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Mathematics

‘The Dance of Number’ Is the Way Forward for Teaching Mathematics in the Classical Christian Tradition

By Terence Gillespie August 13, 2019

I’ve been pouring over James Nickel’s work for the past two months and began vetting his new math curriculum three weeks ago. Since the first four books of his “Dance of Number” arrived I’ve been exploring its structure and going through the lessons. It wasn’t long before deciding it will be the centerpiece of the math education for our boys. I’ll explain why and also present an argument for the title of this article: Nickel’s curriculum is the way forward for teaching mathematics in the classical Christian tradition.

Not Your Father’s Math Textbooks, Please!

My relationship with math textbooks has been no love affair. Whether mathematicians can’t write or clarity is anathema to the profits of their publishers, the words in my books were as clear as mud. That mud trained me to skip right to the examples in the solutions manual (often written by someone else and purchased separately.) Whoever wrote the solutions manual couldn’t play games; they had to list the steps of the derivations. Whatever concepts I managed to grasp were incidental to the derivation steps in the solution manuals.

My “learning process” was devoid of historical context and practical application. Some of the science — made possible by the math — seeped into physics class. However, the only thing beautiful in the whole experience was a GPA that made it possible to get a job.

The Beauty of Math, Revealed

In contrast, Nickel teaches math thoroughly and takes pains to reveal the logic behind the concepts. Math is presented alongside the science, history, theology, and practical applications related to the lesson; and the integration is seamless.

None of the leading contenders for the precalculus stages of mathematics even attempt to do what Nickel has done.

I want our boys to have that keen sense of number you sometimes see in carpenters and engineers. The best way to do that is to provide context, application, and meaning to each building block. James Nickel has done this in beautiful sequence. I’m as excited to teach my sons as to relearn mathematics, myself!

The Way Forward

With the perspective imparted this summer by a slow read of David Hick’s “Norms & Nobility”¹ it seems no risk at all to support Nickel’s curriculum as “The Way Forward.” I also thank Andrew Kern for his distillations of the many terms surrounding the pursuit of Classical Education.²

Hicks defines a classical education as “a spirit of inquiry and a form of instruction concerned with the development of style through language and of conscience through myth.”¹ These are penetrating words but require the context of Hick’s book to unpack and grasp fully.

On the other hand, Kern’s definition is a one-stop-shop:

“A Christian Classical Education is the cultivation of wisdom and virtue by nourishing the soul on truth, goodness, and beauty by means of the seven liberal arts and the four sciences so that, in Christ, the student is enabled to know, glorify, and enjoy God.”²

The Argument for “The Dance…”

On the jacket cover of “The Dance of Number,” Nickel makes lofty promises. He claims his curriculum:

“Teaches mastery of number sense and algebraic syntax.”
- It does. The student also learns how to use an abacus and an improved version of Stoddard’s speed math (having already mastered the abstracts of number.)
“Integrates math themes with history, science, and personalities.”
- It plainly does.
“Coordinates beauty, truth, and goodness with rigor and heuristics.”
- In a math curriculum? Yep.
“Structures mathematics as an interconnected framework, and explores the dynamic interrelatedness of Arithmetic, Algebra, Geometry, Trigonometry, and Science.”
- This is one of Nickel’s passions. He laments of so many students beginning Algebra before mastering Arithmetic. The error is compounded by attempting geometry and trig before learning Algebra. Problem solved in “The Dance …”.
“Brings to light the multiplicities of the perichoretic nature of creation and mathematics.”
- Perichoretic refers to the mutual indwelling nature of the Trinity and is the word that inspired the curriculum’s title. In “Mathematics: Is God Silent?” Nickel traces how impasses in mathematics were overcome by the Christian revelation of the Trinitarian nature of reality. The distinction between Creator and Created — when widely accepted — broke the Platonic spell and paved the way for the technological achievements of the middle-ages (which were anything but “Dark.”)

In short, Nickel’s “Dance” does what no other on the market does; and the classical integration (or interpenetration as James might say) is seamless.

Flipping the Argument

Has any math curriculum you know of even attempted to do what Nickel’s has done?

How do the accomplishments, listed above, compare with the math curriculum deployed at your classical school?

A Whole New World

Do western students know how to use an Abacus? Why not? And what’s the harm in teaching Stoddard’s “Speed Mathematics” (which Nickel further streamlines with Vedic methods) as long as the student has a firm grasp of the fundamentals? These and a seemingly endless stream of surprises are in store for the student. Nickel draws from his 40-year teaching experience and 1400 volume library to show the student the context of the mathematical insights that shape our lives and unify our impression of the Divine Creator.

Nickel’s approach to teaching mathematics can impart that intuitive sense of number you sometimes see in carpenters and engineers. That’s not to say that mathematics is any less abstract than it always has been. But Nickel explicitly reveals its poetry and the stunning natural beauty upholding “The Dance.”

Those with a gift for math will be lit up at the beginning of their study like never before possible. Those less gifted can learn at rest, knowing that a logical and inspiring presentation is in store.

Thoughts on Implementation

This is not an assign-and-forget curriculum; it’ a “hands-on” journey for Teacher and Student to embark on, jointly.

The curriculum is recommended to start at age 12 (through 16). Therefore, a bridge is needed for younger students. Our 11-year-old is ready though we’ll be going through each lesson in tandem.

Nickel recommends the student read through each lesson with the teacher joining in when the student begins the exercises. The lessons are quite accessible but also what one might expect from a curriculum integrating mathematics with history, theology, science, and the beauty of practical applications: Deep with a capital ‘D’.

Until our youngest is ready for “The Dance of Number” we’ll be using Math U See. However, since dad is going through “The Dance …”, in advance, I’ll be able to verbally fill in gaps per Nickel’s framework.

Conclusion

Nickel seems to have used Kern’s definition of a Classical Christian Education as a specification. More surprisingly, his curriculum delivers on that specification. What do you do with something like this and whose first paragraph defines the word “Elohim”?

You’re reading my answer: adopt it as the centerpiece of the mathematics curriculum for your school and tell everyone you know about it!

James Nickel has given us the way forward in Mathematics! For imparting the subject in the classical tradition, there’s not even a close second out there to this monumental achievement.

David Hicks, Norms & Nobility, a Treatise on Education, University Press of America, 1999 ↩
Andrew Kern, Circe Institute’s “Definition of Terms.” ↩

History

Why is ‘separation of church and state’ so misquoted?

By Guest Post February 6, 2019

After King Henry VIII broke from Rome in 1534, England began enforcing Anglican religious uniformity. Some wanted to purify the Anglican Church from the inside, being given the name “Puritans.” Others separated themselves completely from the Anglican Church as dissenters. Of those were Thomas Helwys, John Murton and John Smyth, who founded the Baptist faith in England.

Thomas Helwys wrote “A Short Declaration of the Mystery of Iniquity,” 1612, considered the first English book defending the principle of religious liberty: “Queen Mary … had no power over her subjects consciences … neither hath our Lord the King … power over his subjects consciences. … The King is a mortal man, and not God, therefore he hath no power over the mortal soul of his subjects to make laws and ordinances for them and to set spiritual Lords over them. …”

He continued: “If the King’s people be obedient and true subjects, obeying all humane laws made by the King, our Lord the King can require no more: for men’s religion to God is betwixt God and themselves; the King shall not answer for it, neither may the King be judge between God and man.”

Thomas Helwys was arrested and thrown into London’s notorious Newgate Prison, where he died in 1616.

Another Baptist dissenter, John Murton, was locked in Newgate Prison as punishment for spreading politically incorrect religious views. Prisoners were not fed, but instead relied on charity of friends to bring them food, such as bread or bottles of milk.

Roger Williams referred to John Murton in his work, “The Bloody Tenet (Practice) of Persecution for the Cause of Conscience,” 1644: “The author of these arguments against persecution … being committed (a) prisoner to Newgate for the witness of some truths of Jesus … and having not use of pen and ink, wrote these arguments in milk, in sheets of paper brought to him by the woman, his keeper, from a friend in London as the stopples (corks) of his milk bottle. … In such paper, written with milk, nothing will appear; but the way of reading by fire being known to this friend who received the papers, he transcribed and kept together the papers, although the author himself could not correct nor view what himself had written. … It was in milk, tending to soul nourishment, even for babes and sucklings in Christ … the word of truth … testify against … slaughtering each other for their several respective religions and consciences.”

Williams wrote: “Persecution for cause of conscience is most contrary to the doctrine of Christ Jesus the Prince of Peace. … Enforced uniformity is the greatest occasion of civil war, ravishing of conscience, persecution of Christ Jesus in his servants.”

Roger Williams was a contemporary of John Bunyan, who wrote “Pilgrim’s Progress” while in prison for conscience sake. When the government sought to arrest Roger Williams for preaching religious liberty, he fled to Boston, Massachusetts, on Feb. 5, 1631.

To his dismay, Puritans in Massachusetts had begun enforcing Puritan religious uniformity. Supreme Court Justice Hugo Black wrote in Engel v. Vitale, 1962: “When some of the very groups which had most strenuously opposed the established Church of England found themselves sufficiently in control of colonial governments … they passed laws making their own religion the official religion of their respective colonies.”

A controversy raged among inhabitants of Massachusetts, between “a covenant of grace” versus “a covenant of works.” The “covenant of grace” leaders were Sir Henry Vane, Rev. John Cotton, Rev. John Wheelwright, and his sister-in-law, Anne Hutchinson.

Rev. John Wheelwright fled Puritan uniformity in Massachusetts in 1637 and founded Exeter, New Hampshire. Roger Williams was briefly the pastor a church till “notorious disagreements” caused the Massachusetts General Court to censor his religious speech. Upon hearing the sheriff was on his way to arrest him and send him back to England, Williams fled again, in freezing weather, January of 1636. For weeks he traveled alone till he was befriended by the Indians of Narragansett. He founded Providence Plantation, Rhode Island – the first place where the church was not controlled by state.

Roger Williams wrote in 1661: “I having made covenant of peaceable neighborhood with all the Sachems (Chiefs) and natives round about us, and having in a sense of God’s merciful providence unto me in my distress called the place Providence … a shelter for persons distressed of conscience.”

A historical plaque reads: “To the memory of Roger Williams, the Apostle of Soul Liberty, Founder of the State of Rhode Island and Providence Plantation.”

The reverse of the plaque reads: “Below this spot then at the water’s edge stood the rock on which according to tradition Roger Williams, an exile for the devotion to the freedom of conscience, landed. 1636.”

In 1638, Roger Williams organized the first Baptist Church in America.

A plaque reads: “The First Baptist Church, Founded by Roger Williams, AD 1638, The Oldest Baptist Church in America, The Oldest Church in this State.”

Physician John Clarke came to Rhode Island and founded another Baptist Church in Newport. Other dissenters arrived in Williams’ Rhode Island Colony, such as William Coddington, Philip Sherman, and Anne Hutchinson. Anne soon left again to settle in the Dutch settlement of the Bronx in New York City, where all her family was scalped and beheaded by raiding Indians in 1643. There was only one survivor, Anne’s nine-year-old daughter Susanna, who was taken captive. After several years, she escaped and married an innkeeper, Samuel Cole. Their descendants included three U.S. presidents.

The Governor of Massachusetts from 1636 to 1637 was Sir Henry Vane, who helped found Harvard. He supported the efforts of Roger Williams. Due to the “covenant of grace” versus “covenant of works” controversy, Governor Sir Henry Vane was not reelected, being replaced by John Winthrop.

In 1639, Sir Henry Vane returned to England where he backed the Puritan Revolution, led by Oliver Cromwell, though he did not support the Rump Parliament which beheaded Charles I.

During the brief English Commonwealth, Vane helped draft for Roger Williams the Patent for Providence Plantation, which was unique in that it did not acknowledge a king, and it guaranteed freedom of religion and conscience. Vane later defended the Patent on behalf of Roger Williams against a competing charter.

Roger William wrote of Vane in April of 1664: “Under God, the great anchor of our ship is Sir Henry Vane … an instrument in the hand of God for procuring this island.”

A statue of Sir Henry Vane is in the Boston Public Library with a plaque that reads: “Sir Henry Vane … An ardent defender of civil liberty and advocate of free thought in religion. He maintained that God, Law, and Parliament were superior to the King.”

The Plantation Agreement at Providence, Sept. 6, 1640, stated: “We agree, as formerly hath been the liberties of the town, so still, to hold forth liberty of conscience.”

The Government of Rhode Island, March 19, 1641, stated: “The Government … in this Island … is a Democracy, or Popular Government; that is to say, It is in the Power of the Body of Freemen orderly assembled.”

Roger Williams responded to Puritan leader John Cotton’s accusations by publishing “The Bloody Tenet (Practice) of Persecution for the Cause of Conscience and Mr. Cotton’s Letter Lately Printed, Examined and Answered in 1644.” In this, Williams first mentioned his now famous phrase, “wall of separation”: “Mr. Cotton … hath not duly considered these following particulars. First, the faithful labors of many witnesses of Jesus Christ, existing in the world, abundantly proving, that the Church of the Jews under the Old Testament in the type and the Church of the Christians under the New Testament in the anti-type, were both separate from the world; and that when they have opened a gap in the hedge, or wall of separation, between the garden of the church and the wilderness of the world, God hath ever broken down the wall itself, removed the candlestick, &c. and made his garden a wilderness, as at this day. And that therefore if He will ever please to restore His garden and paradise again, it must of necessity be walled in peculiarly unto Himself from the world, and that all that shall be saved out of the world are to be transplanted out of the wilderness of the world and added unto His Church or garden … a separation of Holy from unHoly, penitent from impenitent, Godly from unGodly.”

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Education

Former Atheist & Philosophy Professor Edward Feser On How Studying Philosophy Convinced Him of God’s Existence

By Guest Post January 31, 2019

By James Bishop

Philosopher Edward Feser perhaps has one of the most well articulated and detailed testimonies I recall having read (which at this point is quite a few). Feser is a professional philosopher after all, so it shouldn’t be too much of a surprise. Nonetheless, in this short post I have attempted to summarize Feser’s journey while also attempting to outline some of the key moments that had taken place within it. I am confident that this summarized testimony will be helpful to those who don’t necessarily have the time to read through the 7000 word testimony on Feser’s own website. However, I do encourage reading the full testimony for there is much in the details not included here.

As a way of biography, Feser is a well-known philosopher in the profession having penned numerous academic articles on several subjects ranging from the philosophy of mind to metaphysics. He is the Associate Professor of Philosophy at Pasadena City College, previously a Visiting Assistant Professor at Loyola Marymount University, and a Visiting Scholar at the Social Philosophy and Policy Center. He has authored numerous books including Aquinas, Five Proofs of the Existence of God, Scholastic Metaphysics: A Contemporary Introduction, and The Last Superstition: A Refutation of the New Atheism. Feser was also once an atheist naturalist until he converted to Christianity.

Feser explains that he was a convinced atheist naturalist for a period of 10 years in the 1990s and that his transition away from it “was no single event, but a gradual transformation.” He was brought up Catholic but ultimately lost his faith while a teenager around the age of 13 or 14. His atheism stayed with him well into his university years as a passionate philosophy student. While at university he discovered a new interest in existentialism and existentialist philosophers, particularly Soren Kierkegaard. This interest led him to discover other existentialists such as Friedrich Nietzsche and Walter Kaufmann of whom he both appreciated but especially Kaufmann in particular. In the more modern philosophical climate, the atheist analytic philosopher J. L. Mackie proved appealing to Feser, and he considered Mackie’s book The Miracle of Theism to be a solid piece of philosophical work. Feser remarks that Mackie’s book was “intellectually serious, which is more than can be said for anything written by a “New Atheist.”” Philosopher Kai Nielsen would also appeal on issues of morality and religion. According to Feser,

What really impressed me was the evidentialist challenge to religious belief. If God really exists there should be solid arguments to that effect, and there just aren’t, or so I then supposed… Atheism was like belief in a spherical earth — something everyone in possession of the relevant facts knows to be true, and therefore not worth getting too worked up over or devoting too much philosophical attention to.

However, when he examined analytic philosophy in some more detail during the course of his studies it would, before long, bring his “youthful atheism down to earth.” The genesis of Feser’s transition away from atheism came about when he first began to look into the philosophy of language and logic. Over the several following years, during which he weighed information and arguments presented in his course materials, he reasoned that the existing naturalistic accounts of language and meaning failed to satisfy,

I already knew from the lay of the land in the philosophy of language and philosophy of mind that the standard naturalist approaches had no solid intellectual foundation, and themselves rested as much on fashion as on anything else.

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