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Walking into her sophomore year math class, Taylor Paris was nervous. She’d had a rocky relationship with the subject ever since long division showed up in elementary school. “I knew I didn’t understand math concepts very well. I knew that it was something that took me a longer time (than classmates),” she recalled.
So she was pleasantly surprised when one of the first assignments from teacher Sarah Strong required no calculating. Instead, Strong asked the class to write a letter to math – as if it were a person. These “Dear Math” letters are a tool that Strong developed as a way to understand students’ relationship to math when they arrive in her classroom, which researchers call mathematical identity. What Strong learns from these letters informs how she teaches individual students and whole classes throughout the year. Often that means working to disrupt the negative beliefs that students hold about their math abilities, which tend to revolve around comparisons to classmates, like “fast” and “slow” or “math person” vs. “not a math person.”
Strong introduces the Dear Math activity by reading her own letter to math as a model. Then she gives students prompts, such as:
- What is one of your greatest mathematical strengths?
- How do you plan to engage with math in the future?
- What would you like more of in math classrooms?
Paris, who is now 20, was excited to apply her writing skills in math, but also, unpack some of her deeply rooted emotions about to math. “I was finally able to write all of the things that made me sad and things that made me mad, like everything into one letter, addressing math directly,” she said. Here’s what she wrote in 10th grade:
Dear Math, Oh, do I have some things to say to you. You’ve followed me through every school year, caused me the worst headaches, and given me numerous counts of anxiety just thinking about you … The memories of my seventh grade math teacher telling me ‘maybe you’re just not a math person’ still ringing in my head and the constant Bs and Cs are still imprinted in my mind. You’ve been a never ending challenge and struggle, and it’s always been hard to understand you. No matter how many times my friends and teachers explain you, I never grasp you completely.
For Paris, having a teacher acknowledge emotions in math class was humanizing. “She recognized my experience as a part of this really big experience that so many other people have. And that was really validating,” Paris said.
Strong devotes a few hours to reading the letters, making notes about broad patterns and individual details. “It’s the beginning of an ongoing story between you and the students and their math experience for that semester or year, and it’s really important to start by listening to them well,” she said.
Hierarchy in math education
Strong teaches at High Tech High and its Graduate School of Education in San Diego. She developed the Dear Math routine almost a decade ago, and she published a book about it, Dear Math: Why Kids Hate Math And What Teachers Can Do About It, co-authored by her former student Gigi Butterfield. In it, the teacher and former student reflect on the themes across hundreds of letters. One pervasive theme is hierarchy.
“Kids as young as kindergarten and first grade are defining themselves as good at math or not good at math,” said Amy Parks, an elementary math education researcher at Michigan State University. Much of that definition comes from how they rank among classmates – from timed tests, to ‘high’ and ‘low’ groups, to subtle cues in teachers’ language. “I’ve been in classrooms where teachers have had kids line up by how many questions they answered or how many things they got right,” Parks said. “These hierarchies get reinforced so often and in so many different ways it’s almost overwhelming.”
For many kids, the comparisons add up to a negative self-perception around math. And by the time they reach high school, that mathematical identity can feel immutable. But math class doesn’t have to be this way. “Teachers and parents can affect the way kids think about these things,” said Rachel Lambert, a professor and researcher at University of California, Santa Barbara.
There’s a stubborn cultural myth that some of us are “math people” and some of us aren’t. This idea gets repeated explicitly all the time, and often implicitly with gendered and racialized associations. But neuroscience shows that everyone is capable of learning math, and Lambert said it matters that kids hear that. “Students connect subjects to teachers in a pretty intense way that I think as adults we often forget. So if they feel their math teacher believes in them as a human being and believes in their competence in mathematics, that can make a huge difference,” she said.
In Strong’s classroom, listening to students’ stories is the first step toward disrupting those hierarchies. She also looks for ways to highlight students’ mathematical thinking on a daily basis. One way she does this is by having multiple students write their problem-solving ideas on the whiteboard and asking other students to comment on what they like about the strategies they see. Another routine is an exit ticket that asks students to share something they learned from a classmate that day. She might share the details the next day with a student who was mentioned or with the whole class if there’s a bigger lesson in it.
Math is for everyone
Isabela Avila, another of Strong’s former students, said these kinds of practices created a sense of community: “It was never even like a question of did you get it right or wrong. It just seemed like we were always just all learning together as a class.” She had Strong as a teacher twice and wrote Dear Math letters both times. In her letter as a sophomore, her self-doubts showed up in the first sentence:
Dear Math, I really like you, but you don’t come naturally to me. I have to work extra hard to understand and fully conceptualize what you have to offer.
In her letter as a senior, Avila wrote about her math growth over the prior two years:
I developed a sense of patience and open mindedness for the first time ever. … I know this will help me a lot in college and beyond, and I look forward to using it in the future.
When Avila got to the highly competitive environment of Johns Hopkins University, however, the usual order of things returned. “I really struggled a lot with comparing myself, especially in math,” she said, discussing her freshman year. “And I just found that to be super, super counterproductive for both my learning and my self esteem.”
Strong said her own math story has had a lot of highs and lows, too. Though she can’t protect students from the ways math is taught and talked about beyond her classroom, her hope is that before they leave high school, “they start to see themselves as mathematicians in new ways and that they start to see their peers as mathematically brilliant in new ways.”
For Avila, the persistence she developed in high school did pay off in the long, emotionally tough hours of college calculus. “I feel like how you think about yourself and how fast you are to get back up and keep trying is really, truly so much more important than if you can actually do the math,” she said.
Fast and slow
Paris, Strong’s former student who liked expressing her emotions in a Dear Math letter, still remembers the heart-racing stress that accompanied timed multiplication tests in third grade. In Strong’s classroom, she said, there was never a timer. When Paris needed extra support, Strong brought out old algebra textbooks to reinforce foundational concepts. She designed projects where Paris could make connections between math and art – a subject that she already loved. Most importantly, Strong helped Paris learn how to break down complex problems into smaller steps. “Which is such a simple concept, but it didn’t even cross my mind that I could do that in math,” said Paris. “And that taking my time in math meant that I was being a mathematician.”
“Many students have this conception that they’re the only one who’s taking time to understand this concept, that everybody around them has already got it,” said Lambert, the UC Santa Barbara professor. Lambert suggested that teachers can reduce the rush of the pacing calendar by thinking of it not as going slowly but choosing where to invest time. “You can’t do every standard every year with your students. You have to figure out what is worth investment, and then spend more time with those topics so that students feel that they have enough time learning those things,” she said.
In Strong’s view, this requires shifting away from math instruction that is built around the ideas the teacher wants to get to in a given period. Student-centered instruction requires a lot more listening, she said: “Listening first off to their stories and how they’re showing up to class, and then second off (listening to) the ways that they are thinking of and understanding and making sense of mathematical ideas.”
Paris, who had Strong as a teacher for three years, said that time transformed her. She now works at a bridal shop, where she was recently promoted from stylist to sales manager – a role that involves a lot of math. “If I want to teach my stylists how to increase their productivity in their sales, then I need to think like a mathematician and come up with the ways that I can do that,” she explained. In tenth grade, that would have scared her. Not now. “There’s no reason for me to be afraid of math because I’ve proven to myself time and time again that I can do it,” she said.
Kara Newhouse: Welcome to MindShift, where we explore the future of learning and how we raise our kids. I’m Kara Newhouse.
Nimah Gobir: And I’m Nimah Gobir.
Kara Newhouse: Today we’re talking about math.
Nimah Gobir: Because it involves numbers and formulas, we often think of math as straightforward and objective.
Kara Newhouse: But learning math is actually packed with emotions. I met a high school teacher who starts the year with an unusual assignment. She has her students write a letter to math, describing their feelings about the subject. Here’s that teacher, Sarah Strong.
Sarah Strong: A Dear Math letter is a letter that students write to math as if math were personified sitting across the table from them. … And it really helps inform teachers better understand the students stories and experiences that they’re coming to class with so that teachers can better design math experiences for students to thrive and flourish in math class.
Kara Newhouse: We’ll hear more from Sarah later in the episode. First, here’s part of a Dear Math letter from one of her former students, Taylor Paris.
Taylor Paris: [Reading letter] Dear math, Oh, do I have some things to say to you. You’ve followed me throughout every school year, caused me the worst headaches, and given me numerous counts of anxiety just thinking about you … The memories of my seventh grade math teacher telling me, ‘Maybe you’re just not a math person’ still ringing in my head, and the constant Bs and Cs are still imprinted in my mind. You’ve been a never ending challenge and struggle, and it’s always been hard to understand you. No matter how many times my friends and teachers explain you, I never grasp you completely.
Kara Newhouse: The anxiety and frustration that Taylor described in her letter are familiar feelings for many young people. And by the time students get to high school, it can feel like if they don’t understand math now, they never will.
Nimah Gobir: But math doesn’t have to be this way.
Kara Newhouse: When we get back from the break, we’ll hear more about Dear Math letters and how they help students like Taylor strengthen their mathematical identities.
Kara Newhouse: Taylor Paris graduated high school a few years ago, but she still remembers the first week of tenth grade math with her teacher Sarah Strong. That’s when students wrote letters to math, as if it were a person.
Taylor Paris: And I remember being so excited because basically you’re writing in math, and that’s never the case.
Kara Newhouse: Interdisciplinary learning allows students to think about a subject from new perspectives. For Taylor, writing the Dear Math letter gave her a chance to reflect on how her early school years shaped her relationship to math.
Taylor Paris: I remember, my first, like, scariness of math was long division, because it was like so abstract to me, and everyone around me understood it and was just like, ‘Yeah, well that’s just the way it is and that’s totally fine.’
Kara Newhouse: Writing about those memories was cathartic. It also helped Taylor feel connected to her teacher.
Taylor Paris: I have never had a math teacher talk about emotions behind math ever. Like, truly ever … She recognized my experience as a part of this really big experience that so many other people have. And that was really validating.
Kara Newhouse: Her teacher, Sarah Strong, also made it clear that it was okay for those feelings to surface throughout the year. Which made it possible for Taylor to focus on actually learning math.
Taylor Paris: She did a great job at making me feel like I could take a really complex problem and break it down to the bare bones of it, which is such a simple concept. But it didn’t even cross my mind that I could do that in math and that taking my time in math meant that I was being a mathematician. And that’s what mathematicians did, was take their time and work on problems slowly to really understand every aspect.
Kara Newhouse: When I met Taylor, she had just been promoted from a stylist to a sales manager at a bridal shop in San Diego. That’s a fashion job that involves a lot of math.
Taylor Paris: So stylists are responsible for obviously, you know, the customer service side of things, but on the sales side, there is a certain goal that you need to meet or would ideally meet day to day and kind of week to day, month to day. … And so when you think about it, sales is like one big math problem every day because there’s a question, there’s an answer that you have to get to, and then there’s variables that go into, you know, the answer to your problem, essentially.
Kara Newhouse: Taylor is 20. Not that long ago, doing a math-related job would have been unimaginable to her.
Taylor Paris: If you told sophomore year Taylor that I would be doing something that was directly correlated with math and numbers all the time, I would be terrified and probably laugh.
Kara Newhouse: Taylor had Sarah Strong as a math teacher from 10th grade through 12th grade. She said that those years totally changed her view of math.
Taylor Paris: And so while I may have been scared to take a sales manager position at, you know, in my sophomore year, it makes a ton of sense for me now because what I do is help people find their wedding dress. And who would have thought that math was in finding a wedding dress?
Kara Newhouse: Taylor now sees herself as a doer of math. This is what’s called mathematical identity.
Nimah Gobir: We did an episode featuring Chris Emdin, who talked about students’ STEM identities. Mathematical identity is one form of a STEM identity.
Sarah Strong: Mathematical identity is a way that students see themselves as a mathematician, and therefore it connects to the ways that they enter into mathematical spaces and connect with other mathematicians around them.
Kara Newhouse: That’s teacher Sarah Strong again. She created the Dear Math activity during a bigger project where students were exploring their mathematical identities. They were using different types of math as metaphors for their experiences. And Sarah wanted to add a writing component to that project.
Sarah Strong: And one of my colleagues shared with me the idea of writing letters to a thing like books or basketball, and how she’d heard of that practice. And she thought I could do Dear Math letters, and I thought that was an amazing idea. So I ran with it.
Kara Newhouse: The letters were powerful. And Sarah realized that having students write them at the beginning of the year could help her teach each class better.
Here’s how she does it now. She introduces the assignment during the first week of school. She reads her own Dear Math letter as a model, because most students aren’t used to writing in math class. Hearing her letter also lets them know that even though she teaches math, it hasn’t always been easy for her.
Nimah Gobir: After reading her letter, Sarah gives her students prompts for writing their own. Questions like…
- What is one of your greatest mathematical strengths?
- How do you plan to engage with math in the future?
- What would you like more of in math classrooms?
Kara Newhouse: They spend 15 to 30 minutes writing in class. Anyone who wants to write more can finish at home.
Nimah Gobir: Then Sarah reads the letters on her own. She says this is the most important step.
Sarah Strong: ‘Cause it’s the beginning of an ongoing story between you and the students and their math experience for that semester or year, and it’s really important to start by listening to them well.
Kara Newhouse: She first looks for broad patterns across the class.
Sarah Strong: If I’ve got a disproportionate amount of students that hate math, don’t think they’re mathematicians, that I have to be really intentional about my class design, where I am regularly noticing and calling out their mathematical strengths and giving them opportunities to see themselves as mathematicians and see each other as mathematicians. Or do I have a lot of students who, who feel like ‘I am a really strong mathematician. Ever since I was young, I get all the right answers. I’m really fast.’ Then I can note that that’s a trend in the class and be thinking how I can continue to push those students while also broadening their understanding of how they are mathematical and how important it is to also listen to other students’ ways of being mathematical.
Kara Newhouse: She also reads the letters for individual details about things students love and things that trip them up. She might make a few notes and …
Sarah Strong: Check in with students like, ‘Gosh, I remember you said that you had a really hard time with the idea of percents and like whenever percents come up, you panic. Well, tomorrow we’re going to need some percents in our work with exponential functions. And so I wanted to make sure that you knew that I believe that you’ve got this. If you want to do a little practice beforehand, we can do that because I want you to feel confident. I don’t want some story from sixth grade impacting your confidence in what we’re working on right now.’
Kara Newhouse: Sarah said that getting to know students was always important to her. Even before she created the Dear Math assignment.
Sarah Strong: I would often try to connect with them in a variety of ways and I would hear their comments here and there that were both positive and negative. And I always tried to be a really good listener and understand my students’ feelings.
Kara Newhouse: But she wasn’t always getting a full picture.
Sarah Strong: Sometimes I think I was being a little delusional before I got to hear their whole stories because I would think, ‘Oh, they had really negative experiences. They don’t like math, but now that they’re in my class, everything’s going to be fine.’
Kara Newhouse: The letters helped her take off her rose-colored glasses.
Sarah Strong: It wasn’t until I started having them write Dear Math letters that I got to hear more complete stories and gain a bigger picture for their previous experience and how those experiences were informing the ways they were showing up to my class.
Kara Newhouse: That knowledge enables her to help students grow as math learners throughout the year.
Sarah Strong: My biggest hope is that they start to see themselves as mathematicians in new ways and that they start to see their peers as mathematically brilliant in new ways.
Kara Newhouse: Nimah, it would be great if writing a Dear Math letter helped all students see themselves as capable of doing math – the way it did for Taylor Paris.
Nimah Gobir: It would. But of course not every student’s math story is linear.
Kara Newhouse: No… Some math stories go up and down over time, like a periodic function.
Nimah Gobir: Hey, nice math analogy!
Kara Newhouse: I got that one from Sarah Strong. She described her own math story that way. It also applies to another of her former students, Isabela Avila. Here’s the start of a Dear Math letter Isabela wrote in tenth grade.
Isabela Avila: [Reading letter] Dear Math, I really like you, but you don’t come naturally to me. I have to work extra hard to understand and fully conceptualize what you have to offer.
Kara Newhouse: In previous math classes, Isabela felt pressure to always be fast and have the right answer. But she told me that expectation wasn’t there in Sarah Strong’s class.
Isabela Avila: It was never even like a question of like, did you get it right or wrong? It was just seemed like we were always just all learning together, as a class.
Kara Newhouse: That sense of togetherness mattered.
Isabela Avila: And like, I think that really helped me like number one, like, think highly of myself as like a problem solver and also … be confident in my ideas.
Kara Newhouse: Isabela had Sarah Strong as a teacher twice, and she wrote a Dear Math letter both times. You can hear her increased confidence in the letter she wrote as a senior.
Isabela Avila: [Reading letter] The most mathematical growth I feel I have ever experienced was during my junior year. I felt confident in my algebra skills for the first time ever. … My mindset also shifted drastically. I developed a sense of patience and open mindedness for the first time ever. … I know this will help me a lot in college and beyond, and I look forward to using it in the future. Sincerely, Isabela Avila.
Kara Newhouse: When Isabela actually got to college, the transition was rocky. She’s a pre-med major at Johns Hopkins University in Baltimore.
Isabela Avila: Our like math department is known for being like notoriously hard.
Kara Newhouse: All around her, Isabela saw classmates who had come from elite high schools and seemed to understand calculus more easily than she did.
Isabela Avila: I really struggled a lot with like comparing myself, especially in math. And I just found that to be super, super counter-productive for both my learning and like my self esteem.
Kara Newhouse: Sometimes she would break down crying while doing homework, which could take eight hours to complete. In class, she didn’t participate as much as she had hoped to.
Isabela Avila: I just really didn’t want to sound like I didn’t know what I was talking about or like, not that I don’t belong there, but I don’t know. It was just, everyone around me was so smart. And I know, like, tests don’t define you, but everyone around me, like, even if they were starting in calc one, they, like, got fives on like the AP calc exams and did exceptionally well.
Kara Newhouse: Back in high school, Isabela had written in one of her letters that she’d had a lot of highs and lows with math. Freshman year of college was definitely another low.
When I talked to her during her sophomore year at Johns Hopkins, being a premed major was still very stressful. Something that helped, though, was making friends who didn’t talk about grades.
Isabela Avila: We don’t talk about, like, what score we got. We don’t talk about how we’re doing in the class. We don’t talk about — honestly we don’t talk that much about like our actual like school.
Kara Newhouse: And she said the persistence that she developed in high school did help her get through calculus.
Isabela Avila: Especially in math here in college, like, I feel like how you think about yourself and like how fast you are to like, get back up and keep trying is really, truly so much more important than if you can actually do the math.
Nimah Gobir: Kara, the way Isabela compared herself to her calculus classmates isn’t unique to being at a university full of high achievers.
Kara Newhouse: That’s right. Sarah Strong said those comparisons have been pervasive in students’ Dear Math letters. And according to experts, this kind of thinking starts early.
Nimah Gobir: Researchers say even kindergarteners start to notice their spot in the pecking order of math ability.
Kara Newhouse: It often starts with those one-minute math quizzes that so many of us remember.
[Sound of pencils scribbling and slamming down]
Nimah Gobir: Students might hear their classmates furiously scribbling answers and slamming their pencils down when they finish. They equate that with being “good” at math.
Kara Newhouse: And there are lots of other ways in school that students are ranked and sorted. In younger grades, teachers often group students by ability when they’re practicing math. In upper grades, students may get tracked into ‘regular’ and ‘advanced’ classes.
Nimah Gobir: Some teachers will even publicly display kids’ progress in certain math skills. This can look like a bulletin board that uses paper ice cream scoops to represent how many multiplication facts each student knows.
Kara Newhouse: One researcher I talked to had a lot of ideas about how to disrupt hierarchies in math education. This is Rachel Lambert, from University of California, Santa Barbara.
Rachel Lambert: I think if there’s one one thing I’d like to communicate, it’s that teachers and parents can affect the way kids think about these things.
Kara Newhouse: Rachel shared five tips that teachers can use to help kids stop comparing themselves to others in math. The first tip is to change the narrative about who can do math.
Rachel Lambert: Students would tell me how much it mattered to them to hear their teacher say, ‘There is no difference in who can be good at math.’ Like very clear messages around race and gender and the clear message that there is no one group of people that is better in math than other people, those students told me that was helpful to them.
Kara Newhouse: Changing the narrative isn’t just about what we say to kids. It’s also about how teachers talk to each other. And how they group students in class.
Rachel Lambert: We might think as teachers – and I was a teacher for over 10 years – that kids don’t know that we might be calling them low kids or high kids when we’re having lunch with other teachers. … But they know, they always know and they know how they’re being grouped and classified and seen. … If we decide that kids are going to do well in mathematics, we do a lot of things in our teaching to set them up for success day after day. If we think kids will fail when we hand them a mathematical task, we’re doing subtle things to set them up for failure every single time we do that. So if we put them in groups that never change, we’re teaching them who they are and we’re also affecting who they become, because we’re only allowing them opportunities to do things quote-unquote at their level.
Kara Newhouse: Rachel’s second tip for teachers is to stop focusing on speed.
Rachel Lambert: Think of it not as a matter of going slow. Think of it as investing in certain things. So you can’t hit everything on your pacing calendar. You can’t do every standard every year with your students. You have to figure out what is worth investment and what is worth extra time, and then spend more time with those topics so that students feel that they have enough time learning those things.
Kara Newhouse: Her third tip is to normalize mistakes. It can help students learn from each other’s thinking when you have them share their mistakes. Rachel told me about a teacher who did this.
Rachel Lambert: She would even put a little heart next to a mistake and she’d be, ‘This was my favorite mistake of the day.’ And she drew a little heart next to it. And the kids would go, ‘awww.’ It’s adorable.
Kara Newhouse: Tip number four is to give students problems that can be approached from multiple angles.
Rachel Lambert: I see that some kids really love to engage in the visual aspect of a problem. Other students like to make, say, an organized list. And that doesn’t mean – there’s no such thing as learning styles; it doesn’t mean that that’s the way they’re going to approach every problem, but it does mean that a problem that draws on multiple ways of engaging can be more rich mathematically and also disrupt ideas of who’s the best at math and who isn’t.
Kara Newhouse: Rachel Lambert’s fifth and final tip is to make supports available to everyone.
Rachel Lambert: That is the one of the simplest interventions you can do in math to make it more equitable … And it doesn’t send any negative messages to kids because they are choosing if they want to use a calculator. They are choosing if they want to hear the directions a second time. They are choosing if they use manipulatives.
Kara Newhouse: Making these resources available to everyone takes the teacher’s assumptions out of the equation. And it helps kids develop the skills to recognize what they need to succeed.
Nimah Gobir: Kara, there are some people who say math teachers should just focus on content. That activities like writing letters to math are more about self-esteem than learning.
Kara Newhouse: These goals don’t have to be separate. Direct instruction and problem-solving practice are essential parts of math education. But like we said at the beginning, doing math involves emotions. Although we’ve heard a lot about the frustrating parts of math, it can also evoke positive emotions.
Nimah Gobir: Kids who are absorbed in math problem-solving often express wonder and excitement.
Kara Newhouse: Listening to young people’s stories and honoring all of these emotions allows students to be more human in math class. And that doesn’t just make them believe in their math abilities, it empowers them to learn math and to do math.
Kara Newhouse: This episode would not have been possible without Sarah Strong. To learn more about Dear Math letters, you can read the book she wrote with her former student, Gigi Butterfield. The book is called, Dear Math: Why Kids Hate Math and What Teachers Can Do About It.
Thanks also to Taylor Paris, Isabela Avila, Rachel Lambert and Amy Parks.
The MindShift team includes Nimah Gobir, Ki Sung, Marlena Jackson-Retondo and me, Kara Newhouse.
Our editor is Chris Hambrick. Chris Hoff engineered this episode.
Additional support from Jen Chien, Katie Sprenger, Cesar Saldaña and Holly Kernan.
MindShift is supported in part by the generosity of the William & Flora Hewlett Foundation and members of KQED.
Nimah Gobir: If you love MindShift, and enjoyed this episode, please share it with a friend. We really appreciate it. You can also read more or subscribe to our newsletter at kqed.org/mindshift.
Kara Newhouse: Thank you for listening to Season 8 of the MindShift podcast. That’s it for these deep dive episodes. We’re taking a little break, but we’ll be back soon with new episodes featuring conversations about big ideas in education. Be sure to follow the show or subscribe so you don’t miss a thing.