Rachel Cromidas

As camps go, the Summer Program in Mathematical Problem Solving might
sound like a recipe for misery: six hours of head-scratching math
instruction each day and nights in a college dorm far from home.But Mattie Williams, 13, who attends Middle School 343 in the Bronx, was
happy to attend, giving up summer barbecues with her parents and
afternoons in the park with her Chihuahua, Pepsi. She and 16 other
adolescents are spending three weeks at Bard College here in a free, new camp for low-income students who are gifted in mathematics.

All are entering eighth grade at New York City public middle schools
where at least 75 percent of the student body is eligible for free
lunches. And all love math. At this camp, asking “What kind of math do
you like, algebra or geometry?” is considered an appropriate icebreaker,
and invoking the newly learned term “the multiplication principle”
elicits whoops and high-fives.

In a Bard classroom one afternoon, it seemed for a moment that Arturo
Portnoy had stumped everyone. Dr. Portnoy, a math professor visiting
from the University of Puerto Rico, posed this question: “The length of a
rectangle is increased by 10 percent and the width is decreased by 10
percent. What percentage of the old area is the new area?” The 17 campers whispered and scribbled. One crumpled his paper into a
ball. Mattie Williams may have looked as if she was doodling as she drew
dozens of tiny rectangles in her notebook, but she was hard at work on
the problem, which was taken from the American Mathematics Competitions,
a contest series known for its difficulty. In less than 10 minutes, she had the answer — 99 percent — and was ready for the next question.

For some schoolchildren, mathematics is a competitive sport, and summer
is the time for training — poring over test-prep books, taking practice
exams and attending selective math camps. But for students who cannot
afford such programs, or have not been exposed to many advanced math
concepts, the avenues to new skills are limited.

Daniel Zaharopol, the director of the camp at Bard,
is trying to change that. He has brought four math educators to the
Bard campus to teach the middle school students concepts as varied as
number theory and cryptography. Among the instructors is Mr. Portnoy, a
director of the Puerto Rico Mathematical Olympiads. The camp is financed by the Art of Problem Solving Foundation, the
nonprofit arm of an online school that promotes math education for gifted students. Classes meet in two-hour sessions and cover topics including voting theory, graph theory, and math and the arts.

The point of the program, Mr. Zaharopol said, is not to offer remedial
instruction to struggling students, but rather to challenge those who
already excel. He also hopes to prepare students to participate in
competitions and independent math seminars called math circles, where
low-income students are typically underrepresented. “These are students who have a tremendous amount of potential and are
really ready for a lot more than they’re able to get in schools,” said
Mr. Zaharopol, who has master’s degrees in mathematics and teaching
mathematics.

But they may lack some basic preparation, he said. “If these students
had just gone to the New York City Math Circle this summer, they would
have felt like a fish out of water,” he said. “They wouldn’t have the
same mathematical background and experience as their peers.”

It is common for young people who later specialize in mathematical
fields to begin studying advanced math concepts before they reach high
school. But Andrew Brantlinger, an assistant professor at the University
of Maryland who has researched secondary-school math education, sees
the math pipeline as “overwhelmingly nondiverse.” “There are very few women, people of color and people from low-income backgrounds,” Dr. Brantlinger said. A summer program designed to address such an achievement gap can be
valuable in theory, he said, but might not be able to accomplish enough
in a short time.

Zvezdelina Stankova, a professor of mathematics at Mills College in
Oakland, Calif., who directs the Berkeley Math Circle at the University
of California, Berkeley, said she had observed the same problem. “Just
like it takes years for a basketball player to develop themselves and
get to the professional league, it’s the same for mathematicians,” Dr.
Stankova said. “By and large they have done something exceptional before
they get into college.”

Jeffrey Pereira, 20, one of the math camp counselors, said he was trying
to impress on the campers the value of their studying math
independently, so they will not simply sit back and coast through
classes that come easy to them when they return to school in September. “In middle school, my experience with math was basically, everything was
really easy to me,” said Mr. Pereira, who attended public school in the
Bronx and is now a math major at Bard. “Some of the things they’re
doing here, I haven’t seen in college yet.” Besides helping the campers during classes, Mr. Pereira plays puzzle games with them during free time.

For Mattie, evenings spent socializing at the two-story residence hall
where the students and counselors live have made the camp feel less like
a school and more like a home away from home. Outside of class time, the math whizzes can hike or lounge in the
computer lab. And at least among the 10 girls, conversations are more
often about what to wear the next day (one recent day, they all agreed
to wear blue) than the merits of a particular counting system. “The first night we all sat in each other’s rooms and talked about what
we wanted to do, and how, oh, I miss my mom, I miss my dad,” Mattie
said. “Then we had a pillow fight.”