program overview - Art of Problem Solving Foundation
A PROGRAM OF THE AOPS FOUNDATION
How can we train the next generation of scientists?
How can we make careers in math, science,
computer science, and engineering accessible to
students from all backgrounds?
The Summer Program in Mathematical Problem
Solving is a transition program that helps talented
young students from low-income backgrounds enter
the same programs for advanced study as their more
affluent peers. Through a summer intensive program
and year-round mentoring for students and families
to help them apply to top opportunities, we make it
possible for students to pursue advanced work that
would otherwise be closed to them.
SPMPS is perhaps the most successful program ever at supporting the proposition that even in the
lowest-income neighborhoods and with underrepresented minority students, there are kids who can
work at the highest mathematical levels (i.e., MathPath level) if only they are given an intervention to
overcome their “enrichment deficit”. — Stephen Maurer, Professor of Mathematics at Swarthmore College and Executive Director at MathPath
The Status of STEM Achievement
Only 9% of low-income students complete a college degree by
age 24, and graduation rates in Science, Technology, Engineering, and Math (STEM)
fields are even lower than
Percent of students beginning
non-STEM fields. In the
a STEM degree who complete it
US, only 6% of 24-yearwithin five years, by race/ethnicty
olds have natural science
and engineering degrees,
compared with over 10%
in Finland, France, Taiwan, Latino
South Korea, and the UK.
We must start early to
address these issues.
By eighth grade, only 3% of low-income students score at the
Advanced level on the National Assessment of Educational Progress, compared with 14% of their peers. Lower-income students
are vastly underrepresented in good high schools or advanced
enrichment programs. SPMPS changes this pathway.
Summer at SPMPS
Students choose their classes each week. They do
seven hours of math per day (and they love it!), choosing
a core course each week and a problem solving course
(either contest problem solving or general problem
solving). Here are some of the courses faculty members
Graph Theory: From Eulerian paths to minimum spanning trees, students worked together to solve interesting
mathematical questions and to see how math can apply
to real-world problems.
Infinity: Students worked together to understand sizes
of infinity and to compare the quantities of the natural
numbers, integers, rational numbers, and real numbers.
Digital Communications: Students learned about
compression techniques and then designed a procedure
to send a photo across a room from one computer to
another, using nothing but sound.
Number Theory: Students developed a standard for
rigorous proof and then proved that there are infinitely
many prime numbers.
Astrophysics: Students discovered how to measure the
cosmos using the properties of light, careful reasoning,
and some clever applications of mathematics.
Andy: Everything was just amazing... I
learned to love math’s beauty.
Joel: I love the college life and I’m not
afraid of living on-campus anymore.
SPMPS works to help students prepare for future
experiences socially and emotionally. Students live
in a college dorm, possibly outside the city or the first
time. Together, they learn games such as Set, chess,
and Dominion. They play sports such as basketball and
Ultimate Frisbee. They might discover a Rubik’s cube for
the first time, enjoy an afternoon of baking, or relax with
arts and crafts, karaoke, or dance. We go stargazing,
take hikes, and ride the rollercoasters at Six Flags. We
become the students’ friends, mentors, and role models.
Our goal is to create a thoughtful environment for the
students, helping to instill in them a growth mindset,
the belief in their ability to succeed, and a better understanding of what mathematics is.
Zereena: I’ve become more independent and less self-conscious and
The Year with SPMPS
During the academic year, SPMPS helps students to:
• Apply to selective and high quality high schools
• Apply to academic programs, including other summer programs
• Develop self-identities as scientists and scholars
Students receive individual mentoring and advice to help
them take advantage of all the opportunities available
to them. As students transition to high school and are
exposed to a more rigorous curriculum than they experienced in middle school, we help with tutoring so that
they can be successful.
Events During the Year
Graduation Ceremony: Parents pick students up from
the summer and learn about the many opportunities
SPMPS creates for them.
Weekly Office Hours: Students and families are invited
to come in with any questions, ranging from applications
to homework to math contest preparation.
High School Admissions: After a session guiding families through the high school admissions process, SPMPS
provides customized recommendations to each student
and checks up on their progress with the applications.
Summer Program Admissions: All alumni receive customized recommendations and help with the process of
applying to academic summer programs in future years.
Splash at Yale: All alumni are invited to Splash at Yale,
where they can choose from hundreds of interesting and
creative classes taught by Yale students.
Google Tour: Alumni are invited to tour Google’s NYC
headquarters and hear Googlers talk about the work
they do and how it involves math.
SPMPS Math Team: Alumni and their schools are invited
to participate in math contests (such as the AMC-8,
MATHCOUNTS, and Purple Comet) and special trainings.
Algebra 1: SPMPS offers an online Algebra 1 course to
8th graders, a crucial factor to ensure they can reach
calculus while in high school.
SAT and College Admissions: Older alumni receive
support with college selection, SAT preparation, scholarships, and college visits.
On the AMC-8, a national competition
for mathematically talented middle
schoolers, students’ median national
ranking rose by 10 percentile points in 3
weeks. (SPMPS 2014)
12 — Center for Talented Youth
2 — MathPath
2 — Specialized high school discovery
1 — Summer Hackers Immersion Program
3 — Other academic summer programs
Out of 39 graduates of SPMPS 2013.
High School Placements
2 — Bronx High School of Science
4 — Brooklyn Technical School
3 — High School of Math, Science, and
Engineering at City College
1 — Staten Island Technical School
4 — Bard High School Early College
1 — Brooklyn Friends School
1 — Townsend Harris High School
1 — Midwood HIgh School
1 — Beacon High School
3 — Manhattan Center for Science and
1 — Fordham High School for the Arts
1 — Academy for Software Engineering
Out of 38 NYC-based graduates of
Suany: Before SPMPS, I saw math as just numbers and not much thinking... but now I see all
the hard work, understanding, proofs, logic and it
changed the way I see [math] completely!... I like
how even though these people have only known
us for a couple of weeks, the amount of love they show us is
heart warming and it tells me that these people really do love
math and want to share their love with us.
Student body: 77 students selected
from 4500 students at 36 partner
Qualify for federally-subsidized school
American Indian or Alaska Native: 3%
Black/African American: 44%
Native Hawaiian or Other Pacific
Self-reported. Students may select
more than one.
We had two students from SPMPS attend our Honors
Summer Math Camp (HSMC) this past year, 2014. The
HSMC has been recognized 12 times by the American
Math Society Epsilon Program as one of the top programs in the country. I was so impressed by the SPMPS
students’ work ethic and enthusiasm for learning. Although not as experienced as many of our participants,
both students demonstrated tremendous potential—all
they needed was an opportunity. I am expecting great
things from both in the future, and look forward to
encouraging other students from SPMPS to attend our
program. SPMPS works hard to place their alums in
settings where they will continue to grow and develop.
The supportive community from SPMPS is reaching out
to and developing talent from all backgrounds, particularly underserved groups who often don’t have access
to advanced learning opportunities. I look forward to
working with Dan and SPMPS in the future.
— Max Warshauer, Professor of Mathematics at Texas
State University and Director at Mathworks’ Honors
Summer Math Camp, where two SPMPS alumni attended on full scholarship.