Welcome to BEAM’s College Prep Panel on Applying to College!

Six rising, current, and former college students from universities across the country joined BEAM's College Prep Week this August to share their experiences applying for college with BEAM rising 11th and 12th graders, currently navigating this process themselves.

Aisha BEAM '13 (Northwestern University) and Edson BEAM '13 (University of Southern California) will both start college this school year. They just recently navigated the confusing world of college applications themselves. Abdel BEAM '12 (NYU Polytechnic), Ana BEAM '12 (Barnard College), and John BEAM '12 (Fordham University) are all rising sophomores and can look back at their college application process with a whole year of college experience under their belt. Finally, Sylvia, BEAM staff and a graduate of SUNY Albany, rounds out our panel with an inside perspective on the SUNY system and the wisdom of several years of work experience.

The panel had a lot to say about their college application process, and answered many important questions: the how’s and the what’s, the in’s and the out’s, the up’s and the downs of getting into college. Our panelists talked about topics like choosing schools and time management skills. If you are applying for college or just want some advice, here are some of the questions and answers of our College Prep Panel!

From left to right: Abdel, Sylvia, Aisha, Edson, John, and Ana address rising 11th and 12th graders during College Prep Week.

How did you choose which colleges to apply to? What kind of things went into that? 

• Aisha: I was looking for schools that were well-rounded. And schools that I could switch majors, because I knew I was coming in undecided. And schools that had good financial aid.

• Abdel: I looked at three things. Money. Location. Major. Location: my parents wanted me to stay close to home. So in the city. In state you get more money, especially since NYU has a HEOP program that covers a lot of costs. In terms of major, engineering.

• Ana: High school affected a lot. I wanted the opposite of my high school experience [at Brooklyn Tech]. Fewer men. Farther from home.

Can you explain a little bit about the common application? 

Sylvia is a Program Assistant at BEAM and one of her major roles is shepherding the current 12th graders through the college process.

• Sylvia: It is like a portal, where you can submit all your applications through this one website.

• John: So it is very convenient.

In your later years of high school, say 11th and 12 grade, how do you split up your time? 

• Aisha: It all depends on what your situation is like. For me I kinda figure out how to split up time in November [of twelfth grade]. It all depended on my schedule; if something was due for school I would just get it out of way right then and there because I needed to use all of my time for applications.

• Sylvia: Something that I prioritized was taking care of myself too. It is important to take care of myself too. Having a planner is important so you can schedule around [taking care of yourself].

• Ana: Time management is definitely important. That is something that I am still learning to do. It is something that I didn't know how to do in high school so I wasn't taking care of myself. So like keeping a planner I can't stress it enough.

Do you use a paper planner? What do you use? 

• Sylvia: I had a paper planner that was really helpful for me. Now, at work, I use an app called Evernote.

• Aisha: I use the reminder app on my phone. Because I procrastinate, I would make a fake deadline that is earlier.

• Ana: I use a paper planner. I think writing down kinda speaks it into existence. If I don't write it down it's not getting done.

A note from BEAM: rising 11th graders who attend Saturday BEAM Next classes get some swanky planners, donated to us by Passion Planner. We may have extra planners for those not going to Saturday classes and 11th and 12th graders can request those!

How early should you start working on things and what should you focus on? 

• Abdel: Start asking for recommendation letters. I'd say recommendation letters should be the first on your list to do. Personal statement. Start thinking about what you are going to write the summer before.

• Sylvia: Just start thinking about your essay in your mind. They have the prompts on common app beforehand. So you can start getting ideas.

• John: Making a spread sheet about yourself, everything you have done. Also... BEAM does give you a calendar of when things should be done. The earliest we started was January of 11th grade, drafting our essays. That is something you can start on just choosing which days, days you are going to thing about college applications, days you are going to study for SAT.

John starts early! Here he is at BEAM College Prep Week 2016 along with Zereena, also BEAM '12, who attends SUNY Binghamton. They're both working on their essays!

Did any of you let average grades discourage you? 

• Edson: I didn't let it discourage me. Mostly because I am a very optimistic. Even if you are doing good, keep shooting to do better. Because what colleges care about is growth.

• Aisha: I realized after all the college stuff was done and people started getting acceptances, I realized that grades are important but that isn't all they look at. They aren't just looking for a good grade, they are looking for someone who can bring something extra to their school as a person.

Someone mentioned something about being well-rounded? What if you don't have the time? 

• Sylvia: There were small clubs that I was part of, and you know being on a club doesn't have to take too much time. So I think it is about finding your own niche, what you can do, what you enjoy and what your school offers.

• John: Basketball. Cross country. Dancing. You can also list taking care of brothers and sisters at home as an activity.

• Abdel: Volunteering. Working. It's not just sports.

How do you figure out how many schools to apply to? 

• Aisha: I applied to too many schools that had a lot of requirements. My case was that 14 of my schools involved writing supplemental essays, sending extra stuff, it was also really expensive.

• Abdel: There are three types of schools that you can apply too. Safety, reach and target. I would just say balance it out and make sure you are not overdoing it.

• Sylvia: I think another way to narrow down your list is actually talking to people who went to the school.

What was something that you don't like about your school that you wished you looked at? 

• Sylvia: How expensive it was.

• Edson: The diversity of the school. USC is still a great school, but the diversity is kinda unbalanced. I wish I would have looked into it.

• Ana: I kinda knew what I was getting myself into as far as the student body looked like and even the social life looks like. One thing that I wish I had known was how economically segregated it is.

How did you brainstorm your ideas for your essay? 

• Aisha: For me, my high school they had for incoming seniors it was mandatory you needed to write two essays about things that you might want to. I didn't want to write about being undecided. But then I heard this song. And it was an awesome song. So I decided to write about being undecided. Because that song was about being undecided. I wrote two sentences and gave it to my teacher and she didn't like it because it was about being undecided. But I liked it so I wrote about that.

• Edson: My teacher said think of something that is really personal to you. I was like I will write about tacos as a joke. Imagine a donut, a jelly donut, the way to structure your essay is to get down to the jelly. Like why you really want to get an education. So I wrote about how tacos are really personal to me. How such a simple food can be a luxury for people who don't have a lot of money.

Final words of wisdom? 

• John: I think the thing that helped me the most was, I play a lot of basketball and I met upperclassmen through basketball. Meet people through whatever activities interest you.

• Aisha: Don't psyche yourself out too much about certain statistics. If you really want to apply for a school then just go for it. For my school, I didn't look at the acceptance rate, and if I had I wouldn't have applied in the first place. And I am really glad that I did.

• Abdel: Try new stuff.

From left to right: Abdel, Ana, John, Aisha, and Edson, each wearing college gear!

Aisha's Off to Northwestern!

BEAM 7 back in 2013; Aisha is standing in a pink t-shirt about one-third of the way from the left. 

Five years ago, 39 seventh graders had just completed their first summer at BEAM. For some of them, it was their first time out of the city, or their first time away from their family. All of them were going to spend three weeks now living away from home and learning advanced math.

This summer, those same students graduated high school (including three with an Associate's Degree) and are just now starting college. Meanwhile, 370 students completed their own first summer at BEAM. It’s a time for looking backward and looking forward, so we asked one of our rising college goers, Aisha, to reflect on the last five years, from the start of BEAM 7 to her journey to college this fall. 

Aisha and Shikya learn to solder, July 2013

In spring 2013, Aisha decided to attend BEAM because she really loved math, especially geometry puzzles. The program also promised a chance to get away from home, make new friends, and have fun. She figured she would learn some new skills, but other than that she wasn’t sure what to expect. 

At BEAM, Aisha took courses on Proofs, Circuit Design, Statistics, and Math Team Strategies. Her instructor in Math Team Strategies described her as “intent on understanding and solving problems.” She loved the math, which she found to be different and more challenging than what she saw in school, but it wasn’t just the math that altered her trajectory. When asked how she had changed during the summer, she wrote, “I have changed because now I don’t give up. I used to give up a lot, so for me to keep going even when I get frustrated is different.” 

We asked all our students what BEAM could do to support them after that summer, and Aisha responded: “I would like to stay in contact because I think I might need help and this camp helped me understand a lot of things I was confused with.”

Aisha, June 2018

And stay in touch she did! In 8th grade, we helped her pick a high school, Manhattan Center for Science and Mathematics. In 9th grade, long before BEAM offered such comprehensive support, we encouraged her to apply to a mentoring program, Minds Matter, where she spent her summers and Saturdays for the next three years. In 11th and 12th grade, when her high school guidance counselor didn’t have the time to give her personal attention, Aisha turned to BEAM to be her college adviser. After being admitted to Northwestern University on a full scholarship, she turned to BEAM again to evaluate her financial aid package and get advice on applying for a summer bridge program to work on her writing skills. This summer, she will be working at BEAM 6 as a Junior Counselor, teaching and inspiring the next generation of BEAM students. 

We asked Aisha to look back and reflect. Here’s what she wrote:

From the summer of 2013 until now, BEAM has been a constant factor in my life. The staff at BEAM have supported me and been there for me during my achievements as well as during my failures. They have aided me in so many ways, enriching my ability and my personality. They helped me find a high school that best fit me and they presented me with opportunities for next steps, preparing me for college and the professional world. 

Most importantly, throughout the entire college process, BEAM has helped me in more ways than I could have imagined. The college process was one of the most difficult and draining times during my high school experience. However, what made it better was BEAM. When I had to change my college list at the last minute or when I was struggling to write essays, or when I cried because things were too expensive and I couldn’t handle the stress, BEAM helped me any way they could. I particularly appreciate the last-minute grant from BEAM’s Last Dollar Fund to cover $132 in SAT score reports that I needed to send in December 2017, just days before my Common Application was due. 

I am grateful to be part of BEAM. I know without them I could never have reached the position I am in today. BEAM has done so much for me. I love being part of this BEAM family. 

Now we’d like to turn around and share our appreciation with the entire community of BEAM supporters. Over the five years that Aisha has been part of BEAM, we have grown both the number of students we serve and the services we offer. When Aisha started BEAM, we didn’t even have an office; our two staff members each worked from home. Today, we have offices on both coasts. At the time, we had little high school support and no college support. Today, we not only offer college admissions advising to a core group of students, we are also adding advising through college to ensure that students like Aisha will graduate with STEM degrees. Aisha will get support from BEAM on how to choose classes, how to build relationships with professors, how to declare a major, and how to land an internship, along with regular reminders for all the logistics like filing her FAFSA. Already, at our 12th grade graduation party, Aisha sat down to discuss how an undecided student selects courses for her first semester. We feel confident that in four short years, we will be announcing her college graduation and exciting next plans. 

Aisha (right) discusses college plans with Ayinde, BEAM's College Support Coordinator.

Thank you to each and every BEAM donor, summer staff members, family member, peer, and cheerleader. Your support of BEAM allows us to turn around and support Aisha in ways both large and small. Aisha says she wouldn’t be here without BEAM; BEAM would not be here without your support. 

PS: Where are the other BEAM students headed?

Aisha in Spain, during her 2017 summer program where she interned at a maker space. 

Aisha (center) rehearses for the BEAM 7 talent show back in 2013. 

Zanahya, a rising 7th grader, learns to solder at BEAM 6 in 2018. Aisha, who learned to solder at BEAM 7 five years earlier was the teaching assistant for this course. 

BEAM students announce their college plans at College Decision Day at the Apollo Theater, May 2018.

Back row: Elijah (Howard), Henry (UMass Amherst), Tanasia (Rochester), Ariel (Brandeis)

Front row: Vielka (SUNY ESF), Aishat (Yale), Will (Haverford), Aisha (Northwestern), Malachi (SUNY Binghamton)

Aisha graduates from Manhattan Center School for Science and Mathematics, June 2018. 

Aisha, front, second from left, sits on a panel of BEAM staff and alums providing college application advice to rising 11th and 12th graders, August 2018. 

4 for 15: An hour of class at BEAM 6 Uptown

This month, we're welcoming three new full-time staff to BEAM! One of them, Alyssa Loving Jung, is BEAM's new Development and Communications Coordinator. She spent her first week at BEAM visiting BEAM 6 and wrote this blog post about her experience. Welcome to the team, Alyssa!

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My goal is to sit in on four of BEAM 6 Uptownʻs math classes in a single hour. While I may have an advanced degree in mathematics (a Master's to be precise), it is an ambitious plan. I am eager to see what mathematics the BEAM 6 students will be tackling today. 

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To start off, I get to join the very beginning of a class that appears to be about exponents… or maybe number theory? I am not quite sure. On the board there is a question that immediately catches my eye. 

What is the ones digit of 569,423^22?

I can't help it. I immediately start scribbling work in my notebook trying to solve the question. But as discussion swirls around me, I am pulled away from my attempts to solve the problem, curious as to what the students are coming up with. Students wonder out loud how to deal with a problem like this without doing a dizzying degree of multiplication. The instructor, Juan, offers a friendly warning that such an approach would take much more time than they have in class. Returning to my page of notes, I gather from my own work that the key to the problem lies in spotting a pattern and not getting lost in the cumbersome calculations. 

Emily works during class. 

Around me, I can hear students closing in on the pattern, and it is such fun that I must force myself to remember that I only have 15 minutes at most with them before I have to head to the next class. 

Even before my time is up, one of the students is up at the board presenting an idea.  

Collaborative mathematics, the courage to expose a budding solution, a still green idea, to an entire class of peers, is a crucial element of pursuing advanced mathematics. I am delighted that BEAM students are engaging with each other and their faculty like this. But glancing at the clock, I must tear myself away and head to the next class. 

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Here there is a very different sort of picture on the board. 

There are intersecting circles drawn and numbers scattered about. A student is at the board placing a number with care. While the numbers seem haphazardly distributed at first, the thoughtfulness of the student is the first clue that something more is going on. Then I notice the labels: factors of 6, multiples of 6, primes. 

They are exploring logic. The strange picture on the board I recognize as a Venn Diagram, a way to visualize the overlap and interplay between different sets. 

They move on from the Venn Diagram on the board to start working on a sheet of problems. A student notices ambiguity in one of the problems. The problem asks them to explore the statement "not A or B". He wonders if the instructor, Sian, means "(not A) or B" or rather "not (A or B)". 

The whole class takes time to investigate this subtlety. The process reminds me of writing math proofs during graduate school. Oftentimes the tiniest turn of phrase, the most minute missing detail, can make or break a complex mathematical argument. I am excited to see that the students are taking such care with the reading and writing of mathematics. But it is time for me to move on to my third class. 

TA Amaya works with student Karen on a problem set during Open Math Time.

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Yorlan works on an advanced geoemetry problem. 

This class says Geometry and Logic in the corner of the chalkboard at the front. Apparently, it is another class on logic, but now there is geometry thrown into the mix. I am intrigued. 

The instructor, Xavier, is energetic and he calls each student by name as he peppers the room with questions. 

He wonders how we can figure out what c is when we know c^2=8. A student calls out that c is the square root of 8.

Xavier follows up, smiling, to see if Eduardo was just guessing, but no: 

"No, I didn’t guess..." Eduardo responds, "It's 'cause taking the square root is the opposite of squaring something." 

I am impressed that in one sentence Eduardo has gotten at the heart of what mathematicians mean by inverse equations. It is a concept that can confound even college students. But I can’t stay for more insights today. 

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I am off to my final class. As I slip into my seat, I am startled to see scrawled across the board: "Are there Aliens in the Milky Way?" 

A massive equation containing many letters is sprawled somewhere beneath it. The students are clearly in the process of grappling with the equation and what it means. The instructor, Susan, asks them to replace L = (1/10)^8 in their previous calculation, with L = (1/10)^2. Immediately, diligent pencil-scratching begins, heads bent, eyebrows furrowed with concentration. 

This is what I call the "dirty work" of mathematics. Complex computations don’t encompass what mathematicians do. Mathematicians are much more than mere human calculators after all. But such calculations do form an important aspect of the job of many mathematicians and scientists. BEAM students in this class are building the patience and the stamina to handle even very complex formulas, and learning some mind-boggling astronomy at the same time. 

Taro, a TA, observes Jamal as he contemplates a large numbers. 

Meanwhile, I have set a new personal record for how many classes I have attended in one hour, and better yet I have had the chance to think about some really cool math. I cannot wait for what the next hour of BEAM 6 has in store!

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Curious about the classes that Alyssa visited? BEAM 6 students all take classes in our four topic areas: Math Fundamentals, Logic, Math Team Strategies, and Applied Math. Within each topic, students get to choose from a menu of classes, so they each take a class that inspires their curiosity. In the mornings, when Alyssa was visiting classes, students were in either their Math Fundamentals class, which explores the why of elementary math, or Logic class, which focuses on how to justify your reasoning. Juan and Susan were each teaching Math Fundamentals courses, while Sian and Xavier teach courses in the Logic track. 

Here are the full course descriptions for the four classes she visited!

Exponents: The Super-Powers of Numbers! (Juan) 

Using the power of multiplication, we will build some really, really big numbers and compare them to see which ones will turn out to be the biggest. We'll also explore a strange planet which only has 11 numbers in it!

Cryptarithms and Other Arithmetic Puzzles (Sian)

If A + B = AC, then what is A + B + C?  Cryptarithms are math puzzles where the arithmetic is simple but the "thinking part" of the puzzle is challenging.  We will start with simple problems and build up a tool chest of logic strategies for solving these problems and all math problems.

Geometry and Logic (Xavier)

Ever look at a problem and not know where to start? This class will develop your ability to solve complex problems. We will learn how seemingly incomplete information can be combined to form complete solutions.

Big numbers, Small numbers, and In between (Susan)

Imagine you have a very long number line, with every number you’ve discussed this year in school on the number line. A new number is introduced. Where does it go? Are you sure? In this class, we will use a variety of tools (brain power, rulers, logic, and more) to identify the big numbers, the small numbers, and the ones in between.

Learning The Game: Po-Shen Loh's Guest Talk at BEAM 6

Po-Shen Loh, mathematics professor at Carnegie Mellon University, coach of the U.S. Math Olympiad team, founder of Expii, and self-professed math enthusiast, takes the stage at BEAM 6. His audience is the nearly one hundred 6th grade students that make up BEAM 6's Uptown site, along with their counselors, a mix of college students and high schoolers, and the faculty and staff members that run the program. 

Po-Shen exudes energy, and it is clear that the BEAM students are prepared to match his exuberance. When he calls for four volunteers, there is an immediate, delighted clamor to be chosen. Amid a tumult of waving hands, the four lucky ones join Po-Shen at the front. 

The student volunteers stand on the stage, two on either side of a waist-high table. Each pair has one die between the two of them. Each person has one responsibility. One of them will role the die, the other will check the number for their team. The rules of "The Game" are simple: 

1. Each team has 4 rolls.
2. After each roll, they switch dice. 
3. After each roll, they add their number to the numbers previously rolled. 
4. Whoever has the highest sum at the end wins The Game. 

Po-Shen along with Nashle, Crisbelly, Angel, and Amire

Is The Game fair? 

Po-Shen drops the question like a firecracker. The room explodes with excitement. 

Ideas dance like dice. Laughter bounces, loud, off the walls. Counselors smile and gently shush. Po-Shen grins and throws his arms outward in a gesture that embraces the raucous enthusiasm. He brings his hands together drawing the room back to focus, channeling the bountiful energy, creating a space for solutions to be spoken. 

Hands shoot up like rockets. He sifts through, shifting from one student to another, piecing together a pattern, a picture. He grabs a question from one student, an answer from another. All of it guides us towards unraveling the mathematical mystery of whether The Game is a fair one or not. 

But scarcely have we settled on an answer to that question, when Po-Shen poses another.

Could there possibly be a strategy to such a game?

Strategy is such an intriguing word. It practically brims with adventure. But how could dice be thrown with strategy? Arenʻt dice devices of chance? What cherished games might be upended by the notion of a strategic dice throw? 

Po-Shen introduces a key element to The Game as he is playing it, which changes the strategy. Have students noticed anything about these dice? How are standard dice constructed? Students note that they tend to have numbers that sum to 7 on opposing faces: 1 is directly opposite 6, 2 is opposite 5, 3 is opposite 4. Why? It turns out that Po-Shen has dice with 1 facing 2, 3 facing 4, and 5 facing 6. How does this change the game? Why did Po-Shen manufacturer such dice? (We'll leave that question open for you to figure out, but it turns out that the answer transforms this game from a game of chance into a game of strategy.)

Some of the BEAM students in the room were especially intrigued by the strategies that Po-Shen explored with them. 

Amire, one of the four BEAM students to play the game, said "I was amazed that there was a strategy. That really amazed me." In fact, when I asked him what his favorite thing about the talk was, he answered, "Learning the strategy. Now I know how to win Monopoly." 

Deanna

For Deanna, one of the BEAM students in the audience, the element of strategy was also memorable. "It was interesting, because he talked about strategies. It was complex because it was something I personally didn't know about."  In talking about Po-Shen, she says, "He was interactive." 

Po-Shenʻs excitement as he shared his game, his questions, and his strategies with the students was tangible. Ultimately, what he communicated was a genuine love for mathematics. 

Amire, who grew animated just as he recalled the talk, said this about Po-Shen: "He is really good at math and he likes it." Amire contrasted this with people who may excel at math, but donʻt enjoy it. The fact that Po-Shen enjoyed his work as a mathematician was not only evident to Amire, it was important.  

As he spoke to us, Po-Shen himself looked beyond skill in mathematics. While his confidence in the mathematical prowess of his audience seemed as clear as his beaming smile, he closed his talk asking for even more than that. 

"Math is power," he said. 

"Now that you have great power, you must use it for good."

There's a lot going on at BEAM 6 NYC!

BEAM 6 NYC has been underway for three weeks, and the students and staff have a lot to show for it! Since the first Monday, binders have been decorated, balls have been spiked, mafia members have been investigated- and that’s all just in activity periods!

For staff members, the fun started a week before the program for setup where they turned New Design High School (NDHS) into the official BEAM 6 Downtown site. There they taught each other new strategies for problem-solving and how to support students throughout this five-week program.

The program officially kicked off officially on Monday morning when the students met with their travel groups (or traveled alone) and came to NDHS. Upon arrival, the students got to know each other, the staff, and an overview of the program.

Throughout the rest of the week students were able to experience four types of classes that they’ll be in for the rest of the program; Logical Reasoning, Math Fundamentals, Math Team Strategies, and Applied Math. Each of these topics have different instructors and each instructor teaches a different course, so there’s never a dull moment during lunch when the students talk about what they learned earlier that day.

All in all the students have had a great start of camp and made connections that will last them throughout the program, and hopefully throughout life!

Check back soon for another post soon: Staff profiles!

A Day in the Life... of Kathy!

This guest post was written by Dan May, a five-time BEAM instructor, who spent a day getting to know Kathy's schedule and thoughts on BEAM!

Kathy on Day 0 in front of Nott. 

“I’m working on a problem.” These are the first words out of Kathy’s mouth as she leaves Richmond Hall, the dorm space where 40 BEAM students and 20 BEAM staff live throughout July. A couple of days ago, it was pouring rain on our 8 AM walk to breakfast. A couple of days before that, it was already sweltering by then. But today the morning is perfect as we walk past the majestic Nott Memorial on the spacious campus at Union College. 

“The problem is about finding a strategy for how many floors up you can drop a spy device before it will break,” Kathy explains. (Here's a recent TedEd video on the same problem!) In the next breath, she worries about her roommate, Nikelisi, who has overslept just a little this morning. BEAM students tend to look out for each other, especially by the second week, and Kathy doesn’t want Nikelisi to be late for class. “The fan in our room helps us sleep – maybe it helped Nikelisi too much!”

Cassie and Kathy later, on Field Day!

As we enter the dining hall, Kathy mentions that she is excited to tie dye her t-shirt later this evening for her field day team, but our attention quickly turns to the many breakfast options available this morning: eggs, bacon, pancakes, oatmeal, cereals, yogurt, fruit – the list goes on. Kathy enjoys the food at Union, but like many BEAM students, she misses her family’s home cooking. 

While we’re taking our seats, a staff member trips and spills coffee and juice onto the table, floor, and himself. Nearby students and adults quickly pitch in to help clean up, and the conversation turns to embarrassment. Kathy mentions that the supportive environment of BEAM makes people feel much less embarrassed about awkward situations than they might in a normal school. “BEAM is like a democratic society,” Kathy says, going on to describe how everyone’s preferences are taken into consideration when making decisions. This is true: Kathy, like all BEAM students, had a voice in choosing the classes and activities that will shape her day, and summer, at BEAM. 

By 8:20 Nikelisi shows up to breakfast, completely nonplussed by Kathy’s joking around that she’s late. (Official BEAM policy: 8:20 is most definitely not late to breakfast.) “What’s your favorite weird math thing?” Kathy asks the table. Claire, a first-time BEAM instructor, mentions the number 0.999…... (that’s zero, then a decimal point followed by an infinite string of 9’s). The ensuing discussion is mathematically rich, as several adolescent women debate whether .999….. is equal to one or not. “The numbers .999….. and one must be different,” Jazz insists. “By how much?” Mikaela replies immediately. It’s exactly the right question to ask, and leads to much more debate, but the issue is not resolved during this breakfast.

Eventually the conversation turns back to the challenge problem, and after Kathy decides that her most recent strategy won’t work she throws up her hands and says “I’m done .....” and then after a beat “ ... I’ll continue.” This kind of persistence is common at BEAM.

Kathy’s first class this morning is Analytic Number Theory, taught by Cory, a veteran BEAM instructor who is an assistant professor of mathematics at Washington and Lee University. Cory deserves his title of Dr. but at BEAM we all go by our first names. Kathy likes this arrangement and feels that it helps her create better bonds with her BEAM instructors. 

Kathy shares an idea with instructor Cory and her group, Madjara, Sam, and Jack, during Analytic Number Theory

The environment of Analytic Number Theory is intentionally collegiate – Cory trusts his students. They are trusted to choose their own groups to work in. They are trusted to understand complicated mathematical ideas that are not watered down. Cory believes that mathematicians begin to use mathematical concepts before they are completely comfortable with formal definitions, and the students in his class this morning are correctly using fundamental calculus concepts like limits, and convergence and divergence before they know precisely what these terms mean. 

Kathy’s group is working on the sequence generated by the function on the right, and trying to determine if there is a number that this sequence seems to be getting closer and closer to. They discuss the problem with their class’s teaching assistant Bobae, a rising sophomore at Harvard. It’s clear the students have already absorbed function notation, and they are discussing with her how different choices of domain might affect their answer. Someone prematurely declares that they’re “done” with the problem, to which Kathy replies “you’re not done if you don’t understand it!” Everyone agrees with this, and they continue on with their work.

Once they’ve decide to expand the domain past {1, 2, 3, 4, 5} into the set of positive integers, Kathy claims that the answer should be 0. Her reasoning? “The denominator increases while the numerator stays the same, so the answer gets smaller and smaller. Zero is nothing, but this function always gives a fraction of something. The space between the numbers is getting smaller and smaller. So they get close to zero but never get there.” Her group mostly agrees with this assessment – perhaps they remember a similar line of reasoning they saw in a problem in Modules, a quiet, late-night mathematics activity.

After the two-hour block of Analytic Number Theory with Cory, it’s time for the first of two scheduled activities. Today Kathy is playing board games in the Union Student Center. Underneath a high, vaulted ceiling of skylights, students spread out across several tables in a large and inviting space, illuminated with late-morning natural light. This year, students’ favorite board games have included Monopoly and Life, but today we’re learning some lesser-known games. Soon lively matches of Tsuro, Blokus and Niya are underway. And Coup. Coup is a card game in which players assume various personas, including the Duke, Assassin, Captain, Ambassador, and Contessa. By carefully deploying these characters’ skills, players can outmatch their opponents. Or you can just lie a lot. At any point in the game, any player may be bluffing about their true persona. So the game rewards strategy, but also deception, and matches usually become very animated. On this occasion, Kathy attempts to wield the powers of the Contessa – a dangerous gambit that doesn’t end well for her when her bluff is called and Kathy is eliminated from the match. 

Kathy plays Coup with staff Don, Claire, and Ayinde as well as students Jade and Andrew

But everyone has fun, and now it’s time to head upstairs in the Student Center for lunch. Kathy’s run of bad luck continues: the current challenge problem has been cancelled. This is a rare occurrence at BEAM, but when the community of students obtain information on a challenge problem in an unauthorized way – well, it’s time for a new problem! Kathy takes this unfortunate piece of news with her characteristic good humor. She even takes an electronics warning in stride. Kathy is an avid music fan, with tastes that run towards songs addressing weighty social topics, and she has been sharing her headphones with a fellow student over lunch. But BEAM has a strict no-electronics policy from 9 AM to 7 PM every day – we’re all here to grow and we believe an essential aspect of that is to be present with each other instead of our devices. 

None of this dampens Kathy’s enthusiasm for heading back to Analytic Number Theory for two more hours directly after lunch. During this class period, Cory introduces the class to some very formal and very essential calculus notation: 

They spend careful time picking apart each piece of that mathematical sentence. What does “lim” mean? The right-pointing arrow? The students mostly have seen the infinity symbol before, but the use of the equals sign is especially tricky. Like Kathy had said in the morning class, the elements in the sequence will get close to zero, but they will never get there. So how can anything equal zero, she wonders. These are the kinds of questions any college freshman should be considering closely when they first encounter this idea, but frequently they don’t have time to. Eventually, Kathy gets it. “Oh, we’re saying the limit equals zero. Not any terms in the sequence.” This is a breakthrough.

TA Bobae oversees Kathy and her group, Madjara, Sam, and Jack, as they work

Fitz and Zeina play "It's Tuesday!" during an improv activity

Between afternoon blocks of class, students have another scheduled activity period, and an opportunity to have a snack. Kathy’s afternoon activity today is Improv with Hector, another Counselor/TA who is a recent graduate of Rochester Institute of Technology, starting a PhD program in mathematics at Lehigh University. Kathy is delighted by how silly some folks are while acting out their roles: “How are you going to act out an emoji?!?!?”

The third two-hour block of class in Kathy’s day is a class called Solving Big Problems (SBP), where students ..... solve big problems. These are math problems designed to take two hours (or more!) to solve. Kathy’s instructor is Claire, a seventh-grade teacher in Brooklyn (and the .999….. fan from breakfast). Claire does a thoughtful job of helping the students to focus at the beginning of her class. By now it is 4:15, and these twelve and thirteen year olds have been going non-stop since 8:00 this morning (or earlier), and have already spent four hours of very taxing math time in the classroom. Claire’s experience with students of this age is evident. She asks them to spend a few minutes in silent consideration of a photograph of various sizes of pizza pans; each pan is labelled (in the actual photograph, by the pizzeria) with various geometric and pizza-metric information, and the students are asked to generate questions and observations. The students had come into the room a bit disorderly, but they are definitely now focused and ready to go.

Another student, Brandon, works on the problem of the day

Claire introduces the “big problem” for the day – which is actually a complicated question from the mathematical field of graph theory. A graph can be thought of as a network of connections between pairs of objects, and is depicted by a diagram of points (“vertices”) and lines (“edges”). A graph is considered “graceful” if its vertices can be labeled in such a way that generates a labeling of the edges in which every edge gets a different label. The BEAM students have been asked to determine whether certain types of graphs are graceful. A variant of this question is actually an open problem in mathematics – Claire has her students working on a problem that professional mathematicians don’t completely know the answer to!

Another group wrote this about star graphs: "All star graphs can be gracefully labelled as long as there is a 0 in the middle"

But that doesn’t deter Kathy, and she conjectures within minutes of hearing the problem that all “star” graphs are graceful – you just have to label the “middle” vertex with zero.  (To be clear – this is not the open problem, but rather one small case of a larger question.) She’s able to write out her conjecture, and a proof, on the whiteboard with her partner Jade. The hardest part for the pair is to determine which part of what they’ve written is the conjecture and which parts are the proof. BEAM students tend to have A LOT of ideas, and one of the skills we work on in all of our classes is how to organize, edit and communicate these ideas cogently. So what goes in the conjecture, and what goes in the proof? Generally speaking, conjectures should be short, concise and clear – the “what” part of whatever you’re doing. Proofs can be longer, more involved, and they contain the outline of how it all works – the “why” part. After some tricky conversations about language, Kathy and Jade revise what they’re written to reflect these ideas.

The SBP class is loud and lively, with many different groups enthusiastically trading ideas. It’s a nice counterpoint to the methodical and deliberate tone of Kathy’s earlier class, Analytic Number Theory. Near the end of the two hours of SBP, Claire brings the students together as a class and asks them to present their findings to each other. Claire then asks them to give “shout-outs” to their peers. “I want to shout-out Jade” Kathy says, and offers public praise to her partner for working out some of the tricky details about the graceful labelling of a path graph.

By 6:15 classes are over for the day, and we are all ready for dinner. Back at the dining hall, Kathy is still thinking over the graceful graph problem, and comes up with a proof that 0 isn’t the only label that could go in the middle of a star graph to give a graceful labelling. The question of counting precisely how many graceful labellings a star graph has gets a bit trickier, and, unprompted, Kathy brings up Alexandria Ocasio-Cortez. The conversation isn’t political per se, but Kathy does mention that successful people often face harsh criticism. She is glad that BEAM is most certainly not like that. “Students are taught to actually use all their tools,” Kathy says. She is beginning to see that mathematics is not something to be thought about in just one, rigid way. There are many paths to success on a problem.

Earlier in the week, Kathy was spotted re-reading Harry Potter and talking with Kenny, an instructor

After dinner, students have 90 minutes of relatively unstructured free time. There is usually an outdoor sport or activity planned, and many students use this time to shower, do laundry, and just hang out with their friends around the dorms. As it turns out, Kathy’s field day team (the Purple team) is tie-dying shirts tomorrow, so she spends her time playing board games in the student lounge. The lounge is a large common area in the basement, and it’s the only air-conditioned space in the dorms. It’s full of comfy chairs, games, and books – both mathematical books such as The Math Book, and non-mathy books like the Harry Potter series (Kathy has some strong opinions about the plot of Harry Potter). Tonight Kathy is learning a game that is new to her, a two-player strategy game called Niya that some others had learned during today’s morning activity.

Kathy (background) works on the board while her modules group members, Brandon, Amber, and Eli, work at a table

Modules start at 8:25. This is quiet, largely self-paced and mostly individual mathematics time. Unlike the rest of the math at BEAM which is exposes students to very challenging topics they might not otherwise see until college, modules is meant to strengthen students’ foundations in school-type math. They work on meticulously chosen problems covering fractions, decimals, exponents, the distributive property and more – basically all the stuff you’ll need to know to excel at algebra. On this particular evening, Kathy is strengthening her knowledge of fractions and decimals, and learning a nice trick: while you would never want to actually report an answer as something like 1.6/400 (a decimal in a fraction? Yuck!), sometimes allowing for something ugly in an intermediate step is exactly the technique you need to complete the problem, and to understand what you are doing more deeply.

After modules, students attend hall meetings. The forty BEAM students live on single-gender floors, and each of these 20-student floors is further halved into “halls”. Each hall is named after a famous mathematician; Kathy’s is named after Grace Hopper, a pioneer of computer science and a Rear Admiral in the US Navy who was born in New York City. From 9:30 – 10:00, students in Hopper (and all the other halls) meet with each other and the two counselor/TA’s assigned to their hall. For Hopper, that is Bobae and B, who is a rising senior, majoring in math, at St. Edward's University in Texas. They talk about what happened that day, discuss any pressing issues the students on their hall may be having, and outline what the next day will look like. This is where students get to pick their activities for the following day, and Kathy is excited to go to Record Club tomorrow, a social music-listening activity.

Student must be in their rooms by 10:30, and lights-out is at 10:45 – lights-out includes no late-night electronics! This means there is generally a little bit of downtime between hall meetings and bedtime. During this late hour tonight, Kathy is playing a low-key game of Uno with several of her friends in the lounge. Earlier in the day, she had joked that “a mathematician is a mythical being like a unicorn! Because who likes math anymore ... says the person at the math camp.” But now she is reflective. “I go to bed much earlier here than usual. BEAM just tires me out way more than regular school.” It’s a feeling all of us at BEAM are familiar with: exhaustion at the end of a mathematically and personally rewarding day. And we know tomorrow will be the same.

Weekend Fun and our Start of week 2!

Week one has come to end and it is time for some off-campus enjoyment!

As the well-anticipated end of the week arrived, BEAM students prepared themselves for a weekend full of activities. Upon Monday morning's arrival, as a part of their daily routine, students headed to the dining hall prepared to stack up on the nutrients which that will help them power through the busy day. After breakfast and a few turns of water bottles filling, kids made their way to the coach bus-- now fully ready to embark on their mini road trip.  

After both check-ins at the water park and applying sunscreen, our young adolescent campers divided into small groups. While in their well-supervised small groups, they then made their way to water slides exploring what the park had to offer.

When lunchtime arrived at around 1 PM,  we once again, gathered as a camp, ate, and then, prepared to head back to Bard College. At the end of this fulfilling day, tired bodies guided themselves to bed expecting to be well rested for days ahead of them.

At BEAM, Tuesdays mark the start of a new week. Just a day after their water park fun,  BEAM students were mentally ready to go in their classes and hold class discussions on Symmetries and problem-solving theories. When completely submerging themselves into their classes either as a group or as individuals, these students have shown an immense amount of improvement. 

 We applaud the hard and effort applied by every student.  As we approach our last week of camp, we can only encouraged that this habit continues to be practiced beyond BEAM.

Field Day at BEAM 7 Union

Sunday at Union was all tie dye and teamwork as students gathered for BEAM's annual field day! Students participated in games such as pool noodle floor hockey, relay races, staff/student basketball, and a photo scavenger hunt. This photo scavenger hunt led to some of our favorite photos of the day! Each team (orange, red, blue, purple) had one hour to take as many of the photos as they could!

Here were the challenges:

The oldest painted sculpture on campus. (Hint: don’t add anything to it!) 

Take a photo with a Union student. Get and send their NAME and their MAJOR.

The orange team with BEAM staffer and Union graduate, Fred, who majored in engineering. 

Find a rabbit. Brownie points for taking a picture with a rabbit.

A very presidential figure on campus, and an alumnus. (Hint: he’s bronze, but not because of a suntan!) 

Speaking of presidents, where does the president live? Take a cool shot. 

Find the building with rainbow stars in the dome. Take a picture from the outside with your finger on the very top! 

Find a flower. Take a close-up. 

Dance with a staff member. Take a photo. 

Find and take a photo of a Minerva House. 

Wow, what a Messa. Take a photo of an iceless rink. 

We all love learning outdoors. Where can you can sit around a chalkboard-- outside?! 

Splish splash. Where is the only pool on campus? Take a photo of the inside. 

Tube of toothpaste.

Quiet time! Take a picture of everyone in your team reading a book.

Thank a Union staff member and take a photo with them (ask politely!) 

Someone on your team, do a cartwheel. Take a photo mid-wheel. 

Form a human pyramid. Please don’t get hurt in the process.

Find a physical map of Union’s campus and point to your location. 

Where’s Union’s main gate? Take a photo next to it. 

Ready SET go! Take a photo of everyone’s favorite game!  

Find a piece of trash on campus and throw it away. Take a picture. 

Everyone drink water! Take a picture.

Compose a haiku. Write it down. Take a picture. Use chalk if you want. Brownie points for BEAM-theme. 

The blue team haiku: "BEAM is amazing / Mod is very confusing / But I learned a lot."

Find Lynn. Take a picture with her. Make it funny.

Week Two Surveys

Analytic Number Theory featuring Jack, Anais, Madjara, TA Bobae, Kathy, and Sam

It's already week three at BEAM 7 (where did the time go?!) so we're looking back on some of our survey responses from week two. Here's what students had to say about their classes and BEAM 7 in general:

What was good about Analytic Number Theory?

• I like how I came into class knowing nothing about this topic and coming out of it learning so much. 
• The calculus.

Zeina and Rose code together in Arduino. 

What was good about Arduino?

• That it was challenging but I was able to learn a lot.
• It taught both genders how to love to code: (girls who code) <- not many! (I might be next)

What was good about Cryptography?

Mekhi works on Cryptography with John and TA Fred in the background. 

• I really liked the debates the class got into regarding mathematical concepts.
• Everything.

What was good about Infinity?

• I loved how we finally solved our theories and definitions of "infinity." Now I know what it is, and how to use it.
• Everything, for example learning what a number actually is.

Chloe and Emmanuela work with instructor Kenny during Math Team Strategies. 

What was good about Math Team Strategies?

• I liked how it helped me explore many math competition problems and it helped me learn alot about interesting strategies to solve them.
• I learned a lot of ways to solve different types of problems very quickly.

What was good about Solving Big Problems?

Alisa and Angie pose with their work after Solving Big Problems. 

• I like all the interesting questions thrown our way and how we learned from each one.
• It made us keep questioning everything.
• It made me think in different ways.

Do you have any other comments on BEAM 7?

• This program is awesome!
• It is an awesome program, and I hope that there's a BEAM 8!
• I like this program.
• I love it. I will miss everyone.
• Nope. Thank you. ⭐⭐⭐⭐⭐
• It's awesome; make it longer. 
• It's great so far.
• Make Beam 8.

Spotlight on Classes: Analytic Number Theory

Each week, the students are able to list their preferences for which classes they would like to take. They take one course for four hours a day, and another for two hours a day. Each week, new classes are offered and the students have the opportunity to immerse themselves in different advanced mathematical topics.

While each of BEAM’s classes explores incredibly interesting and advanced ideas, we’ve put together a spotlight on just one of the six courses offered this week: Analytic Number Theory with Cory. 

The class has just seven students, with a teacher and a teaching assistant—the kids get to really get to know one another and the staff members! In just three days, the class has gone from not knowing what a function is to being able to find the limit as n approaches infinity of f(n) = (-1)n/n: zero. The students are basically doing calculus without using the word “calculus” itself! 

Sitting in on the class, what is most impressive to our staff, even more than the sheer speed and intensity of the class, is how engaged each student is. Cory will give short lectures, but for a majority of the class, the students work in small groups in order to work on difficult problem sets. Mostly, they are teaching themselves the topics! Today in class, we were beyond impressed to see how each of the students was able to find patterns and draw conclusions from sequences of numbers.

When Anaís and Cynthia talked about the class, they said that they couldn’t believe how much they were learning in such a short period of time!

Jack agreed, saying: “I’ve learned more math in the past three days than I did in the last two months.” 

Cynthia, Jack, Anaís, and Alvin work together on the board

Week two classes are now officially over at BEAM 7 Union College. We can't wait to see how much learning takes place in week three!