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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.” ↩

by Gus Lubin

Some prominent voices at are fed up with the agency’s activist stance toward climate change.

The following letter asking the agency to move away from climate models and to limit its stance to what can be empirically proven, was sent by 49 former NASA scientists and astronauts.

The letter criticizes the Goddard Institute For Space Studies especially, where director Jim Hansen and climatologist Gavin Schmidt have been outspoken advocates for action.

The press release with attached letter is below.

FOR IMMEDIATE RELEASE

Contact: Blanquita Cullum 703-307-9510 bqview at mac.com

Joint letter to NASA Administrator blasts agency’s policy of ignoring empirical evidence

HOUSTON, TX – April 10, 2012.

49 former NASA scientists and astronauts sent a letter to NASA Administrator Charles Bolden last week admonishing the agency for it’s role in advocating a high degree of certainty that man-made CO2 is a major cause of climate change while neglecting empirical evidence that calls the theory into question.

The group, which includes seven Apollo astronauts and two former directors of NASA’s Johnson Space Center in Houston, are dismayed over the failure of NASA, and specifically the Goddard Institute For Space Studies (GISS), to make an objective assessment of all available scientific data on climate change. They charge that NASA is relying too heavily on complex climate models that have proven scientifically inadequate in predicting climate only one or two decades in advance.

H. Leighton Steward, chairman of the non-profit Plants Need CO2, noted that many of the former NASA scientists harbored doubts about the significance of the C02-climate change theory and have concerns over NASA’s advocacy on the issue. While making presentations in late 2011 to many of the signatories of the letter, Steward realized that the NASA scientists should make their concerns known to NASA and the GISS.

“These American heroes – the astronauts that took to space and the scientists and engineers that put them there – are simply stating their concern over NASA’s extreme advocacy for an unproven theory,” said Leighton Steward. “There’s a concern that if it turns out that CO2 is not a major cause of climate change, NASA will have put the reputation of NASA, NASA’s current and former employees, and even the very reputation of science itself at risk of public ridicule and distrust.”

Select excerpts from the letter:

“The unbridled advocacy of CO2 being the major cause of climate change is unbecoming of NASA’s history of making an objective assessment of all available scientific data prior to making decisions or public statements.”
“We believe the claims by NASA and GISS, that man-made carbon dioxide is having a catastrophic impact on global climate change are not substantiated.”
“We request that NASA refrain from including unproven and unsupported remarks in its future releases and websites on this subject.”

The full text of the letter:

March 28, 2012

The Honorable Charles Bolden, Jr.
NASA Administrator
NASA Headquarters
Washington, D.C. 20546-0001

Dear Charlie,

We, the undersigned, respectfully request that NASA and the Goddard Institute for Space Studies (GISS) refrain from including unproven remarks in public releases and websites. We believe the claims by NASA and GISS, that man-made carbon dioxide is having a catastrophic impact on global climate change are not substantiated, especially when considering thousands of years of empirical data. With hundreds of well-known climate scientists and tens of thousands of other scientists publicly declaring their disbelief in the catastrophic forecasts, coming particularly from the GISS leadership, it is clear that the science is NOT settled.

The unbridled advocacy of CO2 being the major cause of climate change is unbecoming of NASA’s history of making an objective assessment of all available scientific data prior to making decisions or public statements.

As former NASA employees, we feel that NASA’s advocacy of an extreme position, prior to a thorough study of the possible overwhelming impact of natural climate drivers is inappropriate. We request that NASA refrain from including unproven and unsupported remarks in its future releases and websites on this subject. At risk is damage to the exemplary reputation of NASA, NASA’s current or former scientists and employees, and even the reputation of science itself.

For additional information regarding the science behind our concern, we recommend that you contact Harrison Schmitt or Walter Cunningham, or others they can recommend to you.

Thank you for considering this request.

Sincerely,

(Attached signatures)

CC: Mr. John Grunsfeld, Associate Administrator for Science

CC: Ass Mr. Chris Scolese, Director, Goddard Space Flight Center

Ref: Letter to NASA Administrator Charles Bolden, dated 3-26-12, regarding a request for NASA to refrain from making unsubstantiated claims that human produced CO2 is having a catastrophic impact on climate change.

/s/ Jack Barneburg, Jack – JSC, Space Shuttle Structures, Engineering Directorate, 34 years

/s/ Larry Bell – JSC, Mgr. Crew Systems Div., Engineering Directorate, 32 years

/s/ Dr. Donald Bogard – JSC, Principal Investigator, Science Directorate, 41 years

/s/ Jerry C. Bostick – JSC, Principal Investigator, Science Directorate, 23 years

/s/ Dr. Phillip K. Chapman – JSC, Scientist – astronaut, 5 years

/s/ Michael F. Collins, JSC, Chief, Flight Design and Dynamics Division, MOD, 41 years

/s/ Dr. Kenneth Cox – JSC, Chief Flight Dynamics Div., Engr. Directorate, 40 years

/s/ Walter Cunningham – JSC, Astronaut, Apollo 7, 8 years

/s/ Dr. Donald M. Curry – JSC, Mgr. Shuttle Leading Edge, Thermal Protection Sys., Engr. Dir., 44 years

/s/ Leroy Day – Hdq. Deputy Director, Space Shuttle Program, 19 years

/s/ Dr. Henry P. Decell, Jr. – JSC, Chief, Theory & Analysis Office, 5 years

/s/Charles F. Deiterich – JSC, Mgr., Flight Operations Integration, MOD, 30 years

/s/ Dr. Harold Doiron – JSC, Chairman, Shuttle Pogo Prevention Panel, 16 years

/s/ Charles Duke – JSC, Astronaut, Apollo 16, 10 years

/s/ Anita Gale

/s/ Grace Germany – JSC, Program Analyst, 35 years

/s/ Ed Gibson – JSC, Astronaut Skylab 4, 14 years

/s/ Richard Gordon – JSC, Astronaut, Gemini Xi, Apollo 12, 9 years

/s/ Gerald C. Griffin – JSC, Apollo Flight Director, and Director of Johnson Space Center, 22 years

/s/ Thomas M. Grubbs – JSC, Chief, Aircraft Maintenance and Engineering Branch, 31 years

/s/ Thomas J. Harmon

/s/ David W. Heath – JSC, Reentry Specialist, MOD, 30 years

/s/ Miguel A. Hernandez, Jr. – JSC, Flight crew training and operations, 3 years

/s/ James R. Roundtree – JSC Branch Chief, 26 years

/s/ Enoch Jones – JSC, Mgr. SE&I, Shuttle Program Office, 26 years

/s/ Dr. Joseph Kerwin – JSC, Astronaut, Skylab 2, Director of Space and Life Sciences, 22 years

/s/ Jack Knight – JSC, Chief, Advanced Operations and Development Division, MOD, 40 years

/s/ Dr. Christopher C. Kraft – JSC, Apollo Flight Director and Director of Johnson Space Center, 24 years

/s/ Paul C. Kramer – JSC, Ass.t for Planning Aeroscience and Flight Mechanics Div., Egr. Dir., 34 years

/s/ Alex (Skip) Larsen

/s/ Dr. Lubert Leger – JSC, Ass’t. Chief Materials Division, Engr. Directorate, 30 years

/s/ Dr. Humbolt C. Mandell – JSC, Mgr. Shuttle Program Control and Advance Programs, 40 years

/s/ Donald K. McCutchen – JSC, Project Engineer – Space Shuttle and ISS Program Offices, 33 years

/s/ Thomas L. (Tom) Moser – Hdq. Dep. Assoc. Admin. & Director, Space Station Program, 28 years

/s/ Dr. George Mueller – Hdq., Assoc. Adm., Office of Space Flight, 6 years

/s/ Tom Ohesorge

/s/ James Peacock – JSC, Apollo and Shuttle Program Office, 21 years

/s/ Richard McFarland – JSC, Mgr. Motion Simulators, 28 years

/s/ Joseph E. Rogers – JSC, Chief, Structures and Dynamics Branch, Engr. Directorate,40 years

/s/ Bernard J. Rosenbaum – JSC, Chief Engineer, Propulsion and Power Division, Engr. Dir., 48 years

/s/ Dr. Harrison (Jack) Schmitt – JSC, Astronaut Apollo 17, 10 years

/s/ Gerard C. Shows – JSC, Asst. Manager, Quality Assurance, 30 years

/s/ Kenneth Suit – JSC, Ass’t Mgr., Systems Integration, Space Shuttle, 37 years

/s/ Robert F. Thompson – JSC, Program Manager, Space Shuttle, 44 years/s/ Frank Van Renesselaer – Hdq., Mgr. Shuttle Solid Rocket Boosters, 15 years

/s/ Dr. James Visentine – JSC Materials Branch, Engineering Directorate, 30 years

/s/ Manfred (Dutch) von Ehrenfried – JSC, Flight Controller; Mercury, Gemini & Apollo, MOD, 10 years

/s/ George Weisskopf – JSC, Avionics Systems Division, Engineering Dir., 40 years

/s/ Al Worden – JSC, Astronaut, Apollo 15, 9 years

/s/ Thomas (Tom) Wysmuller – JSC, Meteorologist, 5 years

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