Abstraction is chunking abstracting right is math foundations

Abstraction is chunking information into definitions, axioms, precise theorems, proofs and examples.

Chunking at the right spots is what math foundations does.  Math foundations finds where one idea or concept or procedure ends and another begins.

If the chunking is at the wrong spots, it is not memorable.

The John Sweller video on the right at the link shows chunking at wrong spots destroys the coherence of the message.  It can’t be remembered, since you never knew it.

http://www.instructionaldesign.org/theories/cognitive-load.html

Chun king wor dsatt hew ron gpl ace des troy sco her ence.

Chunking words at the wrong place destroys coherence.

The first sentence is current math education that ignores the Peano Axioms and fractions as object oriented pairs of natural numbers with rules and procedures.

The first sentence is the throw every application, idea or property at the students as if of equal logical value.  This is arithmetic democracy.  It is application democracy.  Every application is equally important logically as the definition or abstract properties of a math object.

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About New Math Done Right

Author of Pre-Algebra New Math Done Right Peano Axioms. A below college level self study book on the Peano Axioms and proofs of the associative and commutative laws of addition. President of Mathematical Finance Company. Provides economic scenario generators to financial institutions.
This entry was posted in Abstraction, Abstraction is Chunking, Chunking, Cognitive Load, Confusion Load, Uncategorized. Bookmark the permalink.

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