Choice Systems and False Agency

I have been reeling for the past few months at the startling erosion of some of the taken-as-shared narratives about public education as the backbone of democracy. I realize that these often came as platitudes and, worse, double-speak, but as long as there was some semblance of a shared commitment for high quality public education, I felt I had something to work with.

The current U.S.Secretary of Education has taken astonishingly hateful positions on protecting students’ civil rights in her valorization of “choice” and “states rights.” Our shameful history of Jim Crow has established latter as a well-known cover for government-sponsored racism. But I want to poke a few holes in “choice” as well.

The following text comes from a paper I published in 2004 in a study of a high school that allowed students “choice” about whether to take a traditional or reform math curriculum. I have edited it for this post.

The traditional US high school curriculum has famously been compared to the stores of a shopping mall, with a broad array of educational choices that provide something for everyone. In making choices, students are asserting a sense of themselves, the kind of socially-rooted self-understandings and social positions that constitute identities. Indeed, by the time students are in high school, because these understandings and positions may have been reinforced by an array of social and interpersonal forces, personal choice may be less of a choice than it seems: by labeling it as such, choice systems effectively erase the social categories that have been associated with different kinds of school curricula.

In the case of mathematics, different courses are often associated with different types of students. Teachers’ talk about courses reveals their notions of students and mathematical ability, and these ideas get built into the organization of the curriculum. For instance, when teachers are mandated to eliminate remedial courses but feel the need to accommodate “slow” or “lazy” students, they may effectively workaround the mandate and create separate tracks for these students. Students, likewise, may occupy the curricular space of a school in ways that are similar to the ways they occupy physical spaces: they gravitate to places of comfort, where their social identities find company among cohorts of similar peers.

It is not surprising then that one of the most robust findings in studies of relationships between curricular organization and student achievement is that a rigorous common curriculum ––– which minimizes such choices on the part of students –– distributes achievement more equitably (Lee, Bryk, & Smith, 1994). A narrow academic curriculum coupled with a strong organizational push for students to enroll in challenging courses leads to more equitable learning in mathematics (Lee, Smith & Croninger, 1997), with students from groups historically disenfranchised from schooling being especially advantaged by such structures (Lee, Bryk, & Smith, 1993). This research signals the kinds of curricular organization that correlates to higher achievement, giving us a broad look at what seems to matter.

When students make “choices” about courses, this narrative represent a false sense of agency and autonomy. More accurately, choices reflect their assertions (or assignments by parents, counselors, or others who advise in these decisions) of identity: an “honors” student, a “pre-algebra” student. Choice, as a force that propels students through the curriculum,  is problematic: the supposed self-determination of course-selection is actually a mechanism for perpetuation of the status quo. By narrowing the array of courses, the social meaning of courses must correspondingly broaden. Rigorous academic courses are no longer the province of some students to the exclusion of others; they must expand to become habitable places for all students.

The same can be said for taking the logic of choice to a district level, only worse. Not only will “choice” provide a false narrative of agency and autonomy, these systems will thrive on families with insider information. I see it in my own children’s education, where parents wonder at each transition from elementary to middle school to high school, how to navigate the system. Choice systems privilege parents with resources, such as access to  insider knowledge and flexibility to drive children around town.

Good public schools matter. Providing all children access to a high quality education matters. When I hear choice, I hear opportunity hoarding and re-segregation.

I cannot stand by silently while we gut our best tools for democracy.


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.

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.

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?

Policy and Math Education: A Conference


This past week, I attended a conference at UC Berkeley about policy and math ed organized by Geoff Saxe, Na’ilah Nasir, and their amazing graduate students. The gathering had two main purposes:  to get a group of math ed researchers together to talk about issues related to the Common Core, and to mentor junior researchers in their work. I think the conference met the second goal very strongly and the first one more loosely.

Let me give a brief overview of the main events.

  • Alan Schoenfeld gave a keynote about his work on TRU Math and the Formative Assessment Lessons. He shared his work, some initial findings, and areas of research opened up by these tools.
  • Marty Simon, Jenny Langer-Osuna, and Elham Kazemi led breakout discussion sessions on learning trajectories, equity, and professional development respectively. (Elham is also on Twitter and worth a follow.)
  • Doctoral and postdoctoral students poster sessions
  • A symposium on improving mathematics teaching and learning. Danny Martin talked about researching issues of race in mathematics education. Paul Cobb shared the district partnership work from the MIST project, pointing to gaps in what we study and what school leaders need. Then I talked about how policy operates as a context for teacher learning, sharing some of my findings about math teachers’ encounters with NCLB.
  • A closing session with commentary on the research shared. Carol Lee talked about different challenges in implementing the Common Core in English Language Arts, as well as what it means to teach in ways that consider children’s cognitive, social, emotional, and physiological development. Rogers Hall provided a synthesis of much of the research, talking about the importance of “mutterings” about research (complaints and dissatisfaction) and what it takes to turn mutterings to utterings so that different voices are heard and valued. Anna Sfard challenged researchers to increase their conceptual accountability in their work by making their language clearer and their communications more accessible.

Of course, this summary does not do justice to the richness of the conversations or the key insights gleaned. (Raymond Johnson storified some of the tweets from the conference if you want to check them out.) Of course, the in-between social time was enriching as well. I had some great conversations with Kris Gutiérrez, Tesha Sengupta Irving, Niral Shah, and Nicole Louie.

The question and answer sessions after the main events had a collegial but challenging tone. The conversations gave us a chance to ask our most pressing questions to people who are great to think with.

I, for one, am left with tremendous humility about the complexity of the research and educational enterprise. The doctoral students and postdocs seemed to really appreciate the experience as well. It seems like these small, focused forums have a value we can’t always get at bigger conferences whose aim is to present finished work instead of share in difficult puzzles.

Making Sense of Student Performance Data

Kim Marshall draws on his 44 years’ experience as a teacher, principal, central office administrator and writer to compile the Marshall Memo, a weekly summary of 64 publications that have articles of interest to busy educators. He shared one of my recent articles, co-authored with doctoral students Britnie Kane and Jonee Wilson, in his latest memo and gave me permission to post her succinct and useful summary.

In this American Educational Research Journal article, Ilana Seidel Horn, Britnie Delinger Kane, and Jonee Wilson (Vanderbilt University) report on their study of how seventh-grade math teams in two urban schools worked with their students’ interim assessment data. The teachers’ district, under pressure to improve test scores, paid teams of teachers and instructional coaches to write interim assessments. These tests, given every six weeks, were designed to measure student achievement and hold teachers accountable. The district also provided time for teacher teams to use the data to inform their instruction. Horn, Kane, and Wilson observed and videotaped seventh-grade data meetings in the two schools, visited classrooms, looked at a range of artifacts, and interviewed and surveyed teachers and district officials. They were struck by how different the team dynamics were in the two schools, which they called Creekside Middle School and Park Falls Middle School. Here’s some of what they found:

  • Creekside’s seventh-grade team operated under what the authors call an instructional management logic, focused primarily on improving the test scores of “bubble” students. The principal, who had been in the building for a number of years, was intensely involved at every level, attending team meetings and pushing hard for improvement on AYP proficiency targets. The school had a full-time data manager who produced displays of interim assessment and state test results. These were displayed (with students’ names) in classrooms and elsewhere around the school. The principal also organized Saturday Math Camps for students who needed improvement. He visited classrooms frequently and had the school’s full-time math coach work with teachers whose students needed improvement. Interestingly, the math coach had a more sophisticated knowledge of math instruction than the principal, but the principal dominated team meetings.

In one data meeting, the principal asked teachers to look at interim assessment data to predict how their African-American students (the school’s biggest subgroup in need of AYP improvement) would do on the upcoming state test. The main focus was on these “bubble” students. “I have 18% passing, 27% bubble, 55% growth,” reported one teacher. The team was urged to motivate the targeted students, especially quiet, borderline kids, to personalize instruction, get marginal students to tutorials, and send them to Math Camp. The meeting spent almost no time looking at item results to diagnose ways in which teaching was effective or ineffective. The outcome: providing attention and resources to identified students. A critique: the team didn’t have at its fingertips the kind of item-by-item analysis of student responses necessary to have a discussion about improving math instruction, and the principal’s priority of improving the scores of the “bubble” students prevented a broader discussion of improving teaching for all seventh graders. “The prospective work of engaging students,” conclude Horn, Kane, and Wilson, “predominantly addressed the problem of improving test scores without substantially re-thinking the work of teaching, thus providing teachers with learning opportunities about redirecting their attention – and very little about the instructional nature of that attention… The summative data scores simply represented whether students had passed: they did not point to troublesome topics… By excluding critical issues of mathematics learning, the majority of the conversation avoided some of the potentially richest sources of supporting African-American bubble kids – and all students… Finally, there was little attention to the underlying reasons that African-American students might be lagging in achievement scores or what it might mean for the mostly white teachers to build motivating rapport, marking this as a colorblind conversation.”

  • The Park Falls seventh-grade team, working in the same district with the same interim assessments and the same pressure to raise test scores, used what the authors call an instructional improvement logic. The school had a brand-new principal, who was rarely in classrooms and team meetings, and an unhelpful math coach who had conflicts with the principal. This meant that teachers were largely on their own when it came to interpreting the interim assessments. In one data meeting, teachers took a diagnostic approach to the test data, using a number of steps that were strikingly different from those at Creekside:
  • Teachers reviewed a spreadsheet of results from the latest interim assessment and identified items that many students missed.
  • One teacher took the test himself to understand what the test was asking of students mathematically.
  • In the meeting, teachers had three things in front of them: the actual test, a data display of students’ correct and incorrect responses, and the marked-up test the teacher had taken.
  • Teachers looked at the low-scoring items one at a time, examined students’ wrong answers, and tried to figure out what students might have been thinking and why they went for certain distractors.
  • The team moved briskly through 18 test items, discussing possible reasons students

missed each one – confusing notation, skipping lengthy questions, mixing up similar-sounding words, etc.

  • Teachers were quite critical of the quality of several test items – rightly so, say Horn, Kane, and Wilson – but this may have distracted them from the practical task of figuring out how to improve their students’ test-taking skills.

The outcome of the meeting: re-teaching topics with attention to sources of confusion. A critique: the team didn’t slow down and spend quality time on a few test items, followed by a more thoughtful discussion about successful and unsuccessful teaching approaches. “The tacit assumption,” conclude Horn, Kane, and Wilson, “seemed to be that understanding student thinking would support more-effective instruction… The Park Falls teachers’ conversation centered squarely on student thinking, with their analysis of frequently missed items and interpretations of student errors. This activity mobilized teachers to modify their instruction in response to identified confusion… Unlike the conversation at Creekside, then, this discussion uncovered many details of students’ mathematical thinking, from their limited grasp of certain topics to miscues resulting from the test’s format to misalignments with instruction.” However, the Park Falls teachers ran out of time and didn’t focus on next instruction steps. After a discussion about students’ confusion about the word “dimension,” for example, one teacher said, “Maybe we should hit that word.” [Creekside and Park Falls meetings each had their strong points, and an ideal team data-analysis process would combine elements from both: the principal providing overall leadership and direction but deferring to expert guidance from a math coach; facilitation to focus the team on a more-thorough analysis of a few items; and follow-up classroom observations and ongoing discussions of effective and less-effective instructional practices. In addition, it would be helpful to have higher-quality interim assessments and longer meetings to allow for fuller discussion. K.M.] “Making Sense of Student Performance Data: Data Use Logics and Mathematics Teachers’ Learning Opportunities” by Ilana Seidel Horn, Britnie Delinger Kane, and Jonee Wilson in American Educational Research Journal, April 2015 (Vol. 52, #2, p. 208-242

Responding to Federal Oversight of Teacher Preparation Programs

Today is the last day to register reactions to the proposed federal policy on teacher preparation programs. The regulations would evaluate teacher preparation programs based on graduates’ value-added scores. If you want to register your opinions, please do so here. This is what I wrote.

I am writing to state my reasons against this proposed policy. It oversimplifies the work of teaching and punishes teachers who want to work in underresourced communities.

One definition of teaching is that it is “the deliberate cultivation of learning in others in distinctive teaching situations.” In other words, teaching involves recruiting other people in a teacher’s goals for *their* development — and with a unbelievably inequitable set of resources for doing so. Variations in class sizes, material resources, and bureaucratic burdens are all beyond the control of individual teachers yet are highly consequential to what is possible in the classroom.

To place the effectiveness of teaching solely within teachers themselves — without truly equitable funding for schools, without universal healthcare, without adequate supports like childcare for families living in poverty — places teachers in the center of blame for learning or not learning when there are many aspects of the teaching situation that are beyond their control.

We have already seen the unintended consequences of mass annual testing of students in the devaluation of untested subjects, the educational triage of re-teaching students on the cusp of proficiency, and other types of number gaming. I predict an unintended consequence of this proposed policy would be to discourage teachers from working in schools and communities who are already disenfranchised and underresourced. It is much easier to move students to “proficiency” cut points when Mom and Dad can afford supplemental tutoring. We already have a teacher maldistribution problem in this country, where the most qualified teachers work disproportionately with the best-resourced students. This policy only stands to exacerbate this problem.

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?

Old people ride bikes. DSC06211 DSC06224

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?

Common Sense About the Common Core

This is a guest post by Alan Schoenfeld, a professor of Mathematics Education at the University of California, Berkeley. Alan has been instrumental in many of the developments in mathematics education over the last few decades. Full disclosure: he was also my dissertation advisor and continues to be a mentor and friend. Faithful readers of this blog will know I have expressed my own views on the Common Core here and here.

Is the Common Core the best thing since sliced bread, or the work of the devil? Is it brand new, or a rehash of old ideas? Is it anything more than a brand name, or is there substance? Can it work, given the implementation challenges in our political and school systems? Opinions about the Common Core are everywhere, but the op-eds I’ve seen are often short on facts, and equally short on common sense. A mathematician by training, I’ve worked for nearly 40 years as an education researcher, curriculum materials developer, test developer, standards writer, and teacher.

What follows is a Q&A based on that experience. I focus on the Common Core State Standards for Mathematics, known as CCSSM, but the issues apply to all standards (descriptions of what students should know and be able to do).

What’s the CCSSM about?

Take a look for yourself – the Common Core documents are available here. If you read the first 8 pages of CCSSM and then sample the rest, you’ll get a good sense of what’s intended. In brief, CCSSM focuses on two deeply intertwined aspects of mathematics: the content people need to know, and the knowhow that makes for its successful use, called mathematical practices. You can think of the content as a set of tools – the things you do mathematics with. The practices emphasize problem solving, reasoning mathematically, and applying mathematical knowledge to solve real world problems. Without the practices, the tools in the content part of the CCSSM don’t do much for you. It’s like being taught to use a saw, hammer, screwdriver, lathe, and other woodworking tools without having any sense of what it means to make furniture.

At heart, the CCSSM are about thinking mathematically. Here are two visions of a third grade class, both taken from real classrooms. In one, students are practicing addition and subtraction, getting help where needed to make sure they get the right answers. In another, the students have noticed that every time they add two odd numbers, the sum is even. A student asks, “Will it always be true?” Another says “but the odd numbers go on forever, we can’t test them all.” Pretty smart for a third grader! But later, a student notices that every odd number is made up of a bunch of pairs, with one left over. When you put two odd numbers together, you have all the pairs you had before, and the two left-overs make another pair – so the sum is even. And this will always be the case, no matter which odd numbers you start with. Now that’s mathematical thinking – and it’s what the core should be about. Of course, kids should do their sums correctly, and, they should be able to think with the mathematics.

It’s important to understand what the Common Core is not. Most importantly, the Common Core is not a curriculum. CCSSM provides an outline of the mathematics that students should learn – an outline endorsed by 43 states. Equally important, the common core does not prescribe a particular teaching style: effective teachers can have very different styles. To date – and despite what you read or hear – the desired reality of the Common Core has not made its way into even a small minority of American classrooms. What happens in classrooms will depend on the curricula that are developed and adopted, on the high stakes tests that shape instruction (for better or worse), on the capacity of teachers to create classrooms that really teach “to the Core,” and on the coherence or incoherence of the whole effort.

What do powerful classrooms look like?

CCSSM describes what kids should be able to do mathematically, including problem solving, producing and critiquing mathematical arguments, and more. Students won’t get good at these things unless they have an opportunity to practice them in the classroom, and get feedback on how they’re doing. (Imagine a sports coach who lectured the team on how to play, and then told the team to practice a lot before the big match. You wouldn’t bet on that coach’s success.) So, classrooms that produce students who are powerful mathematical thinkers must provide meaningful opportunities for students to do mathematics. Just as there are many successful (and different) coaches and coaching styles, there are many ways to run a successful classroom. At the same time, there’s consistent evidence that classrooms that produce powerful mathematical thinkers have these five properties:[i]

  • High quality content and practices. Students have the opportunity to grapple with powerful ideas in meaningful ways, developing and refining skills, understandings, perseverance and other productive “habits of mind” as they do.
  • Meaningful, carefully structured challenge. Solving complex problems takes perseverance; students should neither be spoon-fed nor lost. In powerful classrooms students are supported in “productive struggle,” which helps them build their mathematical muscles.
  • Equitable opportunity. We’ve all seen the classroom where the teacher moves things along by calling on the few kids who “get it,” leaving the rest in the dust. It shouldn’t be that way. In the kind of classroom that lives up to the standards, all students are productively engaged in the mathematics.
  • Students as sense makers. In powerful classrooms students have the opportunity to “talk math,” to exchange ideas, to work collaboratively, and build on each other’s ideas (just as in productive workplaces). In contrast to classrooms where students come to learn that they’re not “math people,” students in these classes come to see themselves as mathematical sense makers.
  • A focus on building and refining student thinking. In powerful classrooms the teachers know the mathematical terrain and how students come to understand that content so well that they can anticipate common difficulties, look for them, and challenge the students in ways that help them make progress, without simply spoon-feeding them.

We call this kind of powerful teaching “Teaching for Robust Understanding”. Our goal should be to provide such learning experiences for all students. It’s very hard to do this well – which is why the issue of supporting teachers’ professional growth is crucially important. There are no quick fixes. We should be thinking in terms of consistent, gradual improvement.

What’s new in the CCSSM?

The ideas behind CCSSM are not new. We’ve known for some time that students need a well rounded diet of skills, conceptual understanding, and problem solving – rich mathematics content and the opportunities to develop strong mathematical practices.[ii] The “standards movement” began in 1989, when the National Council of Teachers of Mathematics issued its Curriculum and Evaluation Standards. NCTM’s (2000) Principles and Standards for School Mathematics represented an updating of the 1989 standards, based on what had been learned, and the fact that technology had changed so much over the 1990s. CCSSM can be seen as the next step in a progression.

So what’s different? First, the organization is new. CCSSM offers grade-by-grade standards for grades K through 8, rather than the “grade band” standards of its predecessors. It represents a particular set of “trajectories” through subject matter, being very specific about what content should be addressed. Second and critically important, the Common Core has been adopted by the vast majority of states. Prior to the Common Core, each of the 50 states had its own standards and tests. Some of these were world class, with a focus on thinking mathematically; some were focused on low-level skills and rote memorization. Some states compared favorably with the best countries in the world, and some scored near the bottom of the international heap. Mathematics education across the US was totally incoherent; where you lived determined whether you got a decent education or not. That’s no way to prepare students across the US for college and careers, or the nation’s work force for the challenges of the decades to come. And it’s inequitable when your zip code determines whether or not you have access to a good education. IF CCSSM are implemented with fidelity in the states that adopted them, we’ll have something like nationwide consistency and opportunity instead of the crazy quilt patchwork that we’ve had.

What’s wrong with CCSSM?

I can find lots of things to complain about – everyone can. Can you think of a class you took that was so perfect that you wouldn’t change a thing? With under 100 pages to outline all of school mathematics, the authors made a series of choices. Those choices can be defended, but so could other choices. However, if schools and classrooms across the US make strides toward implementing the vision of the Common Core described above, we’d make real progress.

What IS wrong is our political system, and the fact that teachers and schools are not being provided adequate preparation and resources to implement the Common Core. This lack of support can destroy the vision, because real change is needed. Teaching the same old way, called “demonstrate and practice,” just doesn’t cut it. (How much of the math that you memorized in school do you remember, and actually use as part of your tool kit?) The math we want kids to get their heads around is deeper and richer. Kids need to work hard to make sense of it; and in order to provide powerful learning environments teachers need to learn how to support students in grappling with much more challenging mathematics. This isn’t a matter of giving teachers a few days of “training” for teaching the Core; it’s a matter of taking teaching seriously, and providing teachers with the kinds of sustained help they need to be able to create classrooms that produce students who are powerful mathematical thinkers. The REAL reason some nations consistently score well on international tests (pick your favorite: Finland, Japan, Singapore…) is that those nations take teaching seriously, providing ongoing support and professional development for teachers. When teachers have a deep understanding of the mathematics, and are supported in building the kinds of rich classroom environments described above, the students who emerge from those classrooms are powerful mathematical thinkers.

What do “Common Core Curricula” look like?

I could say, “Who knows?” It bears repeating that the Common Core is not a curriculum. What might be called Common Core curricula – widely accessible curricula intended to be consistent with the common core – don’t really exist yet, although publishers are rushing to get them out. When those curricula do emerge, we’ll have to see how faithful they are to the vision of problem solving, reasoning, and sense making described here.

One thing is for sure: the vast majority of materials currently labeled “Common Core” don’t come close to that standard. Here’s a case in point: A student recently brought home a homework assignment with “Common Core Mathematics” prominently stamped at the top of the page. The bottom of the page said, “Copyright 1998.” That’s more than a decade before the CCSSM were written. Remember when supermarkets plastered the word “natural” on everything, because it seemed to promise healthy food? That’s what’s being done today with phony “Common Core” labels. To find out whether something is consistent with the values of the Common Core you have to look at it closely, and ask: are kids being asked to use their brains? Are they learning solid mathematics, engaging in problem solving, asked to reason, using the math to model real world problems? In short, are they learning to become mathematical sense makers? If not, the “Common Core” label is just plain baloney.

Now, there are materials that support real mathematical engagement. For one set of such materials, look at the Mathematics Assessment Project’s “Classroom Challenges,” at <;. But, such materials do not a curriculum make – and again, materials without support are not enough. What really counts is how the mathematics comes alive (or doesn’t) in the classroom.

What about testing?

Do you know the phrase “What you test is what you get”? When the stakes are high, teachers will – for their and their students’ survival! – teach to the test. If the tests require thinking, problem solving and reasoning, then teaching to the test can be a good thing. But if a high stakes test doesn’t reflect the kinds of mathematical thinking you want kids to learn, you’re in for trouble. I worked on the specs for one of the big testing consortia, to some good effect – the exams will produce separate scores for content, reasoning, problem solving and modeling – but I’m not very hopeful at this point. To really test for mathematical sense making, we need to offer extended “essay questions” that provide opportunities for students to grapple with complex mathematical situations, demonstrating what they know in the process. Unfortunately, it appears that test makers’ desire for cheap, easy-to-grade, and legally bullet-proof tests may undermine the best of intentions. It takes time to grade essay questions, and time is money. The two main tests being developed to align with the CCSSM[iii] barely scratch the surface of what we can do. That’s an issue of political will (read: it costs money and will shake people up), and the people footing the bill for the tests don’t seem to have it.

The best use of testing is to reveal what individual students know, to help them learn more. That is, the most important consumers of high quality tests should be teachers and students, who can learn from them. It IS possible to build tests that are tied to standards and provide such information; there are plenty of examples at all grade levels. In addition, scores from such tests can be used to tell schools, districts, and states where they’re doing well and where they need to get better. It’s a misuse of testing when test scores are used primarily to penalize “under-performing” students and schools, rather than to help them to improve. (Moreover, high stakes testing leads to cheating. How many testing scandals do we need to make the point?) Finally, it’s just plain immoral to penalize students when they fail to meet standards they were never prepared for. Holding students accountable for test scores without providing meaningful opportunities to learn is abusive.

What’s needed to fix things?

There’s no shortage of “solutions.” To mention one suggestion that’s been bandied about, why not just adopt the curricular materials from high-performing countries? That would be nice, if it would work – but it won’t. If conditions were the same in different countries – that is, if teachers here were provided the same levels of preparation, support, and ongoing opportunities for learning as in high-performing countries, then this approach could make sense. But the US is not Singapore (or Finland, or Japan), and what works in those countries won’t work in the US, until teachers in the US are supported in the ways teachers in those countries are. Singaporean teachers are deeply versed in their curricula and have been prepared to get the most out of the problems in their texts. Japanese teachers are expected to take a decade to evolve into full-fledged professionals, and their work week contains regularly scheduled opportunities for continuous on-the-job training with experienced colleagues. Finnish teachers are carefully selected, have extensive preparation, and are given significant amounts of classroom autonomy.

In short, if importing good curricula would solve the problem, the problem would have been solved by now. It’s been tried, and it failed. Of course, good curricular materials make life better – IF they’re in a context where they can be well used. The same is true of any quick fix you can think of, for example the use of technology. Yes, the use of technology can make a big, positive difference – IF it’s used in thoughtful ways, to enhance students’ experience of the discipline. I started using computers for math instruction in 1981. With computers you can gather and analyze real data instead of using the “cooked” data in a textbook; you can play with and analyze graphs, because the computer can produce graphs easily; and so on. But in those cases, the technology is being used to in the service of mathematical reasoning and problem solving. You can get much deeper into the math if you use the technology well, but the presence of technology in the classroom doesn’t guarantee anything. In particular, putting a curriculum on tablets is like putting a book on an e-reader: it may be lighter to carry, but it’s the same words. The serious question is, how can the technology be used to deepen students’ sense making, problem solving, and reasoning?

The best way to make effective use of technology is to make sure that the teachers who use it in their classrooms are well prepared to use it effectively. Fancy technology isn’t going to make much of a difference in a world where half of the new teacher force each year will drop out within the next 5 years (within 3 years in urban school districts) – a world in which there are more teachers in their first year of teaching than at any other level of experience. In professions with a stable professional core, the number of newcomers is a much smaller percentage of the total population: there are more established professionals to mentor the newcomers, and a much smaller drop-out rate. The best educational investment, as the highest performing nations make clear, is in the professionalization of teachers – so that they can make powerful instruction live in the classroom. In nations where teachers are given consistent growth opportunities, the teachers continue to develop over time. And, they stay in the profession.

Living up to the vision of the Common Core requires focus and coherence. Curricula and technology need to be aligned with the vision, and implemented in ways true to the spirit of sense making described here – including equitable access to the mathematics for all students. Administrators need to understand what counts, and support it. Testing needs to focus on providing useful information to teachers and students. Most important, we need to provide steady support for the teaching profession, so that teachers can make that vision live in their classrooms. We owe this to our kids.

[i] The quickest path to documentation is through the web site <>. The front page shows the big ideas; click on the “tools” page to see evidence about, and tools for, productive thinking.

[ii] There’s a massive amount of research behind this statement. For one early summary, see Schoenfeld, A. H. (2002, January/February). Making mathematics work for all children: Issues of standards, testing, and equity. Educational Researcher, 31(1), 13-25.

[iii] See the web sites of the Partnership for Assessment of Readiness for College and Careers, PARCC, at <;, and the Smarter Balanced Assessment Consortium, SBAC, at <;.

The Calm of Experience

This is a story of my own learning as a teacher.

During my student teaching, I particularly struggled with a boy I will call Aidan. He was a gloomy 7th grader, a social isolate with no particular sense of humor who regularly antagonized other students.

One day, when I was patrolling the hallways between classes, Aidan rolled by a row of lockers on his Heely’s, elbowing several girls along the way. Because I did not have much empathy for the child to begin with, this incident angered me, perhaps more than it should have.

I brought him to the Head of School’s office, ready for him to get his just desserts. After I relayed what I had witnessed to Teacher Celia (her real name — she deserves all the praise I am about to give her), she turned to Aidan with a calm look on her face.

“Aidan, is what Teacher Lani* said accurate?”

Aidan looked at his lap and reluctantly nodded.

“Can you see what the problems are with what you just did?”

Aidan was quiet. She waited, watching him intently.

After a pause that was longer than anything my 21 year-old self would have had the patience to endure, he looked up at her sheepishly.

“Well, yeah.”

In the remainder of the interaction, Aidan admitted to his poor judgment in both wearing Heely’s at school and elbowing the girls. He and Teacher Celia agreed to the consequences.

I no longer recall what they worked out, since I was so dazzled by her calm, accepting presence. I remember that it seemed measured and fair, giving Aidan an opportunity to repair his relationship with his peers and learn from his mistake.

Why am I writing about this now?

I have two reasons.

First, we are in an era that thinks that just because you learn so much about teaching on the job, there are those who would simply put new teachers in the classroom without much student teaching or mentoring.

Watching Teacher Celia with Aidan helped me see that I needed to move past identifying with the elbowed girls and reacting to Aidan as an annoying boy. I needed to figure out how to be his teacher too. Teacher Celia’s poise and humanity in dealing with him became my go-to image when I dealt with a child who I struggled with. I did not spend a lot of time with administrators in my own career as a student, so seeing the right way to handle misbehavior was critical to my own development.

Second, I am concerned that we are normalizing teacher turnover so that the calm presence of experience has become a rarity in many schools. Estimates of teacher turnover in the first five years range from 30% to 50%, with the rates being even higher among TFA teachers (about 80% leave after 3 years). The burdens of turnover are high, impacting everything from achievement to the cost of staffing and retraining.

I think there is another cost to turnover that involves the social well-being of children. When I see the disciplinary statistics in schools, I wonder if the calm wisdom of experience exists on the most afflicted campuses. Aidan was lucky that Teacher Celia was the go-to for the consequences of his misbehavior and that his discipline was not left to me. She was measured, whereas I surely would have been more reactive. Likewise, in the second school I taught at, we had an administrator with the same matter-of-fact calm when dealing with behavior issues; I was always grateful when children in my class had last names that fell in the first third of the alphabet so we could sort things through with her. I could trust her to preserve the student’s and my own humanity and help us arrive at a reasonable solution.

I am not trying to romanticize experience or say that all veteran teachers share this wisdom. However, I do think it is easier to muster a calm perspective when dealing with students from the vantage point of experience. This calm is certainly a rarity in barely-mentored newbies. I believe that the first year of teaching is often so difficult, in part, due to the steep learning curve and constant novelty of high stakes situations. As experience accrues, these situations become more manageable and teachers’ reactivity diminishes. But if we continuously staff our schools with minimally mentored novices, we take away an important resource from children and their development.


* This student teaching placement was in a Quaker school, where teachers are called “Teacher [First Name]”, showing respect and familiarity.