Category Archives: Pair of Number Line Method of Addition

Pair of Number Lines and Successor Identities

This post concerns using a pair of number lines to illustrate the successor identities.  At lower grade levels, we can simply use a pair of number lines to “prove” the successor identities.   We actually make them plausible, but at an … Continue reading

Posted in Addition Right Identities, Addition Right Successor Identity, Addition Right Zero Identity, Lesson Plans, Lessons Lower Elementary Grade Levels, Number Line Induction, Number Line Recursion, Pair of Number Line Method of Addition, Recusive Inductive Definition of Addition, Teaching prime notation with number lines, Teaching x and y with Number Lines | 1 Comment

Is addition just counting?

Suppose you are given two sets.  One contains 2 items and the other 3.  You form a single set and count them 1 to 5.  This is addition.  What is wrong with this? Addition from Peano Axioms is consistent with … Continue reading

Posted in Addition as counting, Addition Definitions, Iterated Succession, Number Line, Pair of Number Line Method of Addition, Repeated Succession, Set theory definition of addition | 15 Comments

Richard Dedekind Essays on Numbers On-line

The Richard Dedekind book from 1888 that contains New Math in all its original glory is available in English for free. The following was typed into latex and then converted to pdf: http://www.gutenberg.org/files/21016/21016-pdf.pdf The Nature and Meaning of Numbers starts … Continue reading

Posted in Confession of Arithmetic Faith, Essays on the Theory of Numbers, Head Segments of Natural Numbers, Initial Segments of Natural Numbers, New Math Done Right, Number Line, Pair of Number Line Method of Addition, Tails of Natural Numbers, The Nature and Meaning of Numbers, Wooster Woodruff Beman | 1 Comment