All of the volumes of “Dance of Number” are available at Amazon.com
The Dance of Number is a sequenced and tightly integrated curriculum involving four textbooks totaling 1924 pages (Grades 7-10). The only prerequisite is above average reading comprehension. We start from ground zero, teach the basics of arithmetic from a fresh, vibrant perspective, and then take the reader on a journey that leads to the borderlands of the mountain range called Calculus. There are plenty of side roads along the way where we stop to gaze at the scenic beauty (i.e., a unified look at principles of Algebra, Geometry, Trigonometry). It is a long trip; its completion is worth the effort.
The texts are not named Algebra I or Algebra II, etc., because the four-volume sequence tells an coordinated story engaging the student in the nature of the structure of number, the development of its history, and its interpenetration with science. As the student takes this journey, all the topics of Arithmetic, high school Algebra, most of Geometry, and a complete study of Trigonometry are unfolded.
Because of this harmonized approach, these texts are different than most of what is on the market. The author wants the student to see how the ideas/branches of mathematics interpenetrate (e.g., you are doing algebraic operations and geometrical procedures as you are learning the elements of trigonometry). Our current textbook structure is not that successful at doing this.
After this sequence is completed, the student would be ready either for a complete course in Geometry (if desired) or PreCalculus.
From James D. Nickel’s website:
“The Dance of Number” covers the concepts pertinent to Arithmetic, Algebra, Geometry, Trigonometry, and mathematical reasoning in two parts, two volumes per part. It is ideal for teachers, parents, or anyone interested in learning how to instill good number sense in students, too often a missing ingredient in the math education of the Western world, Christian home and day schools included.
The revolution the author introduces in the text, albeit not new, is left-to-right methods consistently applied to the four operations of arithmetic. The ease of this method increases speed in computation, guarantees better accuracy, and engenders immediate estimates. This is the way arithmetic is taught in the Far East and in India. For years, the author asked himself why, for example, Japanese students excel in numeracy and Americans lope behind at a far distance. It is because of the Japanese abacus called the Soroban and how it uses number complements, and left to right computation, to instill an astounding mastery of number sense.
The text explains these concepts in detail: a mastery of arithmetic and pre-algebra concepts, including measurement, the solution methods to linear and non-linear equations, an introduction to probability and statistics, a survey of fundamental geometric concepts, a thorough discussion of trigonometric ratios and functions, an exploration of infinite processes, and the mathematical methods of proof. It is aimed at Grades 7-10 and it requires the ability to reason and develops reasoning skills in terms of mastery of concept, while also exacting drill work for reinforcement. The addition of a detailed solutions manual is an important augment to the text.
The Dance of Number systematically explicates and applies the left-to-right paradigm starting from counting as foundation, using the Soroban as an introduction into the fascinating and beautiful world of arithmetical interconnections. Because of this ground up approach, any teacher of arithmetic, from K-5, can reap dividends by studying the text explanations in the first five chapters. Distributed throughout are a plenitude of quotes that serve as a source of entertainment, meditation, and discussion. The text also builds mathematics, as a branch of knowledge, in a way that upholds the Triune God as the ultimate ground of rationality. In a world that assumes the neutrality of knowledge, this emphasis is vital because it unfolds mathematics in its relationship to objective reality and the Creator and Sustainer thereof. If you want a challenging and rigorous demonstration of the beauty and power of number, “The Dance of Number” is for you.
“Technically, “The Dance of Number” is a tightly integrated series of four textbooks, designed for completion in four years. I start from the beginning, assuming the student knows nothing but can read with comprehension, i.e., age 11-13. In the first two texts, I teach the rudiments of arithmetic, engaging a speed paradigm that covers the four operations of arithmetic in relationship to integers. Then, I move to the operations with fractions and decimals. While doing this, I introduce many geometric ideas, along with exercises that carefully introduce the student to algebraic syntax. In the final two texts, I explore the world of algebraic syntax and mathematical reasoning, covering all the necessary topics that will prepare the student for PreCalculus/Calculus. I include most of the concepts in the typical Algebra I/II syllabus, along with a significant amount of requisite two- and three-dimensional Geometry, a complete course in Trigonometry, all the methods of mathematical proofs, and even an introduction to Calculus reasoning.”