Part 1 (Basic Overview: Classical Education and Mathematics)
Part 2 (Day 1 Notes: Cosmos! Memory. Numbers.)
Part 3 (Fibonacci)
Part 4 (Day 2 Notes: Playing With Cosmos (Poetry). Operations.)
Part 5 (Day 3 Notes: Worship. Attention. Rhetoric. Laws.)
(I’ve been sharing my speaking notes from the local Classical Conversations parent practicum, and I think this about wraps it up!)
Math-related books and curricula
I have previously shared a long list of math resources and curricula that we have used in our home. You can find it at this link. (My final post in my curricula series, with links to all the posts, can be found here.)
Math-related books not on that list:
The History of Counting is an excellent picture book introduction to the history of counting across many cultures. I learned a great deal from this simple resource!
Blockhead: The Life of Fibonacci (another delightful picture book)
The Phantom Tollbooth is a fantastically witty and hilarious romp through an imaginative world filled with words and numbers. This chapter book is worth reading whether you are 8 or 80.
Carry On, Mr. Bowditch is a deeply inspirational work of historical fiction based on the life of a self-educated, eighteenth-century nautical and mathematical wonder.
Little Britches: Father and I Were Ranchers is the first book in an autobiographical series by Ralph Moody. While not a book about mathematics, Moody’s childhood is filled with the practical application of a strong education. Excellent.
Classical Educator.com (Videos, forums, blog, groups, and more)
CiRCE (Be sure to check out the blog and also free audio library)
Half-a-Hundred Acre Wood (An impressive resource for anyone involved in Classical Conversations, a plethora of links, lists, planners, ideas, and more—all free.)
Khan Academy (One of the best free resources on the internet. Do. Not. Miss. Math, Science and Economics, and Humanities for all ages.)
A little more math:
:: It’s All About Value! by Kate Deddens @ Classical Conversations (phenomenal, lengthy article—go read it!):
"Mysterious though it may be, and precisely because mathematics does seem to delve down into the bare essences of things, whatever is inessential is removed. Lovely as they can be, all the distractions and bunny trails of other forms of expression (such as rhetorical devices in writing or flourishes in art and music) that seek to enhance reality are eliminated. Indeed, the best mathematical proofs are the ones which come to the concluding point in the fewest steps, using the most appropriate laws and principles; the same is true for proofs in Formal Logic. This could even be argued to be true in many practical areas, such as in cooking; the best cakes are those in which the ingredients come together well in perfect accord, with no extraneous, distracting flavors or textures. Anything that does not speak precisely to the end-goal—even if it may have intrinsic value and even, in fact, add value—is unnecessary to the unadulterated task at hand."
General Quotes on Classical Education:
What is education?
Beauty for Truth's Sake: On the Re-enchantment of Education by Stratford Caldecott:
“As we have seen, the “Liberal” Arts are precisely not “Servile” Arts that can be justified in terms of their immediate practical purpose. “The ‘liberality’ or ‘freedom’ of the Liberal Arts consist in their not being disposable for purposes, that they do not need to be legitimated by a social function, by being ‘work.’” …At the heart of any culture worthy of the name is not work but leisure, schole in Greek, a word that lies at the root of the English word “school.” At its highest, leisure is contemplation. It is an activity that is its own justification, the pure expression of what it is to be human. It is what we do. The “purpose” of the quadrivium was to prepare us to contemplate God in an ordered fashion, to take delight in the source of all truth, beauty, and goodness…"
"Education is simply the soul of a society as it passes from one generation to another." G.K. Chesterton
“Classical education encourages us that we are capable of becoming an Oxford don who builds bicycles, or a plumber who reads Milton, or a business owner who spouts theology. The classically educated are not defined by their occupation so much as by their breadth of knowledge and understanding.”
And page 61:
“We need to offer children a broad, freeing education that allows them to think well and to be lifelong learners. Children need to be prepared for any challenge, even for job opportunities that may not exist until well into the future.”
“The only people who achieve much are those who want knowledge so badly that they seek it while the conditions are still unfavourable. Favourable conditions never come.” ~C.S. Lewis quoted in The Core, p 6
What is a student?
“To make the content of the curriculum relevant to the everyday life of the pupil, it is essential not to shrink the content to match the pupil’s present experience, but to expand the life of the pupil to match the proposed curriculum.” Beauty in the Word: Rethinking the Foundations of Education by Stratford Caldecott, page 35
“We do not know what or how to teach children, because we do not know what a child is, and we do not know what a child is, because we do not know what man is—and Him from whom and for whom man is. How decisive for…any educator of good will, is the revelation that man is made in the image and likeness of the three-Personed God? That is like asking what difference it will make to us if we keep in mind that a human being is made not for the processing of data, but for wisdom; not for the utilitarian satisfaction of appetite, but for love; not for the domination of nature, but for participation in it; not for the autonomy of an isolated self, but for communion.” Anthony Esolen in the foreword to Beauty in the Word (Stratford Caldecott)
Subjects tell us more about God and are connected with one another.
“To all of us who hold the Christian belief that God is truth, anything that is true is a fact about God, and mathematics is a branch of theology.” Hilda Phoebe Hudson, English mathematician in the early 1900s Integration of subjects.
“Do you often come across people for whom, all their lives, a ‘subject’ remains a ‘subject,’ divided by watertight bulkheads from all other ‘subjects,’ so that they experience very great difficulty in making an immediate mental connection between let us say, algebra and detective fiction, sewage disposal and the price of salmon--or, more generally, between such spheres of knowledge as philosophy and economics, or chemistry and art?” Dorothy Sayers, from “The Lost Tools of Learning,” an essay presented at Oxford in 1947
“I am only pointing out that every education teaches a philosophy; if not by dogma then by suggestion, by implication, by atmosphere. Every part of that education has a connection with every other part. If it does not all combine to convey some general view of life, it is not an education at all." -G.K. Chesterton
“Music, architecture, astronomy, and physics—the physical arts and their applications—demonstrate the fundamental intuition behind the Liberal Arts tradition of education, which is that the world is an ordered whole, a “cosmos,” whose beauty becomes more apparent the more carefully and deeply we study it. By preparing ourselves in this way to contemplate the higher mysteries of philosophy and theology, we become more alive, more fully human. This beautiful order can be studied at every level and in every context, from the patterns made by cloud formation or river erosion to that of the leaves around the stem of the most obnoxious weed, from the shape of the human face as it catches the light, or the way keys are ordered in a concerto by Bach, to the collision of stellar nebulae and particles in an atomic furnace.” (Beauty in the Word, pages 116-117)
Susan Wise Bauer writes: “[T]o the classical mind, all knowledge is interrelated. Astronomy, for example, isn’t studied in isolation; it’s learned along with the history of scientific discovery, which leads into the church’s relationship to science and from there to the intricacies of medieval church history. The reading of the Odyssey allows the student to consider Greek history, the nature of heroism, the development of the epic, and humankind’s understanding of the divine.”
Marva Collins states in Marva Collins' Way: “I taught my students how to add and subtract, but I also taught them that arithmetic is a Greek word meaning to count and that numbers were called digits after the Latin word digitus, meaning finger, because people used to count on their fingers. I taught them about Pythagoras, who believed that mathematics made a pupil perfect and ready to meet the gods. I told them what Socrates said about straight thinking leading to straight living.”
And Parker J. Palmer on teaching well (HT: Mental multivitamin): “Good teachers possess a capacity for connectedness. They are able to weave a complex web of connections among themselves, their subjects, and their students so that students can learn to weave a world for themselves. The methods used by these weavers vary widely: Socratic dialogues, laboratory experiments, collaborative problem solving, creative chaos. The connections made by good teachers are not in their methods but in their hearts -- meaning heart in its ancient sense, as the place where intellect and emotion and spirit and will converge in the human self.”
From Cultural Literacy: What Every American Needs To Know by E. D. Hirsch, Jr.: “In the technological age, Washington and the cherry tree, Scrooge and Christmas, the fights historical, the oceans geographical, the "beings animalculus," and all the other shared materials of literate culture have become more, not less, important. The more computers we have, the more we need shared fairy tales, Greek myths, historical images, and so on. That is not really the paradox it seems to be. The more specialized and technical our civilization becomes, the harder it is for nonspecialists to participate in the decisions that deeply affect their lives. If we do not achieve a literate society, the technicians, with their arcane specialties, will not be able to communicate with us nor we with them. That would contradict the basic principles of democracy and must not be allowed to happen.”
“An education worthy of the name would develop an awareness of the totality through art and literature, music, mathematics, physics, biology, and history. Each subject has its own autonomy, but at its heart it connects with every other.” Beauty for Truth’s Sake, page 31
Tools or Arts of Learning
Dorothy Sayers: “For the tools of learning are the same, in any and every subject; and the person who knows how to use them will, at any age, get the mastery of a new subject in half the time and with a quarter of the effort expended by the person who has not the tools at his command. To learn six subjects without remembering how they were learnt does nothing to ease the approach to a seventh; to have learnt and remembered the art of learning makes the approach to every subject an open door. “
“The key for me was to discover that the three elements of the Trivium link us directly with three basic dimensions of our humanity. No wonder they are so fundamental in classical education! ...To become fully human we need to discover who ...we are (Memory), to engage in a continual search for truth (Thought), and to communicate with others (Speech)." ~Stratford Caldecott, about Beauty in the Word
‘According to Hugh of Saint Victor [during the Middle Ages], “Grammar is the knowledge of how to speak without error; dialectic is clear-sighted argument which separates the true from the false; rhetoric is the discipline of persuading to every suitable thing.” Quoted in Beauty in the Word
Ephesians 3:17b-19 “And I pray that you, being rooted and established in love, may have power, together with all the saints, to grasp how wide and long and high and deep is the love of Christ, and to know this love that surpasses knowledge—that you may be filled to the measure of all the fullness of God.
(Roots! Math! Abundance!)
Col 1:19 “We…desire that you might be filled with the knowledge of his will in all wisdom and spiritual understanding.”
Prov 24:3-4 By wisdom a house is built, and through understanding it is established; through knowledge its rooms are filled with rare and beautiful treasures.
Hebrews 1:3a The Son is the radiance of God’s glory and the exact representation of his being, sustaining all things by his powerful word.
(Photosynthesis. Learning environment.)