Saturday, November 6, 2010

Home Schooling - Concept Progression - Learning How To Learn






Alex just finished the First Semester of Algebra II -
He started 3 months ago.

Through Plato Courses, he has advanced far more quickly
than would have been possible in normal school.

Each section is divided into Concepts. 

Each Concept has a mastery test. 

This allows firmly stated objectives to be mastered
before moving on. 

There is no moving on...or lingering...
 because it follows the time line of a class.

 With home schooling...
 the time line serves the needs of the individual student.

 He may advance upon mastery of the concepts.  


In Alex's case...there is no frustration of having to keep
 a slower pace than is exciting to him. 

He strives to master a concept a day. 

He looks forward to achieving a milestone of progression...
and so, the understanding, so he may advance to higher peaks
of the mathematical (and other subjects) mountain range. 

Today's Concept:  Rules for Exponents and Radicals









Alex, while still only 9 years old...
 is learning far more than academics through his studies. 

Through his studies, he is realizing a far more important lesson:

Learning How To Learn

Break down problems into logically ordered
(Category / Sub-Category) and easily digestible bites.

Master each one before moving on (100% of problems correct). 

The thorough understanding of the sub-categories
leads to understanding of the categories and concepts.

The understanding of this fundamental concept leads to
the construction of a logic tree in the mind. 
As knowledge builds upon knowledge...
the interconnections of concepts make sense.

He will have established perspective and a deeper understanding
 not only of his subject, but of its application.

It is this, the correct application, that the world demands.  
You must know, not only how to answer a problem...
but how to recognize when and what type of problem it is...
and how to formulate the correct solution.

Regurgitation supplies the answer to a specifically outlined problem.

True understanding (Mastery) supplies the path to
Problem Detection...Problem Type...Problem Resolution
in the most efficient and effective manner, as well as...
the tying of it into the master plan.  

Just as importantly, it allows the completed run through
 (in the mind) of applied Problem Resolution...
this is the litmus test for its application.

A correct answer allows the movie of the mind to progress....
ex..the bridge span to withstand the calculated strain
without buckling...
or the house to be built using far less timber
while being stronger...etc.

This is how many innovators think...
they see the answer in their minds and merely reverse engineer.

This is possible because of a mastery of concepts.

While this is a very fundamental and simple thought process...
many lessons in normal school are not structured in such a manner.

I am sure many of you have experienced the same growing up in school. 
To have a lesson or course taught out of logical order is in essence....
teaching the leaves of the tree before the roots / trunk / branches. 

Roots...Trunk...Branches...It is this order that allows perspective
and which allows the logic tree of the mind to be constructed.

Each section is a concept to be mastered. 

With each section mastered...
it becomes easier to predict what should come next...
as it becomes intuitive. 

It is this intuition of the next step that allows children
to think laterally...innovatively...creatively.  

Critical Thinking and Creative Thinking

The building blocks to true knowledge

Both dependent upon the logical progression
 of Concept Mastery.

Learning how to learn
through the logical progression of concept mastery. 

A vital lesson that is learned while learning...

What could be more efficient?

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