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
children's 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 children--adults as well--to 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, let's 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.
About the author:
Joe is a prolific writer of self-help and educational material.
Under the penname, JC Page, Joe authored the classic of
mathematical ABC's Arithmetic Magic. 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. For more
information, visit his website at
www.mathbyjoe.com.
