Celebrating a Summer of Growth

For hundreds of students in New York and Los Angeles, BEAM summer programs are something special — a place where they can discover the joy of math, nurture their curiosity and creativity, and build community. 

Lia, who attended BEAM Summer Away, wrote: “BEAM is so much more than math, and so much more than just a summer camp.”

FOSTERING A LOVE OF MATH AT BEAM DISCOVERY

More than 270 rising 7th graders in Los Angeles and New York City spent five weeks at Discovery exploring deep and interesting math. Students chose their own classes — like Truth, Lies, and Logic; Mysterious Patterns; and Astronomy — solved math puzzles on teams as part of relays, and tackled the 100 Problem Challenge (100 brainteaser math problems they can collaborate to solve).

Haneul, a student at Discovery Los Angeles, came away with a new perspective on math: “BEAM encourages us to become our full self in math and to collaborate, share different ideas, and compare and contrast with others. We learn things in more complex and advanced ways that pretty much none of us thought would be possible.”

Some exciting math-y outcomes at Discovery this summer:

At Discovery, students showed growth on a pre-/post-test we use to measure problem solving; when we asked, “How much do you feel your math skills grew this summer?” (on a scale of 1 to 7, with 7 being the most growth), 82% responded with a 5 or higher!

Students also grew in their perseverance at challenging problems. Alonzo described his experience working on a particularly difficult problem: “It was not only devastating when I got it wrong multiple times, but it was also awesome learning from my mistakes and improving from them.”

Many of our Discovery students said they’d recommend BEAM to their friends. Josselyn said: “I would tell my friends that if you think the math is easy at your school and want to challenge yourself you should apply at BEAM. This program is everything: it's fun [and] challenging. This felt like a second home.”

BUILDING SKILLS AND COMMUNITY AT BEAM SUMMER AWAY

116 rising 8th graders attended BEAM’s Summer Away program, held at Marist, Union, and Harvey Mudd colleges. At Summer Away, students spent three weeks on a college campus, where they challenged themselves in classes like Strategic Math Thinking, Graph Theory, and Cryptography. Students participated in math relays and collaborated on special "Challenge Problems," proof-based problems presented to the entire program to solve as a group for which they could earn prizes.

For many students, Summer Away is their first time away from home, so creating a welcoming, caring environment is critical. This year, 85% of students reported a strong sense of community, and 95% of students said they’d recommend BEAM to others. Izamar said: “I promise you, even if you know no one, BEAM will help you make life-long friends and connections with counselors and with teachers that will make you fall in love with math. This program will change your life, your perception, and how you view things. I would do this again in a heartbeat.”

Here are some highlights from our Summer Away outcomes:

At Summer Away at Harvey Mudd College, students left the program loving math more than ever before. At the beginning of Summer Away, 54% of students responded positively to a survey question about enjoying math, and post program, 87% of students responded positively, demonstrating a significant increase in math enjoyment and interest! 

At Marist College, students surpassed our expectations when it came to growing their problem-solving skills — over the course of just three weeks, the median student grew 10.8% in national ranking on the AMC 8 mathematical contest! 

Lastly, BEAM students at Union College left feeling much more confident about their math skills; when asked how much they felt their math skills grew over the summer on a scale of 1 to 7, 83% responded with a 5 or higher, and 20% of the students gave their skills growth a 7 out of 7.

At the end of the summer, Hangsa wrote: “The community, challenges, and fun you will get from BEAM Summer Away are life-changing!”

FAMILIAR FACES IN LEADERSHIP

Every summer, older BEAM students return to give back to the program and mentor younger students, while also gaining valuable (paid) work experience. This year, more than 30 summer program alumni served as counselors, teaching assistants, and in leadership roles, including two alumni who returned to teach.

BEAM student Maya P. reflected on her “full circle moment” returning to Discovery Los Angeles as a counselor: “I got to see [Discovery Los Angeles] from a different perspective, which showed me how much I’ve grown from middle school to now. I saw some of myself in the students and saw them go through obstacles that I dealt with in middle school, which made me even more appreciative of the BEAM program, as I got to truly understand how much it aided in my passion for mathematics.”

Annie, a summer program alumni and Summer Away counselor, emphasized her role in shaping a safe space for students. “Having been a part of BEAM, I understand the importance of giving young, historically marginalized students a place to grow. I love working with students who I share a background with and showing them that BEAM is here to help guide them throughout their academic journey.” Annie came away from her experience feeling proud of being a mentor students could relate to: “A student this summer wrote in our end of camp yearbook that they ‘want to come back and work for BEAM as [I] have.’ Moments like that show me the importance of students having role models, and the lasting impact that that positive influence can have on developing students.”

REFLECTING ON A TRANSFORMATIVE SUMMER

We’re so proud of what our students achieved this summer, and can’t wait to see what the future holds for them. For our students, BEAM is more than just a summer program; in the words of Summer Away student Lia, “You grow to feel at home with the counselors and other campers, so much so that they begin to feel more like your family. BEAM opens your mind to math you never thought possible, and I will never let go of the memories I've made here.”

Congratulations to our College Scholars!

BEAM is thrilled to announce our third class of College Scholars! This year, three students have been awarded a scholarship through Jane Street, a research-driven global trading firm that’s one of BEAM’s amazing corporate partners. Jane Street College Scholarships make it possible for BEAM students to attend strong-fit colleges that meet their academic goals, even when those schools do not meet 100% of financial need. 

Here are the stories of our College Scholar recipients, in their own words.

Happy First Week of School to our BEAM New York High School Freshmen!

With students heading back to school campuses this past week, BEAM is reflecting on the success of our rising high school freshman class in New York. We’re so proud of the achievements of these students:

  • 64% received offers from high schools that we rank as “Tier 1”; these schools offer AP calculus or an equivalent and more than 85% of graduates are college ready — fewer than 10% of schools qualify;

  • 90% received offers from “Trusted” schools with good course offerings and support;

  • 12 students were admitted to specialized high schools including Brooklyn Latin; Brooklyn Technical High School; High School for Math, Science, and Engineering; and Stuyvesant.

...And Now for Some Math on Pi Day!

Curious about more math this Pi Day? Here’s the problem we included in this year’s Pi Day card:

Problem:

Two logicians (A and B) each secretly pick a whole number from 1 to 30, inclusive. They have the following conversation:

A: “Is your number double mine?”
B. “I don’t know. Is your number double mine?”
A. “I don’t know. Is your number half mine?”
B: “I don’t know. Is your number half mine?”
A: “I don’t know.” 

B: “I know your number.”

All the statements are true. What is A’s number and how did B know?

The Pizza Theorem: How Sharing a Pizza Got Even More Fun!

Pizza holds a special place in our hearts at BEAM. From the very beginning, through the challenges of COVID, we’ve shared pizza (even when we could only do it virtually) and built community together. So this Pi Day we’re spotlighting the humble pizza pie. Since it’s impossible to share an actual pizza with you all, we’re doing the next best thing — sharing a theorem about sharing pizza, the aptly named pizza theorem.

A Look Back at an Outstanding Summer!

Mathematical Wins

At Summer Away (our program for rising 8th graders), students were exceptionally engaged both inside and outside the classroom. In particular, they spent many hours outside of instruction time solving Challenge Problems, weekly problems beyond their daily coursework completed in teams or on their own.

Want to try out a challenge problem for yourself? Here’s Oscar and Yanny’s favorite: “What is the digit sum of the product of the 94-digit number consisting of all 9’s and the 94-digit number consisting of all 4’s?” Let us know what you think!

When we asked students, What’s the longest time you spent working on a single problem this summer, the median response of students at Summer Away, Pepperdine, was 48 hours — hats off to their perseverance! The median student at this site also grew an incredible 22% in national ranking on a national math contest (which we use to measure problem-solving growth) over the course of the summer. We consider 10% growth a “great” result, so this was truly exceptional.

This summer at BEAM Discovery (our program for rising 7th graders) in New York City and Los Angeles, students eagerly tackled the 100 Problem Challenge (100 difficult, puzzle-like math problems that involve teamwork, pattern-finding, and strategy). Students at all three sites completed all the problems, earning an ice cream field trip! Consider this problem from the 100 Challenge: Fill in each of the hexagons (at right) with a positive integer so that the number in each hexagon is equal to the smallest positive integer that does not appear in any of the hexagons that touch it.

Learn more about the puzzle and its solution here.

When asked what she would tell another student about BEAM, Alice T said “I’ve never been this excited to do math, especially the 100 Problem Challenge.” 

A New Course

How do mathematicians know that a particular fact is true? For example, how do we know for certain that there are infinitely many prime numbers? It's because we found a proof of that fact: starting from the basics of math, we built out logical reasons for why there must be infinitely many primes. Proofs can be beautiful and elegant, but they also form the underpinning of math, and for students they're a great step to develop rigorous thinking and to work more like a mathematician.

How, then, can we ensure that students develop the skills to create their own proofs? This past summer, at our Summer Away site at Union College, BEAM piloted a new Introduction to Proofs course developed and taught by BEAM’s Learning and Pedagogy Manager, Javier Ronquillo Rivera.

“One of the main goals of the courses at BEAM Summer Away is getting students to start owning the process of proving things mathematically. This involves not only understanding the content that the class is covering, but also developing some habits of mind (and naming them) that mathematicians use every day. For example, looking at patterns, making conjectures from those patterns, trying to find counterexamples, or trying to find ways of being certain that the pattern always holds,” said Javier. “We decided to run this pilot to ensure that every student has the opportunity to develop the habits of mind and to have a common language around them.”

In the second half of the week-long class, Javier introduced the class to the MU puzzle, created by Douglas Hofstadter (and presented in Godel, Escher, Bach). The puzzle contains the letters M, I, and U, which can be combined to produce strings of letters. The solver is asked to start with the string MI and transform it into the string MU using one of four rules in each step. (Spoiler alert: the puzzle can’t be solved. The rules and more here.)

Javier explained, “By introducing this puzzle before developing the tools to prove its impossibility, there were two things I hoped the students would understand and feel: The first one is understanding the subtle difference between knowing that a result is impossible versus having tried many ways of getting to that result and not being able to. In the MU puzzle — without having completely developed the tools needed to prove the impossibility — we fall in the space of saying: ‘Is it really impossible to get the MU word, or have we just not found a way to get there by using the rules we have?’ I call the students’ attention to that uncertainty to show that in order to avoid that feeling, we need proof. The second thing I hoped students would feel, while using the tools we had at that time, is the need for mathematical proof.”

The puzzle stuck with Zayden, who wrote, “Although ‘MU’ is impossible, I built a connection that taught me to see patterns in these problems that I never saw before.” Andrew also reflected, “[I] worked on this for a while…it was very interesting because there are so many ways to try to come up with a solution.”

Led by Javier, students discussed their own definitions of arithmetic properties like even, odd, and divisible. Students explored how utilizing slightly different definitions led to different results, and collaborated to create strong definitions that required abstraction. For example, taking the definition “An even number is divisible by 2” and strengthening it to “An integer n is even if and only if n is twice some integer.” With these strong definitions, they were able to answer a variety of questions about different integers, included in the video below!

Visit Javier’s class [10 minutes].

BEAM Pathway students mentor a new cohort of mathematicians

BEAM students gave back in a big way this summer — 38 BEAM high school and college students served as near-peer counselors and teaching assistants at Discovery and Summer Away, mentoring BEAM middle schoolers while gaining valuable (paid) work experience.

For the first time, BEAM students also held leadership positions at all of our New York summer sites, serving as the Directors of Student Life (DoSL) across these programs. It’s a big job — DoSLs are responsible for coordinating activities, managing counselors, communicating with parents, and more. At Union College, the Guidance Counselor – who supports students in their social growth while at BEAM – and Associate Site Director were also BEAM alumni!

We’re incredibly proud to see BEAM students step up as role models for our newest cohort of students.

BEAM’s Learning and Evaluation team charts success!

The Learning & Evaluation Team at BEAM not only helps us demonstrate our impact, but also drives improvement across BEAM. Established two years ago, the team has brought new rigor to the evaluation of our work, which is, in turn, shaping how we design and implement our programs.

This summer for the first time, the L&E Team measured student growth in six areas that research has shown to be predictive of students’ future STEM success, and that are central to our work:

  • Math appreciation

  • Sense of community with BEAM

  • Growth mindset

  • Math-specific perseverance

  • Math self-efficacy

  • Math enjoyment

Students at both Summer Away and Discovery showed statistically significant growth in all six areas, with large effect size — which means we can attribute the effect to BEAM’s programs. (For all you nerds, we promised we’d get there, so thanks for hanging in.)

We’re incredibly excited by the strong results — and by everything our L&E Team is doing to make our work more effective.

For more information about BEAM’s 10 year vision for supporting our students’ STEM dreams, please read our strategic plan.

Quotable Quotes

We could write so much more about this summer, but our students say it best:

  • “BEAM wasn't just about math, I did learn new things but I was able to make connections with people and learn how some problems [have] a key to solve them.” -Lauren M, Los Angeles

  • “I grew a lot in BEAM. I think I became more independent and mature. I also made friends and the activities are fun.” - Desani M, New York City

  • “BEAM is a very interactive and rewarding program. It manages to make math feel like a sort of reward.” - Brian R, New York City