*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.