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It's a Saturday afternoon at Boston University’s School of Education, where Elliot Kastner, a former Dartmouth College football player turned mechanical engineer, is addressing a group of students.
He works through the geometry, the engineering and the many failures that led to his developing a tackling robot now used for football practice in the NFL and the NCAA.
The kids look wiped out. Some have hoods pulled up, others are leaning on their desks. But when Kastner wraps up his presentation, a few chime in — and soon the room is full of questions. Is the robot able to drive on different terrain? Could the robot go underwater? And what exactly do mechanical engineers do?
Adrian Mims looks on with a smile. He’s a big fan of football — it's a game day and he’s wearing a Patriots T-shirt. And since 2009, Mims has made it his mission to use experiences like this one to help African-American and Latino students get to the highest heights of high school math with The Calculus Project.
On paper, the project looks like math camp for students of color — testing, pre-teaching and teamwork.
But the program has other features. Mims doesn't just invite roboticists and scientists to speak; he's had his students go to Harvard Medical School to work on cloning fruit flies. That afternoon, he gives each student a free movie pass — he asks them to use it to see "Hidden Figures," the Oscar-nominated film about the black women mathematicians behind the American space program.
And he always buys lunch as a preview of campus life, and as an incentive: "You have to reward kids with pizza. That always works. They were grimacing, but I gave 'em pizza, so, all is well." The pizza, the robot, the movie passes are all part of Mims's plan — math, plus more.
Seeing A Problem
For Adrian Mims, math was a liberation.
He grew up in South Carolina, a stone’s throw from two textile mills, now closed, where he might have been expected to work.
Instead, he went to the University of South Carolina as part of the first generation in his family to get a college degree. Getting his bachelor's, in math, was “hard as hell.” Mims says he couldn’t have done it if not for a Nigerian doctoral student named Kofi who tutored him in high-level math. “I grew up in the South, so I called him 'Coffee,' " he laughs.
Mims began his career in Massachusetts as a METCO tutor in Brookline in 1994. He noticed how the ranks of minority students thinned out as the math became more advanced.
In his doctoral dissertation for Boston College's Lynch School of Education, Mims looked for a reason why.
He focused on black students who performed well enough in algebra to be placed in geometry honors; there was no reason to doubt their facility with math. But in Brookline, he found that between 60 and 70 percent of them tended to withdraw from the class during the second quarter of study.
Mims concluded that the problem was that those students had been stranded, in more ways than one.
First, they often didn’t have the same knowledge base as their classmates.
“In geometry honors, you have to write two-column proofs, which you can't do unless you know theorems and postulates,” Mims says. Miss out on those, and you’ll quickly fall behind: “It's like becoming a public defender or prosecutor without knowing the laws. You can’t do it.”
Moreover, the African-American honors students he saw at Brookline High School were socially isolated. It may be that 20 students of color in total were recommended for geometry honors — but they were spread out across eight or nine sections.
“Brookline can be a very intimidating place. You've got some high-powered kids there,” Mims says. "Some of them are doing ‘Russian math’” or other out-of-school enrichment classes. Mims' takeaway was that even the most talented black and Latino students can feel overwhelmed in that company.
The idea for The Calculus Project was borne out of Mims' hope to fix "those two things": knowledge gaps exacerbated by being one of the only students of color in class.
The program focuses on METCO schools, where minority students could theoretically make it to calculus, but where all too often they are tracked into standard or remedial math.
The project starts with building a cohort of students, and asking them to join a summer “preview” of the material they'll come upon that year in math class — like the aforementioned theorems and postulates. And then throughout the year, those students work together regularly with a teacher-coordinator.
Mims' approach was developed in response to scholarship about the effects on learning of racial isolation and prejudice.
For more than 20 years, social psychologist Claude Steele and others have studied the phenomenon of “stereotype threat," when preconceptions about group performance trigger anxiety in individual students. And in a 2011 paper titled "On Defense," researchers Na’ilah Suad Nasir and Niral Shah ask the reader to consider a young black man who plays basketball and studies math.
On the court, he’s seen as a "natural" leader. But in class, he keeps his head down. Like a white athlete being told "white men can’t jump," he's "on defense" in the classroom — working against the weight of expectations: “Even if he wanted to ignore it, awareness of the narrative renders this virtually impossible.”
Whether or not they attribute it to their racial identity, some of Mims' students report feeling the same way.
Kyra Cooper is a ninth-grade METCO student at Lexington High School. Lexington High is, by one measure, the best in the country. But its student body is overwhelmingly white and Asian. Only 5 percent of its students come from low-income households, and only 4 percent are black.
Cooper has trouble with the subject, and learning math in Lexington only added to the stress.
"I would get really annoyed with myself, and I'd feel disappointed. I would just shut down, kind of — I wouldn't really want to talk,” Cooper says, at home in Roxbury. "Everyone around me — I felt like they were smarter than me, because I would, like, struggle with things."
Mims says that in bringing students of color together to study, he's drawing on famous models. In the 1980s, the civil rights legend Bob Moses started The Algebra Project, which sought to share innovative curricula and strategies for teaching algebra to black students in the American South. And Philip Uri Treisman, an education researcher at the University of California at Berkeley, studied social modes of learning around math.
In a 1990 study, Uri Treisman and Robert Fullilove observed that Asian-American students did some schoolwork alone — but then they double-checked it in study groups that arose organically. Also, they didn’t “compartmentalize… academic and social interactions"; schoolwork coincided with music, food and family time.
By contrast, the black students Uri Treisman tracked tended to work on their own from start to finish, on a white campus — rarely blending study with socializing. In the end, Asian students taught each other — and studied twice as many hours as their black counterparts.
'The Only Chocolate Chip'
Mims’ approach doesn't just give black students more time with math — it gives them more time with one another. And he asks administrators to try to group students of color together, in one or two honors classes.
It's an odd proposition that, in practice, looks a little like the resegregation of education.
But Mims says you don't have to be black or Latino to take part in The Calculus Project, but when you're looking to help kids who don't reach their potential in math, those are the students you tend to find.
Plus, he says, you have to consider that the METCO students Mims serves face a "different reality" at school. They're bused into high-performing districts with vanishingly few black students.
"The appearance is that they are integrating in these communities," Mims says. But in reality, they're still held apart: They can be placed on a lower-intensity learning track as early as the sixth grade; they may face racial antipathy or exclusion they wouldn't see at home; and they have less time to spend at school, facing an hour or more on the bus to and from home.
So when Mims gathers those students in a room, he's says he's only acknowledging that segregation already persists inside the state's most prominent program for school integration — and that these students can help one another.
Elizabeth Quiñonez, a graduate of The Calculus Project in Brookline, goes further, saying that it made a difference for her to learn the same tough concepts alongside students who look like her. "It's nice not to be the only chocolate chip in the cookie," she says. Today, Quiñonez is a sophomore at Harvard College, where she works with the admissions office to promote the recruitment of minorities.
Alongside silent practice tests, Mims asks his students to solve problems on the board and work through stumpers in groups — calculating batting averages, or how far a truck has traveled down an incline after x seconds — while he and other staff walk from table to table.
He's tough on noise and disruptive behavior, but even so, after three hours of math, the ninth-graders are getting restless — ready for lunchtime.
During the weekend sessions hosted by Boston University, the math fades away, and the students head to the cafeteria joking and laughing as ninth graders do.
'It’s Not Spectacular'
The pizza isn't the only one way in which The Calculus Project is about more than math.
Mims has heard the criticism that calculus isn't required for most American jobs. He counters that our society uses it for social sorting — as a marker of achievement and proof of academic rigor.
More than once, he tells me the story of his niece, who graduated from Northeastern University to become a speech-and-language therapist. Calculus was a required course on her way to a degree.
“She isn’t calculating the area under a curve,” Mims notes. “She doesn’t use it at all in her day-to-day job.” But it was a hurdle she had to jump to get the job she wanted — working as a speech-and-language pathologist that paid $85,000 as a starting salary. (Mims also uses his niece’s story when he’s trying to sell parents on the program.)
The advanced-math gap is a national problem with deep roots. And, Mims adds, the U.S. is full of advanced-math “deserts.” According to a 2016 report from the Department of Education, less than half of the country’s high schools even offer calculus — and just a third of those with “high black and Latino enrollment” offer it.
If learning calculus is indeed a powerful elevator to better colleges and jobs, then the advanced-math gap is part of a national crisis of racial and economic inequality. But it's not much discussed in public — let alone on the front page of newspapers. Why?
“Here's my take on it. It's not spectacular,” Mims says. “Unfortunately, we’ve had several unarmed black men shot. That's spectacular, and it's visual. You see someone's life being taken away, and it's shocking.
“What's happening with students of color, with regards to their education — the achievement gap — it's just not that spectacular, or gripping. We've always had an achievement gap.”
Mims feels he's identified a few key ingredients to the solution — more learning time and building a network of cooperation and encouragement.
The Calculus Project approach is decidedly lo-fi — teachers print tests and worksheets, and the students meet in an ordinary classroom during free periods, after school, on weekends and during the summer.
So the idea is shareable. And after Brookline, the pilot district, has graduated three cohorts of Calculus Project participants, it's spreading.
Milton and Newton have run their own versions of the program for years, and Mims is planning expansion to Lynn and Somerville. And the Project looks set to take off out-of-state. In Orlando, more than 1,000 students are taking part in 41 schools, and Mims is in talks to bring it to Brooklyn.
The Calculus Project is new, but Mims points to evidence that it works. He compares eighth-grade participants in Malden — 81 percent of whom scored higher than 70 on a midterm algebra exam — with ninth-graders not in the program, just 28 percent of whom reach the same scores.
And last year in Brookline, half of black 10th-graders scored "Advanced" on the math MCAS. That's a 20-point improvement over that cohort's scores in 2009, the year that a Calculus Project pilot program began in that district.
Mims, though, wants more results. He'd like to see a national drive to use some of these practical techniques to tackle inequity — but that would "take a great deal of coordination, determination, and reallocation of resources," he says. People are "leery" about spending the money needed to expand math education for the students who need it. And the teachers who might help are already "spread too thin."
But at Kyra Cooper's family home in Roxbury, they salute the progress Mims has made so far.
Kyra celebrates the non-mathematical parts of The Calculus Project. She smiles all through the practice exam, working question by question with a partner. She says it means a lot to be able to meet and work with other students of color — something that she doesn't get in Lexington.
But to Kyra's mother, Terri Ware, the math has meaning, too. She's thrilled that Kyra's grades have improved, along with her attitude about a critically important subject.
"Having a good analytical mind is paramount for problem solving. You have to learn to break things down and be able to move step-by-step-by-step," Ware says. "Math is a great tool for that. It teaches you to sit, and think, and break things down. It's not as fluid. 'There's a logical solution to this problem — how am I going to get there?'"
That's the question for Mims, too. He says he found his way, almost by accident, to a logical solution for tackling inequality through math — a few small changes that can make a big difference for students who've often been left behind. What's left is the question of how we get there.