CONCEPTUAL
THINKING
Methodical Approach to Education [click]
Clarity of Definitions [click]
The Age Factor [click]
Systemic and Incremental Approach [click]
Fundamental Skills [click]
Conceptual Thinking [click]
Oh! This is yet another skill that is
being held hostage by educational bureaucracies and freelance
drudges, who time after time announce the new "conceptual"
approach and instead get students into the mush of basic
"monkey" skills, without answering the main question
"WHY"? Why this way and not another is what our
children need, and make no mistake about it, they are
completely
ready and capable of understanding this essential "WHY"
thing. You may teach your child how to solve one thing
or another, you may also teach him or her several things,
like changing tires and brakes on the car. But they will
not become a knowledgeable student nor a complete auto
mechanic until the whole story is told. Remember, mathematics
(and algebra in particular) is arithmetic expressed in
general form. That is why European and Asian students
receive more knowledge in virtually any precise and natural
science than do American students, the secret is simple
- they are intensely taught general concepts first, and
then
taught how to apply them. Here, we have the situation
completely reversed: from narrow "monkey" skill
to maybe, under some favorable conditions, an understanding
by
some students of the larger issue and a grasping of the
larger picture.
But what if we say to them, "grasp the
whole picture first and then apply knowledge?" Do not
be afraid - the majority of our students are ready for
that, they want
that. We know this for sure! Our students
want to know not only that 
but
why. They want to know why quadratic equations have one
standard and three substandard forms, plus another, which
is called, derived. They want to know how to prove LaGrange's
Theorem, or how to derive the differential for any power
function, not just a single one. They want and need to
know how to solve most complex word problems involving
calculus or trigonometric transformations, or how to
explain mathematically Toricelli's experiment. They all
need that, because every normal decent child has those
desires naturally and organically arising in him or her
- because the gift of thinking is given to us from above;
it is
our gift and the most precious personal possession. That
is what makes us HUMAN. Let us not deny our children
this right - to be HUMANS!
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