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Nearly two decades ago, when José Vilson was studying to become a teacher, an alarming rise in high school dropout rates was worrying educators and monopolizing news headlines nationwide.

Eager to make an impact, Vilson set his sights on the middle grades: "I thought that if I wanted to make a difference when it came to altering these rates, it would happen in middle school, because that's where you develop the foundational skills to build up your algebraic and geometric thinking."

If he could successfully teach middle school students math-as well as the skills and mindsets to persevere through challenging work-young adolescents would enter high school better prepared for complex math as well as the ups and downs of college and careers, he reasoned.

After teaching math to middle school students in New York City for 15 years, Vilson hasn't wavered from his early-career commitment. In fact, today he's unequivocal in arguing that aiming for mere proficiency in math is inexcusable. Rather, math is an essential "civil right" that's as important to master as reading and writing.

Vilson is the author of This Is Not a Test: A New Narrative on Race, Class, and Education, and his writing has been published by The Atlantic, The New York Times, and CNN. A popular speaker, he's presented at TED, the American Research Association, and the National Council of Teachers of Mathematics. He is cofounder and executive director of EduColor, an organization aimed at increasing the number of educators of color in classrooms. Currently, Vilson is completing his doctorate at Columbia University, researching barriers facing teachers of color in schools.

I spoke with Vilson about the secret sauce for connecting kids to abstract math, the importance of back-pocket questions as a metacognitive tool, and math as a "lever for change."

BORYGA: In a 2017 talk, you discuss the importance of having high expectations for your middle school math students. What do you mean by high expectations?

VILSON: For me, high expectations aren't about using math to challenge kids in a way that punishes them or weeds them out from the field. I fundamentally believe that if I was able to master this complex math, then you can too. It's that simple.

I tell my students, "I don't want to hear about you not being a math person. Math is already within you. You're doing math all the time, voluntarily and involuntarily." The other thing I say is that even if you think you won't use math in your everyday life, you still have the capacity within you to do it.

It's interesting: The times when students believe the math they're learning isn't relevant is when they can't connect with it. When I can find ways to help them connect to the math, those questions never come up. That speaks to the importance of building deep and sustainable connections with the material.

BORYGA: What do you mean when you say that, for students of color in particular, math is a civil right?

VILSON: Educator Robert P. Moses was instrumental in helping me think about how math and numeracy ought to be a civil right in the same way that we think about literacy. In his book Radical Equations: Civil Rights From Mississippi to the Algebra Project, which he cowrote with Charles E. Cobb Jr., he talks about how when someone is illiterate, generally people say, "Oh, that's a crime. We need to fix that." When it comes to math, that usually isn't the case.

And yet, in the media, in policies, or in our personal fiscal matters, numbers matter a ton. But when students don't know how to interpret the numbers in front of them, people say, "Well, they could just use a calculator." They make it seem like it's not that bad. Or they think, "I wasn't good at math; it's OK if my child isn't good at math."

My feeling is that math is not reserved for a specific set of people who may acclimate to narrow expectations of how to do math. It is for everybody. When I say it's a civil right, I mean that we all deserve to learn the best math possible. We should be saying, "Wait, you're innumerate? We need to fix that immediately." Everything we do for reading, we should do for math.

BORYGA: Why is math so important-why should we take an all-hands-on-deck approach to teaching it?

VILSON: When you join numeracy with literacy, you can better understand other subjects, like social studies or science. To understand what is happening with climate change, for example, you need to understand exponential functions and how they work.

Many of us don't know the basic tenets of math that can provide us access to the things that are affecting us right here and now in a profound way. Basic algebra, geometry, statistics-these are foundational texts for how the world works. Giving students the ability, and the right, to access those texts is important.

When I say it's a civil right, I mean that we all deserve to learn the best math possible.

José Vilson

BORYGA: Your new book, due for publication in 2025, explores how to translate "abstract and intangible math concepts" into concrete understanding for students. What types of strategies do you recommend for teachers in classrooms?

VILSON: The idea is to push students to take a step back, tap into what they already know, and use that understanding to help them scale up to more complex concepts that they may not have previously felt they could access.

For example, too often people think the equal sign signifies an answer. But to effectively teach kids algebra, we must explain that an equal sign is also about balance. One of my favorite lessons is to have students imagine we're going to balance two items on a scale. Because I'm in New York, I'll choose items they're familiar with, like bagels and paper bags. I'll draw a set of bags on one side of the scale and bagels on the other side and show them that to achieve balance, I can put any number of bags and bagels on each side of the scale or a mix of each on either side.

This understanding allows us to get into algebraic equations and the idea that when students see the equal sign in Algebra I, their first thought shouldn't be The other side has to be equal to a constant number. No, it could actually be equal to something that is also a variable. And this inevitably leads to understanding polynomials and all sorts of functions.

BORYGA: For many kids, math anxiety can limit their willingness to take risks and make mistakes. How do you work with that reality in your classroom?

VILSON: By the time students got to me, they may have already had at least six years of not feeling confident about math. You can imagine the level of anxiety they have.

Something I do is lean into what I call a questioner stance. It's me saying, "Let me offer questions to you that you can keep in your back pocket whenever you don't feel confident." This posture helps when you're one teacher with 30 or 35 students, but it also improves students' confidence in their ability to learn on their own.

When students get stuck on a problem, I ask them a series of questions to try and figure out where they're having trouble. Then I try to scaffold things for them. But at the precipice, when they're just about to get it, I say, "OK, you got it from here. I'm not going to tell you yes or no." Then I walk away.

At first it's frustrating for students because they want validation. But I delay that gratification enough for them to feel confident in themselves when they're able to figure out the solution. And hopefully, the next time they get stuck, they hear my voice in their head guiding them and ask themselves similar questions. I've found that this usually helps quell some of their math anxiety.

BORYGA: You've said, pretty famously on Twitter, "Most of my work as a math teacher isn't even math. It's helping students believe that they can also do math." Why is belief so important in math class?

VILSON: For me, making students believe they can do math means making it clear there will be errors along the way and that the idea is not that we'll never make errors, but that we will try our best to make fewer errors.

Trial and error allow us to get better. Failing is a part of winning. When we believe in our students, we allow them to believe in themselves and their efficacy and understand that things get better over time. Instead of thinking, "I made that mistake again-I'm not good at math," what you want students to say to themselves is, "I'm going to keep trying, I'm going to keep making errors, but these errors look better and better, and that means I'm getting closer to what we're trying to accomplish here."

Basic algebra, geometry, statistics-these are foundational texts for how the world works.

José Vilson

BORYGA: You prioritize developing what you call "soft skills" in students. What do you say to critics who argue that this takes away valuable time from the essential work of, for example, learning math facts?

VILSON: I would say there is nothing soft about trying to build community. It's actually hard to figure out what's going on with a particular student that isn't allowing them to connect to a problem in front of them. It's a lot easier to just tell them how to do it. But if you do that, the student has no real connection to the procedures. They just follow it, and then they throw it away once they're done, as opposed to being able to carry a set of skills with them, like being able to model, scale, or reason. That is what the soft skills are all about.

BORYGA: Let's talk about your current work and research. What are some of the main barriers to hiring-and retaining-diverse teachers today?

VILSON: The pay issue is huge, but it's important to dig into that. While White teachers are more likely to have the fiscal base to go into teaching, which can pay substandard wages at first, and wait for salaries to build up over years, teachers of color-and particularly those who come from impoverished contexts-don't often have that luxury. Fixing that could include forms of debt forgiveness, stipends, or other ways to augment pay.

Another issue is the profound lack of mobility teachers of color can experience. I've heard from teachers that they often don't get the same flexibility as White colleagues when it comes to having autonomy in pedagogy, curriculum, or assessments. And in frameworks supposedly designed to be objective, they may receive lower ratings than their White counterparts, even when they're using the same pedagogy.

I think, too often, these experiences compound and keep teachers further and further away from the work they actually want to do.

BORYGA: You've been vocal about the need to hire more teachers of color. Why is this so important in schools and in the lives of students?

VILSON: We ought to put adults in our schools who reflect what we mean by public education. More than 50 percent of our student body in public schools are students of color-and they have urgent needs that aren't being met by our education system.

There's a burgeoning body of research that suggests teachers of color can be a good answer to this. It's not a Band-Aid solution, but when you hire people who have a set of experiences that can inform the system about how to do better, then, notably, everybody benefits, including White students.

We need teachers who can create connective tissue among students so they can see what it means to live in a democracy that includes representations of everybody. That's what I believe a public education can do very well.
This interview has been edited for brevity, clarity, and flow.

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José Vilson: Good Math Education Is a 'Civil Right'

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The middle school math teacher, author, and lecturer, on holding high expectations for every child and prioritizing mathematics in the same way we do literacy.

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It's the end of math class at Forest Hills Elementary School in Sidman, Pennsylvania, and after a short break, fourth-grade teacher Dawn McCall's students are getting down to business-with an additional 20 minutes of math work.

McCall's students know the routine: They pair off with a partner-usually a higher-performing student and a lower-performing one-and work through short sets of problems together that target weak or missing skills, like multidigit subtraction or multiplication. One student solves the problem while describing their thinking aloud; the other student offers support and highlights mistakes. Then they switch roles.

This is SpringMath, a short and intensive math intervention that McCall's school is implementing for all students, regardless of their achievement levels. The targeted daily practice is designed to strengthen foundational skills, and it's rapidly putting grade-level math mastery within reach for a lot more students, according to McCall. "To succeed at fractions and decimals, you have to know your multiplication and division facts," McCall said. "If you know those multiplication and division facts, things like reducing fractions is going to be a lot easier. It's that little extra bit of practice every day."

Since Forest Hills Elementary began implementing the math intervention at the beginning of 2018-slowly adding a few grades at a time, beginning with fourth through sixth grade-student test scores for some participating groups have steadily improved, according to assistant superintendent Dr. Rob Dill. In 2022, 56 percent of fourth graders at the school scored proficient or advanced on the Pennsylvania System of School Assessment state test; by fifth grade, 76 percent of those same students scored proficient or above. Meanwhile, math achievement across the nation is headed in the opposite direction. Only 36 percent of fourth graders scored proficient in math on the 2022 National Assessment of Educational Progress (NAEP) after a historic five-point drop following pandemic school closures. For the decade before that, scores had hovered around only 40 percent proficiency. Eighth-grade achievement dropped even more-down eight points from 2019, with only 26 percent of students scoring proficient; 40 percent scored below basic.

Now, a growing number of researchers, school leaders, and educators are calling attention to research-based solutions to combat slippage in math, including the crucial role that adequate practice time plays in student performance. "They are considered dirty words, but drill and practice, and explicit instruction on how to procedurally solve math problems, are evidence-based strategies that work," said SUNY University at Albany math researcher Ben Solomon. There's often a misconception that rote math practice is dull and uninteresting, but "think about how adults thought phonics was boring, but kids actually feel awesome when they can be successful at learning to read," said University of Winnipeg professor of mathematics Anna Stokke. "It's the same with math. Teaching foundational math skills does not need to be mindless and boring. Adults who have already mastered a topic don't view things with the same sense of excitement that kids do. Kids get excited about math when they feel successful, regardless of the topic."

The Fluency Question

A key missing ingredient in higher math achievement is math fluency, especially in the basic operations of addition, subtraction, multiplication, and division. Research shows that fluency in these foundational skills is critical to math performance and achievement, but experts and educators say there's a disconnect between how much practice students need to achieve fluency-especially students who struggle with math-and how much they often get in classrooms. The National Mathematics Advisory Panel includes the importance of practice in basic operations among its top findings and recommendations-"Computational proficiency with whole number operations is dependent on sufficient and appropriate practice to develop automatic recall," the authors write-yet schools and teachers say that, for a variety of reasons, students aren't getting enough practice to solidify foundational concepts.

Researchers like Solomon say that memorizing multiplication tables, timed practice with feedback, and the dreaded worksheet of problems actually matter to long-term math achievement because they help students build the kind of domain knowledge in foundational skills needed to perform more complex math-and that some kinds of math practice are better than others. Evidence shows that procedural and conceptual understanding go hand in hand and are mutually reinforcing, but experts say that in many classrooms an overcorrection has been made that puts too much focus on conceptual understanding at the expense of procedure. "Conceptual understanding really has been overemphasized to the point that students don't have procedural skills," Stokke said.

Lack of procedural skill often keeps students from ever reaching the creative, open-ended side of math. "We need to give them the basic tools and then play with them in many different ways so they can explore the beauty of math," said cognitive scientist Daniel Ansari, professor and Canada research chair at the University of Western Ontario in London, Ontario. "But first they need the basic building blocks."

Obstacles to practice time

Math practice gets shortchanged for a constellation of reasons-an overstuffed curriculum and the drive to cover an overwhelming number of standards; test-prep pressure; and instructional philosophies that consider repetitive practice, sometimes negatively referred to as "rote" or "drill and kill," to be uniformly harmful and to be avoided at all costs.

When Lee Williams, mom to two middle school students in Williamson County, Tennessee, checks in on their homework, she said, the most notable thing is that they're moving through math at lightning speed-a common refrain among parents interviewed for this story. Both kids are tackling complex concepts in math class, yet they haven't mastered the fundamentals of arithmetic that make learning more challenging topics possible. "They move to a new topic every week in elementary and don't ever master the basic functions," she said. "They start with algebraic concepts before they even have multiplication and division facts at the ready-in third grade."

In classrooms, teachers say there's just not enough time for extra practice. Pressured to cover every state standard with equal emphasis, they often can't spend extra time on fundamentals like memorizing multiplication tables, or even on the standards themselves. "It's a huge problem," said Sarah Powell, associate professor at the University of Texas at Austin, who researches math instruction and trains teachers. Some districts go so far as to put out a calendar dictating what every teacher should be working on every week of the year-regardless of how far along (or behind) their students are in the curriculum, Powell noted. "We have trapped ourselves with having so many expectations; at each grade level there are these standards, and you are supposed to cover these 30 things and not let anything go," she said.

But when it comes to standards, it's important to recognize that they're not all of equal importance, said Phil Daro, who helped write the Common Core math standards. Some of the fundamentals, such as single-digit addition, subtraction, multiplication, and division for the youngest students, are critical to spend ample time teaching and have kids practice. "Students need to know foundational math facts fluently," Daro said. "Practice needs to focus on the foundational skills. If you fill that practice bucket with more and more stuff, that will dilute the amount of time and effort available for practicing the real foundation."

Adding to the problem, researchers say that popular math curricula, and even some teacher training programs, de-emphasize practice's crucial role in math learning. "Many of the newer textbooks don't provide enough practice problems," said Doug Rohrer, a professor and math education researcher at the University of South Florida.

Where does practice belong?

A few years ago, SpringMath founder Amanda VanDerHeyden overheard a tutoring session where a student was trying to divide 148 by 3. Instead of doing long division, the student skip-counted by 3s all the way to 148, which didn't work out evenly. After several more attempts, the student finally arrived at the correct solution. "The student has the horsepower, he conceptually understands," she thought to herself at the time. "But he has been deprived of the most efficient way to get there."

Like learning any skill, after students learn a particular concept like long division, in order to consolidate that learning and reproduce it in the most efficient way possible, they have to practice until it becomes second nature. But because learning isn't a linear process, students should regularly be moving between foundational skills and application, with teachers frequently planning tasks that encourage retrieval of that material in a variety of ways. In most math classrooms, says VanDerHeyden, students are required to stop working on a skill too soon, cutting short valuable opportunities for repetition and limiting their ability to lock the learning into long-term memory.

SpringMath is based on a learning framework called the instructional hierarchy, a framework for how students acquire new skills that includes four distinct stages, including acquisition, fluency, generalization, and adaptation. According to this model (and there are a variety of learning frameworks), teaching looks different in the acquisition stage when students are brand-new to a concept, compared with when students can take a skill like long division and adapt it to other things, like complex story problems. A deeper awareness of how learning works, said University of Florida school psychology assistant professor Kathrin Maki, makes it easier to use techniques like inquiry learning at optimal times-but not when kids haven't yet had enough practice to adapt new skills to new problems.

"Inquiry learning isn't necessarily bad," said Maki. "It's that those techniques are only helpful when kids have basic, prerequisite skills. Something we struggle with in math instruction is trying to implement those [inquiry-based] techniques too soon. Kids who are in the acquisition and proficiency stages, those are kids who need a lot of repeated practice and explicit instruction."

The goal of practice is to move foundational skills into long-term memory so they become quick and automatic. Since math constantly builds new skills on top of existing ones, it's "relentlessly hierarchical," said Maki, and once foundational skills like addition and multiplication facts are locked into long-term memory, learning new, more complex math skills like multiplying fractions gets easier; working memory doesn't have to work so hard. "Long-term memory is effectively limitless; that's our superpower," said researcher and teacher Greg Ashman. "Things that are extremely hard to do when you're a novice become easy when you've got lots of stuff in your long-term memory."

Best practice for practice

Improving math fluency doesn't necessarily require endless hours of drilling, research shows. Short but frequent bursts, using a variety of retrieval practice strategies-think flash cards and brain dumps, for example, that get students to identify what they know about a concept, thus strengthening long-term retention-are more effective than longer, less frequent practice. "Teachers tend to focus on getting info into students' heads," said cognitive scientist Pooja Agarwal, coauthor of Powerful Teaching: Unleash the Science of Learning. "But a big component of learning is getting the information out of our heads." Frequent low-stakes quizzes, entry and exit tickets, and some digital games, like FactFreaks, can offer effective retrieval practice.

Retrieval strategies like spaced practice, where students revisit concepts over a period of time with breaks in between, and interleaved practice, where mixing up different types of math problems helps students remember information better than when they work through long blocks of one type of problem, are strongly backed by the science of learning. Interleaving is so effective, University of Florida researcher Rohrer said, because students must decide which problem-solving strategy to use before solving. "In math textbooks, students don't have a chance to choose a strategy because a typical math assignment is devoted to a single concept," he said. "Which means that they usually know the strategy for each problem before they even read it." Interleaving, however, "gives students a chance to learn what they need to know."

In the Forest Hills school district in Pennsylvania, assistant superintendent Dill said a series of evidence-based reforms, including a new curriculum, have rewired how the district teaches math from kindergarten to high school-but the importance of the extra daily practice can't be understated. "Kids who are now fourth- and fifth-graders, they've been doing this for a few years," Dill said of the intervention. "And their skill development is far better than we've ever seen before." And in McCall's classroom, she's seeing overall math confidence blossom. "They know they can do it," she said. "They've learned those math facts."

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Should More Time Be Spent Learning Math Facts?

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As schools nationwide contend with declining math scores, some districts are dedicating more time to the practice of foundational skills.

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Jo Boaler has spent a lot of time thinking and writing about anxiety-math anxiety, in particular-and its impact on kids' learning trajectories.

Mathematics, she writes in her 2019 book, Limitless Mind: Learn, Lead, and Live Without Barriers, is the subject "with the most damaging ideas held by teachers, students, and parents." It's one of the few academic subjects in which multitudes of students, early on, decide they're not cut out for it: We're either a "math person" or we're not. That notion tends to stick well into adulthood. "It is difficult to know how many people walk around in society harboring damaging ideas about their math ability, but I estimate it to be at least half of the population," she writes.

Boaler, a professor of mathematics education at Stanford University, a best-selling author, and the cofounder of the math education site youcubed.org, has spent decades thinking about how to undo the damage. Her work, closely aligned with Stanford psychology professor Carol Dweck's research on growth mindset, explores what Boaler calls "our most harmful and persistent ideas about innate ability." She's a vocal proponent of changing the way we assess mathematics and modernizing the math curriculum-especially in high school-so that it's more engaging, more inclusive, and more likely to prepare kids for the modern workforce.

Critics argue that by insisting on math as a joyful, creative exploration, we're doing kids a disservice, and that by reducing or eliminating memorization and math drills, for example, we're setting kids up for a lack of mathematical fluency. But Boaler says that she's got no quarrel with things like math facts and that teachers should help kids develop these-not by "emphasizing facts for the sake of facts, or using timed tests, but by encouraging students to use, work with, and explore numbers," a process that ultimately builds critical number sense and reinforces math facts in a more organic way.

I sat down with Boaler recently for a Zoom discussion about mathematical freedom, anxiety-producing teaching practices, and the systemic changes she says are critical for modernizing math curricula.

Sarah Gonser: In your book Limitless Mind, you say that learning is about identity. Can you explain?

Jo Boaler: Well, we know that when people learn, it's not just about an accumulation of knowledge; it's really about changing who they are as people.

And we've found over the years that the traditional approach to teaching maths-I'm just going to show you methods; you're going to accept them and use them-is incompatible with the identities kids want, particularly around adolescence. Kids want to have their own ideas; they want to be respected as thinkers; they don't want to just be given information that they simply reproduce.

They see it as a subject area where they can't be their full selves, and it's a large part of why people drop out of maths.

Gonser: It's also a subject that causes a lot of very real anxiety. Why is that?

Boaler: I would say it comes from a few different things: It's a subject that is heavily tested; it's a subject that's often taught as right and wrong answers; and there are these widespread myths that you're either born as a math person or you're not. Somehow, you have the right brain, or you don't.

There's lots of micromessaging in classrooms that might get kids to think they can't be successful. Speed is very much at the heart of it. If you ask the class a question and then take the answer from the first kid who raises their hand, you're sending the message that you value speed. And we know that professional mathematicians are not fast; they're some of the slowest thinkers.

Finally, we have stereotyped ideas about who can be good at maths. So if you're a woman or a person of color, you're dealing with that pressure. If you have fixed ideas about who can do maths, a fixed mindset, then that stereotype can really take root.

Gonser: So how can we slow it all down and avoid making math class a place of stress and anxiety?

Boaler: I think a big part of it is A for L-Assessment for Learning-I just think that's so critical. It changes the whole culture of classrooms for kids.

If we assess kids by giving them diagnostic feedback, not grades, and ask them to do their own reflection so that they're able to see themselves progress on this journey-everything changes when assessment is like that in classrooms.

But we also want to change the way content is taught. Kids don't need lots of short questions with one method and one answer. It can be open questions that students think about creatively and visually.

Gonser: You're also an advocate of encouraging struggle and mistakes in classrooms. In Limitless Mind, you describe high achievers who work "at the edge of their understanding, making mistake after mistake in difficult circumstances, correcting mistakes, moving on and making more mistakes." In the classroom, why is that important?

Boaler: The best times for learning are when you're struggling and finding things difficult; that's when your brain is on fire with activity. I think it's really important to share the value of struggle with students. When I teach, I say to students, "I want you to struggle, because that's really good for you." I think it's freeing for students when they know that's a goal. And I think you should keep sharing that, reinforce it during every lesson.

It's really going to involve changing how we assess kids. If kids take a test and they're penalized for making mistakes, that's a counter message-and studies have shown that this mixed message is worse than no message at all. Don't tell them that struggle is good if you're going to mark them wrong when they struggle.

I think it's important that we always let kids resubmit work. And if you're using grading-I'm not a fan of grading myself-but if students don't do well the first time, to allow them to work on it again sends a great message that learning and struggle are valued.

Gonser: Let's talk about broader, more systemic curricular changes. You're a prominent voice in the conversation about re-sequencing math curricula so that it's more than a gateway to higher-level mathematics. What's changed in our world to make this so urgent?

Boaler: Well, we need to modernize not just how we teach it, but the actual content we're teaching in classrooms. The content we teach in maths was created around the 1800s and really hasn't changed since then. It was created at a time when we needed kids to be calculators. And so learning arithmetic, calculating things quickly-that was important.

But the world has changed dramatically. In high school, in particular, we're teaching a wide array of methods for kids to do by hand that they'll never use in their lives again. You will never go into a workplace and have people, by hand, go through synthetic division. So we're spending too many hours giving kids this outdated content that they're so turned off by. For what reason?

Gonser: What should we be teaching instead?

Boaler: So I'm very excited about bringing data science into mathematics. I am one of the five writers of a new framework in California where we are highlighting data science as a really important part of maths.

Now, it's hard to do that because the Common Core Standards really didn't include data science, and they need to be updated. But what we've done is try and bring a data science perspective to the current standards. This data science initiative is very exciting, not only because it gives teachers of all grades interesting content to work with, but it also helps kids become data literate, which is something they really need in this world.

There are more data points in the world than there are stars in the galaxies right now; the world is filled with data. So even little kids need to prepare to become data literate.

Gonser: You're also leading the charge on changing the high school math sequence, streamlining the algebra-geometry-algebra sandwich so there's room for a data science class-can you tell me more about that?

Boaler: In the high school years, something very exciting is happening. For generations, really, there's been this race to get to calculus because it can get you into college.

It's built on a very inequitable system. Because there are so many courses before calculus in middle school and high school, it's effectively meant we're pushing kids out of the calculus track in sixth grade, which is awful. The content is also not very up-to-date and not very engaging.

There's recently been a dramatic change in California: The UC and Cal State systems will now accept data science as a third-year course instead of Algebra 2. This is amazing and important because Algebra 2 is a course that is the end of the road for most kids, and now they can take data science instead.

Gonser: Why is Algebra 2 the end of the road for so many kids?

Boaler: Because it's so procedural and uninteresting that the vast majority of kids, after they've done Algebra 2, don't take any more maths. Data science is completely different. As we're rolling it out, we're communicating: This can be a course in high school that any student can take. You don't have to be advanced in middle school, and yet it can lead to a high-level STEM career. I see that completely changing who ends up going into STEM.

Gonser: What do you say to critics who argue this is a change that will water down the curriculum, make it less rigorous?

Boaler: It's totally rigorous, actually. Mathematics is a very broad subject. There's no reason that we should say, "Let's just value this part, which is calculus." The mathematics of data science involves matrices and probability and statistics and linear algebra-which is beyond what's often taught in calculus.

Gonser: My last question comes from an Edutopia reader, a teacher, who asks: "What's your greatest piece of advice for early math educators?"

Boaler: My biggest piece of advice is to really spend time trying to change kids' mindsets and ideas about themselves, because that will pay huge dividends. If you encourage struggle, if you remind kids that they can learn anything, we now know there are no limits to what people can learn.

Kids should know that if the kid next to them is solving something more quickly, it doesn't matter. We know that kids enter school with a growth mindset, and that drops with each passing year. And part of that is kids looking at other kids and thinking, "Oh, they can do it better than me." We have to counter those ideas and couple that with math that's open and creative. When you do that, things change.

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Every child possesses vast mathematics potential, says Jo Boaler, Stanford University mathematics professor and best-selling author-but for them to access it, we need to rethink how we teach math.

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Under pressure from an unprecedented constellation of forces-from state lawmakers to prestigious private schools and college admissions offices-the ubiquitous one-page high school transcript lined with A-F letter grades may soon be a relic of the past.

In the last decade, at least 15 state legislatures and boards of education have adopted policies incentivizing their public schools to prioritize measures other than grades when assessing students' skills and competencies. And more recently, over 150 of the top private high schools in the U.S., including Phillips Exeter, Choate, and Dalton-storied institutions which have long relied on the status conveyed by student ranking-have pledged to shift to new transcripts that provide more comprehensive, qualitative feedback on students while ruling out any mention of credit hours, GPAs, or A-F grades.

Somewhat independently, schools and lawmakers have come to the same conclusion: The old models of student assessment are out of step with the needs of the 21st-century workplace and society, with their emphasis on hard-to-measure skills such as creativity, problem solving, persistence, and collaboration.

"Competency-based education is a growing movement driven by educators and communities focused on ensuring that students have the knowledge they need to flourish in a global economy," said Susan Patrick, chief executive officer of iNACOL, a nonprofit that runs the website CompetencyWorks. "The future of jobs and the workforce will demand a new set of skills, and students' capacity to solve complex problems for an unknown future will be essential."

For their part, colleges-the final arbiters of high school performance-are signaling a surprising willingness to depart from traditional assessments that have been in place since the early 19th century. From Harvard and Dartmouth to small community colleges, more than 70 U.S. institutions of higher learning have weighed in, signing formal statements asserting that competency-based transcripts will not hurt students in the admissions process.

The emerging alignment of K-12 schools with colleges and legislators builds on a growing consensus among educators who believe that longstanding benchmarks like grades, SATs, AP test scores, and even homework are poor measures of students' skills and can deepen inequities between them. If the momentum holds, a century-old pillar of the school system could crumble entirely, leading to dramatic transitions and potential pitfalls for students and schools alike.

Picking Up Steam

Scott Looney, head of the Hawken School in Cleveland, was frustrated. His school had recently begun offering real-world, full-day courses in subjects like engineering and entrepreneurship, but he was finding it difficult to measure and credit the new types of skills students were learning using A-F grades. Looney started reaching out to private high schools and colleges looking for alternatives.

Though he found that many educators shared his desires for a new assessment system, he came up empty-handed.

"The grading system right now is demoralizing and is designed to produce winners and losers," said Looney. "The purpose of education is not to sort kids-it's to grow kids. Teachers need to coach and mentor, but with grades, teachers turn into judges. I think we can show the unique abilities of kids without stratifying them."

Looney began brainstorming a new type of transcript for the Hawken School, but quickly realized he would need a critical mass of schools to influence college admissions offices to accept it. With the initial support of 28 other independent schools, Looney formed the Mastery Transcript Consortium (MTC) in April 2017. The group has since expanded to 157 schools, including both historic institutions like Phillips Exeter and newer alternative schools like the Khan Lab School.

In joining the MTC, each school commits to phase out its existing GPA- and grade-based transcripts for a digital, interactive format that showcases students' academic and enrichment skills, areas for growth, and samples of work or talents, such as a video of a public speaking competition or a portfolio of artwork.

The purpose of education is not to sort kids-it's to grow kids. Teachers need to coach and mentor, but with grades, teachers turn into judges.

While the transcript is still in its infancy, organizers say it will resemble a website that each school will be able customize by choosing from a menu of skills like critical thinking, creativity, and self-directed learning, along with core content areas such as algebraic reasoning. Instead of earning credit hours and receiving grades, students will take courses to prove they've developed key skills and competencies. Looney insists that the transcripts will be readable by admissions officers in two minutes or less.

The MTC's work is not entirely original, though, and takes its lead from a number of public schools-most notably in New England-that have been rethinking traditional methods of assessing students for more than a decade.

Some are supported by the nonprofit group Great Schools Partnership, which helped influence Maine, Connecticut, Vermont, Rhode Island, and New Hampshire to adopt state board of education policies or legislation in the last decade on proficiency-based assessment systems. Other districts, in Florida, California, and Georgia, have made similar changes more recently, and pilot programs have emerged in Colorado, Idaho, Utah, Illinois, Ohio, and Oregon.

There's also backing from colleges. The Great Schools Partnership was able to garner the support of more than 70 colleges and universities, suggesting that higher ed admissions offices are ready for the change.

"We are accustomed to academic reports from around the world, including those from students who have been privately instructed and even self-taught," said Marlyn McGrath, Harvard University's director of admissions, replying via email about the transcripts. "In cases where we need additional information, we typically ask for it. So we are not concerned that students presenting alternative transcripts will be disadvantaged because of format."

Mastery Versus Seat Time

But the new transcripts are just the tip of the iceberg, according to supporters, part of a larger movement to do away with a system where kids can progress through grades or courses without really understanding material and be promoted for seat time and good behavior. When students move on to harder topics, they continue to accumulate gaps in their knowledge-a setup for failure in the later grades or collegiate years.

Under a competency model, kids can no longer just "get by," said Derek Pierce, principal of Casco Bay High School in Portland, Maine, which has used a proficiency-based transcript since 2005.

The new transcripts "get kids focused on doing their personal best on meeting or exceeding standards rather than getting a better grade than the kid next to them," said Pierce. "There is no longer a 'gentleman's C'."

However, without widespread agreement on the necessary skills and knowledge required for core classes, proving mastery may be just as elusive and arbitrary as the current system. Even MTC member schools won't rely on a shared understanding of what mastery means. Instead, each school will be able to quantify it independently, leaving college admissions officers-according to critics-without a clear basis of comparison.

Our learning structures have to be much more nimble to allow today's learners to navigate through opportunities where they can see themselves as the authors of their own education.

While competency-based education proponents argue that the new transcripts will identify students with skills that academia has traditionally overlooked, others worry about equity for marginalized students, who already struggle in the current system. Some critics have suggested that the new transcripts may be a way for wealthier schools, especially private schools like those in the MTC, to give their students an even greater advantage when competing for limited positions at the best universities.

There are other unanswered questions and challenges to be worked out, too. Will college admissions counselors have enough time, especially at large public colleges, to look meaningfully at dense digital portfolios of student work? Will the new transcripts create too much work and new training for K-12 teachers, as they struggle to measure hard-to-define categories of learning? Perhaps most importantly, will parents buy in?

"There's still plenty of work ahead and some pretty radical changes taking place," explained Mike Martin, director of curriculum and technology at Montpelier Public Schools in Vermont, whose district starting transitioning to a competency-based model in 2013.

Many public and private schools, like Martin's, are still years away from full implementation, and others are grappling with the nuts and bolts of how to implement dramatically new systems for student learning and assessment. Those on the forefront of these changes, though, remain hopeful that the new system will push all students to develop the skills they need to succeed in college and careers.

"Our learning structures have to be much more nimble to allow today's learners to navigate through opportunities where they can see themselves as the authors of their education," said Martin. "Proficiency-based education is about getting every single student up to a certain skill level and ensuring every student can succeed."

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Under pressure from an unprecedented constellation of forces-from state lawmakers to prestigious private schools and college admissions offices-the ubiquitous one-page high school transcript lined with A-F letter grades may soon be a relic of the past.

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Mathematicians and scientists are socially awkward men who wear glasses-at least, according to children.

In several studies, when children were asked to draw a mathematician or scientist, girls were twice as likely to draw men as they were to draw women, while boys almost universally drew men, often in a lab coat. I decided to try this out at home with my 12-year-old son, who said, "Really anyone can be a mathematician, but this is your average one," and promptly sketched a man in a checked oxford shirt with a pocket protector.

As an English teacher at a STEM magnet high school in New Jersey, I see these gender disparities in our engineering and computer science (CS) academies, even as our dynamic, thoughtful girls work hard to dispel stereotypes and recruit younger girls through coding camps and workshops. Our teachers certainly reflect the STEM fields of a generation ago: Three of our four CS teachers and engineering teachers are male.

The irony is that girls perform as well as boys in math. Nationally, math test scores for girls have been consistently equal to or within two points of boys in fourth and eighth grades over several years; middle school girls pass algebra at higher rates than boys. In science, girls perform on par with boys and enroll in advanced science and math courses at equal rates as they move into high school. And then something happens: A gender gap in participation starts to appear as girls take fewer of the more advanced STEM courses and tests as they get closer to college. This gap widens the longer girls are in school and is often compounded by issues of race and class.

Researchers don't know yet if these continuing disparities in STEM reflect the slow pace of societal change, child-rearing expectations, or something deeper and more entrenched, such as the way we think about girls' minds. But teachers can play a significant role in influencing or dispelling stereotypes in STEM education. Here are some studies from researchers and educators that may offer a few insights-and a few solutions.

Barrier 1: Building a Math Identity

The problem: One explanation for the gender differences in STEM participation may lie with those formative ideas about who a mathematician or scientist is.

Stereotype threat -the mere perception that a group one belongs to is not good at a task-has been linked to lower academic performance, according to researchers. When girls become aware through both subtle and overt cultural messages about male superiority in math, it makes each encounter with math and technology more fraught, triggering self-doubt in even the most studious young girls.

Both teachers and curriculum can inadvertently contribute to these perceptions.

In one striking study from 2015, Israeli researchers divided sixth-grade exams into two sets for grading: One batch was graded by the teachers and included students' names, and the other contained no student names and was graded externally. In math, teachers graded boys higher, while external graders rated girls higher. Those low teacher grades then dissuaded girls for years to come.

Teachers often harbor these biases about themselves, too. Elementary school teachers are predominantly female, and many are anxious about teaching math, which can lead to lower achievement in math for girls. This persists into high school, where anxious teachers might be overly reliant on textbooks and rote methods of instruction. Images in those same textbooks can subconsciously trigger self-doubt in girls. One study found that when female high school students viewed chemistry textbooks containing pictures of female scientists, they performed better than female students who viewed textbooks containing only pictures of males.

Solutions: In response, researchers say teachers can foster a growth mindset in students by emphasizing that practice rather than innate ability improves performance. Other studies show that brief, targeted interventions in which students learn that intelligence is not fixed but can be improved through training and hard work can help them persist through challenges, a trait that, in math and science, should be particularly advantageous for girls.

Adding images of female mathematicians or scientists throughout classroom materials and assigning individual or group work that summarizes or contextualizes women's achievements in these subjects can also shift perceptions about who belongs.
©Theresa Montgomery
Tackling the STEM gender bias can also warrant some self-reflection on the part of teachers.

"For me, it starts with a belief, these expectations I have for all of my students, that all kids can learn-every teacher doesn't have that belief," says Cicely Woodard, a middle school math teacher in Franklin, Tennessee, and the state's 2018 Teacher of the Year. "When the kids walk in the door I immediately believe they will get this content."

Stanford University professor and researcher Jo Boaler recommends that female teachers avoid phrases that imply their discomfort or dislike of math-like "I'm bad at math" or "This is hard"-and get creative with assignments that show they are truly interested in the topic. They may also want to grade papers anonymously, where possible.

Barrier 2: The Question of Race and Class

The problem: Our assumptions about who does math well-and the academic and financial support that follows-may, in fact, impact performance more than raw aptitude. This has particularly profound implications for low-income students and black and Latino females, who are significantly less likely to take advanced STEM courses and pursue STEM professions later in life.

A recent study by Sean Reardon at Stanford University revealed that girls often do better than boys on math in racially diverse districts, while boys perform better in affluent white districts. He theorized that in higher-income communities, parents are more able and more likely to invest in enrichment for their children-like robotics camps or theater classes-that adhere to stereotypes. Children in these communities may also be more likely to see men in positions like doctors or engineers that reinforce the narrative about who pursues STEM careers.

Additionally, research "has clearly [indicated] that black girls view themselves as outsiders in mathematics and teachers view them as outsiders," says Nicole Joseph, assistant professor of mathematics and science education at Vanderbilt University. Joseph points to tracking in math, more common in middle and high school than in the humanities, as a key structure infused with bias that restricts access to rigorous math education for black students.

Solutions: In a review of 62 studies on the perseverance of black women and girls in math, Joseph and her coauthors found that several measures can help build math identity and interest among black girls. For starters, schools can consider "structural disruptions" to how math instruction usually happens. San Francisco Unified School District, for example, recently eliminated accelerated math in middle school and allowed all students to take Algebra I in ninth grade-effectively ending tracking-which led to a rise in algebra test scores and a decrease in repeat rates for all students, including black and Latino students.

Joseph also suggests that "community influences and resilience strategies" from extra- or co-curricular programs, single-sex programs, teacher training in culturally responsive teaching strategies, and black and female role models in STEM can help.

Educators like Norman Alston, a Seattle-based educator, and Patricia Brown, a technology integration specialist in Ladue, Missouri, are fostering mathematical interest in girls through after-school STEM programs. Alston requires middle school graduates of his program to teach younger students, and every speaker or expert Brown brings to talk to her female students is a woman of color, so students can see powerful, successful female mathematicians and scientists who look like them.

Barrier 3: It's Not Just Content-It's Context, Too

The problem: When it comes to teaching and learning STEM, research shows that the format matters.

A recent analysis of the admission tests to elite New York City high schools found that at Stuyvesant High School (considered the most rigorous in the city) girls had better grades in higher-level math, but overall had scored slightly lower on the admissions test, leading to lower admission rates. This is not because girls are worse at math, but may be because they guess less-a disadvantage on a multiple-choice test-and perform better with open-ended answers, according to the study.

Stanford's Reardon and his colleagues drew similar conclusions after analyzing 8 million fourth- and eighth-grade national standardized test scores and finding that gender gaps correlated with multiple choice questions-as opposed to open-ended ones-and attributed to 25 percent of the difference in scores between males and females.
©UTeach Institute
Solutions: Teachers may want to move away from multiple-choice tests-often a staple in math and science-and place more emphasis on open-ended assessments that allow students, especially girls, to demonstrate their proficiency through word problems or writing, where they feel more confident.

Other STEM educators are going beyond traditional STEM instruction in their classrooms to ensure that every child has a fair chance to learn math.

I hate when people say kids need grit-they have resilience, but need understanding of how to frame it in the content of the course.

As part of a pilot project at Georgia Tech to bring AP Computer Science to Atlanta students, teacher Shana White makes sure to use hands-on activities and real-world examples to supplement the online coursework and provide context and purpose for assignments.

"I hate when people say kids need grit-they have resilience, but need understanding of how to frame it in the content of the course," says White, whose students are all African American, half of them girls.

Focusing on the interdisciplinary and problem-focused nature of STEM is key, recommends Dr. Jill Marshall, associate co-director of UTeach at the University of Texas at Austin, a program trying to confront the pipeline problem of STEM teachers from diverse backgrounds.

"Project-based instruction just generally draws in more people because it addresses problems that people see as relevant," said Marshall. She cites a 2008 study from the National Academy of Engineering that asked people if they wanted to be engineers: Girls were twice as likely as boys to say no. But when asked if they would like to design a safe water system, save the rainforest, or use DNA to solve crimes, the girls answered yes.

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Keeping Girls in STEM: 3 Barriers, 3 Solutions

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Stereotypes and cultural norms dampen girls' interest in STEM, but educators can counter the disparities with small changes to their practice.