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 logic. They remind us of ordered pairs, sets, functions, recursion, definition by induction, proof by induction, and so on. These are the basic concepts of math, logic and programming. So we are always getting a reminder of these every time we use numbers when we learn the Peano Axioms.

Recent Posts
Archives
Categories
 #mtt2k Khan Academy Videos Procedural v Conceptual
 20th Century Peano Addition Authors
 21st Century Peano Addition Authors
 408 U.S. 593 (1972)
 470 U.S. 532 (1985)
 5th to 7th grade math fails in prealgebra
 Aaron Swartz
 Abstraction
 Abstraction is Chunking
 Academy of Actuaries
 Actuary
 Addition as counting
 Addition Definitions
 Addition Left Identities
 Addition Left Successor Identity
 Addition Left Zero Identity
 Addition Proofs
 Addition Right Identities
 Addition Right Successor Identity
 Addition Right Zero Identity
 AEI Education
 Al Baker New York Times
 Albemarle County Virginia
 Alexandre Borovik
 Algebra 2/Trigonometry Professional Learning Community
 Algebra functions restricted to naturals
 Algebra functions restricted to rationals
 Algebra on Natural Numbers.
 Algebra on Rational Numbers
 Algebra One
 Algebra One Word Problems
 Algebraic Laws
 Algebraic slope and rational numbers
 American Math Professors
 Analtyic Continuation
 Analtyic Recursive Continuation
 Angela Chen Chronicles Higher Education
 Aon Hewitt
 Arithmetic Laws
 Arithmetic's Relation to Algebra
 Associativity
 Associativity of Functions
 Austin Frakt Health Economist
 Axiom of Proof
 Backpack.tv
 Bank Capital
 Bank executives
 Base Point Test Point Calculus
 Beaglehole Tenney
 Ben Bernanke
 Bertrand Russell on Euclid
 Bessel functions
 Bill and Melinda Gates Foundation
 Bill Gates
 Bill Gates TED talk State budgets schools
 Binomial Lattice
 Book Bank Alexandria VA
 Book Piracy
 Books a Million Alexandria VA
 Bookstores
 Bookstores Alexandria Virginia
 Boris Berezovsky
 Building Arithmetic Project
 Calculus
 Calculus for Deaf
 Cardinality
 Cardinality Definition of Addition
 Carl Lee University of Kentucky
 CC Standards Grade 2 Operations and Algebraic Thinking
 CCPAP
 Center for Improving Learning of Fractions
 Charlottesville VA
 Chicago Math
 Chicago Public Schools
 Chicago Public Schools Teacher Strike 2012
 Christian Spannagel
 Chunking
 Classroom Boredom
 CLEVELAND BOARD OF EDUCATION v. LOUDERMILL
 Cognitive Load
 Collapse of American Cities
 Common Core Logical Inconsistencies
 Common Core Number and Operations Grade 4
 Common Core Peano Axioms Project
 Common Core Standards Grade 2
 Common Core Standards Grade 4
 Common Core Standards Grade K
 Common Core Standards Math
 Common Core Standards Number and Operations
 Common Core Standards Recursion
 Common Logs 2 to 10
 Conceptual v Procedural
 Conceptual v Procedural videos
 Confession of Arithmetic Faith
 Confusing area and rational numbers
 Confusing length and rational numbers
 Confusion Load
 Conspiracy Thread Fridays
 Constructing Logarithm Tables
 Constructivism
 Counterintelligence
 Counting on Definition of Addition
 Counting on Facts
 Counting on Facts of Addition
 Counting on Induction
 Counting on Rules of Arithmetic
 Counting on v Cardinality
 Coursera
 Cox
 Credit Rating US Government
 Crown Books
 Daubert Standard
 David Boies
 David Coffey
 David E. Joyce
 David Groisser
 David Klein math ed history US 20th century
 David Pierce
 Dedekind and Peano Academy
 Dedekind proof Associativity of Functions
 Derek Thompson The Atlantic
 Devlin Mathematical Thinking Coursera
 Difficult Math Problems for Grades 1 to 3
 Difficulties Learning Fractions
 Dr. Mayer Group Work 1905
 Dr. Schmidt No Homework 1905
 dy/dan Dan Meyer
 Dynamic Dynamic Programming Solutions
 Dynamic Programming
 ebook market
 Early 1900s pedagogy
 Easy Algebra Math Induction Proofs
 Econ Profs
 Economic Scenario Generator
 Edmund Landau
 Edmund Landau Peano Axioms
 Education bloggers
 Education Journalist
 Elena Kagan brutal on students Socratic Method
 Emma Brown Education Journalist
 End of Teacher Tenure
 Espresso Book Printing
 Essays on the Theory of Numbers
 Euclid Proportions Video Wildberger
 Euclid's Elements
 Euclis's Concepts of Number
 Euler 1765 Elements of Algebra
 Euler Academy
 Euler's Fallacies
 Euler's Lies
 Experience Unlimited for Job Seekers
 Explicit solutions of recursion
 Exponents
 Failing Algebra
 Fairfax County Performance Evaluations
 Fairfax County Public Schools
 Fairfax County Teacher Evaluations
 Federal Reserve
 Fictional Academies
 Finance Applications
 Financial Math
 Financial Recursion
 Folge der natürlichen Zahlen
 Foundations of Mathematics
 Fraction Algorithm Approach
 Fraction Aristocracy
 Fraction Democracy
 Fraction Learning Ap Mateusz Mucha
 Fraction Learning Aps
 Fraction Mishmash of Concepts
 Fractions
 Fractions as Functions
 Fractions as Operators
 Fractions same or equal
 Frankfurt School
 Frederick M. Hess
 Full and Fair Employment
 Functions and ordered pairs
 Gates Education Network (GEN)
 Gates Institutions Network
 Geometry of Addition
 Giuseppe Peano
 Grassmann
 H1b visas teachers
 Hari Sreenivasan
 Harkness Table
 Harvard Arrogance
 Head Segments of Natural Numbers
 Herbert von Karajan Effect
 Hermann Grassmann
 High School parents
 High Stakes Testing
 House Committee Financial Services
 Housing and Urban Affairs Committee
 HS Math Teacher Bloggers
 http://patrickjmt.com/
 HungHsi Wu
 Implicit Fraction as Function
 Implicit Fraction as Operator
 Induction Infection language
 Inductive Definitions
 Infinitely Many Primes
 Ingersoll and Ross
 Initial Segments Groisser Style
 Initial Segments of Natural Numbers
 Insurance Companies
 Internet People
 Iran Nuclear Program
 Irate Fridays
 It Ain't No Repeated Addition
 Iterated Succession
 J. Darrell Duffie
 J. F. Ptak Science Bookstore
 James Tanton Math Videos
 Jamie Dimon JP Morgan Chase
 Jay Mathews Washington Post
 Jennifer Asmuth
 Jennifer Medina NYT
 Job Market Journalists
 Joe Wagner
 Joel Brenner Counterintelligence
 Joel Feinstein of U Nottingham
 John Dell at Thomas Jefferson
 John Golden Math Hombre
 Journalists
 Joyce Notes on Dedekind Nature of Numbers
 Justin Reich
 Kalmar Definition of Addition
 Karl Shell of Cornell
 Kate Nowak HS Math Teacher blogger
 Keith Devlin Stanford
 Kenneth Arrow
 Khan Academy
 Khan Academy Charges
 Khan Academy Put Call Parity
 Khan Academy Put Call Parity CNBC
 Kindergarten Counting On
 Lacroix
 Lagrange and Laplace Academy
 Lance Rips
 Larry Summers
 Laszlo Kalmar
 Law Professors Patents and IP
 Law Profs
 Lawrence Lessig
 Lawyers
 Length for PreService Teachers
 Length of Natural Number Point Sets
 Leon Henkin
 Leonard Bernstein on Beethoven's 5th Symphony
 Leonard Blackburn
 Leonhard Euler
 Lesson Plans
 Lessons Lower Elementary Grade Levels
 Let's Play Math
 Lisa Gartner Washington Examiner
 Logarithm Table Project
 Logarithms
 March through the Institutions
 Mark A. Lemley
 Math Ed Jobs
 Math ed Mathematicians
 Math Ed Psychology
 Math ed Tribes
 Math Education
 Math Education 20th Century US
 Math Education Bloggers
 Math Facts
 Math for Deaf
 Math Job Retraining
 Math Journalists
 Math Market
 Math Memory Tricks
 Math Prof Bloggers
 Math Professors UK
 Math Projects for Students
 Math Video Series
 Mathematical Finance
 Mathematical Induction
 Mathematical Induction BaHIC
 Mathematical Thinking
 Mathematicians who created New Math
 Mathoscope
 Matthew O'Brien The Atlantic
 Maura Larkins
 MBA pedagogy
 Melinda Gates
 Michael Alison Chandler
 Monad
 MOOC
 MOOCPIT
 MOOCs for Deaf
 Moody's
 Mortimer Adler Socratic Method Public Schools
 Moscow State University
 Mozart Effect
 MTT2k
 MTT2k Prize
 Multiplication Associative
 Multiplication Commutative
 Multiplication Distributive
 Multiplication Proofs
 Multiplication via Fractions
 Music Conductors
 My Math Gal
 Myron Scholes
 Mystery Teacher Theatre 2000
 National Council of Teachers of Mathematics
 Natural Log Memory Pegs
 Natural Number Constructions
 Natural Number Point Sets
 Natural Numbers No Cycles
 NCTM Illuminations Fractions Aps
 New Math
 New Math 1960s
 New Math Done Right
 New New Math
 No child Latex behind
 No Child Left Behind
 Number classes
 Number Line
 Number Line Induction
 Number Line Recursion
 Number Theory
 Number Theory Grade 6 to 8
 Object oriented concepts
 Object Oriented Rational Number
 Olsson's Books and Records Old Town
 Order First
 Oxford Department of Education
 Pair of Number Line Method of Addition
 Parent Tutoring
 Paul Monroe Columbia University 1911
 Paul Samuelson
 PBS News Hour
 PCK and math foundations discord
 PCK and math foundations harmony
 PCK dependence on math foundations
 Peano Axiom Parent Tutoring
 Peano Axiom Root
 Peano Axiom Root for Deaf
 Peano Axiom Tutoring
 Peano Axioms
 Peano Axioms for Number Line
 Peano Axioms for PreService Teachers
 Peano Axioms Implicit First Grade
 Pedagogical Content Knowledge
 PERRY v. SINDERMANN
 PHHeidelberg Teacher Education Math
 Phillips Exeter Academy Harkness Table
 Physics High School Teachers
 Pitch Line Addition
 Pitch Line Definition of Addition
 Place Value Notation
 Politicians
 Politics and Prose bookstore
 PreService Teacher Math Education
 Procedural Levelism
 Procedural Mathematicians
 Procedural Mathematics
 Procedural v Structural math
 Professor Kingsfield
 Projects
 Projects Logarithms
 Proof Addition is Associative
 Proof Addition is Commutative
 Proof and Works
 Proportion and Magnitude
 Psychological
 Psychology of Mathematical Induction
 Public Figure
 Publishing
 RAKSAT
 Ralph Nader on Socratic Method
 Rational Number Projects
 Rational Numbers
 Real Learning Workbooks
 Real numbers
 Real numbers difficulties
 Real World Algebra Problems
 Recursion
 Recursive Continuation
 Recursive Definitions
 Recursive Inductive Definition of Multiplication
 Recursive Mathematics
 Recusive Inductive Definition of Addition
 Reform Math
 Repeated Succession
 Richard Dedekind
 Robert C. Merton
 Robert S. Wilson of Sonoma State U
 Rules for Exponents
 Russia
 Russian Math Education
 Russian Math Oligarchs
 SAT Mathematical Reasoning
 Science Journalists
 SelfPromotion
 Set theory definition of addition
 Sheeple Fridays
 Sheeple Induction
 Sheeple Thinking
 Slope concept on rationals
 Slope Concepts
 Society of Actuaries
 Socratic Method
 Socratic Method Bullying
 Socratic Method Public Schools
 Sphaghetti Proceduralism
 Split the Monad
 Stanford
 Stanford Arrogance
 Stanford Computer Science
 Stanford Misconduct
 Stanford Professors
 Stanley Fischer
 State Budget Deficits Schools Teachers
 Successor Facts
 Tails of Natural Numbers
 Takergeddon
 Teacher Evaluations
 Teacher Quality Roadmap
 Teacher Tenure
 Teaching prime notation with number lines
 Teaching x and y with Number Lines
 Terence Tao
 The Nature and Meaning of Numbers
 Thomas Jefferson
 Thomas Jefferson High School for Science and Technology
 Timothy Gowers
 TJ Letter Algebra 2/Trig PLC
 TJ Summer School for Stragglers
 TJHHS Algebra Admissions Test
 Transition to College Math
 Transition to Proof
 Tricki
 Tricky Exam Questions
 Tutoring
 Uncategorized
 University Education Departments
 US Supremce Court Decisions Tenure
 Use of x early
 Value at Risk
 Vanishing Calculus
 Variable v Function
 Video Vendors
 Virginia lower pass rates algebra
 Virginia Standards of Learning
 Virginia Standards of Learning Algebra One
 Virginia Standards of Learning Math
 Vision and Works
 von Neumann Construction
 Washington DC bookstores
 What is math good for
 William H. Burnham
 Wooster Woodruff Beman
 Zurich and Prussian Homework rules c. 1900
Meta