Teaching Math Classically
with Andrew Elizalde and Bill CareyWelcome!
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?
Instructional Hours: 12.17, CEU Credits: 1
- The History of Math and Math Pedagogy
- The Deterioration of Math Instruction in the US
- 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.

Bill Carey has been involved in the life of Ad Fontes Academy in Centreville, Virginia, 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.
To obtain a certification credit for this course, simply complete each presentation lesson or discussion in the course (by marking it complete or by taking the quiz) and then also take the certification test at the end of the course. The quizzes are designed to ensure that you have understood the essential content of each presentation, and they can be taken more than once if necessary. The cumulative certification test at the end of the course is given as a pass/fail test and requires that you upload one or more essays demonstrating your understanding of the course. (Please note that essays are simply evaluated by word count.) When you have completed the course, a certificate that you can print or email will become available within “My Courses” (accessible under “Courses” in the main menu when you are signed in as an active subscriber).
We recommend previewing the essay question within the end of course test before starting the course. This will help in guiding your note taking as you progress through the course. Please allow approximately 2 weeks for essay submissions to be reviewed.
Lessons

Teaching Math Classically—Introduction: How to Teach Mathematics Well
Preview
Lesson 1: The State of Math Education in America
Preview
Lesson 2: How to Improve Math Education in the US
Lesson 2: How to Improve Math Education in the US Please sign up for the course before starting the lesson.

Lesson 3: The Trivium and Mathematics Education
Lesson 3: The Trivium and Mathematics Education Please sign up for the course before starting the lesson.

Lesson 4: The Grammar of Mathematics
Lesson 4: The Grammar of Mathematics Please sign up for the course before starting the lesson.

Lesson 5: Mathematics, Memory, and Retained Learning
Lesson 5: Mathematics, Memory, and Retained Learning Please sign up for the course before starting the lesson.

Lesson 6: Cultivating a Reflective and Collaborative Faculty
Lesson 6: Cultivating a Reflective and Collaborative Faculty Please sign up for the course before starting the lesson.

Lesson 7: Strategies for Reforming a Math Program
Lesson 7: Strategies for Reforming a Math Program Please sign up for the course before starting the lesson.

Lesson 8: Teaching Math with Socratic Dialogue—Part 1
Lesson 8: Teaching Math with Socratic Dialogue—Part 1 Please sign up for the course before starting the lesson.

Lesson 9: Teaching Math with Socratic Dialogue—Part 2
Lesson 9: Teaching Math with Socratic Dialogue—Part 2 Please sign up for the course before starting the lesson.

Lesson 10: Rhetoric in the Mathematics Classroom
Lesson 10: Rhetoric in the Mathematics Classroom Please sign up for the course before starting the lesson.

Lesson 11: Taking a Liturgical Audit
Lesson 11: Taking a Liturgical Audit Please sign up for the course before starting the lesson.

Lesson 12: Constructing Mathematical Arguments
Lesson 12: Constructing Mathematical Arguments Please sign up for the course before starting the lesson.

Lesson 13: Mathematical Proofs Students Should Know
Lesson 13: Mathematical Proofs Students Should Know Please sign up for the course before starting the lesson.

Lesson 14: The Beauty of Math and Poetic Instruction
Lesson 14: The Beauty of Math and Poetic Instruction Please sign up for the course before starting the lesson.

Lesson 15: Teaching Math as Storytelling
Lesson 15: Teaching Math as Storytelling Please sign up for the course before starting the lesson.

Lesson 16: Essential Elements for Teaching Math
Lesson 16: Essential Elements for Teaching Math Please sign up for the course before starting the lesson.

Lesson 17: Mathematics as a Humanities Subject
Lesson 17: Mathematics as a Humanities Subject Please sign up for the course before starting the lesson.

Interview: Andrew Elizalde on Math Education
Interview: Andrew Elizalde on Math Education Please sign up for the course before starting the lesson.

Interview: Andrew Elizalde on How He Became Interested in Mathematics
Interview: Andrew Elizalde on How He Became Interested in Mathematics Please sign up for the course before starting the lesson.

Interview: Andrew Elizalde on His Journey into Classical Education
Interview: Andrew Elizalde on His Journey into Classical Education Please sign up for the course before starting the lesson.

Interview: Bill Carey on Teaching Math Classically
Interview: Bill Carey on Teaching Math Classically Please sign up for the course before starting the lesson.

End of Course Test: Teaching Math Classically
End of Course Test: Teaching Math Classically Please sign up for the course before starting the lesson.