SYSTEMIC
AND INCREMENTAL APPROACH
Methodical Approach to Education [click]
Clarity of Definitions [click]
The Age Factor [click]
Systemic and Incremental Approach [click]
Fundamental Skills [click]
Conceptual Thinking [click]
Intensive marketing by the education industry of various "incremental" and "systemic"
concepts over the past several decades led to the very meaning
and essence of such methods being washed out and the
principles themselves have been completely discredited. However, when used properly, this methodology is still the best and time-tested educational tool.
We will show how systemic approach to education should be used in the student's best interests.
Let's ask our 12-year-old Johnny or Sally to solve the following equation:
Try it: ask your child to solve this equation. Sure, there will be students who will
find the correct answer by means of sheer brilliance,
or those who will make a lucky guess. Some think this is good enough, as long as the answer is right. We disagree: the true classical
method emphasizes not only getting the right answer, but also how the student arrived at the solution.
Look at the equation above and follow through the entire sequence
of building blocks necessary for a confident and correct
solution:
Block #1: The student should recognize
this equation as an algebraic proportion and thus, he
or she should recall the main property of any
proportionbased on the correct fundamental definition.
It states that the cross products of a proportion are
equal.
That is if: 
,
then ad = bc. Of course, basic arithmetic skills are required in this situation. Once the student recognized this equation as a proportion,
he or she is ready for the second step, which involves transforming
the equation by means of cross multiplication into:
Block #2: Once the student arrives to this form, he or
she should apply another essential bit of knowledge:
multiplication of binomials. This requires
the knowledge of operations with powers and the knowlege of factoring. In this particular case, the
formula of the square of the sum. Why? Because the left
side of this equation (x+1)(x+1) is, of course, the square
of the sum and could be written as: (x+1)2, which is,
of course: x2+2x+1 . And now our equation looks like
this:
Block #3: Once this task is accomplished, the student
should recall two very essential skills: operations with
like terms (which is a part of basic factoring) and properties
of true statements, (which is essential for the solution
of every single equation on earth). Now our equations,
after all simplification, will look like this:
Block #4: Now we reach the form of the equation that
the student should know: the linear equation of form
ax = b ,
which is solved like this: 
or, in our particular case 
Yes, x being positive 3. While solving this, the student
should remember the operations with the positive and
negative numbers and the definitions of the roots of
the equation as well as understand clearly what it means
to solve any equation. This is yet another fundamental
definition, which states that: to solve an equation means
to find its root(s) or to establish the fact that the
equation does not have root(s). (Yes, there will be many
cases when equations will not have roots, that is, solutions).
What are the roots? Enter another definition: the number(s),
which turn the equation into a true statement. Indeed,
plug our root x=3 back into the original equation:
True statement! Isn't it? Thus the equation
is solved.
And now, once this simple routine is over, let us analyze
what system of knowledge and what increments did it take
to solve the equation. After doing this, we will understand
the immense importance of the true systemic and incremental
approach. Let us create the logical sequence:
Well, there you have it - what it takes to be a good handler
of the linear equations of this form. Red arrows show
you the sequence of the knowledge blocks (increments)
and system (formation), which is required for even this
simple algebraic exercise. And now, mentally, unite each
individual rectangle with the rest of the rectangles
in this system by imaginary arrows. What did you get?
Yes, a web of them, when each separate block is connected
to others. Now imagine dozens upon dozens of those rectangles
tied to each other. And each rectangle will stand for
some specific block (increment) of knowledge. What will
you get? Right - the comprehensive knowledge of the subject
and that is what AIMS does: creation of knowledge by
the systemic, incremental approach. Each child has his
or her own way of grasping the subject, and we were able
to implement both group and individualized approaches
to the full extent with tangible success. What stands
behind each of these and other rectangles, is another
matter - it is our secret, but you are welcome to share
in it and see for yourself what magnificent and inspiring
transformations will happen in your child.
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