Abstraction is the way to explain in math

The way to explain something in math is take away what is not the explanation. What is left is the explanation.  This is called abstraction.

Applications do not explain a math concept.  Calculus was applied to physics before the 19th century.  But the correct explanation of calculus was not until the 19th century.

The wrong explanation is not the explanation.  Wrong explanations are the sign that what is being taught is skills and drills.  It is the sign of behavioral teaching.  It is the sign of stimulus and response teaching.

Calculus before the 19th century was stimulus and response teaching as far as what the derivative really meant.

The explanation was finally determined in the 19th century.  Repeating the wrong explanations of the previous 200 years is not shorter than the right explanation.

The right explanation of limit and derivative is shorter than reading all the different attempted explanations in the 17th and 18th centuries.

The same applies to the math of elementary math.  That math starts with the Peano Axioms.

Wrong explanations are not shorter. They divert the student from the right explanation.  That just takes longer.  Most students will never overcome a wrong explanation in elementary math.

The poorer and more disadvantaged the student, the more the wrong explanation diverts their attention and understanding away from the truth.  New Math abstractions are the last best hope for the poorer students.
 

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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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