The Other Side of Math
∞ APPENDIX A ∞
PREVIEW OF OSOM STEP 3
STEPPING OUT OF THE BOX:
ALTERNATIVES
THE ILLUSTRATIONS
The following white on black illustrations contain unusual line drawings around the borders of the images. These border designs are actually numerals taken from older numeration systems. However, I am using these ancient symbols purely as decoration, and they have no literal mathematical importance or meaning as regards the subjects of this paper.
Alternative Subtraction Algorithm: Austrian Subtraction
Definition of Alternative: 1) something different from and able to serve as a substitute for something else; 2) the possibility of choosing between two different things or courses of action; 3) either of two, or one of several things or courses of action to choose between. (Encarta Webster’s Dictionary)
The use of Step 2 helps free students from dependence on their teachers and textbook/video courses. It enhances their ability to create mathematically on their own. With this enhanced freedom of mathematical thought, students (or at least some of them) will be ready for OSOM Step 3 STEPPING OUT OF THE BOX WITH ALTERNATIVES:
- Alternative Axioms
- Alternative Theorems
- Alternative Algorithms
- Alternative Numeration Systems
- Alternative Solutions
- Alternative Methods of Checking Answers
- Alternative Definitions
In Step 3, Alternatives, the student is no longer using only his textbook’s ideas and practices to guide himself in the solution of math problems. The teacher and the OSOM Step 3 curriculum are intentionally directing him to math ideas and math practices that are outside “the box” (the book, teacher, exams, etc. used in his school). Alternatives has a simple aim: to free the student from the mathematical box once and for all by demonstrating to him in the most direct and personal way possible that there exist simple, usable, and interesting alternatives to the math inside the box.
Alternative Division Algorithm: Big 7 Division