# Teaching Math Classically

with Andrew Elizalde and Bill Carey## Welcome!

In this course, veteran math educators and classical school academic leaders Andrew Elizalde and Bill Carey describe the way mathematics should be recovered and renewed as a liberal art and therefore as a humanities subject. Andrew not only traces the history of mathematics education, but also notes how it slowly deteriorated in America. Most importantly, Andrew shows how mathematics can be taught effectively using traditional, classical pedagogies that should engross and delight most students. Andrew advocates teaching math as something beyond a mere utilitarian skill, but rather as a way of understanding the world.

Questions addressed in this course include:

- Why should mathematics be regarded as a humanities art?
- What were the distinctive principles and practices of a classical mathematics curriculum?
- What went wrong in American mathematics education?
- What are the practical ways that one teaches math classically?
- What are the advantages and challenges of using the Singapore method of teaching math?

This course follows the organizational theme that begins with the history of math, its modern deterioration, and its recent renewal as a classical liberal art.

- The History of Math and Math Pedagogy
- The Deterioration of Math Instruction in the U.S.
- Attempts at Reforming Math Instruction
- Classical Mathematics: Art and Pedagogy
- Questions and Answers with Andrew Elizalde
- The Recent Renewal of a Classical Approach to Teaching Math

There are modest reading assignments associated with each video lecture. These will be listed in each session, along with additional resources, recommended readings, and questions for discussion and reflection.

**Andrew Elizalde** earned his BA at Depauw University in Indiana, where he graduated Phi Beta Kappa and magna cum laude, earned a math major, physics minor, and religious studies minor, and received the H.E.H. Greenleaf Award as the most outstanding 2001 graduate of the school’s mathematics program. He later obtained a teaching credential from California State University Long Beach with a *professional-clear* qualification for his coursework regarding exceptional children and technology integration. His teaching experience includes work in both public and private schools in subjects ranging from 5th-grade mathematics to advanced calculus and physics. His past work in classical education has most notably included reforming mathematics programs and building professional learning communities through meaningful professional development. Andrew is glad to now be serving Covenant Classical School in Fort Worth, TX, as the dean of academics. Additionally, Andrew also offers consulting services to classical Christian schools and has been a keynote speaker at both the ICS Math and Science Lyceum and SCL annual conferences. Andrew and his wife, Brooke, have three daughters and attend Fort Worth Presbyterian Church.

**Bill Carey** has been involved in the life of Ad Fontes Academy in Centreville, VA, since he was in high school. He assisted his father at the weekly Latin Club and took Ad Fontes students to many *certamina* and conventions. At the University of Virginia he studied the classics, focusing on Latin. Fresh from college, he joined the Ad Fontes faculty, where he taught Latin, calculus, formal logic, physics, and (for a few months) senior thesis. After five years of teaching, Bill took a sabbatical writing computer programs for a defense contractor to better understand how adults think about and use mathematics. Always drawn to the classroom, he went on to teach a year of physics and classics courses at George Mason and now runs the Techne Society. After seven years he gladly rejoined the full-time faculty at Ad Fontes to teach math and science. Bill is married to Maren Carey, also a teacher, and they both worship at Lord of Life Lutheran Church in Fairfax and Clifton.

## Lessons

## Introduction: How to Teach Mathematics Well (Free Lesson)

## Lesson 1: The State of Math Education in America (Free Lesson)

## Lesson 2: How to Improve Math Education in the U.S.

## Lesson 3: The Trivium and Mathematics Education

## Lesson 4: The Grammar of Mathematics

## Lesson 5: Mathematics, Memory, and Retained Learning

## Lesson 6: Cultivating a Reflective and Collaborative Faculty

## Lesson 7: Strategies for Reforming a Math Program

## Lesson 8: Teaching Math with Socratic Dialogue—Part 1

## Lesson 9: Teaching Math with Socratic Dialogue—Part 2

## Lesson 10: Rhetoric in the Mathematics Classroom

## Lesson 11: Taking a Liturgical Audit

## Lesson 12: Constructing Mathematical Arguments

## Lesson 13: Mathematical Proofs Students Should Know

## Lesson 14: The Beauty of Math and Poetic Instruction

## Lesson 15: Teaching Math as Storytelling

## Lesson 16: 14 Essential Elements for Teaching Math

## Lesson 17: Mathamatics as a Humanities Subject

## Interview: Andrew Elizalde on Math Education

## Interview: Andrew Elizalde on How He Became Interested in Mathematics

## Interview: Andrew Elizalde on His Journey into Classical Education

## Interview: Bill Carey on Teaching Math Classically

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