Boston Grade School Enrichment Tutoring
The child who has learned arithmetic strictly
by memorizing has missed the first great opportunity to develop
his or her intellect. The most fundamental act of the intellect
is to see the same thing in two or more different ways. This act
is at the basis of art, literature, and humor.
The child who has learned that 6 times 8 equals
forty-eight strictly by memorization has missed the chance to develop the
intellect by knowing several different ways to figure that out.
Another problem that comes up in grade school
arithmetic is that some children find it impossible to memorize
the addition and multiplication tables. Some very bright children
find themselves in this situation. These children are at risk for
developing a life-long aversion to arithmetic, and later, to math
of all kinds.
The way out of this dilemma is to teach these
children to understand the addition and multiplication facts. The
understanding of the facts, and the ability to work out several
different approaches for arriving at each fact, provide a pathway
that these children can tread to learn their tables.
Our feelings about the very important addition
and multiplication tables can be summarized as follows:
a fact without knowing how to figure out the fact for oneself
Hard to do
Bad for the mind
Memorizing a fact based on knowing several
ways to figure out the fact for oneself
Easy to do
Good for the mind
Another problem inherent in the math education
that most children receive involves the skill of reducing fractions.
Children learn to reduce 6/8 to 3/4, but even most adults will have
difficulty reducing the fraction 38/57.
I personally remember the distinct feeling that
I experienced in fourth grade in this connection. I realized that
I had been taught to reduce simple fractions, but that larger numbers
(like 38/57) would defeat me. It was my first feeling of loss of
mastery. A child should be taught the basic structure of integers
that would complete the skill of reducing fractions.
Take a look at your child after he or she has
learned to handle the integers and can "flash" on the
addition and multiplication tables. This child walks straighter,
likes school better, and feels good about himself or herself.
This child will no longer have difficulty learning
that there are three feet to a yard and three sides to a triangle.
Arithmetic, and later the higher forms of math, will come easy to
One other thing about grade school arithmetic:
again picture the child that has overcome all difficulties with
arithmetic. The child takes quizzes and tests and gets no scores
below 100%. This child is ready to become a "mathlete"
in the wonderful math competitions that are available
in middle school.