Reflecting on the year at BEAM

It’s been over a year since I’ve posted about BEAM and my own work—of course things have been busy, and I’ve had little time to pause and share. These times have genuinely taught me a lot about myself and about BEAM, and I’m glad to finally write some of that down.

So how has BEAM been doing?

Actually, as an organization, BEAM has been doing remarkably well considering the state of the world. Although diminished by the distance we’ve all felt from each other while working from home, the team has done amazing work and really stuck together in powerful ways. We all miss being in the office, but we still have such a strong sense of camaraderie. It’s an amazing team.

BEAM has also been succeeding in lots of other ways. Most notably, we’ve really gone the extra mile to support our students. We’ve run online summer programs and classes (including delivery of over 400 laptops, individual provision of internet, and more), provided emergency relief funds to families in need, and supported students through the chaos that has been schools trying to respond to the pandemic, college admissions, colleges going remote, and so on and so forth. I could tell you more, but the link above, to our regular donor updates, does a better job than I could. I’m so proud of what we’ve done.

We’ve also hit our fundraising goals, likely raising enough to make some much-needed infrastructure improvements as we grow from “small startup nonprofit” to something approaching mid-size and more professional. (For example, we will soon have an actual HR person, rather than the hodgepodge of roles we’ve all been keeping so far!)

We’re launching a new national program that will begin working with students in elementary school and support many of them through college graduation. The program, which will use donated licenses of Art of Problem Solving’s Beast Academy, could be a real game changer in terms of reaching a lot of students with interesting math and finding students nationwide who can most benefit from BEAM’s work. (By the way, we’re hiring an Executive Director and I’d love your help spreading the word. See below for more details.)

In other words, from an organizational standpoint, BEAM has honestly excelled. It’s a testament to our team.

What that doesn’t capture, though, is the exhaustion. Can I tell you for a moment how hard it is to arrange internet access for families that don’t have it? At first our plan was to get tablets on cell phone plans. Those tablets could act as hot spots to connect to the laptops we provided. However, we discovered (after ordering 80 tablets!) that, while our plan was 50GB/month, the fine print said you could only use 10GB/month for connected devices. After the first week of LA’s programs, students were running out of bandwidth on Zoom.

So then we switched to trying to get wired internet access. But setting aside the coordination of so many different installs, that doesn’t solve the problem for families who had wired internet but fell behind on payments (and thus can’t reinstate it without first paying back charges), families that might live in unregistered housing setups (e.g. basements), or families that live in shelters where such installs aren’t allowed. We had to get a hodgepodge of devices together, including some expensive wireless access points with higher limits, and for some families we simply delivered a new tablet every week so they’d have a fresh 10GB!

Then there was designing a new online program, training our staff, setting up our technology (I can’t thank the tech volunteers who designed the student portal enough), running student registration online instead of by mail, etc. etc. etc.

All of which is to say: the staff were exhausted. (Have I mentioned the personal tolls of the pandemic and the historic, and still horribly unresolved, racial reckoning in the US?) Meanwhile, while I am proud of the new National program and we’ve been planning it for years, I was working to set it up exactly when we were designing our online summer programs. So at the time that everyone was at their busiest, my attention was divided. It’s a hard balance to strike; after all, those plans really had been in motion for years.

So BEAM is doing great, but our staff are tired! Fortunately, once we got past the summer, we were able to return to a much more normal workload, and we’ve put in place the structures to succeed working remotely. I think everyone is also deeply energized by what we accomplished. Nonetheless: I have a lot of reflecting to do as a leader, especially for future times like this. It’s one of the reasons changes such as creating an HR department are so important: it will put us in an even better position to weather the next unexpected challenge.

Leadership reflections

I think that 2020 would have been an interesting year for BEAM no matter what. We’re now at 45 full-time-equivalent people (counting summer staff, part timers, etc.) and that means we need to transition to stronger systems and more refined processes. Communication that used to be easy when we were a three-person office now needs to be structured. Sometimes I just think everyone can read my mind! One key asset as we evolve is the hire of our new Chief of Staff, who started in May and brings experience with exactly the kind of structure BEAM needs so badly. She’s been guiding us to a place where we can have the structure we need while maintaining the flexibility we want.

Moreover, the events of the summer have really brought forth a problematic truth that has been at play throughout the life of BEAM: I’m a white man leading an organization that serves primarily students of color. I don’t share the experiences of the students we serve. I worry, also, that there’s an extent to which BEAM’s priorities impose additional burdens on students already managing their own values, lives, and achievements.

My answer to this has always been to listen a lot and elevate the voices of our staff and students. While I am ultimately responsible for BEAM and the choices we make, it’s my priority to build staff consensus whenever possible, and to make sure I have thoroughly listened to and understood everyone’s point of view when consensus is not possible. That’s my way; I try to really know the bounds of what I know and what I don’t know, and to use the wisdom of others whenever possible.

Unfortunately, that doesn’t always work when you’re supposed to be a leader and the country is going through the kind of events it’s gone through recently. I don’t think I appreciated how much the staff want to know where I stand, not just know that I am listening to their opinions. This is a side of leadership that I had never really considered before, but especially in a mission-driven organization it’s so important.

(It is also, perhaps, complicated by the fact that my own views are more activist than many of my friends, driven in large part by my BEAM work, but less activist than many of the BEAM staff! It can be quite a journey going from friends where I am explaining why I think that addressing systemic racism and white supremacy is so important right now, only to go to a staff meeting where I can feel like I’m playing catch-up in parsing the events of the day. This tension has been profoundly stressful to me personally, especially whenever I feel like I’m not living up to the leadership the staff need.)

Anyway, there’s a lot to think about. My podcast feed has had a lot more about leadership, and I’m so grateful to the two programs I was a part of that provided me with leadership coaching in the past year. It’s made me wonder if I want to find another coach going forward.

Wrapping up

So where does that leave me at the end of the year?

I’m so proud of the work that BEAM has done. We’ve done really important things for our students, while continuing to grow the organization and move into new areas that position us so well for future work. BEAM is stronger than it’s ever been, despite the events of the world.

I’m tired, but also energized in my way. Sometime soon, I am going to take a true and restful vacation, although I don’t know what that means. Historically, I haven’t found rest very restful! Maybe I’ll take a break to write a novel. :)

I’m learning so much about myself, the world, and leadership. I feel like I’ve grown more as a leader in the past year than in the five years prior. It’s also shown me just how much more growing I still have to do.

Regardless, I am excited for 2021. There’s so much work to do, both at BEAM and in society at large, but I feel so energized to see that progress and growth.

Oh, and…

There really wasn’t a good place to put this, but hey, we’re hiring an Executive Director of National Programs to lead that national program I mentioned. Finding the right person is so important. We are especially looking for candidates whose background represents our students, who have experience scaling an educational program, and who can work well with partners at the school and district level. If you’re reading this, can you spread the word to your network? It’s a great job leading a growing new program!

BEAM Update: Fall 2019

Welcome to a regular sequence of blog posts where I’ll give some personal updates on BEAM’s progress as an organization and my journey within it. I’m transitioning from sending these via personal emails to a format that everyone can access.

Summer Program at Harvey Mudd and Reflections on Growth

Last summer I had the pleasure of visiting BEAM’s first-ever residential program for Los Angeles students, held at Harvey Mudd College.

If you haven’t ever been to “BEAM Summer Away,” as it’s called, it’s a magical experience. It’s an amazing group of students developing a community together that is based around math and making friends for a lifetime. They’re also learning all kinds of interesting, deep math unlike anything they’ve ever seen before. It’s especially powerful for me because a similar experience was life-changing for me growing up.

In addition to outstanding courses (everything from projective planes to public-key cryptography), the students just had such a vibrant community. They invented a song and then game based on the Spanish word for lettuce, developed all kinds of little clubs (such as a gang based on slide-on sandals), and more. Board games and Rubik’s cubes were in evidence, as were lots of people working on and enjoying math. They even made a big book of their math work at the end and signed it like a yearbook, where each student had a page dedicated to their favorite problem.

To be sure, there were growing pains at having a new site. We were still learning about the space, and of course we had to expand our staff at all levels to grow, from counselors up to site leadership. All of our sites went well, but there were a few signs that we’re pushing it: the percentage of students who said they were more interested in math dropped a little bit across our summer programs (could be normal variation, could be significant) and we had fewer experienced staff because they had to be spread across more sites. It’s also just harder to provide consistent training across six summer sites!

I’ve often had some minor envy for friends who work at rapidly-growing tech startups, but the truth is that the scale of working directly with students is just different. So while BEAM continues to expand in other ways (see below), summer 2020 will have the same sites as summer 2019. This will allow us to focus on building a larger base of returning staff and more generally ensuring we have the systems to promote quality classes and experiences for students.

BEAM 6 Los Angeles: Week 1

Here’s our amazing staff, on our very first day of training:

Here’s a programming class taught by Lee-kai, a friend of mine from MIT:

One of the new innovations this year is the “100 Problem Challenge.” I’m especially proud of this one: a hundred problems I selected to challenge the students mathematically and bring them just to the edge of mathematical proof. (Those who continue will learn proof in BEAM 7 next year.) There’s a big board with 100 spaces for the 100 problems, and we write in the names of students who’ve completed problems. Here’s the status as of a couple days ago:

(Here are some of the problems they’ve solved if you’re curious!)

One of the interesting effects of the 100 Problem Challenge is just how motivated everyone is to do problems. Two hours of our day are dedicated to “Open Math Time” when students can set and pursue their own mathematical goals. I’m swarmed with students bringing up solutions for the full two hours, and some have even asked, during their activities (time off!) if they can work on these problems. “Aren’t you supposed to be watching the World Cup?” I asked as a couple of kids came in with answers on Thursday.

What’s Up With The Math Revolution

The Atlantic has a new piece about the more and more advanced work now studied by middle school and high school students.  This trend is well recognized among those of us who’ve been working with these students for years, although it was interesting to read about it in a publication intended for a general audience!

The article is largely about math beyond what’s typically taught in school.  You might call it high-level math, more challenging math, more abstract math, or maybe STEM Pathway math because it helps kids develop the skills to succeed on that pathway.  Regardless, it basically doesn’t touch at all on what a school math curriculum should be or what math class should be like.  It’s important to keep that in mind; this is math for kids who want more math.

And let me say, it’s wonderful that kids have so much opportunity to challenge themselves with interesting mathematics.  However, there are two big downsides to the current arrangement.  First, some students may feel pressure to advance themselves for the wrong reasons.  Second, those without access are being left ever further behind the top achievers.

I’m honored that BEAM was discussed in the article as an effort to address inequity in access, and that I get to contribute to this conversation, but we’re still quite a ways away from really closing the gap.  In this post, I want to dive into what’s really going on so that we can understand how the next generation of mathematicians and scientists is growing up.

5 Minute Problems to Five Year Problems

On Saturday, I gave the keynote talk at the Manhattan MATHCOUNTS contest.  I haven’t had so much fun giving a math talk in a long while!

I was never exceptional at math contests, but I love them.  I think they’re fun challenges and they create a vibrant community; used well they are a good tool in mathematics education.  However, most contests also promote bad habits.  They lead students to focus on speed and winning over deep thought.  They encourage students to learn a few tricks well and memorize useless facts.  They further perpetuate the myth that math is about speed, even though real-world problems take days, months, or years to solve.  Hence, my talk was about transitioning to solving “big” problems.  For my own reference later as well as for anyone who is interested, here’s a log of what I said and how I structured the talk.

An Actual Response to Chief Justice Roberts

On December 9, the Supreme Court heard oral arguments (uhhh, again) in Fisher v. University of Texas, a case about affirmative action.  At issue: what measures (if any) can the university use to increase diversity if those measures disadvantage white students?

The case provoked all the expected outrage, especially when Justice Scalia made a half-informed comment about the effects of affirmative action on minority students’ ultimate achievement.  However, while listening to back episodes of the Amicus Podcast, I heard a different comment from Chief Justice John Roberts.

“What unique perspective,” he asked, “does a minority student bring to a physics class?”

The lawyer for the University of Texas, not surprisingly, was tongue-tied.  (Not exactly part of prep for the case, eh?)  A casual internet search revealed many non-response responses explaining why diversity is important and why physics needs underrepresented students to succeed.  (That second link, if you’re curious, is a letter from almost 2500 physicists to the Supreme Court.)  The Atlantic has a lovely piece about Einstein’s journey to discovering relativity and how it relied on philosophy, but the piece still could only hint at an answer to Roberts.  Somehow, none of these responses actually answered the question!

That’s where I’m stepping in.

Unique Perspective #1: Communication

The job of a physicist is centered around two things: making new scientific discoveries and communicating those discoveries.  A discovery that is not communicated is useless.  Physicists write up their work in academic journals and give talks at conferences.  For many of them, the bulk of their academic employment will be based around teaching physics classes.  Those who go into industry must communicate with coworkers, management, and the public on a regular basis.

Successful communication requires being able to phrase your work in a way that can be understood by those of many different backgrounds.  In lab settings, in group projects, in presentations, it provides a key benefit to learn how to communicate with those who don’t share your background.

Unique Perspective #2: Applications

Many people taking physics classes are going on to think about applications of their work to the real world.  Perhaps they are engineers and will be building bridges.  Perhaps they are going to work at NASA or SpaceX or Blue Origin and will lead space exploration.  Perhaps they are going to work in nanotech, or semiconductors, or… you get the idea.

In all of these cases, applications to the real world are essential.  They must design technologies to be used by other people.  They must think about how the bridges they build interact with the communities around those bridges.  Diverse perspectives allow students to better understand the applications of their work, how it will be used, and how to design it for maximal benefit to society.

Unique Perspective #3: Cultural Support

For the sake of argument, let’s suppose that there’s a physics student who gets into UT and she’s be the only Black student in her class.  She’s doubly underrepresented: one of few women, and the only Black student.  Her learning will be negatively impacted because she has no one to talk to about those struggles.  There’s no one who can understand the lack of role models or the biases she faces.  If she comes from an environment that is not middle- or upper-class, there is no one with whom she can discuss the culture shock not just of attending the university, but of physics, which has its own cultural norms.

This student, although admitted on her own merits, is getting an inferior education to others because she does not have a supportive peer group.  This is preventing her successful education, because her class lacks the perspectives of other students that will help her succeed.  Without diversity, the University of Texas cannot do its job for her, cannot give her the service for which she is paying tuition.

Concluding Notes

These are not the only reasons I support affirmative action in educational settings.  However, as someone who has designed numerous educational programs in math and science settings, I have sought diversity of viewpoints and backgrounds not for a social justice purpose, but because that is how I can provide the best educations for my students and create the products that students will want.  As the country becomes more diverse and as students enter a globally competitive marketplace, access to diverse viewpoints is an essential part of a good education.

To put it in the starkest terms, denying the University of Texas the tools to create a diverse class will decrease their educational effectiveness and put them at a competitive disadvantage against other educational options that offer greater diversity.

BEAM Is Hiring!

In case you only follow me on this blog and not other social media, BEAM is hiring faculty (both residential and NYC-based) as well as undergraduate counselors (same).  It’s a fantastic opportunity to work with underserved students doing serious mathematics.  More information on BEAM’s hiring page.

BEAM 6: Designing a Schedule, or How Does It All Fit?

This is part of a sequence of posts developing a new project for Bridge to Enter Advanced Mathematics called BEAM 6.  BEAM 6 will be a non-residential, four-week summer program for underserved 6th grade students in New York City.  You can find the other posts about its design here.

How can we possibly make everything fit?

Seriously, we have a highly ambitious curriculum planned and we must also fit a vibrant social schedule. The community formed at BEAM 6 will carry students through their future studies if we get this right; it will provide a beacon that tells them that they can have good friends and be serious about math at the same time. It will also encourage them to continue on to BEAM 7, and we want them to come! What schedule will let us accomplish these goals?

The Basics

BEAM 6 will run six days per week. Five days will be class days, which will mix both classes and activities. The sixth day will be a field trip or activity of some kind to further build community and friendships.

We need to fit in as much time during the week as possible, but we have a serious limitation: rush hour! Students will be brought to the program by our undergraduate counselors, who will meet them at subway stations near their homes. However, navigating the subway during rush hour with a bunch of 11-year-olds is not a great plan.

We can’t avoid rush hour completely without terribly shortening our day, but we can avoid the worst of it. If we start at 8:15am, then the farther students will be boarding the subway at 7:15am, which is not too bad, and by avoiding an “on the hour” start we also avoid peak times. Then if we end at 3:40pm, we can get on the subway before the afternoon commute.

That’s our day: 8:15am-3:40pm. I’m not crazy about how that schedule makes us feel like a normal school, but we have few other options.

I debated for a while which day should be our sixth day. BEAM 7 runs on a Tuesday-Saturday academic schedule (adopted from Canada/USA Mathcamp), with field trips on Sunday and Monday. The advantage of Monday trips is that you can visit when places are almost entirely empty. However, such a schedule might cause significant confusion among students and families, and the subway has unpredictable problems on weekends that could interfere with students’ on-time arrivals. So, in another compromise, classes will run Monday-Friday, with activities on Saturday. We might reconsider this in future years when we have more capacity to deal with any unexpected challenges an unusual schedule causes.

Program-long Schedule

We have five courses planned: Logical Reasoning, Applied Math, Math Foundations, Math Team Strategies, and Exploring Math. We cannot possibly offer all four in the same day. With lunch, two activities, and study hall, we simply run out of hours.  (Study hall is very important to me, because it gives students time to reflect on their work and instills study habits.)

The first decision I made was that “Exploring Math” can naturally be simply “Afternoon Math Circle”. The last thing in the day, it’s a fun piece of math, different every day, taught by different people. We can also use the time for guest speakers talking about how they use math in their work. Regardless, this will be in the final block, 2:40pm-3:40pm.

For the rest of the courses… well, let’s consider two different options.

Plan #1: Two two-week sessions

The four other courses naturally break up into two groups of two, so we can have 2 two-week sessions. Students would focus on one pair of courses during each two-week session.

Applied Math with Math Foundations. I paired these because Applied Math will likely be the most intrinsically exciting course, and Math Foundations the least exciting. Applied Math needs as much time as it can get: if students are to become independent in programming, then they need to do lots of programming. Hence, while Applied Math can expect to give 1-1.5 hours of homework per day (depending on the day – see below), Math Foundations should give no more than 15-30 minutes per day. Math Foundations is not designed to drill students in procedures, but rather to encourage creative solutions to problems, so it is all right to give less homework.

Logical Reasoning with Math Team Strategies. Math Team Strategies would get the bulk of the homework time, because we want students to become acclimated to using online resources such as Alcumus and the Art of Problem Solving forums.  These classes are both in the middle in terms of intrinsic excitement, so they pair well together.  Additionally, by putting Math Foundations and Math Team Strategies in different sessions, we know that students are always getting something related to math they’ve learned in school.

Plan #2: Odd/Even Days

There is another way to divide the courses. Instead of two groups of two, they could alternate days. One day is Applied Math and Math Foundations courses; the next day is Logical Reasoning and Math Team Strategies. In this plan, all courses run the full four weeks, but every-other-day.

Pros, Cons, and Choosing a Schedule

With Plan #1 (2 two-week sessions), it is easier to find faculty (who can now teach for just two weeks) and students can focus on specific topics as they go along.  Moreover, by studying the same thing each day, teachers don’t have to spend as much time reviewing at the start of class.

On the other hand, with Plan #2 (alternating days), students get more practice balancing competing demands on their time with homework assignments. Moreover, their ultimate recall is stronger because they spend a longer time actively engaged with each topic.  Finally, it makes things more uniform.  For example, suppose that in Plan #1, someone is teaching Math Team Strategies.  For the first two weeks, their students are new to the program and haven’t taken our Math Foundations course yet, so they will struggle.  But when the course is repeated for different students in the latter two weeks, all of those students have had Math Foundations.  If we use Plan #2, this goes away.

After talking with my colleagues, we settled on Plan #2.  We feel that it is a better educational experience for the students.  While finding faculty may be harder, it is worth it for a stronger program.

Daily Schedule

At BEAM 7, the courses provide no homework. Students do all their work in class, with attention from the instructor. This allows for a fast-paced, highly-interactive environment. However, there are disadvantages as well. It doesn’t train students to budget their own time and develop independent work skills. Moreover, it doesn’t fit well with part-time faculty for a day program. At BEAM 6, we’ll have shorter classes and time for students to do work.

My first draft of the schedule came out like this:

8:15am-8:30am: Breakfast
8:30am-9:30am: Class
9:35am-10:35am: Class
10:40am-11:40am: Activity
11:45pm-12:15pm: Lunch
12:20pm-1:30pm: Study Hall
1:35pm-2:35pm: Activity
2:40pm-3:40pm: Afternoon Math Circle

Lunch can be short, because we will almost certainly get catered boxed lunches that students can grab and eat. Since it is right after activity, it still provides a good break from their classes. If we had just one more hour, I could fit two hours of class/study hall/whatever between lunch and activity, but with avoiding rush hour we just don’t have that time.

However, after reflecting on this schedule, I want more time for study hall. Especially for the programming course, there just isn’t much time for student independent work. Currently students would have a total of 20 hours of work on programming (10 with the instructor and 10 in study hall); more time would be a huge asset. Moreover, having 20 Afternoon Math Circle sessions, while delightful, is not really necessary. Hence, on some days we can replace Afternoon Math Circle with a second Study Hall time. In the end, I decided that Monday, Tuesday, and Friday will have Math Circle (good way to end the week!), while Wednesday and Thursday will have extra Study Hall, allowing students to work on projects or longer assignments later in the week when they are in the thick of things.

This is all very complicated.  Now we have odd/even days determine which of the four long-running classes are happening, while days of the week determine if Math Circle is happening.  I think these are all the right decisions, but we will need clear messaging to make it work and make sure that students feel comfortable with their schedule.

Other Times

There are, of course, a whole wealth of other details.  For example, at what point do students select their courses?  Should they do so on the first day of the program (which eats up class time), or in some earlier orientation?  Right now, my plan is to schedule an orientation for students and families before the first day to talk about the program and how it will work, and to include course selection there.  Unfortunately, some students will miss that event, and we will have to give them another time for course selection.

We must also schedule Saturday trips.  We are thinking about movies, or a trip to the Bronx Zoo, or similar events.  These will each have their own schedule based on what we are doing.

We may also want some sort of closing ceremonies with parents.  Again that will require separate scheduling.  Most likely, we will go for Friday night after the program is done, and provide some sort of food.

Finally, we must have training/setup and wrap-up/take-down with staff.  I am planning the Friday before the program for the former (full-day for counselors, half-day for faculty) and the Saturday after the program for the latter.

I’m sure there are other details that we will think of as we go along.

Wrapping Up

Things fit.  They don’t fit as much as I want; the day feels too short to me, making it hard to really bond with everyone as much and get as involved in the classes.  I am worried that we won’t be able to instill in students the habits we want them to have for their educations.  But this is an iterative development process.  We will run a great program, and then make it even better for next year.

Despite any shortcomings in our available time, this will be a tremendous experience for students.  It will open up so many educational pathways.  Seeing a concrete schedule really gets me excited for the summer!

BEAM 6: Designing a Curriculum

This is part of a sequence of posts developing a new project for Bridge to Enter Advanced Mathematics called BEAM 6.  BEAM 6 will be a non-residential, four-week summer program for underserved 6th grade students in New York City.  You can find the other posts about its design here.

 

At BEAM 7 (a program many BEAM 6 students will attend the summer after 7th grade), we tend to throw students off the deep end when it comes to doing math.  I mean it: they come in and we teach them about proofs, and we have them solving MATHCOUNTS problems, and we have them learning number theory and combinatorics and even group theory… and a lot of them are kind-of still weak on fractions, y’know?

It varies by school, of course.  Not surprisingly, some schools tend to give us more prepared students, while others don’t.  BEAM 7 has had seventh graders (top of their class at school!) who were not comfortable multiplying negative numbers.

I’ve been asking myself what I wish our BEAM 7 students knew.  They’re held back constantly by foundational math knowledge.  They also need to learn how to look at a problem and focus on what it’s asking, rather than guessing at a solution mechanism.  Finally, I want them to have more skills in deductive reasoning and case analysis.  It’s a little bit crazy to be thrown into a proofs class without that!

In the end, there are five course tracks that I really want to work into the program.

• Logic
• Math Foundations
• Math Team Training
• Applied Math
• Seminars

I want students to have choice, so each of these topic areas will have different courses within it.  During their summer, each student will take on course from each track.  The exception will be Seminars, where each will be independent (see below).

It’s a minor nightmare to fit all of these classes into a four-week program.  Right now, the best I can do is 10 hours of class time each, plus some homework time depending on the course.  So they have to be compact and get to the punch quite quickly.  Scheduling will be covered in detail in a future post, but lack of time is a huge concern.

Before I get to describing the course tracks, readers who know about BEAM 7’s courses will see right away that this is super different.  BEAM 7 is basically a playground for our faculty to develop all kinds of interesting math courses and then teach them.  These courses are much more structured and targeted.  Why?

The primary reason is simple: BEAM 6 has a very different goal.  BEAM 6’s main goal is to remedy specific gaps that students need to succeed both in BEAM 7 and in their future mathematical studies.  In contract, BEAM 7’s goal is to transition students to other programs for advanced study where they will have to do more abstract thinking.  Hence, BEAM 7 invites faculty to rock out in courses similar to what students will do at future programs.  In contrast, BEAM 6 is a laser aimed at skills and knowledge that students need.  BEAM 6 courses will be lots of fun, but they’ll also have much more concrete goals.

There are advantages and disadvantages to both approaches.  One big advantage of BEAM 6 is that I can develop a strong curriculum for students.  A second advantage is that it opens our program up to more potential instructors, because they do not need the same experience designing enrichment classes.  However, BEAM 6 is still open to those who want to create their own crazy classes through both the Seminars and Applied Math topic areas.

Great!  Let’s figure out what’s actually in the courses.

BEAM 6: Goals

This is part of a sequence of posts developing a new project for Bridge to Enter Advanced Mathematics called BEAM 6.  BEAM 6 will be a non-residential, four-week summer program for underserved 6th grade students in New York City.  You can find the other posts about its design here.

In about seven months, there will be 100 sixth-grade students all ready to learn math.  Almost exclusively, their mathematics educations so far will be designed around memorizing procedures and passing tests.  We have four weeks to change their lives.  What should we do?

No pressure or anything.

It’s rare in education to get an opportunity to work with motivated, talented students with no outside requirements.  We can design the program that is best for them.  This is the first post developing BEAM 6, and so we will set down the program goals.

Goal: Teach Them to Think Deeply

If students leave the program and they have not learned about logical reasoning, I will feel exceptionally disappointed.  I want students to grasp ideas of deductive reasoning.  This might be my single biggest goal.

I also want to change the way they think about mathematics.  For many students, math problems are defined by the solution method.  “Oh, this is an addition problem.”  “Oh, this is a related rates problem.”  “Oh, this is a Pythagorean theorem problem.”  This thinking leads to oversimplification and memorizing procedures.  It makes it more difficult to solve multi-step problems.  Students should engage with the question, understand the problem independent of its solution, and accept or reject solution paths because they do or don’t solve the problem.

This leads to the broader question of mathematical communication.  For example, the equals sign.  Students often interpret the equals sign as asking a question.  In elementary school, it is always used as “2 + 5 = ?”.  By algebra, the question changes — “2x – 3 = 15” means “solve for x” — but the equals sign is still primarily used to express a question.  Students don’t realize that “25 + 7 = 32” is a statement that can be true or false; that the purpose of = is not to ask a question but rather to give a statement.  The result is a failure of both communication and conceptualization.

These goals are less mathematically sophisticated than BEAM 7’s goals.  This is in part because the students are younger.  It’s also to build synergy with BEAM 7.  Students often come out of BEAM 7 with a strong grounding in abstract mathematics but still well behind peers in school-based math.  For example, students often do well taking a number theory course at CTY or going to a program like MathPath, but do relatively poorly in a contest like MATHCOUNTS.  BEAM 6 can close that gap and set students on a path to deepening their facility with school-based math.

Goal: Help Them Love Math

People love math because it is beautiful; because it is thrilling to challenge yourself with a hard problem that you finally solve; and because it is interesting to see how it applies to the real world.  We must show students what math really is.  That it is not about memorization or following procedures.  That it is beautiful and creative and exciting.  A love of math will carry you far, and we should develop it in the students.

Goal: Develop Their Self-Identities

In my experience, self-identity drives a lot about a person.  More than just thinking something is “cool,” self-identity can push someone to pursue an interest; it can create resilience to failure; it can drive life decisions.  If we can develop self-identities in our students as scholars, and furthermore as scientists and mathematicians, they are much more likely to succeed on that path.

What contributes to developing self-identity?  Here are some thoughts:

• Interest/passion for a topic.
• A feeling of self-efficacy; confidence in your abilities.
• Membership in a distinctive community.
• Role models.
• A sense of future (where will it take you?).

We should harness all of these within the program.  We have special expertise in creating a mathematical community.  To drive students’ further engagement, creating a very strong community will be essential.

Goal: Develop Independent Learners

A summer program cannot alone cover the mathematical education of all these students.  If they will be successful, they must continue to pursue learning after the summer is done.

Students should be connected with resources for further study, such as Art of Problem Solving.  They should get used to these tools during the summer and be encouraged to continue using them when they’re done so that they continue to get better.

Concluding Thoughts

These goals feel right.  They cover what I feel is very important to develop in young mathematicians.  However, they are not complete.  While program elements will be tied into these goals, as the program development continues we will also find new goals that we want to achieve.  These will be included below as updates to this post.