Summary

In this episode, Shannon Valenzuela and Peter Ulrickson explore the significance of the Quadrivium in education and Dr. Ulrickson's unique presentation of teaching these arts in his books A Brief Quadrivium and the accompanying teacher's guide. They discuss the interconnectedness of mathematics and the arts and highlight the unique perspectives offered by each discipline. They explore the importance of modeling, proof, and observation and the role of rhetoric and logic in mathematics. The conversation also addresses the sensory engagement in learning and the value of teaching mathematics classically.

Topics Covered:

• The importance of proof and the power of modeling
• The arts of the Quadrivium and their perspectives on cosmic order
• The role of rhetoric and logic in the study of mathematics
• Engaging the senses in the experience of learning mathematics
• The transformation of students' perceptions of mathematics through an encounter with the Quadrivium

Today's Guest:

Peter Ulrickson is a professor of mathematics at the Catholic University of America. In addition to his work on the quadrivium, he publishes original research in various areas of modern mathematics. Professor Ulrickson received his Ph.D. from the University of Notre Dame.

For more information about the books: briefquadrivium.com

Timestamps:

00:00 Introduction
03:28 Introduction to A Brief Quadrivium
04:07 Exploring Music and Astronomy in the Quadrivium
10:01 Proof and Modeling in Mathematics
13:09 Developing the Sense for Order
20:45 Engaging the Senses in Mathematical Inquiry
26:51 The Ordering of the Quadrivial Arts
30:48 Exploring the Teacher's Guide

Resources Mentioned in Today's Episode:

Peter Ulrickson, A Brief Quadrivium (publisher, Amazon) and Teaching the Quadrivium (publisher, Amazon)

"The Quadrivium and the Stakes for Ordering the Mathematical Arts" by Lesley-Anne Dyer Williams

University of Dallas Links:

• Classical Education Master’s Program at the University of Dallas: udallas.edu/classical-ed
• St. Ambrose Center Professional Development for Teachers and Administrators: https://k12classical.udallas.edu/

Support the show

If you enjoyed the show, please leave a rating and review — it helps others find us!

Summary

In this episode, Shannon Valenzuela and Jake Tawney explore the significance of the quadrivium in education, particularly focusing on mathematics as a bridge between the material and the divine and the ability of mathematics to help students access truth. They discuss the eternal nature of language and mathematics, explore music as number in ratio to itself, and consider the importance of proofs in mathematics. The conversation emphasizes the need for pedagogical approaches that prioritize understanding and wonder over mere proficiency, ultimately arguing that the study of mathematics reveals deeper truths about the universe and God.

Topics Covered:

• A different way of understanding the four arts of the quadrivium
• Mathematics as a bridge between the material world and the eternal
• The arts of language and mathematics as foundational to education
• Music and mathematics
• Proofs in mathematics as a form of rhetoric
• The power of lessons that present engaging problems that motivate inquiry
• The study of mathematics and a unique longing in the human soul
• Success measured as love, not just skill proficiency

Today's Guests:

J. Jacob (Jake) Tawney has been enamored by mathematics for as long as he can remember, from kindergarten to calculus. But he truly fell in love with it during his sophomore year at Denison University during a course on mathematical proofs. After completing an undergraduate degree in mathematics and computer science from Denison, he continued his studies at The Ohio State University. There he earned a master’s degree in mathematics, submitting a thesis on the mathematics of juggling. During his time in Ohio, Tawney taught at Upper Arlington High School and the Pontifical College Josephinum, including courses in Euclid and the philosophy of mathematics. In 2014 he relocated his family to Phoenix, Arizona, to join Great Hearts Academies, where he currently serves as the chief academic officer. Jake is the proud husband of Christina and the proud father of eight children, all of whom have something unique in their souls that can only be satisfied by wondering about mathematics.

Timestamps:

00:00 Introduction
03:50 The Eternal and the Earthly: Understanding the Significance of Three and Four
10:34 Music and Mathematics: The Relationship of Ratios and Intervals
14:54 Math's Unique Contribution: Bridging Heaven and Earth
24:48 The Importance of Proof: Rhetoric in Mathematics
33:09 Bridging Theory and Practice in Mathematics Education
39:00 Wonder and Conversation in the Math Classroom
45:14 A Different Way to Measure Success

Resources Mentioned in Today's Episode:

Another Sort of Mathematics by J. Jacob Tawney at Encounter Books and on Amazon

More on the Quadrivium Retrieval: https://quadriviumretrieval.org/

University of Dallas Links:

• Classical Education Master’s Program at the University of Dallas: udallas.edu/classical-ed
• St. Ambrose Center Professional Development for Teachers and Administrators: https://k12classical.udallas.edu/

Support the show

Support the show

If you enjoyed the show, please leave a rating and review — it helps others find us!

Summary

In this episode, Shannon Valenzuela and Dr. Merrill Roberts explore the beauty of the quadrivium for the middle school classroom. They discuss the integration of nature studies, mathematics, and science in middle school education, highlighting the importance of play, joy, and sensory learning. The discussion also delves into the relationship between mathematics and beauty, the role of the imagination in learning, and the interconnectedness of disciplines across the curriculum. The conversation concludes with reflections on the importance of arts and music in education and the profound impact of experiencing the night sky on students' understanding of the universe.

Topics Covered:

• The quadrivium and middle school math and science
• Beauty and wonder in math and science education
• Play and joy as pedagogical tools
• Learning through the senses and working toward abstraction
• The quadrivium across the curriculum
• Arts and music are integral to a classical education
• The power of dark skies

Today's Guests:

Dr. Merrill Roberts received his Bachelor’s in Liberal Arts from Thomas Aquinas College in 2003. He earned his Ph.D. in Physics from The Catholic University of America in 2018, where he has also served as a Lecturer in Physics, teaching multiple courses, including a course in Solar Physics designed for students planning to teach in primary and secondary schools. He worked for over a decade as a researcher at NASA Goddard Space Flight Center in Greenbelt, MD, where he studied solar coronal transients and performed forward modeling for the Parker Solar Probe mission. Dr. Roberts is a Senior Faculty Consultant for the Institute for Catholic Liberal Education (ICLE), giving workshops and developing curriculum centered around the Quadrivial Arts since 2013, and is also an Associate Fellow at the Boethius Institute, helping with the creative retrieval of the Quadrivium. He combines his passions for nature and education as the Nature Studies teacher at St. Jerome Academy in Hyattsville, MD, where he has instructed 5th through 8th graders since 2010. He is also, along with his wife Elizabeth, the Co-director of Music at St. Jerome Parish, where he strives to emphasize the beauty and truth inherent in the Mass.

Timestamps:

00:00 Introduction

03:27 From NASA to the Classroom

06:41 St. Jerome Academy's Model of Education

10:44 Experiential Learning and the Senses

17:09 Playing with What We Don't Fully Understand

24:50 The Relationship Between Questions and Answers

39:16 The Quadrivium and the Imagination

44:28 The Importance of Music

50:19 Experiencing the Night Sky: A Learning Journey

55:25 Conclusion

University of Dallas Links:

• Classical Education Master’s Program at the University of Dallas: udallas.edu/classical-ed
• St. Ambrose Center Professional Development for Teachers and Administrators: https://k12classical.udallas.edu/

Resources Mentioned in Today's Episode:

More on the Quadrivium Retrieval: https://quadriviumretrieval.org/

Support the show

If you enjoyed the show, please leave a rating and review — it helps others find us!