Teaching Mathematics as One of the Humanities was a master class offered to you by Paideia Academics in July of 2021 and taught by William Carey. This version is online and offered to you at your own pace. At the end of this course, you will have grown in confidence in your ability to explore and enjoy mathematical ideas with yourself and with your students. You will have access to a canon of great mathematical works that illuminate truths in mathematics elegantly and clearly. Most importantly, if you’re “not a math person,” you just might decide that there’s something worth loving in mathematics. If you already love mathematics, you’ll cultivate that love with practical examples of how to uncover mathematical truths for yourself and for others. What you’ll get immediately:
- 9 Recorded – Immersive Sessions
- 9 Mathematics-centered Classical Readings
- Watch other teachers work through the Math with William in real-time.
- List of Classical Mathematics Resources & Further Reading
Curriculum
- 10 Sections
- 11 Lessons
- Lifetime
- Video Preview1
- Session One: IntroductionDuring this session, we will talk about the cultural expectations surrounding mathematics and how they shape the learning experience. We’ll introduce ourselves and share what our own mathematical journeys have been like (the good, the bad, and the ugly, often), and reframe the culture of mathematics into something that supports human flourishing.1
- Session Two – Mathematics as Truth PerceptionDuring this session we will examine a problem in solid geometry that illuminates mathematics as an activity of truth perception, contrasting that with the sisyphean grind that often characterizes modern mathematical teaching. We’ll build a shared liturgy of mathematical work that is collaborative and restful.1
- Session Three – The Teacher as Mentor: Mathematical DiscussionDuring this Session we’ll talk about how to host a good mathematical discussion for students (and ourselves!). We’ll focus on establishing norms of charity and valuing the different contributions students can make to a discussion. We’ll think about how to respond to the needs of different students in conversation and how to lead a mathematical discussion with only a single teacher and student.1
- Session Four – Open Q/AQuestion and answer time with the instructor.1
- Session Five – Teacher as Host: ArithmeticIn this session, we’ll introduce one of the two classical mathematical traditions: arithmetic. Arithmetic is the study of the discrete (as opposed to the continuous). We’ll work through some of the foundational material in Euclid and Nicomachus and compare it with the presentation of similar material in a modern curriculum.1
- Session Six – Teacher as Host: GeometryIn this session, we’ll explore the other tradition of classical mathematics: geometry. We’ll look in particular at how the relationship between arithmetic and geometry gave birth to algebra.1
- Session Seven – Teacher as Coach: Managing Table Stakes & the KairosMathematics is shaped more by kairos – ripeness – than by chronos – chronological time. During this session we’ll explore how to assess a text and place it in a curriculum at the right time. We’ll look at how intentional practice (instead of disjointed homework) can support the liturgy and culture we’ve explored so far.1
- Session Eight – Teacher as Philosopher: Reading Modern Mathematics, Tools for UnderstandingWhat does it look like to explore mathematics together? This session will focus on how to engage with an unfamiliar text with students. There’s great value in modeling being an inquisitive mathematician (both for students and teachers!). What does it look like to approach a problem no one in the room knows how to solve with students? We’ll practice building curiosity and humility as we explore a text together.1
- Session Nine – Harmony in the Mathematics Classroom & Next StepsIn our final session together we’ll talk about how to bring the ideas and techniques of this master class into our teaching practice. We’ll talk about what’s happening in the classical mathematical community, and how each of us can be a part of that renewal.2
Instructor
William Carey is a classicist and a mathematician. He has taught at a classical high school since 2003 with a short sabbatical to work as a practicing mathematician and cartographer.
He has taught Latin, Logic, Rhetoric, Physics, Chemistry, Computer Science, and Mathematics from 7th to 12th grade. He’s also taught classics at the university level.
Formally trained as a classicist and self taught as a mathematician, he’s currently pursuing advanced study in mathematics while working with a group of likeminded friends and scholars to recover the Quadrivial arts, particularly arithmetic and geometry, for primary and secondary education.
William has written articles and given talks on the theme of mathematics as one of the humanities, arguing that everyone is a “math person”, and that a vibrant relationship with mathematics is part of what makes us fully human, just like a vibrant relationship with literature!
Read his blog series on the Classical Mathematical Canon on CiRCE https://circeinstitute.org/blog/author/williamcarey/
