Dear New York Times, Do better.

There must be something deeply attractive about the idea that children’s math success can simply be forced upon them. On Aug 7, yet one more opinion piece promoting drill and memorization in children’s math education was published in the New York Times. By the morning of Aug 8th is was trending in the #1 spot. In “Make Your Daughter Practice Math, She’ll Thank You Later,” Barbara Oakley argues for the importance of math in the lives of children. Unfortunately, she does so in a way that is fundamentally misinformed about both the landscape of K-12 mathematics education in the United States and the research-based consensus on learning theory and cognitive development. Also unfortunately, when an opinion piece is written by a professor, even though it is an opinion piece, the assumption is that it is based in research. People take it as truth. The stakes of this misconception are extremely high when talking about the education and futures of of our children.

Dr. Oakley makes two points that are valid:

  1. Having a solid foundation in math can be fundamental to a child’s future, especially in the world of STEM. Mathematics is powerful as both gatekeeper and gateway when it comes to higher education, and employment. [I would add also, democratic participation in civil society as well as many creative endeavors.]
  2. Research shows that all children, regardless of gender (or race, ethnicity, or class, or anything else) have essentially equivalent innate potential in mathematics such that outcomes are shaped by societal inputs and expectations, not by any biological or innate differences between groups.

She makes a third point that is also correct, but not in the way she intended it. She says that the way we teach math in the United States is harmful to all students and especially girls. It is true that traditional ways of teaching mathematics have been shown to be harmful for all students, and even more harmful for non-dominant populations, including girls. This phenomenon has been widely documented by professors of mathematics education such as Rochelle Gutierrez, Jo Boaler, and others. However, Oakley’s characterization of “the way we teach math in the America” is backwards. Whereas she says we have foregone drill and practice for conceptual understanding, our problem in the United States is understood by learning scientists to be precisely the opposite. The United States is behind other countries on international measures of mathematics performance (including PISA and others) because of an overemphasis on procedural, drill-based approaches to math at the expense of conceptual understanding. It is conceptual understanding that is the basis for complex problem-solving, a critical component of 21st Century STEM literacy. Yes, mathematics educators and education policy-makers have been working to shift the way we teach math in the United States toward practices that emphasize conceptual understanding in tandem with procedural fluency. Unfortunately, as a country, the United States K-12 education system is still a far stretch from a system that “downplays practice in favor of emphasizing conceptual understanding.”

Yes, children should have opportunities to mathematize the world around them through conversations with teachers, parents, other adults, and each other on a consistent basis. But these conversations should be based in creative and flexible work with numbers that will build number sense, pattern recognition and fluency in composing and decomposing numbers. This is distinctly not achieved through drill or rote memorization. Number theory is not introduced through recitation of the multiplication tables. Furthermore, research shows that it is precisely these drill-type tasks that teach children that math is a dull, meaningless activity, and turn many away from math at an early age, including and especially girls.

Finally, the attitude that “foundational patterns must be ingrained before you can begin to be creative” is the root of inequitable mathematics education throughout the United States. The belief that children cannot engage in meaningful and creative problem-solving tasks until they have learned how to be compliant calculators leads to education that is training for menial labor, labor that was long ago replaced by calculator technology. “More drilling,” teaching your daughter that “all learning isn’t – and shouldn’t be – fun,” and that, as a girl, there are certain things she should simply suffer through “even if she finds it painful,” will not set her up for success. Anyone who teaches children that they need to silently comply through painful experiences before they will be allowed to let their brilliance shine has no intention of ever allowing that brilliance to shine, and will not be able to see it when it does.

EDIT: A number of people have been wondering about the “research-based consensus” that I refer to above. I am in particular referencing the extensive bodies of research that came out of the research program of Cognitively Guided Instruction as well as the research produced through the QUASAR Classrooms project. I have linked each to a relevant “sample chapter” or Google Book since many of the academic articles are behind paywalls. For people who have access to academic journals, either search term should produce dozens of relevant peer reviewed articles.

*Thank you to everyone who has commented, including the comments that I have not posted. I am closing comments at this point (8.30.18).

’cause silence is violence (and other Ani Difranco lyrics)

The lyrics of my white, problematically lock-headed, high school musical hero echo in my head as I try to grapple with the events of the past two days. An American police officer kills a black man. And then an American police officer kills a black man.

Philando Castile

Alton Sterling

Say their names, because they were human beings, with names, with families, with lives, and with every possible right to life.

I want to pretend that the violence of the past two days is a violence that I don’t know how to handle because I have never known it before, but I have. We have. We have been living in this world my whole life, and my parent’s whole lives, and the whole lives of those before them. America treats black bodies as though they are on the one hand threatening and on the other utterly disposable. It is oxymoronic and yet it is the American way. We would not be the America that Trump supporters believe is worth returning to its original greatness if it were not for this great history of destruction and dismemberment of black and brown bodies since the beginning.

Ani Difranco spoke to me then because she was angry and powerful and in your face, and she speaks to me now as I scroll past the posts of white acquaintances who are “shocked” at one more American disavowal of the black body’s right to exist. Because she knew way back when (in the ’90s) that this violence and injustice was not new then, and it is not now.

If you’re not angry
you’re just stupid
or you don’t care
how else can you react
when you know
something’s so unfair (Out of Range, Ani Difranco, 1994)

Who are these ignorant police officers? my FB feed asks in consternation. Why do we let these bad apples undermine the pastoral peace of our American Dream? Sorry (not sorry), but there was never an American Dream that did not fundamentally depend upon the systematic, ongoing and normalized annihilation of the Black body’s right to exist as anything other than a tool of American capitalism, American nationalism and White supremacy.

I’m learning to laugh as hard
as I can listen
’cause silence
is violence
in women and poor people
if more people were screaming then I could relax (My I.Q., 1993)

I know that I am not screaming loud enough. It is hard to scream when tears choke my throat and rage makes me numb. But I know that I must use my voice, my very white voice and make some fucking noise this time. Music seems to help me get to the places that allows me to feel again. Ani for one, but also Tracy Chapman, Michael Franti, and more recently Beyoncé. I’m sure you have your own musical salve. I hope you use it. I hope you blast it as loud as you need to while you muster your own courage to start screaming with your own voice. I’m working on it.

Black friends, other friends of color, queer friends, female friends, friends and non-friends who are threatened by the white, heteronormative oppression that is so quintessentially American, but especially to my black friends: I want to be able to give you my body. I want to offer it to each and every one of you as accompaniment, as witness, to flop my arms around you like a human shield as long as you need it (and of course only if you want it). A hug-shield. As though my love could conquer the world, or at least some small piece of it. There are places in the world where the Peace Brigades International sends people to provide accompaniment. The idea is that the presence of observers will make local actors less willing to openly use violence against each other. This American war zone in which we live might benefit from a similar intervention. But in the big picture it’s just a band aid, a mitigating action. Not a solution.

I think about my legacy, being a child of civil rights activists who faced guns pointed at them as they registered black voters in Alabama, picked cotton side by side with share croppers in Mississippi or sat with Black colleagues at a lunch counter in Baltimore, and I ask myself, what about me? What will I do? What will our generation do? #BLM makes me excited. The movement is powerful. I cite Chicago as evidence. But as I held the hand of a Black friend today and cried, she reminded me that the movement will only make lasting change if white people show up. White people have to show up in voice and in body, to assert that yes, black lives do in fact matter to “us” as well, not just to black people.

Change happens through many avenues. My parents were friends with some of the Weathermen, but they did not choose that path. These days I struggle to condemn those that did. If you believe I have not yet figured out how to show up, I am working on it, but that does not mean I am asking you to be patient. There is no time for patience. And there is no time for silence. For today I am trusting in the music help me find my way. I thank the musicians and artists that reach with their art the places that I struggle to touch in any other way.

art is why I get up in the morning
but my definition ends there
and it doesn’t seem fair
that I’m living for something I can’t even define (Out of Habit, 1990)


Oh, the places they’ll go

I wish I had taken photos of the top of each graduation cap that I saw on Monday. I can remember a few (and peruse student photos on FB for a few more).

First Generation Latina”

“Well behaved women seldom make history”

“Proud of my B.S.”

“Unless someone like you cares a whole awful lot, nothing is going to get better. It’s not.”


“Goal Digger”

“B.A.B.” (Bad Ass Bitch)

My former students are the quintessential critically conscious, self-aware, proud and bold young people that I dream of when I think about why I teach and who I hope to support young people in becoming. Pride is the wrong word for my own feelings because I think it implies taking some responsibility, and as much as I was present for their high school education, I know that it was them, their families and the community that they created among themselves that got them where they are today.

I don’t know what percentage of the 2016 graduating class from the selective public school where I used to teach in Brooklyn was first-gen college going (I’m guessing more than 50%, maybe close to 75%?), but I do know that 100% of the students got into colleges and many if not the vast majority of them plan to go and are excited about it. It’s not the realization of the college dream that filled me up at graduation but the love and joy that surrounded the students, their families, and their relationships with each other as well as with their teachers and yes, even administrators. Somewhere we did something right enough that they know how special they are, they know they are valued and they value themselves.

One of my biggest fears about being in graduate school is losing the motivation to be here  as I lose my close ties with young people. These kids that graduated Monday are my primary inspiration – so much of what I do is for them and because of them. I will never learn more from my peers and colleagues than I have learned from being close with this particular group of young people, especially my own advisory  who I spent three years with before jumping ship their Senior year. They have each pushed themselves and grown in ways that they never would have expected or articulated way back in 9th grade. Even last year as we began to work on college essays I watched each of them doubt that they had something valuable to say, a worthwhile story to tell. And yet they wrote, and they put their faith in me and all of their other teachers and college counselors and pushed themselves to do the work, submitting one application after the next, sitting for the SAT or the ACT up to three times in order to achieve something that was (and still is) totally unfamiliar – college.

College will be a whole new adventure but I am so impressed with their personal resources already. I spoke with one of my former students, a first-gen Latina woman with a fabulous ‘fro who is going to an elite private, predominantly white college about finding support systems when she gets there. She explained her plans to get there early for the students of color orientation, and to reach out to student groups on campus. She will be more than fine. But I do at times fret, and at other times rage, about what it means for a private, predominantly white college to offer admission without being able to offer acceptance, support, inclusion and validation. The children are ready to take over the world. But we have have some work to do if the world is going to embrace their brilliance. IMG_1496


Ethics of Teaching Mathematics in the #BlackLivesMatter Era

In my final year as a high school mathematics and special education teacher in Brooklyn I turned down a student’s request to forgo 45 minutes of Geometry instruction for a discussion of the previous night’s announcement of non-indictment of the police officer responsible for Michael Brown’s death (11.24.2014, Ferguson, MO). Yes – I had my reasons for rejecting his plea, reasons that other teachers tell me are entirely justified – but I am still not sure. Most immediately, it was 7:58am and I was not prepared to improvise the facilitation of a painful conversation, especially at the risk of doing so poorly. I was prepared to teach Geometry that morning, not to address questions of police violence and racial justice. Yet, this is exactly what haunts me. Not just that I was not prepared on that morning, but my classroom was not designed to be a place where I did not have to sacrifice one for the other – mathematics for meaningful events in the lives of my students – where the two were inherently intertwined. Because we live in a world where I believe they not only should be but they are. But my classroom did not always make that clear.

While I could not articulate it at the time, I often think now that my move from teaching to pursuing a PhD in Mathematics Education and Race, Inequality and Language in Education was driven in part by my increasing failure to juggle the predicament in which I found myself that morning. I did not become a teacher in order to help students achieve passing scores on the New York State Geometry Regents Exam (even while I understand that it can be an a necessary stepping stone to traditional measures of success and access). I became a teacher so that I could participate in the journeys of young people becoming critically conscious citizens prepared with the tools of change necessary for creating a world more just, inclusive, loving and equitable than the one they were brought into. As I became a more experienced teacher I found myself moving farther away from that, rather than getting better at the weaving it together with the demands of the NYS Geometry curriculum.

Over my years teaching I taught almost every content offered in a New York City public high school – that is the nature of being a Special Educator in a city where integrated co-teaching is the norm. I always taught a little bit of everything, and a lot a bit of math. As I looked around I saw Social Studies and Literature teachers finding ways to engage the social and political project of teaching. I worked closely with one colleague teaching a 10th grade Global History and Literature course, who, like me, had training through Facing History and Ourselves, and I was filled up by that collaboration. But not only is a similarly socially and politically engaged classroom challenging to create in the context of our current mathematics education landscape, it seems the aspiration itself is in many places utterly absent. When I tell people that my graduate research looks at issues of race, inequality and language in mathematics education I often get blank stares – what could such a clearly rule-driven, neat and tidy field like mathematics possibly have to do with race or language, or social (in)justice? People scratch their heads, while I think, how could it not?

My questions for academic research will be different from those I hope to use this blog space to pursue, in large part because I believe that many questions worth asking are not answerable through careful academic research. Sometimes the asking is more important than a clear, concise or comprehensive answer. Sometimes our search for easy answers is precisely what endangers the power of the questioning itself.

So, what are the intersections between mathematics education and education as a social and political project for racial and economic justice? What does a classroom look like that finds these interstices?  And what is the work of a teacher who is supporting this classroom, especially a teacher who comes from racial or economic privilege that is not shared with her students? What are the ethics of teaching, and teaching mathematics in particular, in the era of #BlackLivesMatter? For myself I know I must start and end and find myself returning every day in between to a certain soul scrutiny. Next time a child approaches me at 7:58am while I juggle my classroom keys, coffee cup, and an armload of photocopies and says, “Can we talk about Ferguson [or Charleston, Orlando, Freddie Gray or Sandra Bland] during class today?” will I be able to respond differently? And if not, what can I do between now and then to prepare myself to be the type of educator that can take up the call from a child to engage with a world that is so often full of pain an injustice, not just so that we can cry or rage together, but so that we can change it?

I want to thank my dear friend, former colleague, and constant inspiration, Wendy, for introducing me to the world of blogs and blogging. I know that there are many math teachers, math teacher educators and math education researchers out there that are doing this hard work of asking how we connect the social and political world to our students in ways that are meaningful and productive, both in and outside of their classrooms. I hope that as well as giving me a space to develop some of my own thoughts, this blogging project also gives me another means to become more familiar with you, your work, and your thoughts.

Here’s to my attempt at an opening post: Cheers!