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!

Summary

In this episode, Shannon Valenzuela, Dr. Jeff Lehman, and Dr. Andrew Seeley explore the retrieval of the quadrivium and its significance in classical education, particularly in mathematics and science. They discuss their personal journeys in mathematics, the transformative power of the quadrivium, and the importance of integrating imagination and reason in learning. They emphasize the need for a community of educators to foster a deeper understanding of these subjects, and offer suggestions for teaching. The discussion also touches on the moral implications of education and the beauty inherent in mathematics and the arts.

Topics Covered:

• The creative retrieval of the Quadrivium
• The Quadrivium and the formation of the intellect and imagination
• The importance of fellowship among teachers
• Beauty and structure are integral to the arts and sciences.
• The Quadrivium and its contribution to moral formation

Today's Guests:

Jeffrey S. Lehman is co-founder and Dean of Fellows at the Boethius Institute and Professor of Philosophy and Theology and Director of the M.A. in Catholic Education program at the Augustine Institute’s Graduate School of Theology. He is the founder and President of the Arts of Liberty Project, a Founding Fellow of the Center for Thomas More Studies, and he has taught at Biola University, Thomas Aquinas College, Hillsdale College, and the University of Dallas. He is the author of numerous publications, including Socratic Conversation: Bringing the Dialogues of Plato and the Socratic Tradition into Today’s Classroom.

Andrew Seeley is co-founder and President of the Boethius Institute. He also serves as the Director of Advanced Formation for Educators at the Augustine Institute. Over his three decades as a Tutor at Thomas Aquinas College in California, Dr. Seeley taught every subject in its integrated Great Books curriculum. Dr. Seeley co-founded the Institute for Catholic Liberal Education in 2005, where he served as Executive Director for 12 years. He became Executive Director of the Arts of Liberty Project in 2021. He was named the 2023 recipient of the Circe Institute’s Paideia Prize.

Timestamps:

00:00 Introduction to the Quadrivium and the Boethius Institute
03:21 The Creative Retrieval of the Quadrivium
07:16 The Importance of the Quadrivium in Classical Education
12:09 Transformative Experiences in Teaching the Quadrivium
16:27 Understanding the Four Arts of the Quadrivium
20:52 The Role of Imagination in the Quadrivium
23:23 The Interplay of Reason and Imagination
33:46 Mathematics and Moral Formation
39:18 Reimagining Mathematics Education
43:38 Favorite Resources
48:11 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/

Francis Su, Mathematics for Human Flourishing

Stratford Caldecott, Beauty for Truth's Sake

Support the show

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

Summary

In this conversation, Shannon Valenzuela and John Mays explore the principles of teaching science classically. They discuss the importance of beauty to the work of education, the importance of textbook design, and the need for a mastery-oriented curriculum that emphasizes long-term retention of knowledge. Mays introduces his Wonder-Integration-Mastery model for science education, which serves as a framework for teaching that integrates various disciplines and fosters the development of wisdom and virtue in students. The conversation highlights the role of teachers in modeling honesty and virtue, and the importance of effective communication in the classroom.

Topics Covered:

• The role of beauty and wonder in education
• Textbook design
• The Wonder-Integration-Mastery model in education
• Integration of disciplines enriches the learning experience
• The end of a classical education: wisdom and virtue
• Self-reflection and modeling for teachers

Today's Guest:

John D. Mays spent 14 years in industry in engineering and engineering management in the areas of electrical, controls, and telecommunications systems and has completed graduate degrees in Secondary Education (MEd) and Liberal Arts (MLA). John served as the Math-Science Department Chair at Regents School of Austin from 2001 until 2009, when he became Director of the Laser Optics Lab at Regents. He founded Novare Science in 2009 and Centripetal Press in 2015, both of which became part of Classical Academic Press in 2019. John is the author and editor of numerous student science texts and teacher resources.

Timestamps:

00:00 Introduction
04:24 Introduction to Science Education and Curriculum Development
06:18 The Cram-Pass-Forget Cycle
11:39 Mastery-Based Teaching Model
13:55 Textbook Design Philosophy
17:41 The Importance of Beauty in the Education Environment
23:05 Wonder, Integration, and Mastery in Science Education
34:38 Distinctions between Modern and Classical Education
40:40 The Importance of Self-Reflection for Teachers
53:21 Modeling Virtue: The Teacher's Role
55:28 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:

From Wonder to Mastery: A Transformative Model for Science Education

Centripetal Press: https://centripetalpress.com/

Novare Science (Classical Academic Press): https://classicalacademicpress.com/collections/novare-science

Support the show

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

Summary

In this conversation, Shannon Valenzuela, Robert Puschautz, and AnneMarie Johnson explore the profound role of art in education, emphasizing its ability to connect beauty with truth and goodness. They discuss the artist's vocation as a divine calling, the importance of constraints in fostering creativity, and how beauty serves as a powerful tool for evangelization. The conversation also highlights the necessity of creating beautiful learning environments and integrating art into various subjects, and the deep desire for human authenticity in the age of AI.

Resources & Links:

• Stabat Mater Foundation

Topics Covered:

• Art and teaching students to appreciate beauty
• The vocation of the artist
• Art and evangelization
• Beauty and our environment
• The rise of AI and the desire for authentic human experiences

Today's Guests:

Robert Puschautz is a representational artist based out of Tyler, Texas. He received his bachelor’s in Painting and Art Education from the University of Illinois in Urbana-Champaign and continued his studies in classical painting at the Ravenswood Atelier in Chicago. He is the Executive Director of Stabat Mater Foundation, a nonprofit whose mission is the renewal of beauty in our world and culture by praying for and supporting artists. To see more of his work visit robertpuschautz.weebly.com.

AnneMarie Johnson’s work focuses on the relationship between finitude and transcendence in the human experience. She graduated from the University of Dallas in 2018 with a B.A. in Art - Painting. In 2024 she completed the three-year Classical drawing and painting program at the Lyme Academy of Fine Arts. Additional studies include classical drawing at the Florence Academy of Art, U.S., and graduate painting and art history at the University of Dallas (2021). AnneMarie is currently the Art Fellow and an instructor of drawing at the Stabat Mater Foundation in Tyler, TX.

Timestamps:

02:26 The Mission of the Stabat Mater Foundation
04:18 Bringing Beauty into Education
06:49 Art as a Reflection of Divine Creation
12:02 Art as a Means of Evangelization
22:27 Co-Creating with God: Integrating Beauty and Intellect
24:48 Training Discernment: Truth, Goodness, and Beauty
28:33 Bringing Art into the Classroom
33:30 The Human Connection: Art in the Age of Technology

University of Dallas Links:

• The Way of Beauty (Season Two, The Quest television series): quest.udallas.edu
• 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:

Ever Ancient, Ever New: Art History, Appreciation, Theory, and Practice, Level One (Grades 5-9)

Ever Ancient, Ever New: Art History, Appreciation, Theory, and Practice, Level Two (Grades 7-12)

Support the show

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

Summary

In this conversation, Shannon Valenzuela interviews Dr. Joe Carlson, a University of Dallas alumnus and translator of Dante Alighieri's Divine Comedy. They discuss his journey into the world of Dante, focusing on the personal nature of translation and the importance of delight in education. He emphasizes the role of enthusiasm in teaching, the art of translation, and the significance of medieval cosmology in understanding both literature and the sacramental nature of reality. The conversation also explores the distinction between contemplation and analysis in education, advocating for a more immersive and engaging approach to teaching classical texts.

Resources & Links:

• Dr. Carlson's Dante translation and curriculum: dantepoem.com
• Dr. Carlson's editions of John Milton's Paradise Lost and Paradise Regained: miltonpoem.com

Topics Covered:

• Delight as the key to a lasting educational experience
• The process of translating The Divine Comedy
• Medieval cosmology and the sacramental nature of reality
• Practical tips on teaching epic works
• Practical tips on teaching translation in language courses

Today's Guest:

Dr. Joe Carlson lives in Moscow, Idaho with his wife and son. He graduated from New Saint Andrews College with a BA in Liberal Arts in Culture, and from the University of Dallas with an MA in Humanities and a PhD in Literature. He has managed a chain of coffee shops, published (micro) epic poetry, co-pastored a church, co-founded a university campus ministry, and taught many different kinds of classes over the years. Currently, he is an adjunct lecturer at New Saint Andrews College, a humanities teacher with Logos Online School, and a curriculum developer at Roman Roads Press. He is the author of, among other things, the Dante Curriculum, which includes an original blank verse translation of The Divine Comedy, published by Roman Roads.

Timestamps:

00:00 Introduction to Joe Carlson and His Work

08:11 Delight as a Key Ingredient in Learning

17:46 The Teacher as a Leading Learner

21:39 The Process of Translation and Its Challenges

31:32 The Influence of C.S. Lewis and Medieval Cosmology

38:47 Practical Tips for Teaching Dante

45:02 Contemplation and Immersion in Teaching Literary Texts

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/

Books Mentioned in Today's Episode

Dante Alighieri, The Divine Comedy, translated by Dr. Joe Carlson.

John Milton, Paradise Lost and Paradise Regained, edited by Dr. Joe Carlson.

C.S. Lewis, "Meditation in a Tool Shed"

C.S. Lewis, The Voyage of the Dawn Treader

Michael Ward, Planet Narnia

Support the show

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

Summary

In this conversation, Shannon Valenzuela interviews Mandi Gerth, the author of the new book Thoroughness & Charm: Cultivating the Habits of a Classical Classroom. They explore the principles of classical education, focusing on the importance of classroom management, the role of joy and order in learning, and the integration of the imagination and the intellect. They discuss how embodiment and enculturation can enhance the learning experience and delve into the significance of liturgy in the classroom, the concept of ordered loves, and the teacher's role as a lifelong learner. The discussion also touches on insights from Machiavelli regarding classroom management and the importance of establishing authority while fostering a love for learning.

Resources & Links:

• Mandi's Website: https://mrsgerthteaches.com/
• Thoroughness and Charm - CiRCE Institute

Topics Covered:

• Embodiment and enculturation in classical education
• Classroom management
• The formation of the intellect, the imagination, and the heart
• The importance of joy and order in education
• Classroom liturgies and catechisms

Guest:

Mandi Gerth is a teacher and classical education consultant who lives in Dallas, Texas. She currently serves as the Administrative Director of the Cowan Center at the University of Dallas. She holds a master of humanities degree from the University of Dallas with a concentration in classical education. Her first book, Thoroughness & Charm is now available from CiRCE Press. You can find Mandi on LinkedIn, Substack, and Instagram (@mrsgerthteaches).

Timestamps:

00:00 Introduction
02:08 Introduction to Mandi and her work
04:20 Enculturation and the Role of Tradition
05:28 Liturgical Classroom Practices
11:59 Ordered Loves and Their Significance in Education
22:53 Reconnecting with the Joy of Teaching
26:34 The Role of Lifelong Learning in Teaching
30:24 Critical Thinking and Student Engagement
34:39 Classroom Management Insights from Machiavelli
38:33 Balancing Order and Joy in the Classroom

UD 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/

Books Mentioned in Today's Episode

Charles Taylor, Modern Social Imaginaries

Karen Swallow Prior, Evangelical Imagination

Joshua Gibbs, Something They Will Not Forget

David Hicks, Norms & Nobility

Donald Cowan, Unbinding Prometheus

Support the show

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

Support the show

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