds of mathematical competence have a place in your classroom activities? If the mathematics is rich enough, the strengths of different students will come into play, rendering the common mixed-ability grouping strategy useless. Ordering the students by achievement and evenly distributing strong, weak, and average students across the groups will no longer be enough.

In fact, an essential practice for a multiple-ability classroom is random group assignment. If we believe that students can all learn from each other, then group assignments should have no underlying design based on assessments of ability. Teachers often do this by using a wall-hanging seating chart that has pockets for each student’s name. When it is time to rearrange groups, they will shuffle the cards and simply redistribute them in the pockets to make a transparent show of the randomness of group assignments. If a teacher judges a certain pairing of students to be unwise, she can publicly state the reason for this (e.g., “You two tend to get too silly together, so I think I will switch you out”). These reasons are not judgments about smartness but are instead social considerations. Random group assignment, however, is just one component of multiple-ability treatments.

As I said in my post on smartness, in schools, the most valued kind of mathematical competence is typically quick and accurate calculation. Evaluating people on one dimension of mathematical competence will rank students from most to least competent. This rank order usually relates to students’ academic status, and students tend to be aware of it. One way to interrupt status is to recognize multiple mathematical abilities. Instead of a one-dimensional rank order, we create a multidimensional competence space. Although some students may have multiple mathematical strengths, more places in which to get better surely exist. Likewise, a student who ranks low on the hierarchy produced when we focus on quick and accurate calculation may have a real strength at making astute connections, working systematically, or representing ideas clearly. We cannot address status hierarchies without emphasizing multiple mathematical competencies in the classroom.

A multiple-ability classroom represents a dramatic shift in the topography of mathematical ability. Instead of lining students up in a row in order of smartness, a multiple-ability classroom has students standing on different peaks and valleys of a hilly multidimensional terrain. No one student is always clearly above another. This structure may unsettle students who are used to being on top, as well as those whose vantage points and contributions have been presumed less valuable. In other words, challenging the status hierarchy by developing a multiple-ability view can provoke strong emotions from students, positive and negative. Teachers should not be surprised to see this response in their classrooms.

Multiple Ability Treatments

A multiple-ability treatment comes in the launch of a task. After presenting the directions and expectations, teachers list the specific mathematical abilities that students will need for the task and add the phrase, “No one of us has all of these abilities, so you will need each other to get this work done.” By publicly acknowledging the need for more than just quick and accurate calculation, teachers offer an in for a broader range of students. Multiple-ability treatments do other work too, particularly fostering interdependence.

Assigning Competence

The two status interventions described so far operate on the classroom level. Norms give clear expectations for behavior to push students toward more productive mathematical conversations. Multiple-ability treatments highlight teachers’ valuing of broader mathematical competencies.

The next step is to help students recognize where they and their classmates are located on the complex topography of mathematical competence to shift their self-concept and their ideas about others. Students need to recognize these other competencies for themselves so that they know their own strengths and can work confidently on hard problems. They need to recognize the strengths of their peers in order to interrupt assumptions based on a simplistic smartness hierarchy. If students believe their classmates have something to contribute, they have a mathematically motivated reason to listen to and learn from each other.

Teachers can communicate these messages to students through the practice of assigning competence.

Assigning competence is a form of praise where teachers catch students being smart. The praise is public, specific to the task, and intellectually meaningful.

The public part of assigning competence means that this praise is not an aside to an individual student or a communication with the parent. It takes place in the public realm of the classroom, whether in small-group activity or whole-class discussion. It needs to be specific to the task so that students make a connection between their behavior and their mathematical contribution. Simply saying, “Good job!” is not enough. Students need to know exactly what they did that is valued. The praise must be intellectually meaningful so that it contributes to students’ sense of smartness. Praising a student for a “beautiful poster” does not qualify as assigning competence, because making a beautiful poster does not display mathematical intellect. In contrast, if a teacher praises a student for a clear representation on a poster that helps explain an idea, that is intellectually meaningful because it is tied to mathematics.

I hope this post gives you some insight into how to address status and value smartness in your classroom. No doubt, this is challenging work, But I think the payoff in mathematical learning is well worth it.

What does it mean to be smart in mathematics?

In the last two posts, I discussed the idea of status. First, I talked about why status matters, then I talked about how teachers can see it in the classroom.

Sometimes, after I have explained how status plays out in the classroom, somebody will push back by saying, “Yeah, but status is going to happen. Some kids are just smarter than others.”

I am not naive: I do not believe that everybody is the same or has the same abilities. I do not even think this would be desirable. However, I do think that too many kids have gifts that are not recognized or valued in school — especially in mathematics class.

Let me elaborate. In schools, the most valued kind of mathematical competence is typically quick and accurate calculation. There is nothing wrong with being a fast and accurate calculator: a facility with numbers and algorithms no doubt reflects important mathematical proclivities. But if our goal is to address status issues and broaden classroom participation in an authentically mathematical way, we need to broaden our notions of what mathematical competence looks like.

Again, my naysayers roll their eyes and groan, assuming that I want to “soften” mathematics or dilute the curriculum. But I claim that broader notions of mathematical competence are actually more authentic to the subject.


Let’s cherry pick some nice examples from the the history of mathematics. We see very quickly that mathematical competencies other than quick and accurate calculation have helped develop the field. For example, Fermat’s Last Theorem was posed as a question that seemed worth entertaining for more than three centuries because of its compelling intuitiveness. When Andrew Wiles’s solution came in the late twentieth century, it rested on the insightful connection he made between two seemingly disparate topics: number theory and elliptical curves. Hyperbolic geometry became a convincing alternative system for representing space because of Poincaré’s ingenious half-plane and disk models, which helped provide a means for constructions and visualizations in this non-Euclidean space. When the controversy over multiple geometries brewed, Klein’s Erlangen program developed an axiomatic system that helped explain the logic and relationships among these seemingly irreconcilable models. In the 1970s, Kenneth Appel and Wolfgang Haken’s proof of the Four Color Theorem was hotly debated because of its innovative use of computers to systematically consider every possible case. When aberrations have come up over the years, such as irrational or imaginary numbers, ingenious mathematicians have extended systems of calculation to encompass them so that they become number systems in their own right.

This glimpse into the history of mathematics shows that multiple competencies propel mathematical discovery:

  • posing interesting questions (Fermat);
  • making astute connections (Wiles);
  • representing ideas clearly (Poincaré);
  • developing logical explanations (Klein);
  • working systematically (Appel and Haken); and
  • extending ideas (irrational/complex number systems).

These are all vital mathematical competencies. Surprisingly, students have few opportunities to recognize these competencies in themselves or their peers while in school. Our system highlights the competence of calculating quickly and accurately, sometimes at the expense of other competencies that require a different pace of problem solving.

Evaluating people on one dimension of mathematical competence will rank students from most to least competent. This rank order usually relates to students’ academic status, and students tend to be aware of it. One way to interrupt status is to recognize multiple mathematical abilities. Instead of a one-dimensional rank order, we create a multidimensional competence space. Although some students may have multiple mathematical strengths, more places in which to get better surely exist. Likewise, a student who ranks low on the hierarchy produced when we focus on quick and accurate calculation may have a real strength at making astute connections, working systematically, or representing ideas clearly. We cannot address status hierarchies without emphasizing multiple mathematical competencies in the classroom.

A multiple-ability classroom represents a dramatic shift in the topography of mathematical ability. Instead of lining students up in a row in order of smartness, a multiple-ability classroom has students standing on different peaks and valleys of a hilly multidimensional terrain. No one student is always clearly above another. This structure may unsettle students who are used to being on top, as well as those whose vantage points and contributions have been presumed less valuable. In other words, challenging the status hierarchy by developing a multiple-ability view can provoke strong emotions from students, positive and negative. Teachers should not be surprised to see this response in their classrooms.