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Algebra Through Symmetry is a visual method that was prevalent at the dawn of the mathematical sciences. Symmetry is crucial in the formulation of the method and it is symmetry that enables a visual solution of the algebraic equations. The visual method achieves symmetry through a process of axiomatic reformulation. Reformulating an equation to obtain symmetry requires less symbolic logic, fewer arithmetic operations and activates the student's most primitive concepts of one-to-one matching and the symmetry of the human form.
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perrycream
This is an interesting document. I fully agree that many items, such as completing the square as the only way to solve the quadradic equation, need to be changed in our teaching of math .... this is one of the several alternatives. However, as writen, I don't think visually oriented student thinkers could use it ... I will try it in a class with some modification ... or perhaps as a video or powerpoint.
October 1, 2012 
Wm. George Mandras (TpT Seller)
I use the Modified Quadratic Formula in my tutoring.( in the quad formula: divide terms in the numerator by 2 and the square-root of 4 to obtain the Modified Quadratic Formula)
Send me an email at: wmandras@roadrunner.com and I will attach my paper, Modified Quadratic Formula, to my reply.
Send me an email at: wmandras@roadrunner.com and I will attach my paper, Modified Quadratic Formula, to my reply.
October 2, 2012
jackdudley
An excellent approach to helping students develop an intuitive understanding of basic algebra.
August 8, 2010
mcullen
Symmetry is a great addition to the algebra pedagogy. I teach both the axiomatic and visual methods to my HS classes. I allow the students to choose the method that is easiest for them during a test. Most of them choose the visual method because it requires less symbolic logic and it takes less time to obtain a solution.
September 15, 2008
Wm. George Mandras (TpT Seller)
My teaching style is similar; it has definitely benefited the at-risk students
September 21, 2008
djtotten
I am now retired and formerly taught mathematics in HS and Middle school. I am very impressed with Algebra Through Symmetry and regret that it was not available during my teaching years. Many of the students that I taught had extreme difficulty with the traditional axiomatic method. Based upon outside classroom contact with current students, they learn algebra quickly and easily by using the visual method.
September 15, 2008
Wm. George Mandras (TpT Seller)
I was raised in the axiomatic method but my experience has taught that the only way to reach the at-risk students is to simplify the procedures. I read The Elements more than 40 years ago, so when I was looking for an easier method, visual algebra surfaced from memory.
September 21, 2008
BruceKWill
If you find that your students just don't "get" algebra by classical methods, this approach may lead them to a fundamental understanding.
November 23, 2006
Wm. George Mandras (TpT Seller)
Mathematical ability is normally distributed in the K14 student population consequently most students do not learn algebra if the axiomatic method is used exclusively. I teach both methods in parallel, that is, the students are required to solve each equation twice by employing the axiomatic mantra, “whatever you do to one side of an equation you must do to the other“, and the visual mantra, “rewrite the equation until both sides look the same.” Such a mathematical pedagogy more closely matches the profile of a typical class and enables many more students to learn algebra.
November 23, 2006
OrangeMath
I use this approach in my continuing education program in high school. The standard way failed for these students. The symmetry approach baffles them somewhat, but they also find it fun (relatively) to try this. I consider this paper too short for a regular class, but great for shorter classes that can only cover some standards in depth, such as California.
September 8, 2006
Wm. George Mandras (TpT Seller)
Most of my students appreciate an intuitive method that enables them to do and understand algebra, many for the first time. I teach both methods in parallel, explicit-axiomatic and implicit-visual. One of my teaching techniques consists in demonstrating that every example problem in the textbook, which uses the axiomatic method exclusively, can be solved more easily through the use of numerical techniques that produce symmetry. The state-mandated criteria require the solution of at least 70% of the algebra problems to pass with a "C" or better. The criteria do not require that the students solve the equations in the most difficult way possible. The visual method is within the scope of any student skilled in arithmetic and may be the only means available to "rescue" those students whose circumstance place them at high risk of failure in abstract mathematics.
November 13, 2006
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Aerospace engineer, retired 1996: 35-year career as a technical specialist in aircraft and space vehicle structures. 9/89-9/04 Oxnard Community College - part time faculty 9/84-6/86 West Coast University - part time faculty Taught undergraduate students in Engineering Economic Analysis, Experimental Methods for Engineers, Static's & Strength of Materials, Materials Science, Introduction to Engineering, Engineering Design (CAD), Elementary & Intermediate Algebra, Linear Algebra, College Algebra, Fundamentals of Arithmetic. 1/68 - 3/71: College of Aeronautics - Assistant Professor Taught undergraduate students in Strength of Materials, Materials test laboratory, Thermodynamics, Engineering Design, Aircraft Structural Analysis, Mechanics, and Introduction to Computers.
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