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The simplified methods are an attempt to help those students that will have difficulty learning the subject of arithmetic throughout their entire...

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Every young student is aware of symmetry in a non-conceptual way given that the first thing a newborn infant sees, when vision become operational...

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Subtraction By Addition is an attempt to help those students that will have difficulty learning the subject of arithmetic throughout their entire...

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Advanced Instruction Resources (TpT Seller)

I could see this product being used in a variety of math classes. The symmetry connection is a different way to teach math and might work with some students. Thanks for sharing.

December 25, 2013

Buyer

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.

Sharon L.

Great info

September 5, 2012

Buyer

Awesome concept in an easy to figure out form. Thanks!

February 19, 2012

Tracy K.

Clever. Supports multiple learning styles.

February 3, 2012

Buyer

An excellent approach to helping students develop an intuitive understanding of basic algebra.

August 8, 2010

Buyer

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

Donald T.

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.

Bruce W.

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.

Dennis A.

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.

Ask Wm. George Mandras a question. They will receive an automated email and will return to answer you as soon as possible.
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QUESTIONS AND ANSWERS:

Buyer

Sorry, I thought I had already sent you an email. The address of my website is www.universalhomeschool.com/custom It will be a while before it is live, I am in the process of building it, and creating/collecting quality material. It is mainly going to be video based.

Wm. George Mandras (TpT Seller)

Yes, you may use my work on your website as long as it is not for sale.

Buyer

Sorry, I thought I had already sent you an email. The address of my website is www.universalhomeschool.com/custom It will be a while before it is live, I am in the process of building it, and creating/collecting quality material. It is mainly going to be video based.

Wm. George Mandras (TpT Seller)

Yes, you may use my work on your website as long as it is not for sale.

Buyer

Sorry, I thought I had already sent you an email. The address of my website is www.universalhomeschool.com/custom It will be a while before it is live, I am in the process of building it, and creating/collecting quality material. It is mainly going to be video based.

Wm. George Mandras (TpT Seller)

Yes, you may use my work on your website as long as it is not for sale.

Buyer

Dear George,

My name is Jack Dennison. I am the Editor-in-Chief of www.FunnelBrain.com, an educational website. I am writing to you because the quality of the work you have posted to PTP distinguishes you as a talented author. I am looking for teacher-authors to create custom study review materials for FunnelBrain (on a paid basis, of course).

These study materials would take the form of online flashcards, quizzes, and study guides for high school and college level courses, as well as for certain standardized exams such as the GMAT, the SAT or the GRE. We are also interested in lesson plans built around activities that can take place on www.FunnelBrain.com.

If you are interested in a paid writing assignment, please email me at jack@funnelbrain.com, and I will respond with details on the available assignments. In the meantime, please feel free to browse FunnelBrain.com.

I look forward to hearing from you.

Regards,

Jack Dennison

My name is Jack Dennison. I am the Editor-in-Chief of www.FunnelBrain.com, an educational website. I am writing to you because the quality of the work you have posted to PTP distinguishes you as a talented author. I am looking for teacher-authors to create custom study review materials for FunnelBrain (on a paid basis, of course).

These study materials would take the form of online flashcards, quizzes, and study guides for high school and college level courses, as well as for certain standardized exams such as the GMAT, the SAT or the GRE. We are also interested in lesson plans built around activities that can take place on www.FunnelBrain.com.

If you are interested in a paid writing assignment, please email me at jack@funnelbrain.com, and I will respond with details on the available assignments. In the meantime, please feel free to browse FunnelBrain.com.

I look forward to hearing from you.

Regards,

Jack Dennison

TEACHING EXPERIENCE

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.

MY TEACHING STYLE

In mathematics, I teach both the explicit-axiomatic and implicit-visual methods in parallel. 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.

HONORS/AWARDS/SHINING TEACHER MOMENT

Best teacher award 1970 at the College of Aeronautics. Most of my students appreciate an intuitive method that enables them to do and understand algebra, many for the first time. This is evidenced by the written remarks made on the unsigned evaluation sheets which are overwhelmingly positive. These are typical and authentic remarks because they are anonymous: 1.This is the first time I have ever understood math. Mr. Mandras is my favorite Professor. 2. Mr. Mandras is an excellent math instructor and has helped me overcome my math fears. He encourages students to believe that they can achieve. 3. Mr. Mandras has shown me a different side of Algebra. It is not as intimidating once he has explained it. I am thankful for having an instructor like him on this campus.

MY OWN EDUCATIONAL HISTORY

Education: MSME, New York Polytechnic University, New York NY. BSME, Drexel University, Philadelphia PA. Professional: Registered Professional Engineer, CA & CO - Mechanical. California Community College Instructor Credentials: Engineering & Mathematics. Member: American Society for Engineering Education. Member: National Council of Teachers of Mathematics (NCTM)

ADDITIONAL BIOGRAPHICAL INFORMATION

Married to wife Marty for 38 years, two daughters, one granddaughter and one yet-to-be-born grandchild. Daughters are a nurse and a teacher; granddaughter is a biology major at a state university.

GRADES

PreK, Kindergarten, 1^{st}, 2^{nd}, 3^{rd}, 4^{th}, 5^{th}, 6^{th}, 7^{th}, 8^{th}, 9^{th}, 10^{th}, 11^{th}, 12^{th}, Higher Education, Adult Education, Homeschool

SUBJECTS

Math, Algebra, Arithmetic, Basic Operations, Curriculum & Instruction, Mathematics, Basic Reading, Basic Math