How listening to students’ stories can improve math class
How Encouraging Rough Draft Thinking in Math Class Highlights the Strengths of All Students
What It Looks Like When Students Share and Revise Rough Drafts in Math Class
How A Strengths-Based Approach to Math Redefines Who Is 'Smart'
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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.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">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 \u003c/span>\u003ca href=\"https://www.kqed.org/mindshift/60108/using-dear-math-letters-to-overcome-dread-in-math-class\">\u003cspan style=\"font-weight: 400\">“Dear Math” letters\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> are a tool that Strong developed as a way to understand students’ relationship to math when they arrive in her classroom, which researchers call \u003c/span>\u003ca href=\"https://journals.library.columbia.edu/index.php/jmetc/article/view/9187/4897\">\u003cspan style=\"font-weight: 400\">mathematical identity\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">. 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.”\u003c/span>\u003cspan style=\"font-weight: 400\">\u003cbr>\n\u003c/span>\u003cspan style=\"font-weight: 400\">\u003cbr>\n\u003c/span>\u003cspan style=\"font-weight: 400\">Strong introduces the Dear Math activity by reading her own letter to math as a model. Then she gives students prompts, such as:\u003c/span>\u003c/p>\n\u003cul>\n\u003cli style=\"font-weight: 400\">\u003cspan style=\"font-weight: 400\">What is one of your greatest mathematical strengths?\u003c/span>\u003c/li>\n\u003cli style=\"font-weight: 400\">\u003cspan style=\"font-weight: 400\">How do you plan to engage with math in the future?\u003c/span>\u003c/li>\n\u003cli style=\"font-weight: 400\">\u003cspan style=\"font-weight: 400\">What would you like more of in math classrooms?\u003c/span>\u003c/li>\n\u003c/ul>\n\u003cp>\u003cspan style=\"font-weight: 400\">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: \u003c/span>\u003c/p>\n\u003cp style=\"padding-left: 40px\">\u003ci>\u003cspan style=\"font-weight: 400\">Dear Math, \u003c/span>\u003c/i>\u003ci>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/i>\u003c/p>\n\u003cp>[ad fullwidth]\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">For Paris, having a teacher acknowledge emotions in math class was \u003c/span>\u003ca href=\"https://www.kqed.org/mindshift/54980/why-teachers-want-math-with-more-human-ties\">\u003cspan style=\"font-weight: 400\">humanizing\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">. “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.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003ch2>\u003cb>Hierarchy in math education\u003c/b>\u003c/h2>\n\u003cp>\u003cspan style=\"font-weight: 400\">Strong teaches at \u003c/span>\u003ca href=\"https://www.hightechhigh.org/about/\">\u003cspan style=\"font-weight: 400\">High Tech High\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> 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, \u003c/span>\u003ca href=\"https://www.10publications.com/dear-math\">\u003ci>\u003cspan style=\"font-weight: 400\">Dear Math: Why Kids Hate Math And What Teachers Can Do About It\u003c/span>\u003c/i>\u003c/a>\u003cspan style=\"font-weight: 400\">, co-authored by her former\u003c/span> \u003cspan style=\"font-weight: 400\">student Gigi Butterfield. In it, the teacher and former student reflect on the themes across hundreds of letters. One pervasive theme is hierarchy.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">“Kids as young as kindergarten and first grade are defining themselves as good at math or not good at math,” said \u003c/span>\u003ca href=\"https://twitter.com/amynoelleparks\">\u003cspan style=\"font-weight: 400\">Amy Parks\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">, 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.”\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">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 \u003c/span>\u003ca href=\"https://mathematizing4all.com/about-the-author/\">\u003cspan style=\"font-weight: 400\">Rachel Lambert\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">, a professor and researcher at University of California, Santa Barbara.\u003c/span>\u003cspan style=\"font-weight: 400\">\u003cbr>\n\u003c/span>\u003cspan style=\"font-weight: 400\">\u003cbr>\n\u003c/span>\u003cspan style=\"font-weight: 400\">There’s a stubborn cultural \u003c/span>\u003ca href=\"https://www.kqed.org/mindshift/54389/3-ways-to-shape-math-into-a-positive-experience\">\u003cspan style=\"font-weight: 400\">myth that some of us are “math people” and some of us aren’t\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">. This idea gets repeated explicitly all the time, and often \u003c/span>\u003ca href=\"https://www.science.org/doi/10.1126/science.aah6524\">\u003cspan style=\"font-weight: 400\">implicitly with gendered and racialized associations\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">. But neuroscience shows that \u003c/span>\u003ca href=\"https://www.youcubed.org/resources/brain-science/\">\u003cspan style=\"font-weight: 400\">everyone is capable of learning math\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">, and Lambert said \u003c/span>\u003ca href=\"https://www.kqed.org/mindshift/57997/how-to-build-students-math-confidence-with-culturally-sustaining-teaching-practices\">\u003cspan style=\"font-weight: 400\">it matters that kids hear that\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">. “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.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003ch2>\u003cb>Math is for everyone\u003c/b>\u003c/h2>\n\u003cp>\u003cspan style=\"font-weight: 400\">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:\u003c/span>\u003c/p>\n\u003cp style=\"padding-left: 40px\">\u003ci>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/i>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">In her letter as a senior, Avila wrote about her math growth over the prior two years:\u003c/span>\u003c/p>\n\u003cp style=\"padding-left: 40px\">\u003ci>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/i>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">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.”\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">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.”\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003ch2>Fast and slow\u003c/h2>\n\u003cp>\u003cspan style=\"font-weight: 400\">Paris, Strong’s former student who liked expressing her emotions in a Dear Math letter, still remembers the heart-racing stress that accompanied \u003c/span>\u003ca href=\"https://www.kqed.org/mindshift/61712/do-math-drills-help-children-learn\">\u003cspan style=\"font-weight: 400\">timed multiplication tests\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> 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.”\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">“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.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">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.”\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003c!-- iframe plugin v.4.3 wordpress.org/plugins/iframe/ -->\u003cbr>\n\u003ciframe loading=\"lazy\" frameborder=\"0\" height=\"200\" scrolling=\"no\" src=\"https://playlist.megaphone.fm/?e=KQINC8301605465&light=true\" width=\"100%\" class=\"iframe-class\">\u003c/iframe>\u003c/p>\n\u003ch2 id=\"episode-transcript\">Episode transcript\u003c/h2>\n\u003cp>\u003cb>Kara Newhouse:\u003c/b>\u003cspan style=\"font-weight: 400\"> Welcome to MindShift, where we explore the future of learning and how we raise our kids. I’m Kara Newhouse.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Nimah Gobir: \u003c/b>\u003cspan style=\"font-weight: 400\">And I’m Nimah Gobir.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">[\u003c/span>\u003ci>\u003cspan style=\"font-weight: 400\">Music\u003c/span>\u003c/i>\u003cspan style=\"font-weight: 400\">]\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">Today we’re talking about math.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Nimah Gobir:\u003c/b>\u003cspan style=\"font-weight: 400\"> Because it involves numbers and formulas, we often think of math as straightforward and objective.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse:\u003c/b>\u003cspan style=\"font-weight: 400\"> 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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Sarah Strong: \u003c/b>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse:\u003c/b>\u003cspan style=\"font-weight: 400\"> 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.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">[\u003c/span>\u003ci>\u003cspan style=\"font-weight: 400\">Music\u003c/span>\u003c/i>\u003cspan style=\"font-weight: 400\">]\u003c/span>\u003c/p>\n\u003cp>\u003cb>Taylor Paris: \u003c/b>\u003cspan style=\"font-weight: 400\">[\u003c/span>\u003ci>\u003cspan style=\"font-weight: 400\">Reading letter\u003c/span>\u003c/i>\u003cspan style=\"font-weight: 400\">] 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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse:\u003c/b>\u003cspan style=\"font-weight: 400\"> 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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Nimah Gobir:\u003c/b>\u003cspan style=\"font-weight: 400\"> But math doesn’t have to be this way.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse:\u003c/b>\u003cspan style=\"font-weight: 400\"> 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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse:\u003c/b>\u003cspan style=\"font-weight: 400\"> 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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Taylor Paris:\u003c/b> \u003cspan style=\"font-weight: 400\">And I remember being so excited because basically you’re writing in math, and that’s never the case.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Taylor Paris: \u003c/b>\u003cspan style=\"font-weight: 400\">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.’\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">Writing about those memories was cathartic. It also helped Taylor feel connected to her teacher.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Taylor Paris:\u003c/b> \u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Taylor Paris: \u003c/b>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Taylor Paris: \u003c/b>\u003cspan style=\"font-weight: 400\">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. …\u003c/span> \u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse:\u003c/b>\u003cspan style=\"font-weight: 400\"> Taylor is 20. Not that long ago, doing a math-related job would have been unimaginable to her.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Taylor Paris:\u003c/b> \u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Taylor Paris: \u003c/b>\u003cspan style=\"font-weight: 400\">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?\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">[\u003c/span>\u003ci>\u003cspan style=\"font-weight: 400\">Music\u003c/span>\u003c/i>\u003cspan style=\"font-weight: 400\">]\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">Taylor now sees herself as a doer of math. This is what’s called mathematical identity.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Nimah Gobir:\u003c/b>\u003cspan style=\"font-weight: 400\"> We did an episode featuring Chris Emdin, who talked about students’ STEM identities. Mathematical identity is one form of a STEM identity.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Sarah Strong: \u003c/b>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Sarah Strong:\u003c/b> \u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">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. \u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Nimah Gobir: \u003c/b>\u003cspan style=\"font-weight: 400\">After reading her letter, Sarah gives her students prompts for writing their own. Questions like…\u003c/span>\u003c/p>\n\u003cul>\n\u003cli style=\"font-weight: 400\">\u003cspan style=\"font-weight: 400\">What is one of your greatest mathematical strengths?\u003c/span>\u003c/li>\n\u003cli style=\"font-weight: 400\">\u003cspan style=\"font-weight: 400\">How do you plan to engage with math in the future?\u003c/span>\u003c/li>\n\u003cli style=\"font-weight: 400\">\u003cspan style=\"font-weight: 400\">What would you like more of in math classrooms?\u003c/span>\u003c/li>\n\u003c/ul>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">They spend 15 to 30 minutes writing in class. Anyone who wants to write more can finish at home.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Nimah Gobir: \u003c/b>\u003cspan style=\"font-weight: 400\">Then Sarah reads the letters on her own. She says this is the most important step.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Sarah Strong: \u003c/b>\u003cspan style=\"font-weight: 400\">‘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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">She first looks for broad patterns across the class.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Sarah Strong: \u003c/b>\u003cspan style=\"font-weight: 400\">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.\u003c/span> \u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">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 …\u003c/span>\u003c/p>\n\u003cp>\u003cb>Sarah Strong: \u003c/b>\u003cspan style=\"font-weight: 400\">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.’\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">Sarah said that getting to know students was always important to her. Even before she created the Dear Math assignment.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Sarah Strong:\u003c/b> \u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">But she wasn’t always getting a full picture.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Sarah Strong:\u003c/b> \u003cspan style=\"font-weight: 400\">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.’\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">The letters helped her take off her rose-colored glasses.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Sarah Strong:\u003c/b> \u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">That knowledge enables her to help students grow as math learners throughout the year.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Sarah Strong:\u003c/b> \u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">[\u003c/span>\u003ci>\u003cspan style=\"font-weight: 400\">Music\u003c/span>\u003c/i>\u003cspan style=\"font-weight: 400\">]\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Nimah Gobir: \u003c/b>\u003cspan style=\"font-weight: 400\">It would. But of course not every student’s math story is linear.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">No… Some math stories go up and down over time, like a periodic function. \u003c/span>\u003c/p>\n\u003cp>\u003cb>Nimah Gobir: \u003c/b>\u003cspan style=\"font-weight: 400\">Hey, nice math analogy! \u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse:\u003c/b>\u003cspan style=\"font-weight: 400\"> 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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Isabela Avila: \u003c/b>\u003cspan style=\"font-weight: 400\">[\u003c/span>\u003ci>\u003cspan style=\"font-weight: 400\">Reading letter\u003c/span>\u003c/i>\u003cspan style=\"font-weight: 400\">] 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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Isabela Avila: \u003c/b>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse:\u003c/b>\u003cspan style=\"font-weight: 400\"> That sense of togetherness mattered. \u003c/span>\u003c/p>\n\u003cp>\u003cb>Isabela Avila: \u003c/b>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Isabela Avila:\u003c/b> \u003cspan style=\"font-weight: 400\">[\u003c/span>\u003ci>\u003cspan style=\"font-weight: 400\">Reading letter\u003c/span>\u003c/i>\u003cspan style=\"font-weight: 400\">] 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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">When Isabela actually got to college, the transition was rocky. She’s a pre-med major at Johns Hopkins University in Baltimore.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Isabela Avila:\u003c/b> \u003cspan style=\"font-weight: 400\">Our like math department is known for being like notoriously hard.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse:\u003c/b>\u003cspan style=\"font-weight: 400\"> All around her, Isabela saw classmates who had come from elite high schools and seemed to understand calculus more easily than she did.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Isabela Avila: \u003c/b>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Isabela Avila: \u003c/b>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse:\u003c/b>\u003cspan style=\"font-weight: 400\"> 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.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Isabela Avila: \u003c/b>\u003cspan style=\"font-weight: 400\">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. \u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">And she said the persistence that she developed in high school did help her get through calculus.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Isabela Avila:\u003c/b> \u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">[\u003c/span>\u003ci>\u003cspan style=\"font-weight: 400\">Music\u003c/span>\u003c/i>\u003cspan style=\"font-weight: 400\">]\u003c/span>\u003c/p>\n\u003cp>\u003cb>Nimah Gobir:\u003c/b>\u003cspan style=\"font-weight: 400\"> Kara, the way Isabela compared herself to her calculus classmates isn’t unique to being at a university full of high achievers.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse:\u003c/b>\u003cspan style=\"font-weight: 400\"> 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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Nimah Gobir:\u003c/b>\u003cspan style=\"font-weight: 400\"> Researchers say even kindergarteners start to notice their spot in the pecking order of math ability.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">It often starts with those one-minute math quizzes that so many of us remember.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">[\u003c/span>\u003ci>\u003cspan style=\"font-weight: 400\">Sound of pencils scribbling and slamming down\u003c/span>\u003c/i>\u003cspan style=\"font-weight: 400\">]\u003c/span>\u003c/p>\n\u003cp>\u003cb>Nimah Gobir: \u003c/b>\u003cspan style=\"font-weight: 400\">Students might hear their classmates furiously scribbling answers and slamming their pencils down when they finish. They equate that with being “good” at math.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">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. \u003c/span>\u003c/p>\n\u003cp>\u003cb>Nimah Gobir: \u003c/b>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Rachel Lambert: \u003c/b>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Rachel Lambert: \u003c/b>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse:\u003c/b>\u003cspan style=\"font-weight: 400\"> 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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Rachel Lambert: \u003c/b>\u003cspan style=\"font-weight: 400\">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. \u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">Rachel’s second tip for teachers is to stop focusing on speed. \u003c/span>\u003c/p>\n\u003cp>\u003cb>Rachel Lambert:\u003c/b> \u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Rachel Lambert: \u003c/b>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse:\u003c/b>\u003cspan style=\"font-weight: 400\"> Tip number four is to give students problems that can be approached from multiple angles.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Rachel Lambert:\u003c/b> \u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">Rachel Lambert’s fifth and final tip is to make supports available to everyone.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Rachel Lambert: \u003c/b>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">[\u003c/span>\u003ci>\u003cspan style=\"font-weight: 400\">Music\u003c/span>\u003c/i>\u003cspan style=\"font-weight: 400\">]\u003c/span>\u003c/p>\n\u003cp>\u003cb>Nimah Gobir: \u003c/b>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Nimah Gobir: \u003c/b>\u003cspan style=\"font-weight: 400\">Kids who are absorbed in math problem-solving often express wonder and excitement.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">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 \u003c/span>\u003ci>\u003cspan style=\"font-weight: 400\">believe \u003c/span>\u003c/i>\u003cspan style=\"font-weight: 400\">in their math abilities, it empowers them to learn math and to do math.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">[\u003c/span>\u003ci>\u003cspan style=\"font-weight: 400\">Music\u003c/span>\u003c/i>\u003cspan style=\"font-weight: 400\">]\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">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, \u003c/span>\u003ci>\u003cspan style=\"font-weight: 400\">Dear Math: Why Kids Hate Math and What Teachers Can Do About It.\u003c/span>\u003c/i>\u003cspan style=\"font-weight: 400\"> \u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Thanks also to Taylor Paris, Isabela Avila, Rachel Lambert and Amy Parks.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">The MindShift team includes Nimah Gobir, Ki Sung, Marlena Jackson-Retondo and me, Kara Newhouse.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Our editor is Chris Hambrick. Chris Hoff engineered this episode.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Additional support from Jen Chien, Katie Sprenger, Cesar Saldaña and Holly Kernan.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">MindShift is supported in part by the generosity of the William & Flora Hewlett Foundation and members of KQED.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Nimah Gobir:\u003c/b>\u003cspan style=\"font-weight: 400\"> 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 \u003c/span>\u003ca href=\"http://kqed.org/mindshift\">\u003cspan style=\"font-weight: 400\">kqed.org/mindshift\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">.\u003c/span>\u003c/p>\n\u003cp>[ad floatright]\u003c/p>\n\u003cp>\u003cb>Kara Newhouse:\u003c/b>\u003cspan style=\"font-weight: 400\"> 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.\u003c/span>\u003c/p>\n\n","blocks":[],"excerpt":"In this math class, students write letters about their math history. The process can change their future.","status":"publish","parent":0,"modified":1703019996,"stats":{"hasAudio":true,"hasVideo":false,"hasChartOrMap":false,"iframeSrcs":[],"hasGoogleForm":false,"hasGallery":false,"hasHearkenModule":false,"hasPolis":false,"paragraphCount":135,"wordCount":5848},"headData":{"title":"How listening to students’ stories can improve math class | KQED","description":"In this math class, students write letters about their math history. The process can change their future.","ogTitle":"","ogDescription":"","ogImgId":"","twTitle":"","twDescription":"","twImgId":"","socialDescription":"In this math class, students write letters about their math history. The process can change their future."},"audioUrl":"https://www.podtrac.com/pts/redirect.mp3/chrt.fm/track/G6C7C3/traffic.megaphone.fm/KQINC8301605465.mp3?updated=1695679399","sticky":false,"excludeFromSiteSearch":"Include","articleAge":"0","path":"/mindshift/62436/how-listening-to-students-stories-can-improve-math-class","audioTrackLength":null,"parsedContent":[{"type":"contentString","content":"\u003cdiv class=\"post-body\">\u003cp>\u003cp>\u003ca href=\"#episode-transcript\">\u003cem>View the full episode transcript\u003c/em>\u003c/a>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">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 \u003c/span>\u003ca href=\"https://www.kqed.org/mindshift/60108/using-dear-math-letters-to-overcome-dread-in-math-class\">\u003cspan style=\"font-weight: 400\">“Dear Math” letters\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> are a tool that Strong developed as a way to understand students’ relationship to math when they arrive in her classroom, which researchers call \u003c/span>\u003ca href=\"https://journals.library.columbia.edu/index.php/jmetc/article/view/9187/4897\">\u003cspan style=\"font-weight: 400\">mathematical identity\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">. 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.”\u003c/span>\u003cspan style=\"font-weight: 400\">\u003cbr>\n\u003c/span>\u003cspan style=\"font-weight: 400\">\u003cbr>\n\u003c/span>\u003cspan style=\"font-weight: 400\">Strong introduces the Dear Math activity by reading her own letter to math as a model. Then she gives students prompts, such as:\u003c/span>\u003c/p>\n\u003cul>\n\u003cli style=\"font-weight: 400\">\u003cspan style=\"font-weight: 400\">What is one of your greatest mathematical strengths?\u003c/span>\u003c/li>\n\u003cli style=\"font-weight: 400\">\u003cspan style=\"font-weight: 400\">How do you plan to engage with math in the future?\u003c/span>\u003c/li>\n\u003cli style=\"font-weight: 400\">\u003cspan style=\"font-weight: 400\">What would you like more of in math classrooms?\u003c/span>\u003c/li>\n\u003c/ul>\n\u003cp>\u003cspan style=\"font-weight: 400\">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: \u003c/span>\u003c/p>\n\u003cp style=\"padding-left: 40px\">\u003ci>\u003cspan style=\"font-weight: 400\">Dear Math, \u003c/span>\u003c/i>\u003ci>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/i>\u003c/p>\n\u003cp>\u003c/p>\u003c/div>","attributes":{"named":{},"numeric":[]}},{"type":"component","content":"","name":"ad","attributes":{"named":{"label":"fullwidth"},"numeric":["fullwidth"]}},{"type":"contentString","content":"\u003cdiv class=\"post-body\">\u003cp>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">For Paris, having a teacher acknowledge emotions in math class was \u003c/span>\u003ca href=\"https://www.kqed.org/mindshift/54980/why-teachers-want-math-with-more-human-ties\">\u003cspan style=\"font-weight: 400\">humanizing\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">. “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.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003ch2>\u003cb>Hierarchy in math education\u003c/b>\u003c/h2>\n\u003cp>\u003cspan style=\"font-weight: 400\">Strong teaches at \u003c/span>\u003ca href=\"https://www.hightechhigh.org/about/\">\u003cspan style=\"font-weight: 400\">High Tech High\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> 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, \u003c/span>\u003ca href=\"https://www.10publications.com/dear-math\">\u003ci>\u003cspan style=\"font-weight: 400\">Dear Math: Why Kids Hate Math And What Teachers Can Do About It\u003c/span>\u003c/i>\u003c/a>\u003cspan style=\"font-weight: 400\">, co-authored by her former\u003c/span> \u003cspan style=\"font-weight: 400\">student Gigi Butterfield. In it, the teacher and former student reflect on the themes across hundreds of letters. One pervasive theme is hierarchy.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">“Kids as young as kindergarten and first grade are defining themselves as good at math or not good at math,” said \u003c/span>\u003ca href=\"https://twitter.com/amynoelleparks\">\u003cspan style=\"font-weight: 400\">Amy Parks\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">, 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.”\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">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 \u003c/span>\u003ca href=\"https://mathematizing4all.com/about-the-author/\">\u003cspan style=\"font-weight: 400\">Rachel Lambert\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">, a professor and researcher at University of California, Santa Barbara.\u003c/span>\u003cspan style=\"font-weight: 400\">\u003cbr>\n\u003c/span>\u003cspan style=\"font-weight: 400\">\u003cbr>\n\u003c/span>\u003cspan style=\"font-weight: 400\">There’s a stubborn cultural \u003c/span>\u003ca href=\"https://www.kqed.org/mindshift/54389/3-ways-to-shape-math-into-a-positive-experience\">\u003cspan style=\"font-weight: 400\">myth that some of us are “math people” and some of us aren’t\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">. This idea gets repeated explicitly all the time, and often \u003c/span>\u003ca href=\"https://www.science.org/doi/10.1126/science.aah6524\">\u003cspan style=\"font-weight: 400\">implicitly with gendered and racialized associations\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">. But neuroscience shows that \u003c/span>\u003ca href=\"https://www.youcubed.org/resources/brain-science/\">\u003cspan style=\"font-weight: 400\">everyone is capable of learning math\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">, and Lambert said \u003c/span>\u003ca href=\"https://www.kqed.org/mindshift/57997/how-to-build-students-math-confidence-with-culturally-sustaining-teaching-practices\">\u003cspan style=\"font-weight: 400\">it matters that kids hear that\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">. “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.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003ch2>\u003cb>Math is for everyone\u003c/b>\u003c/h2>\n\u003cp>\u003cspan style=\"font-weight: 400\">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:\u003c/span>\u003c/p>\n\u003cp style=\"padding-left: 40px\">\u003ci>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/i>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">In her letter as a senior, Avila wrote about her math growth over the prior two years:\u003c/span>\u003c/p>\n\u003cp style=\"padding-left: 40px\">\u003ci>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/i>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">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.”\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">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.”\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003ch2>Fast and slow\u003c/h2>\n\u003cp>\u003cspan style=\"font-weight: 400\">Paris, Strong’s former student who liked expressing her emotions in a Dear Math letter, still remembers the heart-racing stress that accompanied \u003c/span>\u003ca href=\"https://www.kqed.org/mindshift/61712/do-math-drills-help-children-learn\">\u003cspan style=\"font-weight: 400\">timed multiplication tests\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> 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.”\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">“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.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">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.”\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003c!-- iframe plugin v.4.3 wordpress.org/plugins/iframe/ -->\u003cbr>\n\u003ciframe loading=\"lazy\" frameborder=\"0\" height=\"200\" scrolling=\"no\" src=\"https://playlist.megaphone.fm/?e=KQINC8301605465&light=true\" width=\"100%\" class=\"iframe-class\">\u003c/iframe>\u003c/p>\n\u003ch2 id=\"episode-transcript\">Episode transcript\u003c/h2>\n\u003cp>\u003cb>Kara Newhouse:\u003c/b>\u003cspan style=\"font-weight: 400\"> Welcome to MindShift, where we explore the future of learning and how we raise our kids. I’m Kara Newhouse.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Nimah Gobir: \u003c/b>\u003cspan style=\"font-weight: 400\">And I’m Nimah Gobir.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">[\u003c/span>\u003ci>\u003cspan style=\"font-weight: 400\">Music\u003c/span>\u003c/i>\u003cspan style=\"font-weight: 400\">]\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">Today we’re talking about math.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Nimah Gobir:\u003c/b>\u003cspan style=\"font-weight: 400\"> Because it involves numbers and formulas, we often think of math as straightforward and objective.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse:\u003c/b>\u003cspan style=\"font-weight: 400\"> 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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Sarah Strong: \u003c/b>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse:\u003c/b>\u003cspan style=\"font-weight: 400\"> 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.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">[\u003c/span>\u003ci>\u003cspan style=\"font-weight: 400\">Music\u003c/span>\u003c/i>\u003cspan style=\"font-weight: 400\">]\u003c/span>\u003c/p>\n\u003cp>\u003cb>Taylor Paris: \u003c/b>\u003cspan style=\"font-weight: 400\">[\u003c/span>\u003ci>\u003cspan style=\"font-weight: 400\">Reading letter\u003c/span>\u003c/i>\u003cspan style=\"font-weight: 400\">] 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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse:\u003c/b>\u003cspan style=\"font-weight: 400\"> 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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Nimah Gobir:\u003c/b>\u003cspan style=\"font-weight: 400\"> But math doesn’t have to be this way.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse:\u003c/b>\u003cspan style=\"font-weight: 400\"> 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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse:\u003c/b>\u003cspan style=\"font-weight: 400\"> 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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Taylor Paris:\u003c/b> \u003cspan style=\"font-weight: 400\">And I remember being so excited because basically you’re writing in math, and that’s never the case.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Taylor Paris: \u003c/b>\u003cspan style=\"font-weight: 400\">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.’\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">Writing about those memories was cathartic. It also helped Taylor feel connected to her teacher.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Taylor Paris:\u003c/b> \u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Taylor Paris: \u003c/b>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Taylor Paris: \u003c/b>\u003cspan style=\"font-weight: 400\">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. …\u003c/span> \u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse:\u003c/b>\u003cspan style=\"font-weight: 400\"> Taylor is 20. Not that long ago, doing a math-related job would have been unimaginable to her.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Taylor Paris:\u003c/b> \u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Taylor Paris: \u003c/b>\u003cspan style=\"font-weight: 400\">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?\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">[\u003c/span>\u003ci>\u003cspan style=\"font-weight: 400\">Music\u003c/span>\u003c/i>\u003cspan style=\"font-weight: 400\">]\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">Taylor now sees herself as a doer of math. This is what’s called mathematical identity.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Nimah Gobir:\u003c/b>\u003cspan style=\"font-weight: 400\"> We did an episode featuring Chris Emdin, who talked about students’ STEM identities. Mathematical identity is one form of a STEM identity.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Sarah Strong: \u003c/b>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Sarah Strong:\u003c/b> \u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">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. \u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Nimah Gobir: \u003c/b>\u003cspan style=\"font-weight: 400\">After reading her letter, Sarah gives her students prompts for writing their own. Questions like…\u003c/span>\u003c/p>\n\u003cul>\n\u003cli style=\"font-weight: 400\">\u003cspan style=\"font-weight: 400\">What is one of your greatest mathematical strengths?\u003c/span>\u003c/li>\n\u003cli style=\"font-weight: 400\">\u003cspan style=\"font-weight: 400\">How do you plan to engage with math in the future?\u003c/span>\u003c/li>\n\u003cli style=\"font-weight: 400\">\u003cspan style=\"font-weight: 400\">What would you like more of in math classrooms?\u003c/span>\u003c/li>\n\u003c/ul>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">They spend 15 to 30 minutes writing in class. Anyone who wants to write more can finish at home.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Nimah Gobir: \u003c/b>\u003cspan style=\"font-weight: 400\">Then Sarah reads the letters on her own. She says this is the most important step.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Sarah Strong: \u003c/b>\u003cspan style=\"font-weight: 400\">‘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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">She first looks for broad patterns across the class.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Sarah Strong: \u003c/b>\u003cspan style=\"font-weight: 400\">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.\u003c/span> \u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">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 …\u003c/span>\u003c/p>\n\u003cp>\u003cb>Sarah Strong: \u003c/b>\u003cspan style=\"font-weight: 400\">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.’\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">Sarah said that getting to know students was always important to her. Even before she created the Dear Math assignment.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Sarah Strong:\u003c/b> \u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">But she wasn’t always getting a full picture.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Sarah Strong:\u003c/b> \u003cspan style=\"font-weight: 400\">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.’\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">The letters helped her take off her rose-colored glasses.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Sarah Strong:\u003c/b> \u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">That knowledge enables her to help students grow as math learners throughout the year.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Sarah Strong:\u003c/b> \u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">[\u003c/span>\u003ci>\u003cspan style=\"font-weight: 400\">Music\u003c/span>\u003c/i>\u003cspan style=\"font-weight: 400\">]\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Nimah Gobir: \u003c/b>\u003cspan style=\"font-weight: 400\">It would. But of course not every student’s math story is linear.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">No… Some math stories go up and down over time, like a periodic function. \u003c/span>\u003c/p>\n\u003cp>\u003cb>Nimah Gobir: \u003c/b>\u003cspan style=\"font-weight: 400\">Hey, nice math analogy! \u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse:\u003c/b>\u003cspan style=\"font-weight: 400\"> 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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Isabela Avila: \u003c/b>\u003cspan style=\"font-weight: 400\">[\u003c/span>\u003ci>\u003cspan style=\"font-weight: 400\">Reading letter\u003c/span>\u003c/i>\u003cspan style=\"font-weight: 400\">] 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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Isabela Avila: \u003c/b>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse:\u003c/b>\u003cspan style=\"font-weight: 400\"> That sense of togetherness mattered. \u003c/span>\u003c/p>\n\u003cp>\u003cb>Isabela Avila: \u003c/b>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Isabela Avila:\u003c/b> \u003cspan style=\"font-weight: 400\">[\u003c/span>\u003ci>\u003cspan style=\"font-weight: 400\">Reading letter\u003c/span>\u003c/i>\u003cspan style=\"font-weight: 400\">] 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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">When Isabela actually got to college, the transition was rocky. She’s a pre-med major at Johns Hopkins University in Baltimore.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Isabela Avila:\u003c/b> \u003cspan style=\"font-weight: 400\">Our like math department is known for being like notoriously hard.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse:\u003c/b>\u003cspan style=\"font-weight: 400\"> All around her, Isabela saw classmates who had come from elite high schools and seemed to understand calculus more easily than she did.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Isabela Avila: \u003c/b>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Isabela Avila: \u003c/b>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse:\u003c/b>\u003cspan style=\"font-weight: 400\"> 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.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Isabela Avila: \u003c/b>\u003cspan style=\"font-weight: 400\">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. \u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">And she said the persistence that she developed in high school did help her get through calculus.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Isabela Avila:\u003c/b> \u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">[\u003c/span>\u003ci>\u003cspan style=\"font-weight: 400\">Music\u003c/span>\u003c/i>\u003cspan style=\"font-weight: 400\">]\u003c/span>\u003c/p>\n\u003cp>\u003cb>Nimah Gobir:\u003c/b>\u003cspan style=\"font-weight: 400\"> Kara, the way Isabela compared herself to her calculus classmates isn’t unique to being at a university full of high achievers.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse:\u003c/b>\u003cspan style=\"font-weight: 400\"> 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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Nimah Gobir:\u003c/b>\u003cspan style=\"font-weight: 400\"> Researchers say even kindergarteners start to notice their spot in the pecking order of math ability.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">It often starts with those one-minute math quizzes that so many of us remember.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">[\u003c/span>\u003ci>\u003cspan style=\"font-weight: 400\">Sound of pencils scribbling and slamming down\u003c/span>\u003c/i>\u003cspan style=\"font-weight: 400\">]\u003c/span>\u003c/p>\n\u003cp>\u003cb>Nimah Gobir: \u003c/b>\u003cspan style=\"font-weight: 400\">Students might hear their classmates furiously scribbling answers and slamming their pencils down when they finish. They equate that with being “good” at math.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">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. \u003c/span>\u003c/p>\n\u003cp>\u003cb>Nimah Gobir: \u003c/b>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Rachel Lambert: \u003c/b>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Rachel Lambert: \u003c/b>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse:\u003c/b>\u003cspan style=\"font-weight: 400\"> 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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Rachel Lambert: \u003c/b>\u003cspan style=\"font-weight: 400\">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. \u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">Rachel’s second tip for teachers is to stop focusing on speed. \u003c/span>\u003c/p>\n\u003cp>\u003cb>Rachel Lambert:\u003c/b> \u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Rachel Lambert: \u003c/b>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse:\u003c/b>\u003cspan style=\"font-weight: 400\"> Tip number four is to give students problems that can be approached from multiple angles.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Rachel Lambert:\u003c/b> \u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">Rachel Lambert’s fifth and final tip is to make supports available to everyone.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Rachel Lambert: \u003c/b>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">[\u003c/span>\u003ci>\u003cspan style=\"font-weight: 400\">Music\u003c/span>\u003c/i>\u003cspan style=\"font-weight: 400\">]\u003c/span>\u003c/p>\n\u003cp>\u003cb>Nimah Gobir: \u003c/b>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">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.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Nimah Gobir: \u003c/b>\u003cspan style=\"font-weight: 400\">Kids who are absorbed in math problem-solving often express wonder and excitement.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">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 \u003c/span>\u003ci>\u003cspan style=\"font-weight: 400\">believe \u003c/span>\u003c/i>\u003cspan style=\"font-weight: 400\">in their math abilities, it empowers them to learn math and to do math.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">[\u003c/span>\u003ci>\u003cspan style=\"font-weight: 400\">Music\u003c/span>\u003c/i>\u003cspan style=\"font-weight: 400\">]\u003c/span>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse: \u003c/b>\u003cspan style=\"font-weight: 400\">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, \u003c/span>\u003ci>\u003cspan style=\"font-weight: 400\">Dear Math: Why Kids Hate Math and What Teachers Can Do About It.\u003c/span>\u003c/i>\u003cspan style=\"font-weight: 400\"> \u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Thanks also to Taylor Paris, Isabela Avila, Rachel Lambert and Amy Parks.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">The MindShift team includes Nimah Gobir, Ki Sung, Marlena Jackson-Retondo and me, Kara Newhouse.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Our editor is Chris Hambrick. Chris Hoff engineered this episode.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Additional support from Jen Chien, Katie Sprenger, Cesar Saldaña and Holly Kernan.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">MindShift is supported in part by the generosity of the William & Flora Hewlett Foundation and members of KQED.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Nimah Gobir:\u003c/b>\u003cspan style=\"font-weight: 400\"> 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 \u003c/span>\u003ca href=\"http://kqed.org/mindshift\">\u003cspan style=\"font-weight: 400\">kqed.org/mindshift\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">.\u003c/span>\u003c/p>\n\u003cp>\u003c/p>\u003c/div>","attributes":{"named":{},"numeric":[]}},{"type":"component","content":"","name":"ad","attributes":{"named":{"label":"floatright"},"numeric":["floatright"]}},{"type":"contentString","content":"\u003cdiv class=\"post-body\">\u003cp>\u003c/p>\n\u003cp>\u003cb>Kara Newhouse:\u003c/b>\u003cspan style=\"font-weight: 400\"> 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.\u003c/span>\u003c/p>\n\n\u003c/div>\u003c/p>","attributes":{"named":{},"numeric":[]}}],"link":"/mindshift/62436/how-listening-to-students-stories-can-improve-math-class","authors":["11487"],"categories":["mindshift_192","mindshift_21130","mindshift_193"],"tags":["mindshift_21794","mindshift_20994","mindshift_21792","mindshift_21611","mindshift_21341","mindshift_392","mindshift_20893","mindshift_21795","mindshift_21796","mindshift_46","mindshift_21640","mindshift_21793","mindshift_47","mindshift_20852","mindshift_21642"],"featImg":"mindshift_62441","label":"mindshift"},"mindshift_56564":{"type":"posts","id":"mindshift_56564","meta":{"index":"posts_1591205157","site":"mindshift","id":"56564","score":null,"sort":[1601280711000]},"guestAuthors":[],"slug":"how-encouraging-rough-draft-thinking-in-math-class-highlights-the-strengths-of-all-students","title":"How Encouraging Rough Draft Thinking in Math Class Highlights the Strengths of All Students","publishDate":1601280711,"format":"standard","headTitle":"MindShift | KQED News","labelTerm":{"site":"mindshift"},"content":"\u003cp>\u003ci>\u003cspan style=\"font-weight: 400\">This is the first article in a\u003ca href=\"https://www.kqed.org/mindshift/56566/what-it-looks-like-when-students-share-and-revise-rough-drafts-in-math-class\"> two-part\u003c/a> series about rough draft math, a concept that applies a process from language arts — creating, discussing and revising rough drafts — to math classrooms. In this Q&A, \u003c/span>\u003c/i>\u003ca href=\"https://twitter.com/MandyMathEd\">\u003ci>\u003cspan style=\"font-weight: 400\">Amanda Jansen\u003c/span>\u003c/i>\u003c/a>\u003ci>\u003cspan style=\"font-weight: 400\">, a University of Delaware math education researcher, discusses how framing math as a shared exploration, rather than a set of right or wrong steps, enables more students to develop math competence and confidence. Jansen is the author of \u003c/span>\u003c/i>\u003ca href=\"https://www.stenhouse.com/content/rough-draft-math\">\u003ci>\u003cspan style=\"font-weight: 400\">Rough Draft Math: Revising to Learn\u003c/span>\u003c/i>\u003c/a>\u003ci>\u003cspan style=\"font-weight: 400\">, published this year by Stenhouse. In \u003ca href=\"https://www.kqed.org/mindshift/56566/what-it-looks-like-when-students-share-and-revise-rough-drafts-in-math-class\">part two\u003c/a>, learn some strategies for how to foster rough draft talk and how to structure revisions in math classrooms.\u003c/span>\u003c/i>\u003c/p>\n\u003cp>\u003cb>You wrote that it is your dream for mathematics classrooms to shift from places of performance to places of exploration. What does that mean?\u003c/b>\u003c/p>\n\u003cp>\u003cb>Jansen: \u003c/b>\u003cspan style=\"font-weight: 400\">When I think about math class being a place for performance, I think about the experiences that we may have had when we're asked to talk about our thinking and we find it as if we're being judged. “Correct.” “Not correct.” And it's in public, in front of everyone. It’s more of an evaluation space in that moment. Instead, discussions can be a place where we're all learning together from what anyone shares. If we shift our role as a teacher from an evaluator to more of someone that's making sense out of ideas along with people, that's a very different way of interacting. And the job of a student in the classroom is different. I'm going to \u003c/span>\u003ca href=\"https://www.kqed.org/mindshift/56136/talking-math-with-tweens-how-to-bring-math-into-daily-life-with-middle-schoolers\">\u003cspan style=\"font-weight: 400\">explore with you\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">. I'm going to share that idea. I'm not sure about it. And it's OK. And there's going to be something that we can learn from anyone's idea.\u003c/span>\u003c/p>\n\u003cp>\u003cb>It might be more intuitive the ways that this approach can benefit students who struggle with math. How does it also benefit students who get the correct answer the first time?\u003c/b>\u003c/p>\n\u003cp>\u003cb>Jansen: \u003c/b>\u003cspan style=\"font-weight: 400\">Really it opens up \u003c/span>\u003ca href=\"https://www.kqed.org/mindshift/54389/3-ways-to-shape-math-into-a-positive-experience\">\u003cspan style=\"font-weight: 400\">what it means to be good at math\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">. Not just getting a correct answer quickly. So initially it's hard, but in the bigger picture, it's more liberating for all the students because they can start to see how they're contributing to their colleagues’ learning in a lot of \u003c/span>\u003ca href=\"https://www.kqed.org/mindshift/53767/getting-physical-how-the-flagway-game-sparks-learning-and-love-of-math\">\u003cspan style=\"font-weight: 400\">different ways\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">. Ultimately, after that initial shift, people do start to get more excited, like, “Wow, my ideas actually matter. My thinking actually matters in that space. My ideas have value.” Everyone feels included in that kind of environment.\u003c/span>\u003c/p>\n\u003cp>[ad fullwidth]\u003c/p>\n\u003cp>\u003cb>You alluded to how speed is often seen as the marker of math success. What are some other ways of being smart in math that can be highlighted via rough draft thinking?\u003c/b>\u003c/p>\n\u003cp>\u003cb>Jansen: \u003c/b>\u003cspan style=\"font-weight: 400\">You can ask a question about someone else's thinking, and it could \u003c/span>\u003ca href=\"https://www.kqed.org/mindshift/54504/three-simple-tech-tools-to-make-math-thinking-visible\">\u003cspan style=\"font-weight: 400\">help the whole class learn something more\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">. You can notice how two people's ideas are related, and then you're making a new connection. You can represent somebody else's thinking in a new way, like a \u003c/span>\u003ca href=\"https://www.kqed.org/mindshift/55961/how-sidewalk-math-cultivates-a-playful-curious-attitude-towards-math\">\u003cspan style=\"font-weight: 400\">drawing\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> or a graph. You can write an explanation that makes more sense to the class than what the teacher's explanation communicated. So there are all kinds of ways that the students can then contribute to help the whole class learn more that's not about getting an answer correct quickly. And those ideas are not new for rough draft math. They're really rooted in the ideas of \u003c/span>\u003ca href=\"https://complexinstruction.stanford.edu/\">\u003cspan style=\"font-weight: 400\">complex instruction\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">.\u003c/span>\u003c/p>\n\u003cp>\u003cb>\u003ca href=\"https://www.stenhouse.com/content/rough-draft-math\">\u003cimg class=\"alignright wp-image-56707\" src=\"https://ww2.kqed.org/app/uploads/sites/23/2020/08/Rough-Draft-Math_Jansen_final-cover_web-rgb.jpg\" alt=\"\" width=\"200\" height=\"251\" srcset=\"https://ww2.kqed.org/app/uploads/sites/23/2020/08/Rough-Draft-Math_Jansen_final-cover_web-rgb.jpg 560w, https://ww2.kqed.org/app/uploads/sites/23/2020/08/Rough-Draft-Math_Jansen_final-cover_web-rgb-160x201.jpg 160w\" sizes=\"(max-width: 200px) 100vw, 200px\">\u003c/a>Your book takes us inside some classrooms to show how teachers facilitate students sharing solution strategies before they've refined them. How does this benefit both the speaker and the listener?\u003c/b>\u003c/p>\n\u003cp>\u003cb>Jansen: \u003c/b>\u003cspan style=\"font-weight: 400\">The speaker is benefiting in a few ways. Every time we're being asked to articulate our thinking we make new connections or crystallize our ideas just by trying to put them into words or trying to put them into writing. And the class is going to try and make sense out of what they shared, so then they have that experience of their \u003c/span>\u003ca href=\"https://www.kqed.org/mindshift/54486/how-collaboration-unlocks-learning-and-lessens-student-isolation\">\u003cspan style=\"font-weight: 400\">ideas being taken seriously in the community\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">. Hopefully multiple people are asked to share and there's a conversation about that person's thinking, so who’s the speaker and who's the listener should start shifting pretty quickly. But if you are listening in whatever moment, you're benefiting because you're thinking about what they said, you may get a new perspective on how to think about an idea that you hadn't thought about before. You might feel validated, as if, “Oh, this person thinks in ways that are similar to me.” You could feel challenged. And you could feel interested in helping that person revise.\u003c/span>\u003c/p>\n\u003cp>\u003cb>The book also includes different methods for enabling students to \u003c/b>\u003ca href=\"https://www.kqed.org/mindshift/53524/how-revising-math-exams-turns-students-into-learners-not-processors\">\u003cb>revise their work\u003c/b>\u003c/a>\u003cb> and to reflect on their revisions. Why is reflection important?\u003c/b>\u003c/p>\n\u003cp>\u003cb>Jansen:\u003c/b>\u003cspan style=\"font-weight: 400\"> There's a phenomenon that when you understand something new and you develop a deep understanding for it, you feel like you've always known it. \u003c/span>\u003ca href=\"https://www.kqed.org/mindshift/54983/10-nonfiction-childrens-books-that-humanize-mathematics\">\u003cspan style=\"font-weight: 400\">Honoring that history\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> of how the idea came to evolve helps you when you hit a new topic that's very amorphous and challenging to understand. It \u003c/span>\u003ca href=\"https://www.kqed.org/mindshift/53404/why-normalizing-struggle-can-create-a-better-math-experience-for-kids\">\u003cspan style=\"font-weight: 400\">normalizes\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> and reminds you about the ongoing learning process. At the same time, I think it creates this sense of intellectual connection to the other people in the room. You realize that we all need each other, that it's a great opportunity to be able to \u003c/span>\u003ca href=\"https://www.kqed.org/mindshift/55327/how-hands-on-projects-can-deepen-math-learning-for-teens\">\u003cspan style=\"font-weight: 400\">learn with other people\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">.\u003c/span>\u003c/p>\n\u003cp>\u003cb>How might these practices improve racial, gender or socioeconomic equity in math classrooms?\u003c/b>\u003c/p>\n\u003cp>\u003cb>Jansen: \u003c/b>\u003cspan style=\"font-weight: 400\">There may be students who are consistently seen by their peers as not being academically strong in whatever way. Sometimes those ways of seeing their peers might fall under racial lines or gender lines. And if, through rough drafts, everyone's ideas have strengths in them and the teacher points out what's valuable about the drafts, and then their peers start to point out what's valuable, then everyone is seeing each other as having some mathematical strengths. That's a powerful thing that we should all be doing for each other all the time.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">There are things to be concerned about so we don't create \u003c/span>\u003ca href=\"https://www.kqed.org/mindshift/43704/is-quality-math-preparation-the-next-equity-battleground\">\u003cspan style=\"font-weight: 400\">additional equity dilemmas\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> when we're dealing with rough drafts. One is whose work is being positioned as being rough, and whose work is being positioned as more refined. So I started keeping track in my own class with a clipboard: Who is being called upon in what time in the lesson? Are we only calling on girls in the rough drafts or positioning Black or brown students as having rough draft thinking? They can also have \u003c/span>\u003ca href=\"https://www.kqed.org/mindshift/54986/how-black-girls-benefit-when-math-has-social-interaction-and-ways-to-learn-together\">\u003cspan style=\"font-weight: 400\">brilliant, refined thinking\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> and we need to make sure not only are they having a \u003c/span>\u003ca href=\"https://www.kqed.org/mindshift/56393/why-student-voice-is-critical-for-managing-discipline-when-schools-reopen\">\u003cspan style=\"font-weight: 400\">voice\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">, but their strengths are being really looked at.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Rough draft math involves more discussion of problems than many of us experienced in math class. How does this work out for \u003c/b>\u003ca href=\"https://www.kqed.org/mindshift/tag/introvert\">\u003cb>quiet kids\u003c/b>\u003c/a>\u003cb>?\u003c/b>\u003c/p>\n\u003cp>\u003cb>Jansen:\u003c/b>\u003cspan style=\"font-weight: 400\"> I think that also rough draft math should involve \u003c/span>\u003ca href=\"https://www.kqed.org/mindshift/50640/how-reading-novels-in-math-class-can-strengthen-student-engagement\">\u003cspan style=\"font-weight: 400\">writing\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">. A lot of the revision practices are individual. So there is a lot of discussion with rough draft spaces, but there's also these built-in individual revision opportunities that everyone should be experiencing because individual writing is also the space where your thinking continues to grow. However, when I have (quieter students), I do gently challenge them to share, because if they aren't sharing in the public space, their colleagues are missing out on their ideas.\u003c/span>\u003c/p>\n\u003cp>\u003cb>What differences do you see in students’ affect and engagement when they feel safe to refine and revise their thinking?\u003c/b>\u003c/p>\n\u003cp>\u003cb>Jansen:\u003c/b>\u003cspan style=\"font-weight: 400\"> People show up with this sense of just feeling happy to be there. They are uniquely interested in each other's thinking because they know that they're learning in community to develop ideas together. They are more likely to just put something out there, whether it's in the group work that they're working on or coming up to the document camera to share their thinking. There's less waiting for a student to volunteer. There just seems to be a little less \u003c/span>\u003ca href=\"https://www.kqed.org/mindshift/tag/math-anxiety\">\u003cspan style=\"font-weight: 400\">stress\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">. People also tend to feel proud. If someone's recognizing that their ideas helped them, they feel this sense of pride.\u003c/span>\u003c/p>\n\u003cp>\u003cb>What are some of the barriers to teachers adopting this approach?\u003c/b>\u003c/p>\n\u003cp>\u003cb>Jansen: \u003c/b>\u003cspan style=\"font-weight: 400\">If you've never experienced a space that encourages those ideas, that's hard to recreate. If you do have this vision rooted in some experiences, what takes more time for folks is building in revision experiences. At first it’s the initial setting up of revision expectations that takes more time. Then, over time, adding in the revision isn't as much work. It takes less time than we think it will after we do this many times with students. And teachers I have known have used rough drafts with honors classes, with classes that have a lot of special education students, English language learners, and they’ve reported benefits.\u003c/span>\u003c/p>\n\u003cp>\u003cb>What can rough draft math look like in \u003c/b>\u003ca href=\"https://www.kqed.org/mindshift/tag/distance-learning\">\u003cb>online teaching\u003c/b>\u003c/a>\u003cb>?\u003c/b>\u003c/p>\n\u003cp>\u003cb>Jansen: \u003c/b>\u003cspan style=\"font-weight: 400\">(For synchronous learning), you can do a lot of communicating to students that \u003ca href=\"https://www.kqed.org/mindshift/56570/6-classroom-strategies-that-work-for-generating-student-discussions-online\">their ideas are valuable\u003c/a> and making sure you're helping them elicit the drafts. A lot of people have had success using Google slides where you can still put the students in small groups to write up their thinking and then have the groups look at each other's slides and talk in the in the whole group and then go back and revise your slides and then write in the notes how you changed your ideas and why. You can even, at the end of class, have them write a Google form reflection about how their thinking changed and why. For asynchronous, I've seen folks have some success using discussion boards. So essentially the principle of giving people the opportunity to share their first thinking and then revise it. You can imagine different structures online that people have had success with. But it's also a lot of us, this year, we knew folks face to face for a period of time before we went online. So now people are talking about what does it take to set up the classroom culture when we may need to be online from the beginning? What kinds of \u003c/span>\u003ca href=\"https://www.kqed.org/mindshift/54980/why-teachers-want-math-with-more-human-ties\">\u003cspan style=\"font-weight: 400\">relationship building experiences\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> do we need to do?\u003c/span>\u003c/p>\n\u003cp>\u003cb>How can teachers apply the principles of rough draft thinking to how they reflect their own successes and failures in the classroom?\u003c/b>\u003c/p>\n\u003cp>[ad floatright]\u003c/p>\n\u003cp>\u003cb>Jansen: \u003c/b>\u003cspan style=\"font-weight: 400\">I've found that if I treat my work as a teacher as a draft, then a misstep is a \u003c/span>\u003ca href=\"https://www.kqed.org/mindshift/tag/growth-mindset\">\u003cspan style=\"font-weight: 400\">learning opportunity\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">, not something to get frustrated about. I can be proud of trying out the new things I'm trying out and my revisions that I can even apply to the next class. I don't have to wait until the next year or revise. I'm also growing as a learner about the mathematics, because I learn from how my students are making sense out of things, too. I think that's an important thing as a teacher to really make it clear: that we are all learning together.\u003c/span>\u003c/p>\n\n","blocks":[],"excerpt":null,"status":"publish","parent":0,"modified":1601310235,"stats":{"hasAudio":false,"hasVideo":false,"hasChartOrMap":false,"iframeSrcs":[],"hasGoogleForm":false,"hasGallery":false,"hasHearkenModule":false,"hasPolis":false,"paragraphCount":26,"wordCount":1880},"headData":{"title":"How Encouraging Rough Draft Thinking in Math Class Highlights the Strengths of All Students - MindShift","description":"This is the first article in a two-part series about rough draft math, a concept that applies a process from language arts — creating, discussing and revising rough drafts — to math classrooms. In this Q&A, Amanda Jansen, a University of Delaware math education researcher, discusses how framing math as a shared exploration, rather than","ogTitle":"","ogDescription":"","ogImgId":"","twTitle":"","twDescription":"","twImgId":""},"disqusIdentifier":"56564 https://ww2.kqed.org/mindshift/?p=56564","disqusUrl":"https://ww2.kqed.org/mindshift/2020/09/28/how-encouraging-rough-draft-thinking-in-math-class-highlights-the-strengths-of-all-students/","disqusTitle":"How Encouraging Rough Draft Thinking in Math Class Highlights the Strengths of All Students","path":"/mindshift/56564/how-encouraging-rough-draft-thinking-in-math-class-highlights-the-strengths-of-all-students","audioTrackLength":null,"parsedContent":[{"type":"contentString","content":"\u003cdiv class=\"post-body\">\u003cp>\u003cp>\u003ci>\u003cspan style=\"font-weight: 400\">This is the first article in a\u003ca href=\"https://www.kqed.org/mindshift/56566/what-it-looks-like-when-students-share-and-revise-rough-drafts-in-math-class\"> two-part\u003c/a> series about rough draft math, a concept that applies a process from language arts — creating, discussing and revising rough drafts — to math classrooms. In this Q&A, \u003c/span>\u003c/i>\u003ca href=\"https://twitter.com/MandyMathEd\">\u003ci>\u003cspan style=\"font-weight: 400\">Amanda Jansen\u003c/span>\u003c/i>\u003c/a>\u003ci>\u003cspan style=\"font-weight: 400\">, a University of Delaware math education researcher, discusses how framing math as a shared exploration, rather than a set of right or wrong steps, enables more students to develop math competence and confidence. Jansen is the author of \u003c/span>\u003c/i>\u003ca href=\"https://www.stenhouse.com/content/rough-draft-math\">\u003ci>\u003cspan style=\"font-weight: 400\">Rough Draft Math: Revising to Learn\u003c/span>\u003c/i>\u003c/a>\u003ci>\u003cspan style=\"font-weight: 400\">, published this year by Stenhouse. In \u003ca href=\"https://www.kqed.org/mindshift/56566/what-it-looks-like-when-students-share-and-revise-rough-drafts-in-math-class\">part two\u003c/a>, learn some strategies for how to foster rough draft talk and how to structure revisions in math classrooms.\u003c/span>\u003c/i>\u003c/p>\n\u003cp>\u003cb>You wrote that it is your dream for mathematics classrooms to shift from places of performance to places of exploration. What does that mean?\u003c/b>\u003c/p>\n\u003cp>\u003cb>Jansen: \u003c/b>\u003cspan style=\"font-weight: 400\">When I think about math class being a place for performance, I think about the experiences that we may have had when we're asked to talk about our thinking and we find it as if we're being judged. “Correct.” “Not correct.” And it's in public, in front of everyone. It’s more of an evaluation space in that moment. Instead, discussions can be a place where we're all learning together from what anyone shares. If we shift our role as a teacher from an evaluator to more of someone that's making sense out of ideas along with people, that's a very different way of interacting. And the job of a student in the classroom is different. I'm going to \u003c/span>\u003ca href=\"https://www.kqed.org/mindshift/56136/talking-math-with-tweens-how-to-bring-math-into-daily-life-with-middle-schoolers\">\u003cspan style=\"font-weight: 400\">explore with you\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">. I'm going to share that idea. I'm not sure about it. And it's OK. And there's going to be something that we can learn from anyone's idea.\u003c/span>\u003c/p>\n\u003cp>\u003cb>It might be more intuitive the ways that this approach can benefit students who struggle with math. How does it also benefit students who get the correct answer the first time?\u003c/b>\u003c/p>\n\u003cp>\u003cb>Jansen: \u003c/b>\u003cspan style=\"font-weight: 400\">Really it opens up \u003c/span>\u003ca href=\"https://www.kqed.org/mindshift/54389/3-ways-to-shape-math-into-a-positive-experience\">\u003cspan style=\"font-weight: 400\">what it means to be good at math\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">. Not just getting a correct answer quickly. So initially it's hard, but in the bigger picture, it's more liberating for all the students because they can start to see how they're contributing to their colleagues’ learning in a lot of \u003c/span>\u003ca href=\"https://www.kqed.org/mindshift/53767/getting-physical-how-the-flagway-game-sparks-learning-and-love-of-math\">\u003cspan style=\"font-weight: 400\">different ways\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">. Ultimately, after that initial shift, people do start to get more excited, like, “Wow, my ideas actually matter. My thinking actually matters in that space. My ideas have value.” Everyone feels included in that kind of environment.\u003c/span>\u003c/p>\n\u003cp>\u003c/p>\u003c/div>","attributes":{"named":{},"numeric":[]}},{"type":"component","content":"","name":"ad","attributes":{"named":{"label":"fullwidth"},"numeric":["fullwidth"]}},{"type":"contentString","content":"\u003cdiv class=\"post-body\">\u003cp>\u003c/p>\n\u003cp>\u003cb>You alluded to how speed is often seen as the marker of math success. What are some other ways of being smart in math that can be highlighted via rough draft thinking?\u003c/b>\u003c/p>\n\u003cp>\u003cb>Jansen: \u003c/b>\u003cspan style=\"font-weight: 400\">You can ask a question about someone else's thinking, and it could \u003c/span>\u003ca href=\"https://www.kqed.org/mindshift/54504/three-simple-tech-tools-to-make-math-thinking-visible\">\u003cspan style=\"font-weight: 400\">help the whole class learn something more\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">. You can notice how two people's ideas are related, and then you're making a new connection. You can represent somebody else's thinking in a new way, like a \u003c/span>\u003ca href=\"https://www.kqed.org/mindshift/55961/how-sidewalk-math-cultivates-a-playful-curious-attitude-towards-math\">\u003cspan style=\"font-weight: 400\">drawing\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> or a graph. You can write an explanation that makes more sense to the class than what the teacher's explanation communicated. So there are all kinds of ways that the students can then contribute to help the whole class learn more that's not about getting an answer correct quickly. And those ideas are not new for rough draft math. They're really rooted in the ideas of \u003c/span>\u003ca href=\"https://complexinstruction.stanford.edu/\">\u003cspan style=\"font-weight: 400\">complex instruction\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">.\u003c/span>\u003c/p>\n\u003cp>\u003cb>\u003ca href=\"https://www.stenhouse.com/content/rough-draft-math\">\u003cimg class=\"alignright wp-image-56707\" src=\"https://ww2.kqed.org/app/uploads/sites/23/2020/08/Rough-Draft-Math_Jansen_final-cover_web-rgb.jpg\" alt=\"\" width=\"200\" height=\"251\" srcset=\"https://ww2.kqed.org/app/uploads/sites/23/2020/08/Rough-Draft-Math_Jansen_final-cover_web-rgb.jpg 560w, https://ww2.kqed.org/app/uploads/sites/23/2020/08/Rough-Draft-Math_Jansen_final-cover_web-rgb-160x201.jpg 160w\" sizes=\"(max-width: 200px) 100vw, 200px\">\u003c/a>Your book takes us inside some classrooms to show how teachers facilitate students sharing solution strategies before they've refined them. How does this benefit both the speaker and the listener?\u003c/b>\u003c/p>\n\u003cp>\u003cb>Jansen: \u003c/b>\u003cspan style=\"font-weight: 400\">The speaker is benefiting in a few ways. Every time we're being asked to articulate our thinking we make new connections or crystallize our ideas just by trying to put them into words or trying to put them into writing. And the class is going to try and make sense out of what they shared, so then they have that experience of their \u003c/span>\u003ca href=\"https://www.kqed.org/mindshift/54486/how-collaboration-unlocks-learning-and-lessens-student-isolation\">\u003cspan style=\"font-weight: 400\">ideas being taken seriously in the community\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">. Hopefully multiple people are asked to share and there's a conversation about that person's thinking, so who’s the speaker and who's the listener should start shifting pretty quickly. But if you are listening in whatever moment, you're benefiting because you're thinking about what they said, you may get a new perspective on how to think about an idea that you hadn't thought about before. You might feel validated, as if, “Oh, this person thinks in ways that are similar to me.” You could feel challenged. And you could feel interested in helping that person revise.\u003c/span>\u003c/p>\n\u003cp>\u003cb>The book also includes different methods for enabling students to \u003c/b>\u003ca href=\"https://www.kqed.org/mindshift/53524/how-revising-math-exams-turns-students-into-learners-not-processors\">\u003cb>revise their work\u003c/b>\u003c/a>\u003cb> and to reflect on their revisions. Why is reflection important?\u003c/b>\u003c/p>\n\u003cp>\u003cb>Jansen:\u003c/b>\u003cspan style=\"font-weight: 400\"> There's a phenomenon that when you understand something new and you develop a deep understanding for it, you feel like you've always known it. \u003c/span>\u003ca href=\"https://www.kqed.org/mindshift/54983/10-nonfiction-childrens-books-that-humanize-mathematics\">\u003cspan style=\"font-weight: 400\">Honoring that history\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> of how the idea came to evolve helps you when you hit a new topic that's very amorphous and challenging to understand. It \u003c/span>\u003ca href=\"https://www.kqed.org/mindshift/53404/why-normalizing-struggle-can-create-a-better-math-experience-for-kids\">\u003cspan style=\"font-weight: 400\">normalizes\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> and reminds you about the ongoing learning process. At the same time, I think it creates this sense of intellectual connection to the other people in the room. You realize that we all need each other, that it's a great opportunity to be able to \u003c/span>\u003ca href=\"https://www.kqed.org/mindshift/55327/how-hands-on-projects-can-deepen-math-learning-for-teens\">\u003cspan style=\"font-weight: 400\">learn with other people\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">.\u003c/span>\u003c/p>\n\u003cp>\u003cb>How might these practices improve racial, gender or socioeconomic equity in math classrooms?\u003c/b>\u003c/p>\n\u003cp>\u003cb>Jansen: \u003c/b>\u003cspan style=\"font-weight: 400\">There may be students who are consistently seen by their peers as not being academically strong in whatever way. Sometimes those ways of seeing their peers might fall under racial lines or gender lines. And if, through rough drafts, everyone's ideas have strengths in them and the teacher points out what's valuable about the drafts, and then their peers start to point out what's valuable, then everyone is seeing each other as having some mathematical strengths. That's a powerful thing that we should all be doing for each other all the time.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">There are things to be concerned about so we don't create \u003c/span>\u003ca href=\"https://www.kqed.org/mindshift/43704/is-quality-math-preparation-the-next-equity-battleground\">\u003cspan style=\"font-weight: 400\">additional equity dilemmas\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> when we're dealing with rough drafts. One is whose work is being positioned as being rough, and whose work is being positioned as more refined. So I started keeping track in my own class with a clipboard: Who is being called upon in what time in the lesson? Are we only calling on girls in the rough drafts or positioning Black or brown students as having rough draft thinking? They can also have \u003c/span>\u003ca href=\"https://www.kqed.org/mindshift/54986/how-black-girls-benefit-when-math-has-social-interaction-and-ways-to-learn-together\">\u003cspan style=\"font-weight: 400\">brilliant, refined thinking\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> and we need to make sure not only are they having a \u003c/span>\u003ca href=\"https://www.kqed.org/mindshift/56393/why-student-voice-is-critical-for-managing-discipline-when-schools-reopen\">\u003cspan style=\"font-weight: 400\">voice\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">, but their strengths are being really looked at.\u003c/span>\u003c/p>\n\u003cp>\u003cb>Rough draft math involves more discussion of problems than many of us experienced in math class. How does this work out for \u003c/b>\u003ca href=\"https://www.kqed.org/mindshift/tag/introvert\">\u003cb>quiet kids\u003c/b>\u003c/a>\u003cb>?\u003c/b>\u003c/p>\n\u003cp>\u003cb>Jansen:\u003c/b>\u003cspan style=\"font-weight: 400\"> I think that also rough draft math should involve \u003c/span>\u003ca href=\"https://www.kqed.org/mindshift/50640/how-reading-novels-in-math-class-can-strengthen-student-engagement\">\u003cspan style=\"font-weight: 400\">writing\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">. A lot of the revision practices are individual. So there is a lot of discussion with rough draft spaces, but there's also these built-in individual revision opportunities that everyone should be experiencing because individual writing is also the space where your thinking continues to grow. However, when I have (quieter students), I do gently challenge them to share, because if they aren't sharing in the public space, their colleagues are missing out on their ideas.\u003c/span>\u003c/p>\n\u003cp>\u003cb>What differences do you see in students’ affect and engagement when they feel safe to refine and revise their thinking?\u003c/b>\u003c/p>\n\u003cp>\u003cb>Jansen:\u003c/b>\u003cspan style=\"font-weight: 400\"> People show up with this sense of just feeling happy to be there. They are uniquely interested in each other's thinking because they know that they're learning in community to develop ideas together. They are more likely to just put something out there, whether it's in the group work that they're working on or coming up to the document camera to share their thinking. There's less waiting for a student to volunteer. There just seems to be a little less \u003c/span>\u003ca href=\"https://www.kqed.org/mindshift/tag/math-anxiety\">\u003cspan style=\"font-weight: 400\">stress\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">. People also tend to feel proud. If someone's recognizing that their ideas helped them, they feel this sense of pride.\u003c/span>\u003c/p>\n\u003cp>\u003cb>What are some of the barriers to teachers adopting this approach?\u003c/b>\u003c/p>\n\u003cp>\u003cb>Jansen: \u003c/b>\u003cspan style=\"font-weight: 400\">If you've never experienced a space that encourages those ideas, that's hard to recreate. If you do have this vision rooted in some experiences, what takes more time for folks is building in revision experiences. At first it’s the initial setting up of revision expectations that takes more time. Then, over time, adding in the revision isn't as much work. It takes less time than we think it will after we do this many times with students. And teachers I have known have used rough drafts with honors classes, with classes that have a lot of special education students, English language learners, and they’ve reported benefits.\u003c/span>\u003c/p>\n\u003cp>\u003cb>What can rough draft math look like in \u003c/b>\u003ca href=\"https://www.kqed.org/mindshift/tag/distance-learning\">\u003cb>online teaching\u003c/b>\u003c/a>\u003cb>?\u003c/b>\u003c/p>\n\u003cp>\u003cb>Jansen: \u003c/b>\u003cspan style=\"font-weight: 400\">(For synchronous learning), you can do a lot of communicating to students that \u003ca href=\"https://www.kqed.org/mindshift/56570/6-classroom-strategies-that-work-for-generating-student-discussions-online\">their ideas are valuable\u003c/a> and making sure you're helping them elicit the drafts. A lot of people have had success using Google slides where you can still put the students in small groups to write up their thinking and then have the groups look at each other's slides and talk in the in the whole group and then go back and revise your slides and then write in the notes how you changed your ideas and why. You can even, at the end of class, have them write a Google form reflection about how their thinking changed and why. For asynchronous, I've seen folks have some success using discussion boards. So essentially the principle of giving people the opportunity to share their first thinking and then revise it. You can imagine different structures online that people have had success with. But it's also a lot of us, this year, we knew folks face to face for a period of time before we went online. So now people are talking about what does it take to set up the classroom culture when we may need to be online from the beginning? What kinds of \u003c/span>\u003ca href=\"https://www.kqed.org/mindshift/54980/why-teachers-want-math-with-more-human-ties\">\u003cspan style=\"font-weight: 400\">relationship building experiences\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\"> do we need to do?\u003c/span>\u003c/p>\n\u003cp>\u003cb>How can teachers apply the principles of rough draft thinking to how they reflect their own successes and failures in the classroom?\u003c/b>\u003c/p>\n\u003cp>\u003c/p>\u003c/div>","attributes":{"named":{},"numeric":[]}},{"type":"component","content":"","name":"ad","attributes":{"named":{"label":"floatright"},"numeric":["floatright"]}},{"type":"contentString","content":"\u003cdiv class=\"post-body\">\u003cp>\u003c/p>\n\u003cp>\u003cb>Jansen: \u003c/b>\u003cspan style=\"font-weight: 400\">I've found that if I treat my work as a teacher as a draft, then a misstep is a \u003c/span>\u003ca href=\"https://www.kqed.org/mindshift/tag/growth-mindset\">\u003cspan style=\"font-weight: 400\">learning opportunity\u003c/span>\u003c/a>\u003cspan style=\"font-weight: 400\">, not something to get frustrated about. I can be proud of trying out the new things I'm trying out and my revisions that I can even apply to the next class. I don't have to wait until the next year or revise. I'm also growing as a learner about the mathematics, because I learn from how my students are making sense out of things, too. I think that's an important thing as a teacher to really make it clear: that we are all learning together.\u003c/span>\u003c/p>\n\n\u003c/div>\u003c/p>","attributes":{"named":{},"numeric":[]}}],"link":"/mindshift/56564/how-encouraging-rough-draft-thinking-in-math-class-highlights-the-strengths-of-all-students","authors":["11487"],"categories":["mindshift_193"],"tags":["mindshift_20994","mindshift_392","mindshift_20893"],"featImg":"mindshift_56712","label":"mindshift"},"mindshift_56566":{"type":"posts","id":"mindshift_56566","meta":{"index":"posts_1591205157","site":"mindshift","id":"56566","score":null,"sort":[1601280681000]},"guestAuthors":[],"slug":"what-it-looks-like-when-students-share-and-revise-rough-drafts-in-math-class","title":"What It Looks Like When Students Share and Revise Rough Drafts in Math Class ","publishDate":1601280681,"format":"standard","headTitle":"MindShift | KQED News","labelTerm":{"site":"mindshift"},"content":"\u003cp>\u003ci>\u003cspan style=\"font-weight: 400\">Excerpted from \u003c/span>\u003c/i>\u003ca href=\"https://www.stenhouse.com/content/rough-draft-math\">\u003ci>\u003cspan style=\"font-weight: 400\">Rough Draft Math: Revising to Learn\u003c/span>\u003c/i>\u003c/a>\u003ci>\u003cspan style=\"font-weight: 400\"> by Amanda Jansen, copyright © 2020, reproduced with permission of Stenhouse Publishers. www.stenhouse.com\u003c/span>\u003c/i>\u003c/p>\n\u003cp>\u003ci>\u003cspan style=\"font-weight: 400\">This is the second article in a two-part series about rough draft math. In the \u003ca href=\"https://www.kqed.org/mindshift/56564/how-encouraging-rough-draft-thinking-in-math-class-highlights-the-strengths-of-all-students\">first post\u003c/a>, University of Delaware professor \u003c/span>\u003c/i>\u003ca href=\"https://twitter.com/MandyMathEd\">\u003ci>\u003cspan style=\"font-weight: 400\">Amanda Jansen\u003c/span>\u003c/i>\u003c/a>\u003ci>\u003cspan style=\"font-weight: 400\"> discusses how framing math as a shared exploration enables more students to develop math competence and confidence. This post uses classroom examples to show some of the ways teachers can foster rough draft talk and set up students to revise their solutions.\u003c/span>\u003c/i>\u003c/p>\n\u003cp>\u003cstrong>By Amanda Jansen\u003c/strong>\u003c/p>\n\u003ch1>\u003cb>Talking about Rough Draft Talk: Christine’s Classroom\u003c/b>\u003c/h1>\n\u003cp>\u003cspan style=\"font-weight: 400\">Christine Hubbard teaches seventh-grade at Meredith Middle School in Middletown, Delaware. She starts her school year by talking with her students about the role of rough drafts in learning. … It is helpful, then, for students to engage in rough draft talk soon after defining it with them. By trying out rough draft talk, they learn to believe in its usefulness through reflecting on their experience. After talking with her students about rough draft thinking, Christine engaged her students in a Number Talk about ways to visualize chunking a set of dots to make the set easier to count.\u003c/span>\u003c/p>\n\u003cp>\u003cb>\u003ci>Christine:\u003c/i>\u003c/b>\u003ci>\u003cspan style=\"font-weight: 400\"> I want you in your mind to be thinking about how many dots there are.\u003c/span>\u003c/i>\u003c/p>\n\u003cp>[ad fullwidth]\u003c/p>\n\u003cp>\u003cb>\u003ci>Caleb: \u003c/i>\u003c/b>\u003ci>\u003cspan style=\"font-weight: 400\">It’s like dominoes.\u003c/span>\u003c/i>\u003c/p>\n\u003cp>\u003cb>\u003ci>Christine: \u003c/i>\u003c/b>\u003ci>\u003cspan style=\"font-weight: 400\">Yeah, you’re going to see that some patterns might remind you of dominoes. I’m going to flash it up there. Try and see how you can figure out how many are up there without counting one by one.\u003c/span>\u003c/i>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Christine also introduced hand signals for Number Talks, specifically putting a number of fingers at your chest to indicate how many strategies you have. A student asked, “A strategy is a different way of counting?” Christine said, “Exactly.” After flashing up the image of the dots (Figure 2.5), Christine then collected answers—how many dots students saw. They all reported seeing eight dots.\u003c/span>\u003c/p>\n\u003cp>\u003cimg class=\"aligncenter size-full wp-image-56567\" src=\"https://ww2.kqed.org/app/uploads/sites/23/2020/08/Number-Talk-1.png\" alt=\"\" width=\"738\" height=\"438\" srcset=\"https://ww2.kqed.org/app/uploads/sites/23/2020/08/Number-Talk-1.png 738w, https://ww2.kqed.org/app/uploads/sites/23/2020/08/Number-Talk-1-160x95.png 160w\" sizes=\"(max-width: 738px) 100vw, 738px\">\u003c/p>\n\u003cp style=\"text-align: center\">\u003cspan style=\"font-weight: 400\">Figure 2.5 Dot Pattern for Christine’s Number Talk\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Christine then invited students to share: “Can anybody be brave enough to share and justify why they think there’s eight dots up there?” A number of students went up to the whiteboard to draw how they grouped and chunked the diagram to count. The first student saw a set of five, as if it was a side of dice, plus three more. The second student saw the three on top, the three on the bottom, and the two in the middle. Another student came up to the front of the room and gestured to indicate diagonal lines:\u003c/span>\u003c/p>\n\u003cp>\u003cb>\u003ci>Jason: \u003c/i>\u003c/b>\u003ci>\u003cspan style=\"font-weight: 400\">So I saw these three and then these three. So there were six and then I made them into one sideways diamond. Then I added the two on the ends. To me this looks like a diamond.\u003c/span>\u003c/i>\u003c/p>\n\u003cp>\u003cb>\u003ci>Christine: \u003c/i>\u003c/b>\u003ci>\u003cspan style=\"font-weight: 400\">Jason’s saying he sees a shape, is this what you’re showing? What shape is that? (Christine drew in lines as seen in Figure 2.6).\u003c/span>\u003c/i>\u003c/p>\n\u003cp>\u003cimg class=\"aligncenter size-full wp-image-56568\" src=\"https://ww2.kqed.org/app/uploads/sites/23/2020/08/Number-Talk-2.png\" alt=\"\" width=\"512\" height=\"264\" srcset=\"https://ww2.kqed.org/app/uploads/sites/23/2020/08/Number-Talk-2.png 512w, https://ww2.kqed.org/app/uploads/sites/23/2020/08/Number-Talk-2-160x83.png 160w\" sizes=\"(max-width: 512px) 100vw, 512px\">\u003c/p>\n\u003cp style=\"text-align: center\">\u003cspan style=\"font-weight: 400\">Figure 2.6 Jason sees a shape\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Students brainstormed names for the shape, saying things like pentagon, parallelogram, rhombus, or “I can’t remember.” Christine identified the terms that students used and asked them to describe what they are (e.g., “What’s a pentagon?”). Then she asked, “So what can we call that shape?” Jason replied, “A weird rectangle thing.” Calista said, “It’s a parallelogram.” Another student shouted out, “It’s a thingy!” Christine said, “Calista is telling us that it’s a parallelogram.” Then she went on to say, “Yeah, we could describe it either way, but if we call it a parallelogram, that’s using more precise language that we can all visualize.” Michael Reitemeyer, the math coach in Christine’s district, was also in the room and asked, “So is it okay during rough draft talk to maybe call it a weird rectangle?” Christine turned to her students and said, “What do we think, as a class?” Students said, yes, so she said “Sure, we can accept it. Absolutely. Rough draft talk helps us.”\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">There were multiple moments when students engaged in rough draft sharing during this Number Talk. The first was the moment the teacher intended, which was when students shared multiple ways of seeing how to chunk the diagram to count the total. This sort of exploratory talk invites multiple ways of seeing mathematical relationships. But there was a moment that Christine did not necessarily anticipate, which was rough draft talk around how Jason named the shape he saw in the diagram. She shifted back and forth with students from rough draft to more formal language to begin refining their rough draft talk, but then affirmed that the rough draft language of “a weird rectangle” was a useful way to get started talking about the shape. Taking moments to talk about talking is important, but it is even more important to give students firsthand experience engaging in rough draft talk and to name and label those rough draft moments. … \u003c/span>\u003c/p>\n\u003ch1>\u003cb>Revise Solutions: My Favorite Rough Draft\u003c/b>\u003c/h1>\n\u003cp>\u003cspan style=\"font-weight: 400\">Stefanie Vascellaro, a sixth-grade teacher at Meredith Middle School in the Appoquinimink School District in Middletown, Delaware, created an instructional routine that she called My Favorite Rough Draft.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">First, Stefanie’s students work in pairs to write a rough draft of an explanation. While students are working, Stefanie circulates and considers which explanations might be fruitful to revise together. She selects one based on her mathematical and social goals for the class and then pulls the large group together to discuss it. She displays it anonymously, and the class works together to improve the explanation. She modified this routine from My Favorite No (Teaching Channel 2011), which is when a teacher chooses a common procedural error and discusses with the class what was correct about the work and where it needed to be improved. Stefanie has her students write explanations for why procedural mistakes were errors rather than explaining the error to her students herself.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">As an example, she asked pairs of students to write about the following:\u003c/span>\u003c/p>\n\u003cp>\u003ci>\u003cspan style=\"font-weight: 400\">Read and answer the problem with your shoulder partner. Explain whether the expression on the left side of the equal sign is equivalent to the expression on the right side. Show all work.\u003c/span>\u003c/i>\u003c/p>\n\u003cp>\u003ci>\u003cspan style=\"font-weight: 400\">14x^2 + 6 – 9x^2\u003c/span>\u003c/i>\u003ci>\u003cspan style=\"font-weight: 400\"> + 4x = 9x^2\u003c/span>\u003c/i>\u003ci>\u003cspan style=\"font-weight: 400\"> + 6\u003c/span>\u003c/i>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">She assumed that students would combine 14x^2 \u003c/span>\u003cspan style=\"font-weight: 400\">and -9x^2\u003c/span>\u003cspan style=\"font-weight: 400\"> with 4x rather than recognize that 4x was a term that could not be combined with the other two terms. One of the goals for this task was for students to go beyond catching an error to interpreting why someone might do this. Students were expected to reflect on the meaning of “combining like terms.” Stefanie also wanted students to practice using language of the discipline of mathematics, such as\u003c/span>\u003ci>\u003cspan style=\"font-weight: 400\"> combine like terms\u003c/span>\u003c/i>\u003cspan style=\"font-weight: 400\">, \u003c/span>\u003ci>\u003cspan style=\"font-weight: 400\">coefficient\u003c/span>\u003c/i>\u003cspan style=\"font-weight: 400\">, \u003c/span>\u003ci>\u003cspan style=\"font-weight: 400\">constant\u003c/span>\u003c/i>\u003cspan style=\"font-weight: 400\">, \u003c/span>\u003ci>\u003cspan style=\"font-weight: 400\">variable\u003c/span>\u003c/i>\u003cspan style=\"font-weight: 400\">, \u003c/span>\u003ci>\u003cspan style=\"font-weight: 400\">expression\u003c/span>\u003c/i>\u003cspan style=\"font-weight: 400\">, and \u003c/span>\u003ci>\u003cspan style=\"font-weight: 400\">exponent\u003c/span>\u003c/i>\u003cspan style=\"font-weight: 400\">.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">During My Favorite Rough Draft, students’ thinking is first elicited when they talk through their initial explanations—before they write. When sixth grader Arturo talked through his ideas for his explanation with his partner, his rough draft thinking sounded like this:\u003c/span>\u003c/p>\n\u003cp>\u003ci>\u003cspan style=\"font-weight: 400\">Arturo: But then you have to think about it. You can’t do an exponent if you’re using—so, it’s 5x to the second power (after combining 14x^2 \u003c/span>\u003c/i>\u003ci>\u003cspan style=\"font-weight: 400\">with -9x^2\u003c/span>\u003c/i>\u003ci>\u003cspan style=\"font-weight: 400\">). You can’t do 5x to the second power plus 4x. It doesn’t work. Because 4x, it would have to go to the second power. You can’t add a second power to that.\u003c/span>\u003c/i>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">You can hear the initial roughness in Arturo’s thinking when he cuts himself off (“if you’re using—”). Also, the repetitiveness in his talk is what often happens when we’re sorting out our thoughts.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">After each pair talked and then wrote a draft, Stefanie had two pairs of students join to make groups of four, which is a structure she used frequently so students gain additional perspectives. The pairs swapped their drafts and edited one another’s work by suggesting revisions to their peers’ drafts. After a few minutes of editing, they got to see revisions from their peers.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">When Stefanie circulated the class to choose her Favorite Rough Draft, many of the drafts were correct, so Stefanie chose a draft to revise with the class that could have included more mathematical terms. For instance, Stefanie wanted students to use terminology such as exponents. We can see in the students’ rough draft talk that they did not use that term.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Choosing a draft to revise as a class involves choosing student work that needs improving in a particular way for a particular reason. Perhaps we want students’ revisions to include more visual illustrations, to use precise vocabulary, to make their points more clearly, or to make connec-tions more explicit. But when looking for a Favorite Rough Draft, whether or not it is correct, it is useful to look for the strengths in that draft so the class can build on them. In other words, even as we select a goal for improvement, we should also notice and highlight the productive thinking in the original draft, which helps us all learn what to do similarly next time. Critique involves recognizing what is working as well as improving what is not working.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">\u003ca href=\"https://www.stenhouse.com/content/rough-draft-math\">\u003cimg class=\"alignright wp-image-56707\" src=\"https://ww2.kqed.org/app/uploads/sites/23/2020/08/Rough-Draft-Math_Jansen_final-cover_web-rgb.jpg\" alt=\"\" width=\"200\" height=\"251\" srcset=\"https://ww2.kqed.org/app/uploads/sites/23/2020/08/Rough-Draft-Math_Jansen_final-cover_web-rgb.jpg 560w, https://ww2.kqed.org/app/uploads/sites/23/2020/08/Rough-Draft-Math_Jansen_final-cover_web-rgb-160x201.jpg 160w\" sizes=\"(max-width: 200px) 100vw, 200px\">\u003c/a>While revising the draft, Stefanie asked students to recommend changes and to give justifications for those suggestions. Not all changes are improvements! Suggestions for changes are stronger when the people making the suggestions justify why the change makes the draft stronger. In addition to revealing students’ mathematical thinking, hearing students’ justifications also provides insight as to whether students are attending to the goal for revision. Revising work as a class helps students learn to accept feedback as well.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">To validate students’ thinking, Stefanie explained how revising the draft supported the group’s learning. She said that she displayed the students’ draft anonymously to protect students who may otherwise feel uncomfort-able having their work critiqued by peers. A second benefit is that an anonymous draft can help the revision process feel collectively owned by the group: the draft becomes the class’s draft, and the entire class benefits from the opportunity to think it through. If we make this explicit—the ways in which the draft helps everyone’s thinking improve—then the author of the draft is positioned as having contributed something valuable to the class.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Consider phasing out the use of anonymous drafts. After norms are in place such that in-progress thinking is seen as valuable, students can feel safer having their work publicly revised with their name attached to it. If we highlight strengths in the draft while revising, students might even feel proud of their drafts.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">My Favorite Rough Draft involves multiple cycles of revision. After thinking individually, students share that initial thinking with their partners. Through cocreating a written draft with a peer, their own ideas might shift. Pairs of students then trade with another pair of students and receive feedback on their drafts that they can apply toward another revision. A further opportunity to revise thinking occurs when the class revises the Favorite Rough Draft selected by the teacher. In this particular example, Stefanie used this revision structure to analyze students’ explanations of a procedural mistake, but you could use My Favorite Rough Draft to analyze drafts of proofs, justifications, or other forms of mathematical reasoning.\u003c/span>\u003c/p>\n\u003cp>\u003cem>*Note: due to an earlier error, exponents did not appear properly in the sample equations. This except has been updated. \u003c/em>\u003c/p>\n\u003cp>[ad floatright]\u003c/p>\n\u003cp>\u003cem>Amanda (Mandy) Jansen is a Professor in the School of Education at the University of Delaware where she teaches future elementary and middle school mathematics teachers. Prior to becoming a professor, she taught junior high (grades 7-9) mathematics in Mesa, Arizona. You can follow Amanda at \u003ca href=\"https://twitter.com/MandyMathEd\">@MandyMathEd\u003c/a>. \u003c/em>\u003c/p>\n\n","blocks":[],"excerpt":null,"status":"publish","parent":0,"modified":1601316156,"stats":{"hasAudio":false,"hasVideo":false,"hasChartOrMap":false,"iframeSrcs":[],"hasGoogleForm":false,"hasGallery":false,"hasHearkenModule":false,"hasPolis":false,"paragraphCount":35,"wordCount":2057},"headData":{"title":"What It Looks Like When Students Share and Revise Rough Drafts in Math Class - MindShift","description":"Excerpted from Rough Draft Math: Revising to Learn by Amanda Jansen, copyright © 2020, reproduced with permission of Stenhouse Publishers. www.stenhouse.com This is the second article in a two-part series about rough draft math. In the first post, University of Delaware professor Amanda Jansen discusses how framing math as a shared exploration enables more students","ogTitle":"","ogDescription":"","ogImgId":"","twTitle":"","twDescription":"","twImgId":""},"disqusIdentifier":"56566 https://ww2.kqed.org/mindshift/?p=56566","disqusUrl":"https://ww2.kqed.org/mindshift/2020/09/28/what-it-looks-like-when-students-share-and-revise-rough-drafts-in-math-class/","disqusTitle":"What It Looks Like When Students Share and Revise Rough Drafts in Math Class ","path":"/mindshift/56566/what-it-looks-like-when-students-share-and-revise-rough-drafts-in-math-class","audioTrackLength":null,"parsedContent":[{"type":"contentString","content":"\u003cdiv class=\"post-body\">\u003cp>\u003cp>\u003ci>\u003cspan style=\"font-weight: 400\">Excerpted from \u003c/span>\u003c/i>\u003ca href=\"https://www.stenhouse.com/content/rough-draft-math\">\u003ci>\u003cspan style=\"font-weight: 400\">Rough Draft Math: Revising to Learn\u003c/span>\u003c/i>\u003c/a>\u003ci>\u003cspan style=\"font-weight: 400\"> by Amanda Jansen, copyright © 2020, reproduced with permission of Stenhouse Publishers. www.stenhouse.com\u003c/span>\u003c/i>\u003c/p>\n\u003cp>\u003ci>\u003cspan style=\"font-weight: 400\">This is the second article in a two-part series about rough draft math. In the \u003ca href=\"https://www.kqed.org/mindshift/56564/how-encouraging-rough-draft-thinking-in-math-class-highlights-the-strengths-of-all-students\">first post\u003c/a>, University of Delaware professor \u003c/span>\u003c/i>\u003ca href=\"https://twitter.com/MandyMathEd\">\u003ci>\u003cspan style=\"font-weight: 400\">Amanda Jansen\u003c/span>\u003c/i>\u003c/a>\u003ci>\u003cspan style=\"font-weight: 400\"> discusses how framing math as a shared exploration enables more students to develop math competence and confidence. This post uses classroom examples to show some of the ways teachers can foster rough draft talk and set up students to revise their solutions.\u003c/span>\u003c/i>\u003c/p>\n\u003cp>\u003cstrong>By Amanda Jansen\u003c/strong>\u003c/p>\n\u003ch1>\u003cb>Talking about Rough Draft Talk: Christine’s Classroom\u003c/b>\u003c/h1>\n\u003cp>\u003cspan style=\"font-weight: 400\">Christine Hubbard teaches seventh-grade at Meredith Middle School in Middletown, Delaware. She starts her school year by talking with her students about the role of rough drafts in learning. … It is helpful, then, for students to engage in rough draft talk soon after defining it with them. By trying out rough draft talk, they learn to believe in its usefulness through reflecting on their experience. After talking with her students about rough draft thinking, Christine engaged her students in a Number Talk about ways to visualize chunking a set of dots to make the set easier to count.\u003c/span>\u003c/p>\n\u003cp>\u003cb>\u003ci>Christine:\u003c/i>\u003c/b>\u003ci>\u003cspan style=\"font-weight: 400\"> I want you in your mind to be thinking about how many dots there are.\u003c/span>\u003c/i>\u003c/p>\n\u003cp>\u003c/p>\u003c/div>","attributes":{"named":{},"numeric":[]}},{"type":"component","content":"","name":"ad","attributes":{"named":{"label":"fullwidth"},"numeric":["fullwidth"]}},{"type":"contentString","content":"\u003cdiv class=\"post-body\">\u003cp>\u003c/p>\n\u003cp>\u003cb>\u003ci>Caleb: \u003c/i>\u003c/b>\u003ci>\u003cspan style=\"font-weight: 400\">It’s like dominoes.\u003c/span>\u003c/i>\u003c/p>\n\u003cp>\u003cb>\u003ci>Christine: \u003c/i>\u003c/b>\u003ci>\u003cspan style=\"font-weight: 400\">Yeah, you’re going to see that some patterns might remind you of dominoes. I’m going to flash it up there. Try and see how you can figure out how many are up there without counting one by one.\u003c/span>\u003c/i>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Christine also introduced hand signals for Number Talks, specifically putting a number of fingers at your chest to indicate how many strategies you have. A student asked, “A strategy is a different way of counting?” Christine said, “Exactly.” After flashing up the image of the dots (Figure 2.5), Christine then collected answers—how many dots students saw. They all reported seeing eight dots.\u003c/span>\u003c/p>\n\u003cp>\u003cimg class=\"aligncenter size-full wp-image-56567\" src=\"https://ww2.kqed.org/app/uploads/sites/23/2020/08/Number-Talk-1.png\" alt=\"\" width=\"738\" height=\"438\" srcset=\"https://ww2.kqed.org/app/uploads/sites/23/2020/08/Number-Talk-1.png 738w, https://ww2.kqed.org/app/uploads/sites/23/2020/08/Number-Talk-1-160x95.png 160w\" sizes=\"(max-width: 738px) 100vw, 738px\">\u003c/p>\n\u003cp style=\"text-align: center\">\u003cspan style=\"font-weight: 400\">Figure 2.5 Dot Pattern for Christine’s Number Talk\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Christine then invited students to share: “Can anybody be brave enough to share and justify why they think there’s eight dots up there?” A number of students went up to the whiteboard to draw how they grouped and chunked the diagram to count. The first student saw a set of five, as if it was a side of dice, plus three more. The second student saw the three on top, the three on the bottom, and the two in the middle. Another student came up to the front of the room and gestured to indicate diagonal lines:\u003c/span>\u003c/p>\n\u003cp>\u003cb>\u003ci>Jason: \u003c/i>\u003c/b>\u003ci>\u003cspan style=\"font-weight: 400\">So I saw these three and then these three. So there were six and then I made them into one sideways diamond. Then I added the two on the ends. To me this looks like a diamond.\u003c/span>\u003c/i>\u003c/p>\n\u003cp>\u003cb>\u003ci>Christine: \u003c/i>\u003c/b>\u003ci>\u003cspan style=\"font-weight: 400\">Jason’s saying he sees a shape, is this what you’re showing? What shape is that? (Christine drew in lines as seen in Figure 2.6).\u003c/span>\u003c/i>\u003c/p>\n\u003cp>\u003cimg class=\"aligncenter size-full wp-image-56568\" src=\"https://ww2.kqed.org/app/uploads/sites/23/2020/08/Number-Talk-2.png\" alt=\"\" width=\"512\" height=\"264\" srcset=\"https://ww2.kqed.org/app/uploads/sites/23/2020/08/Number-Talk-2.png 512w, https://ww2.kqed.org/app/uploads/sites/23/2020/08/Number-Talk-2-160x83.png 160w\" sizes=\"(max-width: 512px) 100vw, 512px\">\u003c/p>\n\u003cp style=\"text-align: center\">\u003cspan style=\"font-weight: 400\">Figure 2.6 Jason sees a shape\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Students brainstormed names for the shape, saying things like pentagon, parallelogram, rhombus, or “I can’t remember.” Christine identified the terms that students used and asked them to describe what they are (e.g., “What’s a pentagon?”). Then she asked, “So what can we call that shape?” Jason replied, “A weird rectangle thing.” Calista said, “It’s a parallelogram.” Another student shouted out, “It’s a thingy!” Christine said, “Calista is telling us that it’s a parallelogram.” Then she went on to say, “Yeah, we could describe it either way, but if we call it a parallelogram, that’s using more precise language that we can all visualize.” Michael Reitemeyer, the math coach in Christine’s district, was also in the room and asked, “So is it okay during rough draft talk to maybe call it a weird rectangle?” Christine turned to her students and said, “What do we think, as a class?” Students said, yes, so she said “Sure, we can accept it. Absolutely. Rough draft talk helps us.”\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">There were multiple moments when students engaged in rough draft sharing during this Number Talk. The first was the moment the teacher intended, which was when students shared multiple ways of seeing how to chunk the diagram to count the total. This sort of exploratory talk invites multiple ways of seeing mathematical relationships. But there was a moment that Christine did not necessarily anticipate, which was rough draft talk around how Jason named the shape he saw in the diagram. She shifted back and forth with students from rough draft to more formal language to begin refining their rough draft talk, but then affirmed that the rough draft language of “a weird rectangle” was a useful way to get started talking about the shape. Taking moments to talk about talking is important, but it is even more important to give students firsthand experience engaging in rough draft talk and to name and label those rough draft moments. … \u003c/span>\u003c/p>\n\u003ch1>\u003cb>Revise Solutions: My Favorite Rough Draft\u003c/b>\u003c/h1>\n\u003cp>\u003cspan style=\"font-weight: 400\">Stefanie Vascellaro, a sixth-grade teacher at Meredith Middle School in the Appoquinimink School District in Middletown, Delaware, created an instructional routine that she called My Favorite Rough Draft.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">First, Stefanie’s students work in pairs to write a rough draft of an explanation. While students are working, Stefanie circulates and considers which explanations might be fruitful to revise together. She selects one based on her mathematical and social goals for the class and then pulls the large group together to discuss it. She displays it anonymously, and the class works together to improve the explanation. She modified this routine from My Favorite No (Teaching Channel 2011), which is when a teacher chooses a common procedural error and discusses with the class what was correct about the work and where it needed to be improved. Stefanie has her students write explanations for why procedural mistakes were errors rather than explaining the error to her students herself.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">As an example, she asked pairs of students to write about the following:\u003c/span>\u003c/p>\n\u003cp>\u003ci>\u003cspan style=\"font-weight: 400\">Read and answer the problem with your shoulder partner. Explain whether the expression on the left side of the equal sign is equivalent to the expression on the right side. Show all work.\u003c/span>\u003c/i>\u003c/p>\n\u003cp>\u003ci>\u003cspan style=\"font-weight: 400\">14x^2 + 6 – 9x^2\u003c/span>\u003c/i>\u003ci>\u003cspan style=\"font-weight: 400\"> + 4x = 9x^2\u003c/span>\u003c/i>\u003ci>\u003cspan style=\"font-weight: 400\"> + 6\u003c/span>\u003c/i>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">She assumed that students would combine 14x^2 \u003c/span>\u003cspan style=\"font-weight: 400\">and -9x^2\u003c/span>\u003cspan style=\"font-weight: 400\"> with 4x rather than recognize that 4x was a term that could not be combined with the other two terms. One of the goals for this task was for students to go beyond catching an error to interpreting why someone might do this. Students were expected to reflect on the meaning of “combining like terms.” Stefanie also wanted students to practice using language of the discipline of mathematics, such as\u003c/span>\u003ci>\u003cspan style=\"font-weight: 400\"> combine like terms\u003c/span>\u003c/i>\u003cspan style=\"font-weight: 400\">, \u003c/span>\u003ci>\u003cspan style=\"font-weight: 400\">coefficient\u003c/span>\u003c/i>\u003cspan style=\"font-weight: 400\">, \u003c/span>\u003ci>\u003cspan style=\"font-weight: 400\">constant\u003c/span>\u003c/i>\u003cspan style=\"font-weight: 400\">, \u003c/span>\u003ci>\u003cspan style=\"font-weight: 400\">variable\u003c/span>\u003c/i>\u003cspan style=\"font-weight: 400\">, \u003c/span>\u003ci>\u003cspan style=\"font-weight: 400\">expression\u003c/span>\u003c/i>\u003cspan style=\"font-weight: 400\">, and \u003c/span>\u003ci>\u003cspan style=\"font-weight: 400\">exponent\u003c/span>\u003c/i>\u003cspan style=\"font-weight: 400\">.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">During My Favorite Rough Draft, students’ thinking is first elicited when they talk through their initial explanations—before they write. When sixth grader Arturo talked through his ideas for his explanation with his partner, his rough draft thinking sounded like this:\u003c/span>\u003c/p>\n\u003cp>\u003ci>\u003cspan style=\"font-weight: 400\">Arturo: But then you have to think about it. You can’t do an exponent if you’re using—so, it’s 5x to the second power (after combining 14x^2 \u003c/span>\u003c/i>\u003ci>\u003cspan style=\"font-weight: 400\">with -9x^2\u003c/span>\u003c/i>\u003ci>\u003cspan style=\"font-weight: 400\">). You can’t do 5x to the second power plus 4x. It doesn’t work. Because 4x, it would have to go to the second power. You can’t add a second power to that.\u003c/span>\u003c/i>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">You can hear the initial roughness in Arturo’s thinking when he cuts himself off (“if you’re using—”). Also, the repetitiveness in his talk is what often happens when we’re sorting out our thoughts.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">After each pair talked and then wrote a draft, Stefanie had two pairs of students join to make groups of four, which is a structure she used frequently so students gain additional perspectives. The pairs swapped their drafts and edited one another’s work by suggesting revisions to their peers’ drafts. After a few minutes of editing, they got to see revisions from their peers.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">When Stefanie circulated the class to choose her Favorite Rough Draft, many of the drafts were correct, so Stefanie chose a draft to revise with the class that could have included more mathematical terms. For instance, Stefanie wanted students to use terminology such as exponents. We can see in the students’ rough draft talk that they did not use that term.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Choosing a draft to revise as a class involves choosing student work that needs improving in a particular way for a particular reason. Perhaps we want students’ revisions to include more visual illustrations, to use precise vocabulary, to make their points more clearly, or to make connec-tions more explicit. But when looking for a Favorite Rough Draft, whether or not it is correct, it is useful to look for the strengths in that draft so the class can build on them. In other words, even as we select a goal for improvement, we should also notice and highlight the productive thinking in the original draft, which helps us all learn what to do similarly next time. Critique involves recognizing what is working as well as improving what is not working.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">\u003ca href=\"https://www.stenhouse.com/content/rough-draft-math\">\u003cimg class=\"alignright wp-image-56707\" src=\"https://ww2.kqed.org/app/uploads/sites/23/2020/08/Rough-Draft-Math_Jansen_final-cover_web-rgb.jpg\" alt=\"\" width=\"200\" height=\"251\" srcset=\"https://ww2.kqed.org/app/uploads/sites/23/2020/08/Rough-Draft-Math_Jansen_final-cover_web-rgb.jpg 560w, https://ww2.kqed.org/app/uploads/sites/23/2020/08/Rough-Draft-Math_Jansen_final-cover_web-rgb-160x201.jpg 160w\" sizes=\"(max-width: 200px) 100vw, 200px\">\u003c/a>While revising the draft, Stefanie asked students to recommend changes and to give justifications for those suggestions. Not all changes are improvements! Suggestions for changes are stronger when the people making the suggestions justify why the change makes the draft stronger. In addition to revealing students’ mathematical thinking, hearing students’ justifications also provides insight as to whether students are attending to the goal for revision. Revising work as a class helps students learn to accept feedback as well.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">To validate students’ thinking, Stefanie explained how revising the draft supported the group’s learning. She said that she displayed the students’ draft anonymously to protect students who may otherwise feel uncomfort-able having their work critiqued by peers. A second benefit is that an anonymous draft can help the revision process feel collectively owned by the group: the draft becomes the class’s draft, and the entire class benefits from the opportunity to think it through. If we make this explicit—the ways in which the draft helps everyone’s thinking improve—then the author of the draft is positioned as having contributed something valuable to the class.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">Consider phasing out the use of anonymous drafts. After norms are in place such that in-progress thinking is seen as valuable, students can feel safer having their work publicly revised with their name attached to it. If we highlight strengths in the draft while revising, students might even feel proud of their drafts.\u003c/span>\u003c/p>\n\u003cp>\u003cspan style=\"font-weight: 400\">My Favorite Rough Draft involves multiple cycles of revision. After thinking individually, students share that initial thinking with their partners. Through cocreating a written draft with a peer, their own ideas might shift. Pairs of students then trade with another pair of students and receive feedback on their drafts that they can apply toward another revision. A further opportunity to revise thinking occurs when the class revises the Favorite Rough Draft selected by the teacher. In this particular example, Stefanie used this revision structure to analyze students’ explanations of a procedural mistake, but you could use My Favorite Rough Draft to analyze drafts of proofs, justifications, or other forms of mathematical reasoning.\u003c/span>\u003c/p>\n\u003cp>\u003cem>*Note: due to an earlier error, exponents did not appear properly in the sample equations. This except has been updated. \u003c/em>\u003c/p>\n\u003cp>\u003c/p>\u003c/div>","attributes":{"named":{},"numeric":[]}},{"type":"component","content":"","name":"ad","attributes":{"named":{"label":"floatright"},"numeric":["floatright"]}},{"type":"contentString","content":"\u003cdiv class=\"post-body\">\u003cp>\u003c/p>\n\u003cp>\u003cem>Amanda (Mandy) Jansen is a Professor in the School of Education at the University of Delaware where she teaches future elementary and middle school mathematics teachers. Prior to becoming a professor, she taught junior high (grades 7-9) mathematics in Mesa, Arizona. You can follow Amanda at \u003ca href=\"https://twitter.com/MandyMathEd\">@MandyMathEd\u003c/a>. \u003c/em>\u003c/p>\n\n\u003c/div>\u003c/p>","attributes":{"named":{},"numeric":[]}}],"link":"/mindshift/56566/what-it-looks-like-when-students-share-and-revise-rough-drafts-in-math-class","authors":["4354"],"categories":["mindshift_193"],"tags":["mindshift_20994","mindshift_392","mindshift_20893"],"featImg":"mindshift_56567","label":"mindshift"},"mindshift_45012":{"type":"posts","id":"mindshift_45012","meta":{"index":"posts_1591205157","site":"mindshift","id":"45012","score":null,"sort":[1463994515000]},"guestAuthors":[],"slug":"how-a-strengths-based-approach-to-math-redefines-who-is-smart","title":"How A Strengths-Based Approach to Math Redefines Who Is 'Smart'","publishDate":1463994515,"format":"standard","headTitle":"MindShift | KQED News","labelTerm":{"site":"mindshift"},"content":"\u003cp>A group of young women who had graduated from high school between 1997 and 2006 sat at the front of the room crying and laughing about their experiences \u003ca href=\"http://fairfieldmathadvocates.com/wp-content/uploads/2013/01/Case-of-Railside.pdf\" target=\"_blank\">learning math at Railside High\u003c/a> (a research pseudonym for the school). This session of the \u003ca href=\"http://www.nctm.org/\" target=\"_blank\">National Council of Teachers of Mathematics\u003c/a> annual meeting didn’t focus on any specific mathematical practice and yet it was enlightening -- with the right approach, teachers can help kids who hate math feel like it’s their best subject.\u003c/p>\n\u003cp>One after another, these young women, who had all graduated from an urban high school serving many kids living in poverty, described how math class made them feel safe, heard and able to express their ideas without fear.\u003c/p>\n\u003cp>“I felt like they cared for me,” said Martha Hernandez, who graduated in 2002 and is now a social worker. “They cared for my education and they wanted me to succeed.”\u003c/p>\n\u003cp>Hernandez was designated an English language learner in high school and was the first in her family to go to college. She loved her math classes so much that almost 15 years later, in the NCTM session, she held out physical examples of her work as she cried about the impact the non-traditional math program at Railside High had on her confidence and future success.\u003c/p>\n\u003caside class=\"pullquote alignright\">'It has expanded my thinking about what makes you smart at math.'\u003ccite>Tracy Thompson, High school math teacher\u003c/cite>\u003c/aside>\n\u003cp>“It changed what math meant,” said Maria Velazquez, who now studies education policy at the University of Wisconsin. “It was a process and it required other people. It wasn’t just you and your work and not talking.”\u003c/p>\n\u003cp>[ad fullwidth]\u003c/p>\n\u003cp>Before high school, these young women, like many students in the U.S., experienced math as lecture, sitting at desks quietly. Many believed they weren’t good at math because they didn’t understand or compute quickly. But the math program at Railside High changed that for each of these women, showing them their strengths and allowing them to bring all of themselves to the pursuit of mathematics.\u003c/p>\n\u003cp>But what was so different about how these women learned math in high school? How did their math teachers form bonds so strong that years later they were attending students’ weddings in Mexico?\u003c/p>\n\u003cp>The answer: \u003ca href=\"http://cgi.stanford.edu/group/pci/cgi-bin/site.cgi\" target=\"_blank\">Complex Instruction\u003c/a>. This pedagogy is not specific to math and has been \u003ca href=\"http://cgi.stanford.edu/group/pci/cgi-bin/site.cgi?page=research.html\" target=\"_blank\">in the literature\u003c/a> for decades, originally researched by \u003ca href=\"http://cgi.stanford.edu/group/pci/cgi-bin/site.cgi?page=whos_who.html\" target=\"_blank\">Elizabeth Cohen and Rachel Lotan\u003c/a> at Stanford University. Teachers at Railside High discovered the methodology when they were undergoing an accreditation review and were told they needed to drastically change something to improve their results. The ultimatum prompted teachers to try something different -- heterogeneous classes, high expectations for all students and, above all, approaching math with an eye to students’ strengths.\u003c/p>\n\u003cfigure id=\"attachment_45185\" class=\"wp-caption alignnone\" style=\"max-width: 1920px\">\u003cimg class=\"wp-image-45185 size-full\" src=\"http://ww2.kqed.org/mindshift/wp-content/uploads/sites/23/2016/05/Railside-2-e1463987977561.jpg\" alt=\"Railside 2\" width=\"1920\" height=\"1440\">\u003cfigcaption class=\"wp-caption-text\">Courtesy of Yuka Walton\u003c/figcaption>\u003c/figure>\n\u003cp>The three main tenets of Complex Instruction are that learning should have multi-ability access points, norms and roles that support interdependency between students, and attention to status and accountability for learning. In most Complex Instruction classrooms the majority of class time is spent with students working in groups of four on a rich task that has multiple entry points and ways it could be solved. If one student can solve the problem in his or her head, it’s not a rich task.\u003c/p>\n\u003cp>Each student in the group has a role: team captain, resource manager, recorder-reporter and facilitator. While these roles might sound cheesy to some students, they are important for helping groups to work equitably, ensuring that every group member has a crucial and intellectual task. The roles help students learn how to effectively participate and, because each role is necessary to solve a task, everyone must share their ideas.\u003c/p>\n\u003caside class=\"alignleft\">\n\u003ch3>More Resources on Complex Instruction\u003c/h3>\n\u003cp>These books delve more deeply into student experiences of Complex Instruction, details on how to create equitable groups and how to mitigate status issues.\u003c/p>\n\u003cul>\n\u003cli>\u003ca href=\"http://store.tcpress.com/0807755664.shtml\">\u003ci>Designing Groupwork\u003c/i>\u003c/a>\u003c/li>\n\u003cli>\u003ca href=\"http://www.nctm.org/store/Products/Smarter-Together!-Collaboration-and-Equity-in-the-Elementary-Math-Classroom/\">\u003ci>Smarter Together! Collaboration and Equity in the Elementary Math Classroom\u003c/i>\u003c/a>\u003c/li>\n\u003cli>\u003ca href=\"http://store.tcpress.com/0807755419.shtml\">\u003ci>Mathematics For Equity: A Framework For Successful Practice\u003c/i>\u003c/a>\u003c/li>\n\u003cli>\u003ca href=\"http://store.tcpress.com/0807752460.shtml\">\u003ci>\"Heterogeneous\" Classrooms: Detracking Math and Science -- A Look at Groupwork in Action\u003c/i>\u003c/a>\u003c/li>\n\u003c/ul>\n\u003c/aside>\n\u003cp>“Participation leads to more learning because learning is a socially constructed activity,” said \u003ca href=\"http://washington.academia.edu/LisaJilk/Papers\" target=\"_blank\">Lisa Jilk\u003c/a>, program director of Reculturing Math Departments for Excellence & Equity, part of the \u003ca href=\"http://www.matheducation.uw.edu/\" target=\"_blank\">Mathematics Education Project\u003c/a> at the University of Washington. Jilk taught at Railside High, and when she left to get her doctorate she studied how and why Complex Instruction worked for so many students from various backgrounds. Now she’s dedicated to helping other math departments around the country “reculture” themselves to think about what learners bring to math that will help them, rather than only about the information they are missing.\u003c/p>\n\u003cp>When the three tenets of Complex Instruction are all working together simultaneously it can feel like a magical experience. But getting there takes a lot of work. When Jilk starts training teachers, one of the first things that must be discussed is the idea of status in the classroom and how to break that down. Teaching with Complex Instruction is intimately tied to research in educational psychology, which says that to succeed students need more than content knowledge -- they need to see themselves as efficacious learners.\u003c/p>\n\u003cp>That is particularly hard in math, where many students believe they are dumb or incapable because of past math learning experiences. To combat that, a core part of Complex Instruction is to teach with a strengths-based approach, rather than only seeing student deficits.\u003c/p>\n\u003cp>“Every person who walks through our doors has mathematical strengths,” Jilk said. “They also have mathematical needs or weaknesses, things they have yet to learn. So we need each other.”\u003c/p>\n\u003cp>https://twitter.com/SFComplex_Instr/status/695004370312671232\u003c/p>\n\u003cp>The Complex Instruction model works because when students work in groups to grapple with a rich math task (Jilk says \u003ca href=\"http://cpm.org/textbooks/\" target=\"_blank\">College Prep Math\u003c/a> is a good place to look), they are each encouraged to bring their full personality and ways of seeing math to the task. The teacher’s job is to observe what’s going on within groups and assign status when she sees a great idea, technique or way of thinking.\u003c/p>\n\u003cp>“You definitely can’t fake these moments,” said Yuka Walton, a seventh- and eighth-grade math teacher at \u003ca href=\"http://www.sfusd.edu/en/schools/school-information/james-denman.html\" target=\"_blank\">James Denman Middle School\u003c/a> in San Francisco. “You can’t assign competence or publicly acknowledge kids for things that aren’t meaningful because then it feels super fake.” Kids are great at detecting inauthentic praise, which ends up sounding condescending.\u003c/p>\n\u003cp>But when a teacher recognizes competence in students who don’t often feel like they have much status as a math learner, it can make a huge difference. Walton remembers one student, Alexis, who would often push the limits in class and consistently referred to herself as bad at math. One day in group work, Walton’s Complex Instruction coach noticed that Alexis was using a really smart, unique technique to organize the numbers in the problem, and her method was propelling her group’s thinking forward. Walton publicly acknowledged how smart that specific technique was and why it was adding value to the group. From then on, the whole class started calling that technique the “Alexis Method.”\u003c/p>\n\u003cp>“It helped her feel ownership over her own learning and her own smartness and power,” Walton said. Over time, Alexis built an identity as a math person, and as she had more confidence in her ability to contribute to her group, other students started assigning her status on their own by asking her for help. In order for teachers to assign competence well, they need to be open to many ways of solving the problem and many kinds of “smartness.”\u003c/p>\n\u003cp>Tracy Thompson teaches math at \u003ca href=\"http://www.sfusd.edu/en/schools/school-information/george-washington.html\" target=\"_blank\">George Washington High School\u003c/a> in San Francisco. Her math department was one of the first in the district to take on Complex Instruction seven years ago, before San Francisco made the \u003ca href=\"http://ww2.kqed.org/news/2015/07/22/san-francisco-middle-schools-no-longer-teaching-algebra-1\" target=\"_blank\">decision to detrack \u003c/a>math classes through sophomore year of high school. When Thompson started trying this approach, she had a group of juniors taking a class called “Applied Math,” an alternative to Algebra II that mostly low-performing math students chose to take. The class counted for graduation credit, but many students couldn’t wait to finish and be done with their math requirements.\u003c/p>\n\u003cp>By the end of that year, students had changed their tune. “Most of the kids that were juniors told me on their own that they wanted to go to Algebra II now,” Thompson said. Even though these students came from 10 years of school where they felt bad at math, with one year of strengths-based instruction that focused on kids working together to figure out interesting problems, they wanted to take on more challenging math.\u003c/p>\n\u003cp>Both Thompson and Walton were clear that this is difficult work and that it doesn’t happen overnight. It can be overwhelming for teachers to balance all the elements: designing or choosing a rich task for every lesson, monitoring status issues, holding students accountable to the norms and roles of group work, and not helping too much when students struggle. It doesn’t always go perfectly. But both teachers say they’d never go back to teaching any other way.\u003c/p>\n\u003cp>“The most important thing is it makes you see so much more clearly,” Thompson said. “Even though things aren’t perfect, it gives me these tools to work with and it just becomes part of the lesson planning process.” Now, when a student is unengaged in the lesson she doesn’t assume he’s lazy. Instead, she tries to find ways to make the classroom a dynamic, comfortable place for him to share his ideas and to participate.\u003c/p>\n\u003cp>“It has expanded my thinking about what makes you smart at math,” Thompson said. “It’s really helped me understand that there are different strengths that people have and that also the fastest calculator is not the best math student always.” Thompson now teaches both Algebra II (which all juniors take) and Calculus BC, one of the few tracked classes for high achievers. She says she has more trouble getting her calculus students to explain their thinking because they believe the best students are godlike and don’t push on their thinking.\u003c/p>\n\u003cp>\u003cstrong>RECULTURING MATH DEPARTMENTS\u003c/strong>\u003c/p>\n\u003cp>San Francisco has been training teachers in Complex Instruction for seven years. The district started by focusing on high schools, bringing in cohorts of teachers who worked at the same school in order to build a community that could collaborate on this difficult and transformative work.\u003c/p>\n\u003cp>“We’re broadening this idea of smart,” said Angela Torres, high school math content specialist for SFUSD. She and Ho Nguyen have championed the Complex Instruction program within the district, slowly broadening its reach as teachers heard about the program and expressed interest.\u003c/p>\n\u003cp>“We literally have to reculture these spaces so we are providing people with a new message and a new narrative about what they bring, the strengths and smartness they bring, and redefine what they’re capable of,” Jilk said.\u003c/p>\n\u003cp>\u003c!-- iframe plugin v.4.3 wordpress.org/plugins/iframe/ -->\u003cbr>\n\u003ciframe width=\"640\" height=\"360\" src=\"https://www.youtube.com/embed/6b-WnJ3c2lo?rel=0\" frameborder=\"0\" scrolling=\"yes\" class=\"iframe-class\">\u003c/iframe>\u003c/p>\n\u003cp>Just a few years after San Francisco began dabbling in Complex Instruction, California adopted Common Core standards, which require more focus on the conceptual underpinnings of math, explaining thinking and reasoning, and less focus on procedural quickness. The SFUSD math department responded to the new standards by inviting teacher leaders to help them write the new math curriculum, pilot test it and offer feedback. They’re still iterating on that work, but the result has been a more engaged math team throughout the district, and more interest in strategies like Complex Instruction that can help teachers get students where they need to go.\u003c/p>\n\u003cp>“It took us really about four years to really understand what it takes,” Nguyen said. “And it wasn’t just about teacher change. It was really about reculturing the math department. We had to go through our own struggles.” SFUSD teachers have received training from Lisa Jilk’s organization, including classroom coaching.\u003c/p>\n\u003cp>The district has also been working to build up its own capacity to coach teachers through Complex Instruction so they can continue sustaining and broadening the program’s reach throughout the district. Coaches watch teachers as they teach and often provide on-the-spot feedback when they notice a student displaying a strength that the teacher missed. The coach will often nudge the teacher to acknowledge that student, sometimes to the whole class, as a way of breaking down some of the status issues in the classroom.\u003c/p>\n\u003cp>\u003c!-- iframe plugin v.4.3 wordpress.org/plugins/iframe/ -->\u003cbr>\n\u003ciframe width=\"640\" height=\"360\" src=\"https://www.youtube.com/embed/ZUKue1upMv0?rel=0\" frameborder=\"0\" scrolling=\"yes\" class=\"iframe-class\">\u003c/iframe>\u003c/p>\n\u003cp>Torres and Nguyen have strategically tried to build teams of teachers at school sites who have incubated the ideas and continue pushing each other. As with students, teachers each have their own strengths and issues of status. Working together to develop rich math tasks, align assessments and discuss strategies has helped them experience the kind of learning environment they are trying to create. And there are meetings to connect educators across the district doing Complex Instruction, as well as a \"video club\" to practice identifying and assigning competence to different students.\u003c/p>\n\u003cp>“When grading we see students are able to think in this critical way that they weren’t able to do before,” Walton said. She used to teach in a district that used direct instruction, a type of teaching that came naturally to her. But she noticed that her students struggled as soon as a problem involved something that had not been explicitly taught.\u003c/p>\n\u003cp>“After doing Complex Instruction, it didn’t matter how complicated the problem was. Even if kids hadn’t seen it before, they would dive right in and get started,” Walton said. Even better, “you see these moments where these kids who before were so discouraged, brighten up and engage and feel more empowered. It has made it so much more meaningful.”\u003c/p>\n\u003cp>All the teachers and coaches involved in Complex Instruction stress that like any other truly transformative teaching practice, getting good takes time. For this style of pedagogy to work well all three elements of the program must be in place and functioning simultaneously. Teachers have to have high expectations for all students, and a real belief that each learner is coming to the experience of learning math with strengths, not just gaps in learning. It takes time to get good at listening for authentic moments of brilliance in student work, and to help students create the interdependence on one another necessary for strong group work.\u003c/p>\n\u003cp>“If you do only one thing, and that is to create opportunities for kids to leverage their strengths in your classroom activities and then name those strengths for them, if you can create those strengths for them, you will already be changing things for most kids in ways that are otherwise not possible,” said Jilk.\u003c/p>\n\u003cp>[ad floatright]\u003c/p>\n\u003cp>And when it all starts to come together, and every student is in the “sweet spot,” it’s like magic. That’s when students start to feel the connection and recognition that the graduates of Railside High were so grateful to have experienced.\u003c/p>\n\n","blocks":[],"excerpt":"Math teachers in San Francisco are using Complex Instruction to see the brilliance in all their students and help them to see it too.","status":"publish","parent":0,"modified":1492624001,"stats":{"hasAudio":false,"hasVideo":true,"hasChartOrMap":true,"iframeSrcs":["https://www.youtube.com/embed/6b-WnJ3c2lo","https://www.youtube.com/embed/ZUKue1upMv0"],"hasGoogleForm":false,"hasGallery":false,"hasHearkenModule":false,"hasPolis":false,"paragraphCount":41,"wordCount":2586},"headData":{"title":"How A Strengths-Based Approach to Math Redefines Who Is 'Smart' | KQED","description":"Math teachers in San Francisco are using Complex Instruction to see the brilliance in all their students and help them to see it too.","ogTitle":"","ogDescription":"","ogImgId":"","twTitle":"","twDescription":"","twImgId":""},"disqusIdentifier":"45012 http://ww2.kqed.org/mindshift/?p=45012","disqusUrl":"https://ww2.kqed.org/mindshift/2016/05/23/how-a-strengths-based-approach-to-math-redefines-who-is-smart/","disqusTitle":"How A Strengths-Based Approach to Math Redefines Who Is 'Smart'","path":"/mindshift/45012/how-a-strengths-based-approach-to-math-redefines-who-is-smart","audioTrackLength":null,"parsedContent":[{"type":"contentString","content":"\u003cdiv class=\"post-body\">\u003cp>\u003cp>A group of young women who had graduated from high school between 1997 and 2006 sat at the front of the room crying and laughing about their experiences \u003ca href=\"http://fairfieldmathadvocates.com/wp-content/uploads/2013/01/Case-of-Railside.pdf\" target=\"_blank\">learning math at Railside High\u003c/a> (a research pseudonym for the school). This session of the \u003ca href=\"http://www.nctm.org/\" target=\"_blank\">National Council of Teachers of Mathematics\u003c/a> annual meeting didn’t focus on any specific mathematical practice and yet it was enlightening -- with the right approach, teachers can help kids who hate math feel like it’s their best subject.\u003c/p>\n\u003cp>One after another, these young women, who had all graduated from an urban high school serving many kids living in poverty, described how math class made them feel safe, heard and able to express their ideas without fear.\u003c/p>\n\u003cp>“I felt like they cared for me,” said Martha Hernandez, who graduated in 2002 and is now a social worker. “They cared for my education and they wanted me to succeed.”\u003c/p>\n\u003cp>Hernandez was designated an English language learner in high school and was the first in her family to go to college. She loved her math classes so much that almost 15 years later, in the NCTM session, she held out physical examples of her work as she cried about the impact the non-traditional math program at Railside High had on her confidence and future success.\u003c/p>\n\u003caside class=\"pullquote alignright\">'It has expanded my thinking about what makes you smart at math.'\u003ccite>Tracy Thompson, High school math teacher\u003c/cite>\u003c/aside>\n\u003cp>“It changed what math meant,” said Maria Velazquez, who now studies education policy at the University of Wisconsin. “It was a process and it required other people. It wasn’t just you and your work and not talking.”\u003c/p>\n\u003cp>\u003c/p>\u003c/div>","attributes":{"named":{},"numeric":[]}},{"type":"component","content":"","name":"ad","attributes":{"named":{"label":"fullwidth"},"numeric":["fullwidth"]}},{"type":"contentString","content":"\u003cdiv class=\"post-body\">\u003cp>\u003c/p>\n\u003cp>Before high school, these young women, like many students in the U.S., experienced math as lecture, sitting at desks quietly. Many believed they weren’t good at math because they didn’t understand or compute quickly. But the math program at Railside High changed that for each of these women, showing them their strengths and allowing them to bring all of themselves to the pursuit of mathematics.\u003c/p>\n\u003cp>But what was so different about how these women learned math in high school? How did their math teachers form bonds so strong that years later they were attending students’ weddings in Mexico?\u003c/p>\n\u003cp>The answer: \u003ca href=\"http://cgi.stanford.edu/group/pci/cgi-bin/site.cgi\" target=\"_blank\">Complex Instruction\u003c/a>. This pedagogy is not specific to math and has been \u003ca href=\"http://cgi.stanford.edu/group/pci/cgi-bin/site.cgi?page=research.html\" target=\"_blank\">in the literature\u003c/a> for decades, originally researched by \u003ca href=\"http://cgi.stanford.edu/group/pci/cgi-bin/site.cgi?page=whos_who.html\" target=\"_blank\">Elizabeth Cohen and Rachel Lotan\u003c/a> at Stanford University. Teachers at Railside High discovered the methodology when they were undergoing an accreditation review and were told they needed to drastically change something to improve their results. The ultimatum prompted teachers to try something different -- heterogeneous classes, high expectations for all students and, above all, approaching math with an eye to students’ strengths.\u003c/p>\n\u003cfigure id=\"attachment_45185\" class=\"wp-caption alignnone\" style=\"max-width: 1920px\">\u003cimg class=\"wp-image-45185 size-full\" src=\"http://ww2.kqed.org/mindshift/wp-content/uploads/sites/23/2016/05/Railside-2-e1463987977561.jpg\" alt=\"Railside 2\" width=\"1920\" height=\"1440\">\u003cfigcaption class=\"wp-caption-text\">Courtesy of Yuka Walton\u003c/figcaption>\u003c/figure>\n\u003cp>The three main tenets of Complex Instruction are that learning should have multi-ability access points, norms and roles that support interdependency between students, and attention to status and accountability for learning. In most Complex Instruction classrooms the majority of class time is spent with students working in groups of four on a rich task that has multiple entry points and ways it could be solved. If one student can solve the problem in his or her head, it’s not a rich task.\u003c/p>\n\u003cp>Each student in the group has a role: team captain, resource manager, recorder-reporter and facilitator. While these roles might sound cheesy to some students, they are important for helping groups to work equitably, ensuring that every group member has a crucial and intellectual task. The roles help students learn how to effectively participate and, because each role is necessary to solve a task, everyone must share their ideas.\u003c/p>\n\u003caside class=\"alignleft\">\n\u003ch3>More Resources on Complex Instruction\u003c/h3>\n\u003cp>These books delve more deeply into student experiences of Complex Instruction, details on how to create equitable groups and how to mitigate status issues.\u003c/p>\n\u003cul>\n\u003cli>\u003ca href=\"http://store.tcpress.com/0807755664.shtml\">\u003ci>Designing Groupwork\u003c/i>\u003c/a>\u003c/li>\n\u003cli>\u003ca href=\"http://www.nctm.org/store/Products/Smarter-Together!-Collaboration-and-Equity-in-the-Elementary-Math-Classroom/\">\u003ci>Smarter Together! Collaboration and Equity in the Elementary Math Classroom\u003c/i>\u003c/a>\u003c/li>\n\u003cli>\u003ca href=\"http://store.tcpress.com/0807755419.shtml\">\u003ci>Mathematics For Equity: A Framework For Successful Practice\u003c/i>\u003c/a>\u003c/li>\n\u003cli>\u003ca href=\"http://store.tcpress.com/0807752460.shtml\">\u003ci>\"Heterogeneous\" Classrooms: Detracking Math and Science -- A Look at Groupwork in Action\u003c/i>\u003c/a>\u003c/li>\n\u003c/ul>\n\u003c/aside>\n\u003cp>“Participation leads to more learning because learning is a socially constructed activity,” said \u003ca href=\"http://washington.academia.edu/LisaJilk/Papers\" target=\"_blank\">Lisa Jilk\u003c/a>, program director of Reculturing Math Departments for Excellence & Equity, part of the \u003ca href=\"http://www.matheducation.uw.edu/\" target=\"_blank\">Mathematics Education Project\u003c/a> at the University of Washington. Jilk taught at Railside High, and when she left to get her doctorate she studied how and why Complex Instruction worked for so many students from various backgrounds. Now she’s dedicated to helping other math departments around the country “reculture” themselves to think about what learners bring to math that will help them, rather than only about the information they are missing.\u003c/p>\n\u003cp>When the three tenets of Complex Instruction are all working together simultaneously it can feel like a magical experience. But getting there takes a lot of work. When Jilk starts training teachers, one of the first things that must be discussed is the idea of status in the classroom and how to break that down. Teaching with Complex Instruction is intimately tied to research in educational psychology, which says that to succeed students need more than content knowledge -- they need to see themselves as efficacious learners.\u003c/p>\n\u003cp>That is particularly hard in math, where many students believe they are dumb or incapable because of past math learning experiences. To combat that, a core part of Complex Instruction is to teach with a strengths-based approach, rather than only seeing student deficits.\u003c/p>\n\u003cp>“Every person who walks through our doors has mathematical strengths,” Jilk said. “They also have mathematical needs or weaknesses, things they have yet to learn. So we need each other.”\u003c/p>\u003c/p>\u003c/div>","attributes":{"named":{},"numeric":[]}},{"type":"component","content":"","name":"singleTwitterStatus","attributes":{"named":{"id":"695004370312671232"},"numeric":[]}},{"type":"contentString","content":"\u003cdiv class=\"post-body\">\u003cp>\n\u003cp>The Complex Instruction model works because when students work in groups to grapple with a rich math task (Jilk says \u003ca href=\"http://cpm.org/textbooks/\" target=\"_blank\">College Prep Math\u003c/a> is a good place to look), they are each encouraged to bring their full personality and ways of seeing math to the task. The teacher’s job is to observe what’s going on within groups and assign status when she sees a great idea, technique or way of thinking.\u003c/p>\n\u003cp>“You definitely can’t fake these moments,” said Yuka Walton, a seventh- and eighth-grade math teacher at \u003ca href=\"http://www.sfusd.edu/en/schools/school-information/james-denman.html\" target=\"_blank\">James Denman Middle School\u003c/a> in San Francisco. “You can’t assign competence or publicly acknowledge kids for things that aren’t meaningful because then it feels super fake.” Kids are great at detecting inauthentic praise, which ends up sounding condescending.\u003c/p>\n\u003cp>But when a teacher recognizes competence in students who don’t often feel like they have much status as a math learner, it can make a huge difference. Walton remembers one student, Alexis, who would often push the limits in class and consistently referred to herself as bad at math. One day in group work, Walton’s Complex Instruction coach noticed that Alexis was using a really smart, unique technique to organize the numbers in the problem, and her method was propelling her group’s thinking forward. Walton publicly acknowledged how smart that specific technique was and why it was adding value to the group. From then on, the whole class started calling that technique the “Alexis Method.”\u003c/p>\n\u003cp>“It helped her feel ownership over her own learning and her own smartness and power,” Walton said. Over time, Alexis built an identity as a math person, and as she had more confidence in her ability to contribute to her group, other students started assigning her status on their own by asking her for help. In order for teachers to assign competence well, they need to be open to many ways of solving the problem and many kinds of “smartness.”\u003c/p>\n\u003cp>Tracy Thompson teaches math at \u003ca href=\"http://www.sfusd.edu/en/schools/school-information/george-washington.html\" target=\"_blank\">George Washington High School\u003c/a> in San Francisco. Her math department was one of the first in the district to take on Complex Instruction seven years ago, before San Francisco made the \u003ca href=\"http://ww2.kqed.org/news/2015/07/22/san-francisco-middle-schools-no-longer-teaching-algebra-1\" target=\"_blank\">decision to detrack \u003c/a>math classes through sophomore year of high school. When Thompson started trying this approach, she had a group of juniors taking a class called “Applied Math,” an alternative to Algebra II that mostly low-performing math students chose to take. The class counted for graduation credit, but many students couldn’t wait to finish and be done with their math requirements.\u003c/p>\n\u003cp>By the end of that year, students had changed their tune. “Most of the kids that were juniors told me on their own that they wanted to go to Algebra II now,” Thompson said. Even though these students came from 10 years of school where they felt bad at math, with one year of strengths-based instruction that focused on kids working together to figure out interesting problems, they wanted to take on more challenging math.\u003c/p>\n\u003cp>Both Thompson and Walton were clear that this is difficult work and that it doesn’t happen overnight. It can be overwhelming for teachers to balance all the elements: designing or choosing a rich task for every lesson, monitoring status issues, holding students accountable to the norms and roles of group work, and not helping too much when students struggle. It doesn’t always go perfectly. But both teachers say they’d never go back to teaching any other way.\u003c/p>\n\u003cp>“The most important thing is it makes you see so much more clearly,” Thompson said. “Even though things aren’t perfect, it gives me these tools to work with and it just becomes part of the lesson planning process.” Now, when a student is unengaged in the lesson she doesn’t assume he’s lazy. Instead, she tries to find ways to make the classroom a dynamic, comfortable place for him to share his ideas and to participate.\u003c/p>\n\u003cp>“It has expanded my thinking about what makes you smart at math,” Thompson said. “It’s really helped me understand that there are different strengths that people have and that also the fastest calculator is not the best math student always.” Thompson now teaches both Algebra II (which all juniors take) and Calculus BC, one of the few tracked classes for high achievers. She says she has more trouble getting her calculus students to explain their thinking because they believe the best students are godlike and don’t push on their thinking.\u003c/p>\n\u003cp>\u003cstrong>RECULTURING MATH DEPARTMENTS\u003c/strong>\u003c/p>\n\u003cp>San Francisco has been training teachers in Complex Instruction for seven years. The district started by focusing on high schools, bringing in cohorts of teachers who worked at the same school in order to build a community that could collaborate on this difficult and transformative work.\u003c/p>\n\u003cp>“We’re broadening this idea of smart,” said Angela Torres, high school math content specialist for SFUSD. She and Ho Nguyen have championed the Complex Instruction program within the district, slowly broadening its reach as teachers heard about the program and expressed interest.\u003c/p>\n\u003cp>“We literally have to reculture these spaces so we are providing people with a new message and a new narrative about what they bring, the strengths and smartness they bring, and redefine what they’re capable of,” Jilk said.\u003c/p>\n\u003cp>\u003c!-- iframe plugin v.4.3 wordpress.org/plugins/iframe/ -->\u003cbr>\n\u003ciframe width=\"640\" height=\"360\" src=\"https://www.youtube.com/embed/6b-WnJ3c2lo?rel=0\" frameborder=\"0\" scrolling=\"yes\" class=\"iframe-class\">\u003c/iframe>\u003c/p>\n\u003cp>Just a few years after San Francisco began dabbling in Complex Instruction, California adopted Common Core standards, which require more focus on the conceptual underpinnings of math, explaining thinking and reasoning, and less focus on procedural quickness. The SFUSD math department responded to the new standards by inviting teacher leaders to help them write the new math curriculum, pilot test it and offer feedback. They’re still iterating on that work, but the result has been a more engaged math team throughout the district, and more interest in strategies like Complex Instruction that can help teachers get students where they need to go.\u003c/p>\n\u003cp>“It took us really about four years to really understand what it takes,” Nguyen said. “And it wasn’t just about teacher change. It was really about reculturing the math department. We had to go through our own struggles.” SFUSD teachers have received training from Lisa Jilk’s organization, including classroom coaching.\u003c/p>\n\u003cp>The district has also been working to build up its own capacity to coach teachers through Complex Instruction so they can continue sustaining and broadening the program’s reach throughout the district. Coaches watch teachers as they teach and often provide on-the-spot feedback when they notice a student displaying a strength that the teacher missed. The coach will often nudge the teacher to acknowledge that student, sometimes to the whole class, as a way of breaking down some of the status issues in the classroom.\u003c/p>\n\u003cp>\u003c!-- iframe plugin v.4.3 wordpress.org/plugins/iframe/ -->\u003cbr>\n\u003ciframe width=\"640\" height=\"360\" src=\"https://www.youtube.com/embed/ZUKue1upMv0?rel=0\" frameborder=\"0\" scrolling=\"yes\" class=\"iframe-class\">\u003c/iframe>\u003c/p>\n\u003cp>Torres and Nguyen have strategically tried to build teams of teachers at school sites who have incubated the ideas and continue pushing each other. As with students, teachers each have their own strengths and issues of status. Working together to develop rich math tasks, align assessments and discuss strategies has helped them experience the kind of learning environment they are trying to create. And there are meetings to connect educators across the district doing Complex Instruction, as well as a \"video club\" to practice identifying and assigning competence to different students.\u003c/p>\n\u003cp>“When grading we see students are able to think in this critical way that they weren’t able to do before,” Walton said. She used to teach in a district that used direct instruction, a type of teaching that came naturally to her. But she noticed that her students struggled as soon as a problem involved something that had not been explicitly taught.\u003c/p>\n\u003cp>“After doing Complex Instruction, it didn’t matter how complicated the problem was. Even if kids hadn’t seen it before, they would dive right in and get started,” Walton said. Even better, “you see these moments where these kids who before were so discouraged, brighten up and engage and feel more empowered. It has made it so much more meaningful.”\u003c/p>\n\u003cp>All the teachers and coaches involved in Complex Instruction stress that like any other truly transformative teaching practice, getting good takes time. For this style of pedagogy to work well all three elements of the program must be in place and functioning simultaneously. Teachers have to have high expectations for all students, and a real belief that each learner is coming to the experience of learning math with strengths, not just gaps in learning. It takes time to get good at listening for authentic moments of brilliance in student work, and to help students create the interdependence on one another necessary for strong group work.\u003c/p>\n\u003cp>“If you do only one thing, and that is to create opportunities for kids to leverage their strengths in your classroom activities and then name those strengths for them, if you can create those strengths for them, you will already be changing things for most kids in ways that are otherwise not possible,” said Jilk.\u003c/p>\n\u003cp>\u003c/p>\u003c/div>","attributes":{"named":{},"numeric":[]}},{"type":"component","content":"","name":"ad","attributes":{"named":{"label":"floatright"},"numeric":["floatright"]}},{"type":"contentString","content":"\u003cdiv class=\"post-body\">\u003cp>\u003c/p>\n\u003cp>And when it all starts to come together, and every student is in the “sweet spot,” it’s like magic. That’s when students start to feel the connection and recognition that the graduates of Railside High were so grateful to have experienced.\u003c/p>\n\n\u003c/div>\u003c/p>","attributes":{"named":{},"numeric":[]}}],"link":"/mindshift/45012/how-a-strengths-based-approach-to-math-redefines-who-is-smart","authors":["234"],"categories":["mindshift_193"],"tags":["mindshift_21089","mindshift_20994","mindshift_20784","mindshift_1040","mindshift_20762","mindshift_20512","mindshift_392","mindshift_20993"],"featImg":"mindshift_45189","label":"mindshift"}},"programsReducer":{"possible":{"id":"possible","title":"Possible","info":"Possible is hosted by entrepreneur Reid Hoffman and writer Aria Finger. Together in Possible, Hoffman and Finger lead enlightening discussions about building a brighter collective future. The show features interviews with visionary guests like Trevor Noah, Sam Altman and Janette Sadik-Khan. 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Hosted by journalists of color, the show tackles the subject of race head-on, exploring how it impacts every part of society — from politics and pop culture to history, sports and more.\u003cbr />\u003cbr />\u003cem>Life Kit\u003c/em>, which will be in the second part of the hour, guides you through spaces and feelings no one prepares you for — from finances to mental health, from workplace microaggressions to imposter syndrome, from relationships to parenting. The show features experts with real world experience and shares their knowledge. Because everyone needs a little help being human.\u003cbr />\u003cbr />\u003ca href=\"https://www.npr.org/podcasts/510312/codeswitch\">\u003cem>Code Switch\u003c/em> offical site and podcast\u003c/a>\u003cbr />\u003ca href=\"https://www.npr.org/lifekit\">\u003cem>Life Kit\u003c/em> offical site and podcast\u003c/a>\u003cbr />","airtime":"SUN 9pm-10pm","imageSrc":"https://cdn.kqed.org/wp-content/uploads/2021/12/CodeSwitchLifeKit_StationGraphics_300x300EmailGraphic.png","meta":{"site":"radio","source":"npr"},"link":"/radio/program/code-switch-life-kit","subscribe":{"apple":"https://podcasts.apple.com/podcast/1112190608?mt=2&at=11l79Y&ct=nprdirectory","google":"https://podcasts.google.com/feed/aHR0cHM6Ly93d3cubnByLm9yZy9yc3MvcG9kY2FzdC5waHA_aWQ9NTEwMzEy","spotify":"https://open.spotify.com/show/3bExJ9JQpkwNhoHvaIIuyV","rss":"https://feeds.npr.org/510312/podcast.xml"}},"commonwealth-club":{"id":"commonwealth-club","title":"Commonwealth Club of California Podcast","info":"The Commonwealth Club of California is the nation's oldest and largest public affairs forum. As a non-partisan forum, The Club brings to the public airwaves diverse viewpoints on important topics. The Club's weekly radio broadcast - the oldest in the U.S., dating back to 1924 - is carried across the nation on public radio stations and is now podcasting. Our website archive features audio of our recent programs, as well as selected speeches from our long and distinguished history. 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We cover topics like how fed-up administrators are developing surprising tactics to deal with classroom disruptions; how listening to podcasts are helping kids develop reading skills; the consequences of overparenting; and why interdisciplinary learning can engage students on all ends of the traditional achievement spectrum. This podcast is part of the MindShift education site, a division of KQED News. KQED is an NPR/PBS member station based in San Francisco. You can also visit the MindShift website for episodes and supplemental blog posts or tweet us \u003ca href=\"https://twitter.com/MindShiftKQED\">@MindShiftKQED\u003c/a> or visit us at \u003ca href=\"/mindshift\">MindShift.KQED.org\u003c/a>","imageSrc":"https://cdn.kqed.org/wp-content/uploads/2022/02/mindshift2021-tile-3000x3000-1-scaled-1.jpg","imageAlt":"KQED MindShift: How We Will Learn","officialWebsiteLink":"/mindshift/","meta":{"site":"news","source":"kqed","order":"2"},"link":"/podcasts/mindshift","subscribe":{"apple":"https://podcasts.apple.com/us/podcast/mindshift-podcast/id1078765985","google":"https://podcasts.google.com/feed/aHR0cHM6Ly9mZWVkcy5tZWdhcGhvbmUuZm0vS1FJTkM1NzY0NjAwNDI5","npr":"https://www.npr.org/podcasts/464615685/mind-shift-podcast","stitcher":"https://www.stitcher.com/podcast/kqed/stories-teachers-share","spotify":"https://open.spotify.com/show/0MxSpNYZKNprFLCl7eEtyx"}},"morning-edition":{"id":"morning-edition","title":"Morning Edition","info":"\u003cem>Morning Edition\u003c/em> takes listeners around the country and the world with multi-faceted stories and commentaries every weekday. 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