Academics

Our Curriculum

Bread & Roses

Our curriculum is split into Bread and Roses. We want to give our students the basics that they need to survive. But we also want them to do more than just survive.

Flexibility of Mind

Richard Feynman’s Vision

As described by the great physicist Richard Feynman, we see our subject less specifically in terms of math and more generally in terms of developing habits of mind: “What we have been doing in the past is teaching just one fixed way to do arithmetic problems, instead of teaching flexibility of mind — the various possible ways of writing down a problem, the possible ways of thinking about it, and the possible ways of getting at the problem.”

Teamwork

Problem Solving Together

We approach math with problem solving, teamwork, and near-peer mentoring. While each student must ultimately see for themselves how to approach a given topic, we support each other in the process. Teams of middle school students work together, with high school students serving as paid mentors who work closely with their students.

Bread Curriculum

The Essentials

The goal of the Bread curriculum is to ensure that our students:

• Are numerate and proficient in algebra by the end of middle school, and;
• Are exposed to the intuition, formal theory, and applications of calculus while in high school.

These courses follow the textbook Math As Flexibility of Mind, written by The Math Movement’s Director Dionissi Aliprantis.

Roses Curriculum

Mathematical Beauty

The goal of the Roses curriculum is to expose our students to beautiful math.

Course offerings tend to be idiosyncratic and driven by the passions of a given summer camp’s instructors.

Roses courses are more open-ended, but always approach material with a team attitude.

7th Grade — Bread

Ordering and Operations

We begin with the idea of ordering objects, discussing arbitrary sets and leaning on the number line to look at the ordering of natural numbers, integers, and rationals. We introduce multiplication to allow ordering fractions, and study how to multiply fractions and get common denominators.

7th Grade — Roses

Infinite Series

We reinforce concepts by teaching students a course on infinite series that introduces ideas in integral calculus. We explore: What is an infinite sum? What is a limit? Can an infinite sum have a finite limit? What idea(s) might help us find the limit of an infinite sum?

8th Grade — Bread

Operations and Equations

We introduce the operation of addition and study adding and simplifying fractions. Then we turn toward solving equations using the additive and multiplicative inverses, along with the order of operations. We conclude with translating words into equations and solving inequalities.

8th Grade — Roses

Statistical Decision Theory

We discuss how to make predictions about uncertain outcomes, starting with flipping a coin. This leads to discussions about statistical statements about samples we have observed and experiments yet to be realized. We conclude with a look at how statistics can play a role in our decision making.

9th Grade — Bread

Functions

We introduce students to functions as a subset of the Cartesian plane and define specific functions using their domain, range, and rule. We examine graphs of functions, study conic sections and separating curves, and define a continuous function. We conclude with asymptotes and fixed points.

9th Grade — Roses

Geometry

We take students on a guided tour of Euclid’s Elements. The emphasis is placed on beauty and demonstration. We want our kids to learn how to provide logical arguments for why something is true, and we want them to see the beauty of geometry.

10th Grade — Bread

Introduction to Calculus

We begin by asking the question Archimedes studied thousands of years ago: How do we find the area of a circle? We generalize this to finding the area under a function, introduce the Riemann Integral, then introduce the derivative in terms of describing motion. This course is focused on building intuition.

10th Grade — Roses

Graph Theory

We define what a graph is and then let the students do their own research on a pursuit-evasion game with a chaser and a runner. We also discuss other topics including coloring planar graphs.

11th Grade — Bread

Applications of Calculus

We give students a taste of how calculus is often used in applications. We start with introductory statistics, build from frequency distributions to Probability Mass Functions, introduce the Cumulative Distribution Function as an integral, use these ideas to look at data including income inequality, and conclude with numerical optimization.

11th Grade — Roses

Game Theory

We define choice sets and strategies and search for optimal strategies in several games. We consider winning strategies via planning ahead in a “Stones” game and consider isomorphisms between a “Sum to 15” card game and Tic-Tac-Toe. We introduce students to the idea of equilibrium strategies and Nash equilibrium.

12th Grade — Bread

Calculus

We begin with an overview of the Fundamental Theorem of Calculus. We derive rules for computing derivatives and integrals and practice applying those rules. We study sum, product, power, and chain rules, and conclude with a look at convex sets and how derivatives can be used to understand optimization.

12th Grade — Roses

Set Theory

The crown jewel of our curriculum is a course on transfinite set theory. Students explore ideas related to the cardinality of infinite sets, with goals including struggling with the Continuum Hypothesis and writing a version of Cantor’s diagonalization proof for themselves.