EPIC | Curriculum

"If you wish to build a ship, don't drum up people to collect wood and don't assign them
tasks and work, but rather teach them to long for the endless immensity of the sea."
-Antoine de Saint-Exupéry







Overview


Our Academic Goal

To foster creativity

We want to get kids excited about learning. We think the best way to foster this excitement is to share beautiful ideas with our kids and then to practice creativity, giving students problems along with the autonomy to find new directions for solving them. Our approach to learning aims to help students let go of motivation based on fear and the need for status, and instead to develop motivation based on possibility, self-expression, and the desire to create. In a country where children are growing up surrounded by violence and trauma, engaging kids' minds creates opportunities for healing centered engagement.



Our Curriculum | Teams

We approach learning as a team effort

We approach math with problem solving, teamwork, and near-peer mentoring. We start by giving students problems to solve. While each student must ultimately see for themselves how to approach a given topic, we support each other in the process of solving problems. Teams of middle school students work together, with high school students serving as paid mentors who work closely with their students. College students lead teams of students, tracking students' progress and working with mentors to create an individualized curriculum for each student. While we do have brief lectures, the emphasis is placed on students engaging with the material and learning how to think logically to solve the problems they face.


Our Curriculum | Inspiration

We try to inspire our students

We agree with Albert Einstein that "The most valuable thing a teacher can impart to children is not knowledge and understanding per se but a longing for knowledge and understanding, and an appreciation for intellectual values, whether they be artistic, scientific, or moral. It is the supreme art of the teacher to awaken joy in creative expression and knowledge." We try to awaken joy in our students by sharing mathematical beauty with them. This means that we don't just teach our 7th graders a course concerned with comparing fractions, but we also teach them a course on adding an infinite number of fractions, using these infinite series to explore the beauty of ideas like partial sums and limits. Playing with ideas and experiencing the pleasure of finding things out are the basis for our camp, just as painting would be for an art camp or shooting would be for a basketball camp.



Courses

Standard Curriculum

Discovery Math




7th Grade

The Real Numbers

Intro to Calculus

We begin by introducing students to the Real Numbers, with a focus on the expansion from the Natural and Whole Numbers to the Rational Numbers. We emphasize that fractions are numbers, and we use number lines as a central tool in teaching how fractions expand the number system, as well as other concepts like ordering (ie, comparing fractions). We always try to follow best practices as informed by research and mathematicians.

We reinforce concepts and provide inspiration for students to learn about fractions by also teaching students a course on infinite series that introduces students to concepts in integral calculus. We explore ideas like: What is an infinite sum? What is a limit and what does it mean for a sequence to converge? Can an infinite sum have a finite limit? What idea(s) might help us find the limit of an infinite sum? Can we find common patterns in different infinite sums?



8th Grade

Operations on the Real Numbers

Instructor's Choice

We continue our study of the real numbers, now with a focus on the operations of addition and multiplication. We establish the idea of an identity for each operation, and introduce the commutative and associative properties of each operation. We explore ideas related to exponents and engage in practice arithmetic problems to solidify these ideas.

Our 8th grade Discovery course is open to the instructor's choice, with the goal being for the instructor to share their passion for a subject with the students. Some examples of courses include a study of fractals that explores ideas like the Coastline Paradox, the Cantor Set, and Cantor Dust; a course on social choice that explores ideas like voting rules, Condorcet's Paradox, and Arrow's Impossibility Theorem; and a course on statistics that explores ideas around theories, prediction, sampling, and the law of large numbers.


9th Grade

Applications with Real Numbers I

Geometry

We provide students with examples of how using the operations on the Real Numbers can solve real world applications. We focus on equations and inequalities, begining with word problems and finishing by posing open-ended questions to our students.

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

Functions

Proofs I

We introduce students to functions as a subset of the Cartesian plane and define specific functions using their domain, range, and rule. We examine the graphs of functions and, focusing on linear and polynomial functions, explore properties of functions and how they can be used in applications. We informally introduce ideas related to inequalities and linear algebra.

In our introductory proof class we try to avoid asking our kids to follow directions. We ask our kids open-ended questions and give them full autonomy to find new directions for solving these problems. We aim to provide our students experience with the intellectual struggle and the ultimate joy of figuring something out. Emphasis is again placed on students making sound arguments. This course will vary from teacher to teacher, but will typically be based on the first half of Paul Lockhart's Measurement.



11th Grade

Applications II

Proofs II

In our continuation of applications, we now incorporate ideas from our study of functions and geometry alongside the operations on the Real Numbers. We solve word problems and now pose open-ended questions like: How tall is this pyramid? We informally explore ideas from physics and calculus.

Our proof class continues, focusing on the remaining material in Paul Lockhart's Measurement.


12th Grade

Calculus

Set Theory

We formalize the ideas from calculus that students were introduced to in their 7th grade Discovery course and their 11th grade Applications course. An emphasis is placed on giving students a deep understanding of the big ideas.

The crown jewel of the Epic curriculum is a course on transfinite set theory. In this course students explore ideas related to the cardinality of infinite sets, with some goals being for students to struggle a bit with the Continuum Hypothesis and to write a version of Cantor's diagonalization proof for themselves.