The textbook method, Axiomatic Reduction to obtain Reflective Symmetry, (x = a), currently in vogue in all the algebra textbooks in print, is arguably the most difficult way possible to find the solution of an algebraic equation. Because all students must be proficient in algebra in order to graduate from high school or proceed in their college major, this book presents the alternative methods for the solution of algebraic equations that provides a resource, other than a textbook, for the students to refer to. The methods are visual, negate the use of abstract symbolic logic and reformulate the equations to solve for the variables by the one-to-one matching of terms.
The basis of visual algebra is one-to-one matching and the reflective symmetry of the human form, which are natural concepts that implies a one-to-one matching of parts, is an organic part of human understanding, is ingrained very early in life (crib-phase) and is independent of one’s mathematical ability. Considering the remarks written on the instructor evaluation forms by students that were taught visual algebra, strongly suggests that every student may have a natural propensity towards mathematics, that is, if the pedagogy is in sync with the student’s most ingrained concepts of symmetry and one-to-one matching. One way to help all students is to simplify the mathematical procedures as much as possible; to that end this book was written.
What method should be taught for the solution of algebraic equations? The 3-known methods: Axiomatic Reduction to obtain Reflective Symmetry (textbook), Axiomatic Reformulation to obtain Translational Symmetry, Numerical methods and Geometric Algebra after a hiatus of 2300 years; Euclid’s students were equipped with a straight edge and compass and could draw the geometric diagrams to scale (See bottom of Page 3). Then allow the students, themselves, to decide which method is most conducive to their understanding. Such pedagogy is more likely to fit the mathematical abilities of a typical class in algebra.
The numerical and visual methods for the solution of algebraic equations are intended to augment what is currently taught in the algebra curriculum.