# About Math Fundamentals

Welcome! We're excited that you are interested in teaching Math Fundamentals at BEAM 6.

## Why Math Fundamentals?

Over the years we've run BEAM 7, our program for students who have just finished seventh grade, we've found that certain basic skills are consistently missing from even the strongest students at many of our partner schools. Those gaps have consistently prevented some students from pursuing more advanced work. Math Fundamentals is designed to fill in key gaps so that students can attend BEAM 7 more prepared.

In particular, students' backgrounds are often centered around procedural fluency, and as a result students can do only the specific types of problems they are used to. Math Fundamentals is a chance to break free of that, by exploring topics in mathematics and doing novel problems that require students to reflect on their knowledge.

At BEAM 7, we developed "modules", designed to help students break free of procedural thinking. You may use problems from our modules (they provide a ready bank of problems) or you may develop your own. (However, beware that modules contain very few basic problems to build student knowledge, and you may need to supplement them.)

## Different Classes

Students will be placed into a Math Fundamentals course by considering both a pre-program assessment and their own preferences for what skills they want to strengthen.

Perhaps the biggest gap our students face is in their knowledge of fractions. Hence, any student whose fractions knowledge is weak will focus on that topic. We are likely to have a "basic fractions" course, for students who lack procedural fluency with fractions (for example, those who have not mastered adding fractions).

For students whose grasp of fractions is strong, there are several other possible Math Fundamentals courses for them to take. For example, here are some potential courses with links to modules we have used at BEAM 7:

- Fractions (but more advanced and conceptual) [sample problems 1, sample problems 2]
- The Distributive Property and Mental Math Tricks [sample problems]
- Exponents [sample problems]
- Introductory Geometry. [There are currently no geometry-based modules. If you would like to teach geometry, you will need to develop all of the problems for the course.]

The first part of every Math Fundamentals course will focus on common difficulties that students face. Most notably, we want to give students a proper introduction to the meaning of the = sign.

## DETAILed Overview

There are two key aspects to the Math Fundamentals course: the *skills* students get in interpreting mathematics, understanding definitions, and processing how subjects should connect to one-another; and the *knowledge* they gain in whatever topic they are studying. It is our hope that the course will help students in both ways. There is no way you can possibly cover all of the topics we want students to know, but you can model for them how they should be learning through a deep exploration of one topic.

In addition to the modules we've used at BEAM 7, we have copies of the Art of Problem Solving's *Prealgebra* book, which can provide additional problems. The questions in our modules are relatively sophisticated, and you may need some scaffolding to get to them, including more basic questions or some time to teach students directly. You may also want to include more motivation or applications for students. Ultimately, the course is yours to direct. You will have the flexibility (and responsibility) for developing your day-to-day lesson plans, selecting problems, and creating handouts.

## An Important Note

Math Fundamentals is, in some sense, the course that is most in danger of "feeling like school". Although it is the closest to covering school topics, it is very important that students treat this course as an exploration of interesting problems. They should be constantly challenged and enjoying the greater depth of knowledge they are gaining about math that they thought they knew.

## Ready to Apply?

Our applications all involve giving a course description about how you would teach your course. For the Math Fundamentals course, please include:

- Within whatever topic you have chosen (fractions, exponents, distributive property, geometry, etc.), what do you expect would give students trouble? How would you help students overcome that difficulty?
- A short description of how your classroom would lead students through a particular math problem, for example in the modules above.

In addition, we ask that you send us a copy of your CV or resume, or a short summary of your education and work experience. (In particular, please don't spend hours polishing your CV on our account if you do not have one ready!)

Once we have received your application, our hiring committee will review it and then get back to schedule an interview if we feel you're a good fit.

Ready to apply? Want to preview the application? Please click the button below!