Abstraction reduces cognitive load

Abstraction reduces cognitive load.  Abstraction is you remove what is not the explanation and what is left, if you did it right, is the explanation.  Math foundations has already done it right for elementary math.

When we use the abstractions of math foundations, then we reduce the cognitive load of learning elementary math.

One sees diagrams for teaching where every type of sensory experience of fractions is to be thrown at the student.  This is confusing the student.  They don’t reconstruct a math foundations book from that.  Instead they shut down in learning more math.

Abstraction is the opposite of throw every idea at them as equal.  Abstraction pares away most of those ideas and all of the applications.  Applications are not part of the abstract idea of fraction.  Geometry, area and length are not part of the abstract idea of fraction.

The cognitive load link with short videos is given again here.

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

The video on the right gives a cognitive load task and shows that meaning lightens the cognitive load. The same is true in elementary math.  The meaning of elementary math is not applications.  The meaning of elementary math is math foundations.  It is the Peano Axioms through fractions as object oriented data with procedures.

Structure also reduces cognitive load.  Abstraction and structure go together.  Abstraction takes away what is not the structure and we are left, with luck and the work of mathematicians over many years, with the the structure of what we know in elementary math.  It is the structure of what it means.

The weakest students are helped the most by reducing the cognitive load. Abstraction helps the weakest students.   The pared down structure of math foundations helps the weakest students have a structured path through elementary math.

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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.
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