Summary: This is a very long post about essentially this: Young children are brilliant. Traditional schooling, whether at home or in brick and mortar buildings, socializes a lot of the brilliance out of them, including their intuition around mathematics. At the same time, we know that young children are capable of and should engage in conversations about race and racism. I’ve been thinking about how we bring these two worlds closer together. Quantitative literacy is a powerful tool and can be part and parcel of how we engage children in antiracism. Quantitative literacy can be fostered in young children by inviting them to notice and wonder about the world through mathematical lenses (eg questions of fairness, pattern noticing, relationships between quantities, measurement, etc). Two suggested avenues for this are 1) mathematizing children’s books that both celebrate the lives of Black and Indigenous people, as well as portray the history of racism in the United State, through read-alouds and 2) utilizing those same books as the contexts for mathematics tasks.
Teaching and Learning in Pain
As we reel from the multiple murders of black people at the hands of police, continued state sanctioned violence against indigenous and Latinx immigrant populations incarcerated at the border, and continued silence around the disappearance of indigenous women, we are all likely so tired and so angry that we need to take our breaks. Perhaps you are risking your own life for change, participating in protests where you are likely to experience police violence first hand, gassed, shot at by rubber bullets, maced, arrested, or run over.
My heart hurts, but I am also angry .
A quick stock-taking of my own positionality and privilege is I am an elementary mathematics education-focused professional, who identifies as a lighter-skinned Latina and mother of two white cisgendered boys (they are mixed-heritage, white presenting, so white is how they read to others). My husband is white, his parents are from Canada but he grew up in the US. I am working to acknowledge my own growth as well as continuing to challenge myself to grow. Through this I am asking myself, what can and should we consider as we teach mathematics to younger children so that math can be a tool in the struggle, and not a tool for oppression? In particular, what does it mean to engage the quantitative lenses of our young children in a struggle for a racially just (read, humanized) society? And outside of the classroom setting, how can parents, myself included, raise antiracist children?
There are many websites out there curated specifically for this need, and that in particular are responding with resources for teaching to, through and beyond our #blacklivesmatter moment. For our youngest children, here’s a quick reminder that yes, we can talk about race with toddlers (not just can, should/must/need to). Teaching Tolerance has been at the forefront of developing materials for teachers for a long time, as has Rethinking Schools. In addition, Raising Race-Conscious Children is a site with loads of resources for parents and teachers. Citizen-run databases such as Mapping Police Violence create data and data displays that some middle and high school mathematics teachers in particular may be interested in. Individual teachers develop and share curriculum all the time. Check out the work of Classroom Clapback , high school teacher, from her store at teacherspayteachers*, for tools for young and old adults alike to learn more about Black culture and excellence.
If you are feeling like you just need to get to reading, thinking, buying books, I suggest you head over to Ashay by the Bay, a local-to-me black-owned bookstore, or your own local black-owned books store. Ashay by the Bay is a beautiful bookstore for literature on the multiple stories of Black people, joy and love and just being kids. If you’re ready, head over there. I’m going to continue with my long post about infusing math into read alouds for social justice.
Quantitative Lenses in Literacy as Everyday Practice
One tool that has come out for all of us are curated lists of books for children that help take up these issues and spark conversations. As an example here is a good one from Embrace Race, that was curated by two critical literacy organizations, The Conscious Kid and American Indians in Children’s Literature. Another favorite, the Social Justice Books Project. What I would argue is that in addition to reading these books and having discussions around the characters and content, that we make small shifts in questioning to engage students in practicing using their quantitative lens (which they have, as math people that we all are) to notice, wonder, question, and analyze what the heck is going on in the world, and how they move through it.
What’s a quantitative lens with little kids even mean?
Before the COVID pandemic I had the opportunity to interview Marian Dingle as part of the TODOS podcast. Something that she said struck me as related to what I’m trying to say here. She said that she doesn’t really think of herself necessarily as having become a math person, rather she just thinks this way and always has. What we recognize as mathematical thinking is embedded in her way of moving through the word. Like let’s say she’s planning some social studies lessons, she would maybe find herself calculating how many years since the march on washington, or to notice patterns or lack of patterns in police on citizen violence, or wonder what the graph looks like when we read about shifts in immigration populations. I made up those examples because I can’t remember the exact ones we talked about, but the effect is the same: the quantitative piece isn’t separate from her thinking process and doesn’t always have to be prompted. Rather, the mathematical questioning and analysis is just a part of her thinking, and I think that’s really beautiful. But more than beautiful, it’s an undervalued lens on discussion of race and racism with young people.
However, I am not suggesting that we take the focus on racial justice off the table in the name of making kids more academically prepared to do mathematics. Rather what I’m proposing is re-asserting or re-imagining what racial literacy could be, to include quantitative reasoning alongside all of our other reasoning even with young children, especially in ways that honor the quantitative thinking of young BIPOC children.
What might this look like?
I’m envisioning building on the routines of read -alouds (found across the elementary school curriculum, mostly in language arts) and noticing and wondering (more commonly found in mathematics and science) and using anchor texts in mathematics activities we do with children.
What I’m suggesting is to take these really wonderful lists that people have been developing, of good books to spark conversations about race and racial identity, and infuse questions that engage and sharpen the mathematical lenses kids bring to the world. The next two sections are specifically for teaching drawing on two pedagogical practices, however parents can engage in the same practices at home with children.
Read Aloud Routine
Often when we preview the book with children we ask them what do they notice about the cover, we listen to their ideas of what they think the book will be about. This is our first opportunity to listen to the mathematical noticings, and occasionally encourage them.
A picture walk often comes next. As you move from one page to the next you could ask children to notice what do they see in the pictures including how many of something they see, for example if you’re reading a book about a janitor strike in Los Angeles you might ask the students when you turn to a page about the strike to say well how many people do you think are in this picture… how many people do you think that means we’re at this strike? What’s a reasonable number? what’s the number that sounds too low, how about too high? You don’t need to belabor the point – you know the rhythms that work for your picture walks.
Typically we choose points in a read aloud to pause and ask students either comprehension questions, or for reactions. Questions like, what has happened so far? How do you think José feels at this point? Depending on the book, the questions might be more specific to the situation, “have you ever been to a demonstration with your family? What was it like?” This is another point where you might consider if there is a math-related question you could bring up, or a number or math concept mentioned that you could explore a little further.
For example suppose you are reading the book Child of the Civil Rights Movement with your kindergarten class, a book recommended by https://socialjusticebooks.org/child-of-the-civil-rights-movement/. It might unfold like this. You read the page:
You wonder aloud and discuss questions like “This page says that she heard her parents talking about marching and they had marched twice before. How many times is twice? Which number march are they planning? Why do you think they are planning this 3rd march?”
You keep going with your read aloud, maybe another opportunity comes up. “And look at this, she’s imagining her symphony of voices planning this march. Who’s here? How many people are in this symphony?…”
I didn’t say the questions need to be profound, rather just that we notice and talk about the mathy aspects. And likely these questions are embedded among the other questions you are asking.
Another technique is to introduce some quantities to take the reasoning further: Suppose you are reading the book Sí Se Puede/Yes We Can with your second graders about the janitor’s strike in LA. You just read about how Mama works all night downtown cleaning offices. You could wonder aloud with the students, “You know so if her son goes to bed around 8:00 o’clock and then she goes to work and she’s back there when it’s breakfast time how many hours is she out there cleaning buildings every night?” Some kids might say, if breakfast is at 6, how do we figure it out? You might help them count on our fingers, starting with 1 hr is to 9 o’clock, 2 hours to get to 10, et …. Or you might reference the clock on your wall (it is even analog anymore? Mine is)… You do a little math. You talk about, how do you think José feels knowing his mom has to work 10 hours every night, and still work weekends to pay rent? A child might cut you off and say “but Ms. Maria, she’s not working the whole time, she’s getting there and back too”, and they are right. You continue, “José’s mom is working somewhere around 8 or 9 hours a night, and then has to work more on the weekends. What does it make you wonder about?” etc…
And the math goes on.
The discussion we have with students after we finish reading a book can also have quantitative questions embedded, or the space can be opened up for quantitative exploration. Wanting to know the numbers, the meaning of the numbers, is very likely intuitive for many children. However, I bet that we socialize them into not asking these kinds of questions in relation to read-alouds because we don’t see mathematical sounding questions as part of our literacy goals in the classroom. But we can change that.
Again, I’d like to underscore that the goal is not to undermine a lesson on social and emotional learning or one embedded with ELA goals, rather to keep the door open for some kids and open the door for everyone so that a different kind of thinking is introduced alongside the kinds of analysis that we’re hoping to begin to foster in young children. My hope is that as they get older they have had more practice with the kinds of questions they can ask looking at the world through a lens of quantification. Maybe I’m also hoping that it means that the generations of activists-citizens coming up after us have much more practice in interdisciplinary perspectives on the world.
Developing Math Tasks Situated in the Contexts of Books
Again, not a new teaching idea but one that is perhaps worth adding some additional considerations on to. One of my favorite things to see in math lessons planned for young children is a launch or hook connected to a book they read. I also see how excited children are when we plan math activities related to books because they bring explicit expertise to the math lesson. It can help close the gap of understanding between life and math to draw on the contexts children are familiar with presented through books. So many excellent books are out there now that have explicit connections to various grade level mathematics standards. However, few if any of these books also engage with race and racism, in ways that further necessary conversations with children or celebrate Black and indigenous excellence.
We can draw on the contexts of books we read with children to be antiracist explicitly for mathematics tasks. First a word of caution: it pains me to say that there are a lot of bad examples out there of teachers creatively modifying the context of word problems to make them “relatable” to current events. I won’t reproduce them here, suffice it to say word problems some teachers made to make math “relatable” during Black History Month through contexts of slavery and slave masters caused more harm than good**. However, we shouldn’t throw the whole idea out because of the learning curve. Rather, we should be thoughtful in how we mathematize situations with students.
We can take the same books from my examples above and create lessons that either launch with the reading of the book, or build off of having read the book a prior day. I’m basically following the guidance of Bill Bigelow and what he wrote in his chapter of Rethinking Mathematics, which I’ll paraphrase: word problems all have contexts, so it’s up to us as teachers if the contexts advance an understanding of social justice with and for students we are teaching.
One entry point might be developing mathematics tasks around just one situation from a text. For example, in this part of the book Child of the Civil Rights Movement, Paula is reminiscing about how the organizers of the march from Selma to Montgomery, which included her parents, would gather and break bread at her home. She observes that there is alway more than enough food. Young children could be reminded that there were 8 people over, not including Paula and her sisters. They could be asked to make a picture of the dinner table and include their favorite food. They could be asked to write how much of that food should be on the table to feed all the people there, and why? They are employing quantitative reasoning, and engaging in open-ended mathematics that leaves a lot up to themselves to draw, label, and explain. (See Figure below.) But they are also drawing on their understandings of fairness, sharing food, how to ensure everyone has enough.
Notice, this isn’t a situation that directly engages with race or racism. I think we might ask the question, does it have to be? See my comments about harm above. It doesn’t necessarily get us into issues of social justice yet either, so there’s the drawback. But I’m writing it for a fake audience as an example, and I think the questions as to whom the task would be appropriate for are best answered when you have real children to consider, not the fake classroom I’m making up for this example.
Here is another page in the book that has rich information for children to engage with. What do you notice and wonder? After you do that, go buy the book from your closest Black-owned bookstore!
Summary of Suggestions
- Use noticing and wondering routines. Yes, noticing and wondering is everywhere now. Reading children’s books that help students understand racism and engage them in being antiracist is an excellent time to also notice and wonder about mathematics. You can support students to notice and wonder through a variety of lenses, including quantitative, racial literacy, empathetic, analytic, etc. What it might sound like:
- I notice many different kinds of people in the crowd at this protest. Wow, I wonder how many people are there. I wonder how they all knew to gather here.
- I notice many people are carrying signs. I wonder what they say…. etc
- Note: it might not sound mathy all the time. That’s fine. But the goal is to not forget to also support the mathematical noticing as well as make space for exploring the ideas kids bring up, instead of moving past them because it’s not what we ourselves thought of.
- Ask the quantitative reasoning questions regularly as a part of your read aloud routine, not just for math books, and especially for books about social justice issues, racism, and biographies about people of color. What it might sound like:
- I noticed in the book that they said she had to work overtime just to pay the rent. I find myself wondering about how much she was paid for every hour. How could we figure that out?
- I noticed in the book about Katherine that they said she was on the team to ensure the calculations were right, and I wonder how many problems she solved every day! What is a good estimate?
- Utilize recommended books for children on racial justice to lead-off mathematics lessons. IE, the launch for your math lesson doesn’t have to be mathematics-specific books or the traditional texts we are used to reading (which are also great!). Rather, we can build our mathematics lessons out of the contexts in these books too. Lesson planning in this manner also helps situate the mathematics task that could follow from the book within real-world contexts. What it might look like:
- Open ended tasks, even mathematical modeling tasks, developed around what’s happening the text. For example, drawing on the Child of the Civil Rights, Paula notes that it took 4 days for the march to go 50 miles from Selma to Montgomery. You might write a task that focuses on students making sense of the distance, both from a mathematical and social justice lens.
- You can connect to local events: Last Friday there was a march from Mission High to the Mission Police Department. How does it compare to the march from Selma to Montgomery in terms of 1) estimated number of people? 2) distance? 3) issues? How does doing the mathematics add to your understanding of why we march?
There are many directions you can take this work. I encourage you start somewhere, asking the questions and leaving the discussion open to the direction it goes. That’s in part why it’s very important that you have done your own reflecting and researching before diving in with excitement to make what you think is an awesome lesson.
Be selective on what you mathematize: Similar to the hippocratic oath of physicians, teachers take an oath to do no harm to students. However, there is a vast grey area between what is harmful to one person, or what is uncomfortable but useful for a person, and what is healing.
Check Yourself and Ask:
- What are the assumptions about people, racial identities, etc in this story or context of the task?
- Is this context possibly retraumatizing for any students? That is to say, could I work on the ideas that need to get across in other ways that will not be triggering or harmful to some or all students in the class? (trickiest question, since you have to weigh who stands to benefit)
When in doubt, run your idea past a teaching partner (note, I did not say find a person of the same cultural or racial group of the characters in your anchor text if you are white and think you need a person of color, rather find a teacher or parent collaborator you trust), and ask them the same questions.
Some Concluding Thoughts
To me it’s a question of making the world a better place. Having everything in our toolbox to make sense of an act on racial injustice includes mathematical processes. Mathematics and quantitative literacy for young children should be included in that toolbox and can be developed through the same practices we use when we read stories together. And to be perfectly clear, young children are already mathematically brilliant. We socialize their brilliance out of them through schooling, in particular through the policing of their minds and bodies, and in particular young BIPOC. We have to build from the brilliance, which includes sometimes getting out of their way and letting them shine!
Ultimately, we can’t just get all up in arms and excited about teaching about racial justice during times of heightened racial conflict. It has to be regular, consistent, disciplined work to make our homes and classrooms antiracist. We can take our resources and embed it in our days: our books, our activities, our questions, our words, how we show up, how we vote, how we show each other love on the daily – all together is ultimately how we keep striving towards the world we want to see.
Even when the current protests cycle out of the news, don’t forget to do the work. Put it on your calendar or whatever you need to do. I’m doing the same.
akiea “ki” gross’ Woke Kindergarten, powerful read alouds: https://www.wokekindergarten.org/
And in the words of Carla Shalaby, YOU are the most immediate resource for yourself. Look at yourself, look at the children around you, start there.
*I have a lot of mixed feelings about teachers pay teachers as a resource, because there’s a lot of worksheets that taken out of context helps reproduce bad math teaching, however there is also a lot of good stuff on it as a platform for teachers to get really great curriculum out that and get paid for their work. My recommendation is to be savvy, find the teachers doing the work you are looking for, which tends to be Black, Latinx, and Indigenous folx for me, and happily pay them for their resources.
**Conversations about harm versus guarding privilege are very context specific, so I don’t have a clear recommendation at this time. Dedicated scholars, teachers, and researchers in math ed are taking up this question of whose development and emotional safety are taken into account when designing mathematics lessons around hard-to-broach topics, as interest in teaching mathematics for social justice increases.