Descriptions of the Books
1. Ah, So She Ate a Cookie or Learning to Add $17
In this book I emphasize four basic concepts of math: (1) that the number one is an important number, (2) the Associative Rule, (3) the Replacement Rule, and (4) the concept of notation, upon which I build the logic and understanding of mathematics. I introduce words such as concatenation to clear up the vagueness in the conventional language of elementary mathematics. Then I teach three basic patterns that make it easy for children to learn the facts table. The book includes first lessons on number structure and the theory behind multi-column addition. Lessons on Roman Numbers and time are cleverly integrated into the lessons along with strategies for solving the magic square. I introduce "silly arithmetic" so that children can better understand how and why the rules of addition work. Grades 1, 2, 3.
2. One Blue Penny Learns to Subtract $17
Students are lead to discover negative numbers. They learn that subtraction is the inverse process of addition, and use this understanding to master their subtraction facts. This approach for teaching negative numbers provides a model for learning fractions at a later date. The rules for subtracting negative numbers unfold through manipulatives and the process of deduction. Students are shown how the rules for multiplying negative numbers are developed and again use silly arithmetic to better understand our number system and multi-column subtraction. Grades 1, 2, 3.
3. To Multiply or to Add, That is the Question $17
Because the Distributive Rule is key to learning multiplication, fractions, number structure, and algebra, this book develops and illustrates that rule by application. Multiplication offers students the opportunity to understand the fourth basic concept: notation. Special attention is paid to patterns and how they can help make it easy to learn multiplication. Silly arithmetic is illustrated through Roman Numbers in this book. Besides reducing the effort for students to understand multi-digit multiplication, I introduce other base number systems and the multiplication of negative numbers. Grades 2, 3, 4.
4. Division and Fractions: Half a Loaf is Better Than None $17
In this book we teach fractions using the paradigm of negative numbers and the application of the Distributive Rule for multiplication. This gives an opportunity to bring together many of the components of number structure. We conclude with teaching the mechanics and the explanations for long division. Grades 4, 5, 6.
5. Algebra: Solving the Puzzle $17
This book teaches about functions. It also suggests how students can organize their thinking processes to solve problems systematically. This fosters the ability to identify the tools they need to solve problems that arise outside of textbooks. Grades 3 to 6.
6. Geometry or Picture It, Think It $17
Using the definition of parallel lines, this book develops geometry for elementary school students through the use of construction and measurement, and for high school students by relying on logical proof. It defines the components of the triangle and shows how the triangle is the building block for all polygons. Grades 2 to 6 and grade 9.
7. Number Structure: No Nonsense Number Sense $22
This book is the link between elementary and middle school math. It is designed for high achieving students. In dealing with exponents, logarithms, and modulo numbers, it shows how these concepts all explain the structure of numbers as we know them and beyond what we have been taught. It then reviews all of elementary math. Grades 5, 6, 7.
8. Counting and Measuring: They came, They saw, They measured $17
This book links math and physics and shows how measurement and scientific thought are interrelated. It also discusses the uncertainty in measurements. It maps all forms of measuring into an understanding of how to use a ruler. Grades 2 through 5.
9. An Ideal Way To Learn Addition (A Teacher's Guide) $17
This book is organized into lesson plans that lead readers to learn two simple patterns that make it easy to learn addition: (1) counting forward or backward up to twenty, and (2) decomposing numbers into parts such that some of the parts will add to ten. This foundation makes it easy for a child to learn, remember, and retain. Grades 1 to 3.
10. An Ideal Way To Learn Multiplication (A Teacher's Guide) $17
This book is organized into lesson plans that lead readers to learn three simple patterns that make it easy to learn multiplication: (1) extension of the addition rules to learn to multiply by nines, (2) the "nickel" analogy to make it easy to multiply by five and six, and (3) the "double trouble" analogy for the twos and fours. Students see the importance of the Distributive Rule which they use in learning to multiply by three. Grades 2, 3, 4.
11. Computational Mathematics - Irrational and Complex $33
This book is designed for high achieving students in middle school. Because I feel that current mathematics educational is greatly flawed, I designed this book to go somewhat beyond what is conventionally taught in middle school. The book bases the teaching of number structure on the use of Euler's Formula and prepares students for an engineering and scientific education by encouraging them to seek ways to solve problems that they have not seen previously. The book also discusses polynomials, probability, trigonometry and computational skills. Grades 6, 7, 8.
12. One Step Beyond Number Structure: Soaring with the Eagles of
Mathematical Knowledge $44
This book is designed for high achieving math students to show the interconnections among several topics: series, logarithms, differential and integral calculus, trigonometry, and analytic geometry. It emphasizes the importance of exponents and logarithms in advanced topics and shows how Euler's Theorem links all of these topics together. It culminates by applying all that is learned into solving the cubic equation in closed form. This book helps hone students' computational and study skills and shows them how to remember and recall everything that they learned in math. It re-emphasizes studying, learning, and thinking skills. Grades 9 to 12.
13. Patterns to Success: Nurturing Your Child's Innate Giftedness $17
This book uses the Pascal Triangle as the basis for discovering arithmetic, geometric, and other patterns, and organizing the thought processes to encourage creativity in almost every child. It using as examples the magic square and Roman Numbers to teach how to learn, study, remember, and think. With clever use of manipulatives and novel notations, the book teaches how to understand the often unexplained reasons for the rules of subtraction, division, and decimals. This book breaks with the conventional teaching techniques to encompass an understanding of why we do mathematics the way we do. It can make children think and become their own teachers. Grades 2 to 5.
14. Roman Numbers: Challenging Mathematics Education $17
This book explodes some myths about Roman Numbers and uncovers some of their interesting characteristics. Using Roman Numbers as a reference, the book interrelates our monetary system, the abacus, and techniques to make learning addition easy. The book is organized in a way that students can easily learn half a dozen other number systems and gain an understanding of the strengths, weakness, and peculiarities of each. More importantly, the book explains patterns and consequences of other number systems that are overlooked in conventional education. The book uses these observations to criticize the way math has been taught to date. Readers will be awakened to organizing the many meaningless and seemingly unrelated facts stored in the recesses of their minds into simple, well-organized thoughts. They will learn how to think and develop the confidence to challenge what is told to them. Grades 3 through 7.
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