Category Archives: Number Line

Counting on Rules of Arithmetic CORA

Counting on Rules of Arithmetic. We count on from a starting number like 3 by a second number, the count on number or shift number like 2. 3+2 means start at 3 and count on by 2. We imagine we … Continue reading

Posted in Counting on Definition of Addition, Counting on Rules of Arithmetic, Kindergarten Counting On, Peano Axioms for Number Line | 3 Comments

WaPo Emma Brown Parent group pushing for TJ admission changes

The Thomas Jefferson High School admissions test is not hard enough and doesn’t qualify students good enough or advanced enough in intro algebra for the work at TJ.  This results in the need for remedial teaching this summer at TJ … Continue reading

Posted in Emma Brown Education Journalist, Peano Axioms for Number Line, Thomas Jefferson High School for Science and Technology, TJ Summer School for Stragglers, TJHHS Algebra Admissions Test, Vision and Works | Leave a comment

Peano Axioms Number Line

Peano Axioms for the Number Line.  Think of a number line that starts at 0.  It only has the natural numbers as ticks, so 0, 1, 2, etc.  It has no fractions marked and it has no signs positive or … Continue reading

Posted in Number Line, Peano Axioms, Peano Axioms for Number Line | 11 Comments

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: 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