As a continuation in my series of articles on the merits of mathematics, I submit this topic for consideration by parents who want to give their children a serious edge in mathematics. You see folks, it all begins with the basics. Give your children the basics and then the rest is assured. You cannot build a house on a weak foundation, nor can you expect to build your childrens education on a weak substructure. One of the problems with education today is that we have moved away from stressing the importance of the basics. Although this pedagogical approach is still adhered to in many school districts, too much tampering with basic approaches to the learning of mathematics has resulted in a perversion of this basic tenet. Because mathematics is inherently difficult to learn, the common frustration which results from its study has led educators and parents to seek alternative learning approaches.

Over the years, I have developed independently a series of techniques to help childrenadults as wellto do arithmetic with more confidence. After I started cataloguing my system of techniques toward the aim of producing a DVD series, I discovered that certain aspects of my teaching were similar to the methods taught in the Vedic system of mathematics. This system is based on the sutras of Sri Bharati Tirthaji Krishna (1884-1960) and such system is a beautifully catalogued compilation for showing how to do mathematics more naturally and efficiently. A sutra is a Hindu piece of writing meant to teach aphoristically, and such sutras were produced for the purpose of study, meditation, and indeed memorization. When I discovered the Vedic system and immersed myself into some of its sutras, I became quite amused at how pieces of certain discoveries, throughout history, can be made by independent parties.

Armed with the knowledge of the Vedic system as well as my own independently discovered methods, I am placed in a unique position to propagate these methods and to aid children in their efforts to become more efficient and more confident in doing mathematics. Although the arithmetic techniques are interrelated and often build upon one another, the best approach is to teach them in parts, allowing the children to absorb one aspect before moving on to the next. The beauty of these techniques is their simplicity of use and their ability to boost the confidence in students who have incorporated them into their learning repertoire.

Toward this end, lets look at one technique, which I have named the Nifty Five Square Technique. This method teaches students to take the numbers that end in five (called five numbers) and calculate the multiplication of each number by itself. When a number is multiplied by itself, such as 3 x 3, we say we are squaring 3 or squaring the number. Specifically, this method teaches students how to square each of the numbers 15, 25, 35,...,95.

The Nifty Five Square Technique takes each of the numbers and produces their square instantly. No calculator required. The method, with appropriate modifications, will work for all five numbers, even numbers like 115 or 225. For the purposes of this article, however, I will confine myself to the set of five numbers from 15-95. This is a sufficient subset of five numbers for one to garner a particular appreciation of the beauty of this method. Now, let us begin with the method.

In order to calculate the product of 15 x 15, all one need do is take the digit 1, which is the tens digit and multiply that by one more than the tens digit. Thus 1 + 1 = 2, and 1 x 2 = 2. Then just attach 25 to the number 2 to get your product. Thus 15 x 15 = 225. For the other numbers we have the following:

25 x 25 = 625 (2 x 3 = 6)
35 x 35 = 1225 (3 x 4 = 12)
45 x 45 = 2025 (4 x 5 = 20)
55 x 55 = 3025 (5 x 6 = 30)
65 x 65 = 4225 (6 x 7 = 42)
75 x 75 = 5625 (7 x 8 = 56)
85 x 85 = 7225 ( 8 x 9 = 72)
95 x 95 = 9025 (9 x 10 = 90)

What could be easier than that! Start showing your kids this stuff and you will be amazed at how quickly they start to excel in mathematics. Their defeatist attitudes in mathematics will quickly change to more confident and self-assured ones. Children armed with these techniques will feel a sense of positivity toward the subject and no longer dread doing their basic arithmetic homework. With this shift in attitude, children become successful in a difficult subject, become more poised toward challenges, and ultimately become more effective problem solvers. Try it out.

Joe Pagano

Joe is a prolific writer of self-help and educational material and an award-winning former teacher of both college and high school mathematics. Under the penname, JC Page, Joe authored Arithmetic Magic. As a result of this publication, Joe was invited to be a guest on the television show the Book Authority. Joe is also author of the charmingly pithy and popular ebook, Make a Good Impression Every Time: The Secret to Instant Popularity; the seminal collection of verse, Poems for the Mathematically Insecure, which teaches a number of valuable math lessons (often in a humorous way) and even demonstrates famous proofs in both free and formal verse; and the creator and scriptwriter of an upcoming DVD series that is both visionary and highly educational. The diverse genre of his writings (novel, short story, essay, script, and poetry)?particularly in regard to its educational flavor? continues to captivate readers and to earn him recognition.

With a renaissance approach to learning and with over twenty years experience in the science and mathematical disciplines, Joe, through his novel and engaging style of teaching mathematics, has won success for students who attempt to learn this most difficult subject. One of Joe?s principal endeavors is to give individuals---children in particular---the tools and confidence to do basic mathematics. Once obtained, these tools steer students into gradually increasing levels of mathematical study. Ultimately these same students become effective problem solvers with access to many doors of opportunity.

Joe propagates his teaching philosophy through his articles and books and is dedicated to helping educate children living in impoverished countries. Toward this end, he donates a portion of the proceeds from the sale of every ebook. Joe makes himself available for speaking, consulting, teaching and inspiration. For more information on Joe, his teaching style, as well as information on how to purchase his books or other writings, please visit his website.