Monday, June 3, 2013

James D Nickel and The Dance of Number (Part 1)

In 1990 James D. Nickel's Mathematics: Is God Silent? was published by Ross House Books, then updated and expanded in 2001. For more than three decades he has been an educator, author and public speaker. He has also served many years as an IT professional. His demeanor is best characterized by the words joy and laughter, not entirely how you'd picture of math man. He's no clown, though. He has an acute mind and a lifelong devotion to sharing his understanding of math with students, fellow teachers and readers. Later this summer his new book The Dance of Number will be published. The title was so intriguing I had to reach out and ask Nickel to elaborate as to what it was all about.

EN: Why is it essential that children understand mathematics?
JDN: The principles of number and space are imbedded in created reality, the way the universe works and the way we think. It is the beauty and power of this reality that should be the primary motivation for studying and understanding mathematics, but in most cases it is not. Since utilitarianism governs most of math instruction (K-12), there is a tendency to focus on dictating rules without the requisite understanding, but it is in understanding why a principle works that a student is (1) introduced to the beauty of mathematics and (2) learns to master its unique symbolic language. And, in understanding the laws of mathematics, one becomes comfortable in the world of God’s making and how man has developed it. We don’t trump utility with beauty because both go together. They are two sides of the same coin. Mathematics is a unique tool of wonder.

EN: What is “good number sense” and why is it important?
JDN: Number sense is a “feel” for numbers. Number sense comes from understanding why, not just following a set of rules. As a high school teacher of mathematics, I have had a front row seat sampling a good number of incoming students. I have observed far too many students who “can’t do the work” simply because they have not mastered arithmetic. When it comes to dividing by a fraction, many cannot remember what to “invert,” a symptom of a deeper conceptual issue, “What does it mean to divide a number by a fraction and what will my answer approximately be?” I have also noted that very few students possess what I call the joy of “number sense”or the pulse of numerical patterns … how they work, how they interact, and how they reveal rational order.

EN: Your book speaks of a “revolution” in the way math is taught. In what ways do we teach arithmetic differently in the U.S. from the way it’s taught in India and the Far East?
JDN: The fundamental paradigm that I use for teaching addition, subtraction, multiplication, and division is based upon the “left to right” methods based upon a book by Edward Stoddard entitled Speed Mathematics Simplified (New York: Dover Publications, [1962, 1965] 1994). Unlike most “speed math” books, rather than providing a series of disjointed “tricks,” Stoddard teaches a streamlined and consistent method of speed arithmetic, based upon the Japanese abacus called the Soroban and its use of complements (1) , that integrates the same principles throughout. I have also incorporated some revisions to Stoddard’s methods using some of the techniques taught in the schools of India, commonly called Vedic mathematics.

EN: What difference does it make?
JDN: The connections and techniques I explore are sound, sensible, interesting, fascinating, and enjoyable. The ease of this method increases speed in computation, guarantees better accuracy, and engenders immediate estimates. For years, I asked myself why, for example, Japanese students excel in numeracy and Americans lope behind at a far distance. It is because of the Soroban and how it uses number complements, and left to right computation, to instill an astounding mastery of number sense.

EN: What is the essence of algebra and what are some of the benefits understanding algebra brings?
JDN: Algebra is the language of mathematics and mathematics is the language of science. You will never understand the nature and structure of mathematics, or the nature and structure of the physical world, unless you master the language of Algebra. As a language, Algebra has its own syntax that requires one to be conversant with it. If these symbols are not mastered, the symphony of mathematics is played in silence and you will never appreciate its profound beauty. In its history, Algebra, as a language, has resolutely pointed to a given order, a specificity of order, in the universe. Naturalistic mathematicians and scientists have done their best to avoid the implications of such order; i.e., the revelation of consistent rationality in the universe points to an ultimate ground of rationality beyond it. The beauty, symmetry, and wonder revealed in the harmonious dance of number is a portal through which one, who has eyes to see, can catch a faint glimpse, an infinitesimal glimmer, of the beauty and wonder of the Author and Sustainer of number.


(1) In the Hindu-Arabic Base Ten Positional System, the complement of a single digit number is the number you must add to it to get the sum of 10. The complement of 1, therefore, is 9, the complement of 2 is 8, the complement of 3 is 7, etc.

CONTINUED TOMORROW

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