Category Archives: Uncategorized

Peano Axioms 2015 Never more important

Learning the Peano Axioms has never been more important than in 2015 and the years to come.  The Peano Axioms mean that when we do elementary math at any time, we are thinking in terms of foundations of math and … Continue reading

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Learning different multiplication methods is a sound idea

Schools are sometimes ridiculed for teaching different ways of doing multiplication.  However, if this was so bad, then how can we teach applications of multiplication at all?  Isn’t another method to do multiplication an easy application of a first method? … Continue reading

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Structure and abstraction fight the math is random drills feeling

Many students and teachers complain that math is a sequence of random drills with no connection or structure.  What is the plan? How does it fit together? The answers to these questions comes from structure.  Structure is how parts of … Continue reading

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Same 5 rules over and over again in Peano arithmetic

The same 5 rules of the Peano Axioms repeat over and over again as we develop elementary arithmetic of whole numbers. The 5 rules apply not just to the natural numbers, but can be restated to apply to the head … Continue reading

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Head sets v tail sets the unknown controversy

Head sets of natural numbers starting from 0 are sets like 0 0,1 0,1,2 etc. Tail sets are all the numbers starting from and after that number. 0 to infinity, including 0 1 to infinity including 1 but not 0 … Continue reading

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Why good theory must inform pedagogy

If we understand the theory first and then rework it into slogans for children to learn, then we give them a path to understanding. If we invent slogans first and they don’t line up exactly with theory, then there are … Continue reading

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If your students can’t do the associative law proof they have gaps

If your students can’t do the proof of the associative law of addition of whole numbers, then they have gaps in their knowledge.  Moreover, they don’t know they have them.  They will think they know common core math principles but … Continue reading

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