Original Site Title: Appetizers and Lessons for Mathematics and Reason, June 1995 to April 2012. New site title:
Logic and Mathematics Skill & Concept Development with How-TOs Français: 26 pages
for college students, gifted teens, home-tutoring and K1-12 schooling. Avid readers in school and out may like Site Volumes.

Logic 5 Chapters Arithmetic 10 Steps Algebra 12 Starter Steps & 5 Advanced Steps
Work & Study 23 Tips Geometry 15 Steps Calculus 70 Lessons. See Site Map

Ages 15+: Why study slopes Polynomials Quadratics Why factor polynomials Logarithms Functions
What is similarity Euclidean geometry leanly Coordinates + complex no.s Vectors DC Electric Circuits
Ages 12+: Prime factorization Written work formats Decimal place value Extend arithmetic skills orally
What is a variable 5. Fraction Operations by Raising Terms Solving Linear Equations: Take I Take II

Online Volumes: 1 - Elements of Reason, 2 - 3 Skills For Algebra, 3 - Why Slopes and
More Math, 1A - Pattern Based Reason, 1B - Skill Development Principles + Troubles

Welcome: Site content may develop critical thinking, improve reading and writing, and build mathematics skills. See online chapters on on logic and pattern based reason.

Teachers: This December 2011, 5-phase framework offers a context for mathematics & logic instruction. Phases 1 to 3 focus on skills with actual or potential value for adult & daily life. College-oriented phases 5 & 4 focus on calculus & preparation for it. Phases 1 to 4 may also serve trades & professions not dependent on calculus.

Site Review: Math resources ... span ... arithmetic, logic, algebra, calculus, complex numbers, and Euclidean geometry. Lessons and how-tos .... provide a good foundation for high school and college ... mathematics. Read more.

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19 matches:

  1.    wt: 6:   Volume 1A Pattern Based Reason/
  2.    wt: 3:   Volume 1 Elements of Reason/
  3.    wt: 2:   Volume 1A Regles et modeles/
  4.    wt: 2:   10 Examples of Algebraic Reasoning/
  5.    wt: 2:   Volume 1B Mathematics Curriculum Notes/
  6.    wt: 1:   LAMP Lean Applied Mathematics Program/
  7.    wt: 1:   Progressive Observable Motivated Mathematics Education/
  8.    wt: 1:   Mathematics Education Essays/
  9.    wt: 1:   Mathematics Skills Year by Year/
  10.    wt: 1:   A Origins of Counting and Figuring Methods/
  11.    wt: 1:   12 Comparison of Unsigned and Signed Numbers/
  12.    wt: 1:   12 Webvideo Lessons on Area and Volume Calculation/
  13.    wt: 1:   Advanced Calculus Volume 3 Appendices/
  14.    wt: 1:   Volume 3 Why Slopes A Calculus Intro Etc/
  15.    wt: 1:   Volume 2 Three Skills For Algebra/
  16.    wt: 1:   Mathematics 506 Lessons/
  17.    wt: 1:   Secondary Mathematics A Practical Approach/
  18.    wt: 1:   PreSchool and Primary Mathematics or Quantitative Skills/
  19.    wt: 1:   Mathematics Skill Development Framework/

Web Page Search

236 matches:

  1.    wt: 3:   Education in mathematics science and technology
  2.    wt: 3:   Different Kinds of Reasoning in maths
  3.    wt: 3:   three kinds of reason in mathematics
  4.    wt: 3:   Chapter 6 Rule Based Reason in Mathematics
  5.    wt: 2:   Mathematics Education Professors
  6.    wt: 2:   19 Extending the Oral Dimension of Mathematics
  7.    wt: 2:   4 Resultant of a Sum of Movements
  8.    wt: 2:   27 Logarithmic use of products of sines and cosines
  9.    wt: 2:   5 An Easy Proof of the Distributive Law
  10.    wt: 2:   10 Similarity of Triangles Equivalent of Two Criteria
  11.    wt: 2:   21 Addition of Multiples of a Single Vector
  12.    wt: 2:   11 Volume of Sphere
  13.    wt: 2:   10 Volume of Pyramid
  14.    wt: 2:   9 Volume of Cone
  15.    wt: 2:   Quick history of numbers and algebra
  16.    wt: 2:   Example 2 volume of a cone
  17.    wt: 2:   Example 1 volume of a pyramid
  18.    wt: 2:   Volume of Solid by Cross Sections Lesson
  19.    wt: 2:   17 Derivatives of quotients of sine and cosine
  20.    wt: 2:   16 Derivatives of reciprocals of sine and cosine
  21.    wt: 2:   Chapter 4 Longer Chains of Reason
  22.    wt: 2:   Chapter 3 Chains of Reason
  23.    wt: 2:   Chapter 16 Origins and Limitations of Rules and Patterns
  24.    wt: 2:   Chapter 14 Deductive and Empirical Views of Mathematics
  25.    wt: 2:   Chapter 7 Longer Chains of Reason
  26.    wt: 2:   Chapter 6 Chains of Reason
  27.    wt: 2:   V Reasons and Motivations for Logic and Mathematics
  28.    wt: 2:   O On Learning Mathematics and Science
  29.    wt: 1:   Appendix 1 primary and preschool mathematic
  30.    wt: 1:   K LAMP Musings Science Education
  31.    wt: 1:   E LAMP Introduction Modern Mathematics
  32.    wt: 1:   C LAMP Introduction Culture in Mathematics Education
  33.    wt: 1:   11 pure mathematics
  34.    wt: 1:   Math Ed if it must be short make it lean effective
  35.    wt: 1:   Applied Maths Program14092009 POMME variant
  36.    wt: 1:   mathematics in context
  37.    wt: 1:   Secondary Three Mathematics
  38.    wt: 1:   Secondary Two Mathematics
  39.    wt: 1:   Secondary One Mathematics
  40.    wt: 1:   mathematics curriculum shifts
  41.    wt: 1:   teaching tutoring algebraic reason
  42.    wt: 1:   three goals for Mathematics Education
  43.    wt: 1:   04 29 New Mathematics Curriculum
  44.    wt: 1:   04 25 when to stop or suspend mathemat
  45.    wt: 1:   02 20 mathematics education references
  46.    wt: 1:   three aims for mathematics students
  47.    wt: 1:   Theory of Knowledge
  48.    wt: 1:   mathematics instruction in general
  49.    wt: 1:   need for a mixed mathematics curriculum
  50.    wt: 1:   Leaner mathematics curriculum
  51.    wt: 1:   words for mathematics instructor
  52.    wt: 1:   chapitre 07 01 principle D induction mathematique
  53.    wt: 1:   Quebec cahiers d apprentissage en mathematiques pour 4 16
  54.    wt: 1:   E Kirchoffs Second Law
  55.    wt: 1:   D Kirchoff First Law
  56.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  57.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  58.    wt: 1:   22 Student Centered Highschool Mathematics
  59.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  60.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  61.    wt: 1:   18 Primary School Mathematics
  62.    wt: 1:   17 Math Booklets for children and young teenagers
  63.    wt: 1:   16 Secondary Mathematics Tips
  64.    wt: 1:   12 Goals and Objectives For Mathematics
  65.    wt: 1:   8 The Effect of Negative Remarks
  66.    wt: 1:   3 Preparing for Science Studies
  67.    wt: 1:   21 Graphs of functions given by Horizontal Line Method
  68.    wt: 1:   15 Sign analysis of functions
  69.    wt: 1:   8 Set view of relations and functions
  70.    wt: 1:   4 Function notation in and beyond mathematics
  71.    wt: 1:   2 Algebraic use of function notation
  72.    wt: 1:   1 Geometric Introduction of Function Notation
  73.    wt: 1:   8 quadratics backward use of various formulas
  74.    wt: 1:   4 quadratics difference of two squares
  75.    wt: 1:   11 arctan left inverse of tangent Graph
  76.    wt: 1:   10 arctan left inverse of tangent Definition
  77.    wt: 1:   8 arcsin left inverse of sine Graph
  78.    wt: 1:   7 arcsin left inverse of sine Definition
  79.    wt: 1:   6 Graph of arccos function
  80.    wt: 1:   3 Left Inverse of cosine arccos definition
  81.    wt: 1:   8 Radian Measures of Common Angles
  82.    wt: 1:   2 Radian Measure Numerical Value of one degree
  83.    wt: 1:   12 From Applied To Pure Mathematics
  84.    wt: 1:   Proportionality of Line Segments From Parallel Transversals
  85.    wt: 1:   Analytic View of Triangle Construction or Line Instersection More
  86.    wt: 1:   Straight Lines Intersection of
  87.    wt: 1:   3 Straight Lines Slope as Tangent of Inclination Angle
  88.    wt: 1:   35 sines and cosines of 2A 3A 4A 5A
  89.    wt: 1:   34 sines and cosines of 2A 3A 4A 5A
  90.    wt: 1:   33 sines and cosines of 2A 3A 4A 5A
  91.    wt: 1:   32 seven rows of pascals triangle
  92.    wt: 1:   30 unit circle calculation of six trigonometric functions
  93.    wt: 1:   28 Expressing products of sines cosines as sums
  94.    wt: 1:   26 Formulas for products of sines and cosines
  95.    wt: 1:   23 sine and cosine of 180 plus 22.5 degrees
  96.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  97.    wt: 1:   18 sum of sinusoidal waves as a single wave
  98.    wt: 1:   17F Law of cosines
  99.    wt: 1:   13 Graph of tangent function many periods
  100.    wt: 1:   12 Graph of tangent function for one period
  101.    wt: 1:   10 Graphs of sines and cosines many periods
  102.    wt: 1:   9 Graphs of sine and cosine over one period
  103.    wt: 1:   8 period of tangent function
  104.    wt: 1:   7 period of sine and cosine
  105.    wt: 1:   Unit Circle Development of Trigonometry
  106.    wt: 1:   20 N th Roots of Complex Numbers
  107.    wt: 1:   19 N th Roots of Unity
  108.    wt: 1:   18 Sixth Roots of Unity
  109.    wt: 1:   17 Cube Roots of unity
  110.    wt: 1:   14 Law of cosines
  111.    wt: 1:   8 Unit Circle Development of Trigonometry
  112.    wt: 1:   6 Field Properties of Complex Number
  113.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  114.    wt: 1:   2 Similar Triangles Equality of Corresponding Side Ratios
  115.    wt: 1:   9 Similarity of Triangles Usual Criteria
  116.    wt: 1:   8 Similarity of Triangles and Polygons
  117.    wt: 1:   5 Similarity of Circles Squares and Rectangles
  118.    wt: 1:   1 Early Concept of Like or Similar Shapes
  119.    wt: 1:   10 Midpoint of [a b] and [b a]
  120.    wt: 1:   6 Intersection of lines by solving linear systems
  121.    wt: 1:   5 Algebraic View of Slopes
  122.    wt: 1:   1 Numerical view of lines and their equations
  123.    wt: 1:   9 Pythagorean Theorem Chinese Square Proof
  124.    wt: 1:   17 Right Bisectors of Triangle Sides
  125.    wt: 1:   9 Construction of a right bisector
  126.    wt: 1:   3 Isometry of Triangles Congruence
  127.    wt: 1:   8 More Use of Maps Not Drawn to Scale
  128.    wt: 1:   22 Multiplication of Signed Numbers
  129.    wt: 1:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  130.    wt: 1:   19 Signed Multiples of Vectors
  131.    wt: 1:   8 Division and Mulplication of Compound Fractions
  132.    wt: 1:   4 Location of Point in Decimal Addition
  133.    wt: 1:   3 Location of Point in Decimal Multiplication
  134.    wt: 1:   1 The Counting Origins of Numbers
  135.    wt: 1:   5 Areas of Rectangles Revisited
  136.    wt: 1:   7 Pythagorean Theorem Chinese Square Proof
  137.    wt: 1:   4 Comparison of Negative Numbers
  138.    wt: 1:   5 Box Volume Formula Example
  139.    wt: 1:   10 Set View of Wordy Extensions To Arithmetic
  140.    wt: 1:   8 Sets of Numbers
  141.    wt: 1:   6 Three Notions of What is a Variable
  142.    wt: 1:   4 A Brief Story of numbers and algebra
  143.    wt: 1:   3 Comparison of Negative Numbers
  144.    wt: 1:   3 Properties of Square Roots with example
  145.    wt: 1:   17 GCD LCM of 85 and 60 via Prime
  146.    wt: 1:   16 GCD and LCM of 650 225 via Prime
  147.    wt: 1:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  148.    wt: 1:   14 GCD of 650 110 via Primes LCM via Product Rule
  149.    wt: 1:   9 GCD of 360 110 via Primes and Euclid Algorithm
  150.    wt: 1:   4 LCM of 8 and 10 via Prime
  151.    wt: 1:   5 lengths and signs of numbers
  152.    wt: 1:   6 Simplification of Fractions with Units
  153.    wt: 1:   10 Simplification of Fractions and Mixed Numerals
  154.    wt: 1:   6 Multiplication of Mixed Numbers
  155.    wt: 1:   3 Unit fraction of a fraction
  156.    wt: 1:   2 Integers Multiplies of a Unit Moverment
  157.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  158.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  159.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  160.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  161.    wt: 1:   20 Uniqueness of Prime Factorization
  162.    wt: 1:   16 video Factors of 980 using prime
  163.    wt: 1:   15 video Factors of 20 using Prime Factorization
  164.    wt: 1:   14 video Factors of 24 Take II
  165.    wt: 1:   13 video Factors of 24 using prime
  166.    wt: 1:   6 Sieve of Eratosthenes and Square Rule
  167.    wt: 1:   C Counting Areas with Powers of Ten
  168.    wt: 1:   B Powers of Ten
  169.    wt: 1:   8 Subtraction with Units of Measure
  170.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  171.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  172.    wt: 1:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  173.    wt: 1:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  174.    wt: 1:   5 More on Groups of 3 Place Value in Decimal Fractions
  175.    wt: 1:   4 Groups of 3 Place Value in Decimal Fractions
  176.    wt: 1:   3 More on Groups of 3 Multi Digit Place Value
  177.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  178.    wt: 1:   012 Division of Time Intervals by Time Intervals
  179.    wt: 1:   011 Division of Time Intervals By Numbers
  180.    wt: 1:   010 Repeated Addition of Time Intervals
  181.    wt: 1:   9 Comparison and Subtraction of Time Intervals
  182.    wt: 1:   8 Addition of Time Intervals via subtotaling
  183.    wt: 1:   7 Addition of Time Intervals
  184.    wt: 1:   4 Mixing and Changing Units of Time
  185.    wt: 1:   3 Units and Lengths of Time
  186.    wt: 1:   1 Intro of Kids To Time Date Skills
  187.    wt: 1:   Example 4 with x function of y
  188.    wt: 1:   A Related Material in Volume 3
  189.    wt: 1:   A Related lessons in Volume 3
  190.    wt: 1:   34 Derivative of exponential function
  191.    wt: 1:   31 Derivatives of inverse functions
  192.    wt: 1:   30Chain Rule A Proof
  193.    wt: 1:   28 Chain Rule Preparation for a Proof
  194.    wt: 1:   8 Differentiation of polynomials
  195.    wt: 1:   5 Jumps and absence of unlimited error control
  196.    wt: 1:   G.1 First Fundamental Theorem of Calculus
  197.    wt: 1:   G.3 Constant Difference Theorem Proof
  198.    wt: 1:   E2 Algebraic Properties of Limits
  199.    wt: 1:   D2 Limits of Monotone Sequences
  200.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  201.    wt: 1:   Postscript Pythagorean Theorem yet another proof
  202.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  203.    wt: 1:   Appendix E. How To Study Mathematics and Why
  204.    wt: 1:   Chapter 31 Direct and Indirect Reason
  205.    wt: 1:   Chapter 25. Mathematical Induction Examples
  206.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  207.    wt: 1:   Chapter 14. Forward and Backward Use of a Formula
  208.    wt: 1:   Chapter 6 Change of Language
  209.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  210.    wt: 1:   Postscript B Mathematics Education References
  211.    wt: 1:   Chapter 7 Two Treatments of Geometry
  212.    wt: 1:   Chapter 2 For and Against Mathematics
  213.    wt: 1:   Postscript D Reflections on Law of the Excluded Middle
  214.    wt: 1:   Postscript C Consistency as a Tool for Reason
  215.    wt: 1:   Postscript B More on Story Telling and Reason
  216.    wt: 1:   Chapter 24 Direct and Indirect Reason
  217.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  218.    wt: 1:   Chapter 12 Islands and Divisions of Knowledge
  219.    wt: 1:   Chapter 11 Accidental Patterns
  220.    wt: 1:   Chapter 8 Change of Language
  221.    wt: 1:   R Why Learn Mathematics Skills
  222.    wt: 1:   Q How Logic and Proofs extend Show Work Practices
  223.    wt: 1:   N Mathematics Prepare for College Studies
  224.    wt: 1:   C. Domino effect of being careful
  225.    wt: 1:   B. Domino effect of errors
  226.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  227.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  228.    wt: 1:   6 Measuring via counting or arithmetic the role of fractions
  229.    wt: 1:   Helping the Blind in Logic and Mathematics
  230.    wt: 1:   Mathematics Education References
  231.    wt: 1:   Mathematics Education References
  232.    wt: 1:   Multiple Ways to Improve Mathematics Skill Development
  233.    wt: 1:   More Algebra and Slope based Calculus Preview
  234.    wt: 1:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  235.    wt: 1:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  236.    wt: 1:   The Math Forum and Site Content

Extended Search

496 matches:

  1.    wt: 8:   Chapter 16 Origins and Limitations of Rules and Patterns
  2.    wt: 8:   Chapter 14 Deductive and Empirical Views of Mathematics
  3.    wt: 8:   Chapter 7 Longer Chains of Reason
  4.    wt: 8:   Chapter 6 Chains of Reason
  5.    wt: 7:   Postscript D Reflections on Law of the Excluded Middle
  6.    wt: 7:   Postscript C Consistency as a Tool for Reason
  7.    wt: 7:   Postscript B More on Story Telling and Reason
  8.    wt: 7:   Chapter 24 Direct and Indirect Reason
  9.    wt: 7:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  10.    wt: 7:   Chapter 12 Islands and Divisions of Knowledge
  11.    wt: 7:   Chapter 11 Accidental Patterns
  12.    wt: 7:   Chapter 8 Change of Language
  13.    wt: 6:   Postscript A Story Telling
  14.    wt: 6:   Chapter 23 Truth Tables
  15.    wt: 6:   Chapter 22 Contrapositive and Vacuously True Implications
  16.    wt: 6:   Chapter 21 Occurrence Tables
  17.    wt: 6:   Chapter 20 Shorthand Symbols as Pronouns
  18.    wt: 6:   Chapter 19 What is in chapters 20 to 24
  19.    wt: 6:   Chapter 18 Sense and Knowledge
  20.    wt: 6:   Chapter 17 Objective Ways Trial and Error Discovery
  21.    wt: 6:   Chapter 15 Objective Processes
  22.    wt: 6:   Chapter 10 Responsibility
  23.    wt: 6:   Chapter 9 What is in Chapters 10 to 18
  24.    wt: 6:   Chapter 5 Deception
  25.    wt: 6:   Chapter 4 Implication Rules Forwards and Backwards
  26.    wt: 6:   Chapter 3 What is in chapters 4 to 8
  27.    wt: 6:   Chapter 2 Skill Development
  28.    wt: 6:   Chapter 1 Introduction
  29.    wt: 6:   Three Remarks
  30.    wt: 6:   Foreword
  31.    wt: 5:   Chapter 6 Rule Based Reason in Mathematics
  32.    wt: 4:   Education in mathematics science and technology
  33.    wt: 4:   Different Kinds of Reasoning in maths
  34.    wt: 4:   three kinds of reason in mathematics
  35.    wt: 3:   Mathematics Education Professors
  36.    wt: 3:   chapitre 07 01 principle D induction mathematique
  37.    wt: 3:   5 Areas of Rectangles Revisited
  38.    wt: 3:   Example 2 volume of a cone
  39.    wt: 3:   Example 1 volume of a pyramid
  40.    wt: 3:   Volume of Solid by Cross Sections Lesson
  41.    wt: 3:   Chapter 4 Longer Chains of Reason
  42.    wt: 3:   Chapter 3 Chains of Reason
  43.    wt: 3:   Postscript B Mathematics Education References
  44.    wt: 3:   Chapter 7 Two Treatments of Geometry
  45.    wt: 3:   Chapter 2 For and Against Mathematics
  46.    wt: 2:   Appendix 1 primary and preschool mathematic
  47.    wt: 2:   K LAMP Musings Science Education
  48.    wt: 2:   E LAMP Introduction Modern Mathematics
  49.    wt: 2:   C LAMP Introduction Culture in Mathematics Education
  50.    wt: 2:   11 pure mathematics
  51.    wt: 2:   Math Ed if it must be short make it lean effective
  52.    wt: 2:   Applied Maths Program14092009 POMME variant
  53.    wt: 2:   mathematics in context
  54.    wt: 2:   Secondary Three Mathematics
  55.    wt: 2:   Secondary Two Mathematics
  56.    wt: 2:   Secondary One Mathematics
  57.    wt: 2:   mathematics curriculum shifts
  58.    wt: 2:   teaching tutoring algebraic reason
  59.    wt: 2:   three goals for Mathematics Education
  60.    wt: 2:   04 29 New Mathematics Curriculum
  61.    wt: 2:   04 25 when to stop or suspend mathemat
  62.    wt: 2:   02 20 mathematics education references
  63.    wt: 2:   three aims for mathematics students
  64.    wt: 2:   Theory of Knowledge
  65.    wt: 2:   mathematics instruction in general
  66.    wt: 2:   need for a mixed mathematics curriculum
  67.    wt: 2:   Leaner mathematics curriculum
  68.    wt: 2:   words for mathematics instructor
  69.    wt: 2:   chapitre 12 00 les iles et division
  70.    wt: 2:   chapitre 07 00 Des chaines plus longues de la raison
  71.    wt: 2:   chapitre 06 00 Chaines de la raison
  72.    wt: 2:   chapitre 05 00 Deception
  73.    wt: 2:   chapitre 04 10 Etapes pour une meilleur raison
  74.    wt: 2:   chapitre 04 09 Regles accidentelles
  75.    wt: 2:   chapitre 04 08 Limitations et benefices
  76.    wt: 2:   chapitre 04 07 RepetablesEtReproductibles
  77.    wt: 2:   chapitre 04 06 engagements
  78.    wt: 2:   chapitre 04 05 Implication versus suggestion
  79.    wt: 2:   chapitre 04 04 Parlons de la logique
  80.    wt: 2:   chapitre 04 03 Unidirectionnel versus bidirectionnel
  81.    wt: 2:   chapitre 04 02 Deuxieme enigme
  82.    wt: 2:   chapitre 04 01 Premiere enigme
  83.    wt: 2:   chapitre 04 00 Les regles d implication
  84.    wt: 2:   chapitre 03 A Propos Des Prochains Chapitre
  85.    wt: 2:   chapitre 02 00 La Communication des idees
  86.    wt: 2:   chapitre 01 00 Introduction
  87.    wt: 2:   19 Extending the Oral Dimension of Mathematics
  88.    wt: 2:   4 Resultant of a Sum of Movements
  89.    wt: 2:   27 Logarithmic use of products of sines and cosines
  90.    wt: 2:   5 An Easy Proof of the Distributive Law
  91.    wt: 2:   10 Similarity of Triangles Equivalent of Two Criteria
  92.    wt: 2:   21 Addition of Multiples of a Single Vector
  93.    wt: 2:   1 The Counting Origins of Numbers
  94.    wt: 2:   4 Fraction Operations Axiomatic Development
  95.    wt: 2:   3 Inequalities Algebraically
  96.    wt: 2:   2 Fraction Operations Physical Development
  97.    wt: 2:   1 Decimals Modular and Remainder Arithmetic
  98.    wt: 2:   11 Volume of Sphere
  99.    wt: 2:   10 Volume of Pyramid
  100.    wt: 2:   9 Volume of Cone
  101.    wt: 2:   3 Comparison of Negative Numbers
  102.    wt: 2:   Quick history of numbers and algebra
  103.    wt: 2:   Example 4 with x function of y
  104.    wt: 2:   Area Between Curves Lesson Take 2
  105.    wt: 2:   A Related Material in Volume 3
  106.    wt: 2:   17 Derivatives of quotients of sine and cosine
  107.    wt: 2:   16 Derivatives of reciprocals of sine and cosine
  108.    wt: 2:   G.1 First Fundamental Theorem of Calculus
  109.    wt: 2:   G.3 Constant Difference Theorem Proof
  110.    wt: 2:   E2 Algebraic Properties of Limits
  111.    wt: 2:   D2 Limits of Monotone Sequences
  112.    wt: 2:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  113.    wt: 2:   Postscript Pythagorean Theorem yet another proof
  114.    wt: 2:   Chapter 15. Algebraic Evaluation of Limits
  115.    wt: 2:   Appendix E. How To Study Mathematics and Why
  116.    wt: 2:   Chapter 31 Direct and Indirect Reason
  117.    wt: 2:   Chapter 25. Mathematical Induction Examples
  118.    wt: 2:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  119.    wt: 2:   Chapter 14. Forward and Backward Use of a Formula
  120.    wt: 2:   Chapter 6 Change of Language
  121.    wt: 2:   Chapter 5 Islands and Divisions of Knowledge
  122.    wt: 2:   Annotated Links to Material Elsehwere
  123.    wt: 2:   Postscript A Three Remarks
  124.    wt: 2:   Chapter 12 Four Phases
  125.    wt: 2:   Chapter 11 Elementary Instruction
  126.    wt: 2:   Chapter 10 Transition
  127.    wt: 2:   Chapter 9 The Two Ends
  128.    wt: 2:   Chapter 8 Modern Instruction
  129.    wt: 2:   Chapter 5 Four References
  130.    wt: 2:   Chapter 4 Complex Numbers and Why Slopes
  131.    wt: 2:   Chapter 3 Algebra Difficulties
  132.    wt: 2:   Chapter 1 Introduction
  133.    wt: 2:   Foreword
  134.    wt: 2:   V Reasons and Motivations for Logic and Mathematics
  135.    wt: 2:   O On Learning Mathematics and Science
  136.    wt: 2:   Appendix A Calculus with Proofs for Keen or Gifted
  137.    wt: 2:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  138.    wt: 2:   6 Measuring via counting or arithmetic the role of fractions
  139.    wt: 2:   Helping the Blind in Logic and Mathematics
  140.    wt: 2:   Mathematics Education References
  141.    wt: 2:   Mathematics Education References
  142.    wt: 2:   Multiple Ways to Improve Mathematics Skill Development
  143.    wt: 2:   More Algebra and Slope based Calculus Preview
  144.    wt: 2:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  145.    wt: 2:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  146.    wt: 1:   Appendix 2 primary school Arithmetic 01
  147.    wt: 1:   J LAMP Introduction Extrinsic Origins
  148.    wt: 1:   I LAMP Introduction Study Habits
  149.    wt: 1:   H LAMP Introduction Instructional Concepts
  150.    wt: 1:   G LAMP Introduction Problem Solving Skills
  151.    wt: 1:   F LAMP Introduction Prerequisites
  152.    wt: 1:   B LAMP Introduction Curriculum Development Standards
  153.    wt: 1:   A Introduction Objectives
  154.    wt: 1:   Skills Chapter 5 Calculus
  155.    wt: 1:   Skills Chapter 4 Logic
  156.    wt: 1:   Ramblings Extrinsic numbers theory
  157.    wt: 1:   Ramblings Introduction Algebra Essay
  158.    wt: 1:   Skills Chapter 3 Algebra
  159.    wt: 1:   Skills Chapter 2 Geometry
  160.    wt: 1:   Skills Chapter 1 Arithmetic
  161.    wt: 1:   Skills Chapter 0 Introduction
  162.    wt: 1:   10 statistics
  163.    wt: 1:   9 combinatorics probability sets
  164.    wt: 1:   8 analytic geometry etc
  165.    wt: 1:   7 logic review and decimals an odd combination
  166.    wt: 1:   6 polynomials etc
  167.    wt: 1:   5 logarithms and exponentials etc
  168.    wt: 1:   4 algebra
  169.    wt: 1:   3 Euclidean Geometry Leanly
  170.    wt: 1:   2 arithmetic with signed numbers
  171.    wt: 1:   1 arithmetic with unsigned numbers
  172.    wt: 1:   What is POMME
  173.    wt: 1:   why bother
  174.    wt: 1:   which way to go
  175.    wt: 1:   website reviews
  176.    wt: 1:   three goals to set for students
  177.    wt: 1:   Teach the teachers plus goals
  178.    wt: 1:   permissions for teachers
  179.    wt: 1:   activities for students
  180.    wt: 1:   links Education Resources online
  181.    wt: 1:   site origins
  182.    wt: 1:   site eurekas
  183.    wt: 1:   About site lesson plans
  184.    wt: 1:   key notes and themes
  185.    wt: 1:   teacher certification
  186.    wt: 1:   modern education
  187.    wt: 1:   learning takes time
  188.    wt: 1:   grouping students according to ability
  189.    wt: 1:   what should be learnt and When
  190.    wt: 1:   Postscript 2007 01 10
  191.    wt: 1:   Education Reform Inconsistencies
  192.    wt: 1:   five decades make a difference
  193.    wt: 1:   Maps Plans Drawings
  194.    wt: 1:   how letters appear
  195.    wt: 1:   talk the algebra talk
  196.    wt: 1:   three difficulties
  197.    wt: 1:   teaching tips
  198.    wt: 1:   What to Tell Students
  199.    wt: 1:   geometric implications for algebra
  200.    wt: 1:   Lessening Algebra Difficulties
  201.    wt: 1:   the trouble with algebra
  202.    wt: 1:   05 13 OldSiteEntrancePage
  203.    wt: 1:   02 21 words for teachers
  204.    wt: 1:   standards for course material
  205.    wt: 1:   Operational Viewpoint to Value
  206.    wt: 1:   formal or informal peer review
  207.    wt: 1:   cultivating intelligence
  208.    wt: 1:   Four ways to improve education reform
  209.    wt: 1:   How to be a better instructor
  210.    wt: 1:   Motivation and Context Problem
  211.    wt: 1:   Prequel In For A Penny In For A Pound
  212.    wt: 1:   education an empirical art
  213.    wt: 1:   fairness and inductive principles for instruction
  214.    wt: 1:   Quebec cahiers d apprentissage en mathematiques pour 4 16
  215.    wt: 1:   E Kirchoffs Second Law
  216.    wt: 1:   D Kirchoff First Law
  217.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  218.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  219.    wt: 1:   22 Student Centered Highschool Mathematics
  220.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  221.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  222.    wt: 1:   18 Primary School Mathematics
  223.    wt: 1:   17 Math Booklets for children and young teenagers
  224.    wt: 1:   16 Secondary Mathematics Tips
  225.    wt: 1:   12 Goals and Objectives For Mathematics
  226.    wt: 1:   8 The Effect of Negative Remarks
  227.    wt: 1:   3 Preparing for Science Studies
  228.    wt: 1:   Ages 12 to 14 Skills with take home value
  229.    wt: 1:   Ages 12 to 14 Geometry
  230.    wt: 1:   Ages 12 to 14 Arithmetic
  231.    wt: 1:   Ages 10 to 12 Geometry
  232.    wt: 1:   Ages 10 to 12 Arithmetic
  233.    wt: 1:   Ages 9 to 10
  234.    wt: 1:   Ages 8 to 9
  235.    wt: 1:   Ages 7 to 8
  236.    wt: 1:   Ages 6 to 7
  237.    wt: 1:   Ages 4 plus to 5 plus
  238.    wt: 1:   Ages 3 plus to 4 plus
  239.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  240.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  241.    wt: 1:   21 Graphs of functions given by Horizontal Line Method
  242.    wt: 1:   15 Sign analysis of functions
  243.    wt: 1:   8 Set view of relations and functions
  244.    wt: 1:   4 Function notation in and beyond mathematics
  245.    wt: 1:   2 Algebraic use of function notation
  246.    wt: 1:   1 Geometric Introduction of Function Notation
  247.    wt: 1:   8 quadratics backward use of various formulas
  248.    wt: 1:   4 quadratics difference of two squares
  249.    wt: 1:   11 arctan left inverse of tangent Graph
  250.    wt: 1:   10 arctan left inverse of tangent Definition
  251.    wt: 1:   8 arcsin left inverse of sine Graph
  252.    wt: 1:   7 arcsin left inverse of sine Definition
  253.    wt: 1:   6 Graph of arccos function
  254.    wt: 1:   3 Left Inverse of cosine arccos definition
  255.    wt: 1:   8 Radian Measures of Common Angles
  256.    wt: 1:   2 Radian Measure Numerical Value of one degree
  257.    wt: 1:   12 From Applied To Pure Mathematics
  258.    wt: 1:   Proportionality of Line Segments From Parallel Transversals
  259.    wt: 1:   Analytic View of Triangle Construction or Line Instersection More
  260.    wt: 1:   Straight Lines Intersection of
  261.    wt: 1:   3 Straight Lines Slope as Tangent of Inclination Angle
  262.    wt: 1:   35 sines and cosines of 2A 3A 4A 5A
  263.    wt: 1:   34 sines and cosines of 2A 3A 4A 5A
  264.    wt: 1:   33 sines and cosines of 2A 3A 4A 5A
  265.    wt: 1:   32 seven rows of pascals triangle
  266.    wt: 1:   30 unit circle calculation of six trigonometric functions
  267.    wt: 1:   28 Expressing products of sines cosines as sums
  268.    wt: 1:   26 Formulas for products of sines and cosines
  269.    wt: 1:   23 sine and cosine of 180 plus 22.5 degrees
  270.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  271.    wt: 1:   18 sum of sinusoidal waves as a single wave
  272.    wt: 1:   17F Law of cosines
  273.    wt: 1:   13 Graph of tangent function many periods
  274.    wt: 1:   12 Graph of tangent function for one period
  275.    wt: 1:   10 Graphs of sines and cosines many periods
  276.    wt: 1:   9 Graphs of sine and cosine over one period
  277.    wt: 1:   8 period of tangent function
  278.    wt: 1:   7 period of sine and cosine
  279.    wt: 1:   Unit Circle Development of Trigonometry
  280.    wt: 1:   20 N th Roots of Complex Numbers
  281.    wt: 1:   19 N th Roots of Unity
  282.    wt: 1:   18 Sixth Roots of Unity
  283.    wt: 1:   17 Cube Roots of unity
  284.    wt: 1:   14 Law of cosines
  285.    wt: 1:   8 Unit Circle Development of Trigonometry
  286.    wt: 1:   6 Field Properties of Complex Number
  287.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  288.    wt: 1:   2 Similar Triangles Equality of Corresponding Side Ratios
  289.    wt: 1:   9 Similarity of Triangles Usual Criteria
  290.    wt: 1:   8 Similarity of Triangles and Polygons
  291.    wt: 1:   5 Similarity of Circles Squares and Rectangles
  292.    wt: 1:   1 Early Concept of Like or Similar Shapes
  293.    wt: 1:   10 Midpoint of [a b] and [b a]
  294.    wt: 1:   6 Intersection of lines by solving linear systems
  295.    wt: 1:   5 Algebraic View of Slopes
  296.    wt: 1:   1 Numerical view of lines and their equations
  297.    wt: 1:   9 Pythagorean Theorem Chinese Square Proof
  298.    wt: 1:   17 Right Bisectors of Triangle Sides
  299.    wt: 1:   9 Construction of a right bisector
  300.    wt: 1:   3 Isometry of Triangles Congruence
  301.    wt: 1:   8 More Use of Maps Not Drawn to Scale
  302.    wt: 1:   22 Multiplication of Signed Numbers
  303.    wt: 1:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  304.    wt: 1:   19 Signed Multiples of Vectors
  305.    wt: 1:   8 Division and Mulplication of Compound Fractions
  306.    wt: 1:   4 Location of Point in Decimal Addition
  307.    wt: 1:   3 Location of Point in Decimal Multiplication
  308.    wt: 1:   E Long Division Methods more
  309.    wt: 1:   D Long Division Methods
  310.    wt: 1:   C Three Decimal Subtraction Methods
  311.    wt: 1:   B Decimal Comparison and Subtraction
  312.    wt: 1:   A Decimal Addition Columm Methods
  313.    wt: 1:   8 Column Multiplication Methods in General
  314.    wt: 1:   7 Decimals Multiplication Methods Examples
  315.    wt: 1:   6 Column Methods for Decimal Multiplication
  316.    wt: 1:   5 Distributive Law for Whole Numbers
  317.    wt: 1:   4 Commutative Law Groups Counting Form
  318.    wt: 1:   3 Multiplicative Counting Skills Principles
  319.    wt: 1:   2 Combing Counts Addition Skills and Principles
  320.    wt: 1:   7 Pythagorean Theorem Chinese Square Proof
  321.    wt: 1:   4 Comparison of Negative Numbers
  322.    wt: 1:   5 Box Volume Formula Example
  323.    wt: 1:   10 Set View of Wordy Extensions To Arithmetic
  324.    wt: 1:   8 Sets of Numbers
  325.    wt: 1:   6 Three Notions of What is a Variable
  326.    wt: 1:   4 A Brief Story of numbers and algebra
  327.    wt: 1:   4 Greater More Less Than Signs in General
  328.    wt: 1:   2 More and Less Than with Unlike Signs
  329.    wt: 1:   1 More and Less Than for Counts and Measures
  330.    wt: 1:   3 Properties of Square Roots with example
  331.    wt: 1:   17 GCD LCM of 85 and 60 via Prime
  332.    wt: 1:   16 GCD and LCM of 650 225 via Prime
  333.    wt: 1:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  334.    wt: 1:   14 GCD of 650 110 via Primes LCM via Product Rule
  335.    wt: 1:   9 GCD of 360 110 via Primes and Euclid Algorithm
  336.    wt: 1:   4 LCM of 8 and 10 via Prime
  337.    wt: 1:   5 lengths and signs of numbers
  338.    wt: 1:   6 Simplification of Fractions with Units
  339.    wt: 1:   10 Simplification of Fractions and Mixed Numerals
  340.    wt: 1:   6 Multiplication of Mixed Numbers
  341.    wt: 1:   3 Unit fraction of a fraction
  342.    wt: 1:   2 Integers Multiplies of a Unit Moverment
  343.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  344.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  345.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  346.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  347.    wt: 1:   20 Uniqueness of Prime Factorization
  348.    wt: 1:   16 video Factors of 980 using prime
  349.    wt: 1:   15 video Factors of 20 using Prime Factorization
  350.    wt: 1:   14 video Factors of 24 Take II
  351.    wt: 1:   13 video Factors of 24 using prime
  352.    wt: 1:   6 Sieve of Eratosthenes and Square Rule
  353.    wt: 1:   C Counting Areas with Powers of Ten
  354.    wt: 1:   B Powers of Ten
  355.    wt: 1:   8 Subtraction with Units of Measure
  356.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  357.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  358.    wt: 1:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  359.    wt: 1:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  360.    wt: 1:   5 More on Groups of 3 Place Value in Decimal Fractions
  361.    wt: 1:   4 Groups of 3 Place Value in Decimal Fractions
  362.    wt: 1:   3 More on Groups of 3 Multi Digit Place Value
  363.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  364.    wt: 1:   012 Division of Time Intervals by Time Intervals
  365.    wt: 1:   011 Division of Time Intervals By Numbers
  366.    wt: 1:   010 Repeated Addition of Time Intervals
  367.    wt: 1:   9 Comparison and Subtraction of Time Intervals
  368.    wt: 1:   8 Addition of Time Intervals via subtotaling
  369.    wt: 1:   7 Addition of Time Intervals
  370.    wt: 1:   4 Mixing and Changing Units of Time
  371.    wt: 1:   3 Units and Lengths of Time
  372.    wt: 1:   1 Intro of Kids To Time Date Skills
  373.    wt: 1:   Example 1. Area Between x and x squared
  374.    wt: 1:   Area Between Crossing Curves Lesson Take 2
  375.    wt: 1:   Area Between Crossing Curves Lesson Take 1
  376.    wt: 1:   Example 3
  377.    wt: 1:   Example 2
  378.    wt: 1:   Example 1
  379.    wt: 1:   Area Between Curves Lesson Take 1
  380.    wt: 1:   Summary
  381.    wt: 1:   A Related lessons in Volume 3
  382.    wt: 1:   34 Derivative of exponential function
  383.    wt: 1:   31 Derivatives of inverse functions
  384.    wt: 1:   30Chain Rule A Proof
  385.    wt: 1:   28 Chain Rule Preparation for a Proof
  386.    wt: 1:   8 Differentiation of polynomials
  387.    wt: 1:   5 Jumps and absence of unlimited error control
  388.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  389.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  390.    wt: 1:   G.6 Bounded Derivatives implies Lipshitz Continuity
  391.    wt: 1:   G.5 Motions With Bounded Velocities
  392.    wt: 1:   G.4 Lipschitz Continuity implies EquiContinuity
  393.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  394.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  395.    wt: 1:   F.5b Extreme Value Theorem
  396.    wt: 1:   F.5a Equicontinuity Theorems
  397.    wt: 1:   F.4 Finite Covering Theorem
  398.    wt: 1:   F.3 Intermediate Value Theorem
  399.    wt: 1:   F.2 Closed Range Theorem
  400.    wt: 1:   F.1 What Functions are Continuous
  401.    wt: 1:   E1 Error Control Inequalities
  402.    wt: 1:   D1 Sets and Sequences GLBs and LGBs
  403.    wt: 1:   C Triangle Inequalities
  404.    wt: 1:   B3 Bolzano Weierstrass Theorem
  405.    wt: 1:   B1 Pigeon Hole Principles from combinatorics
  406.    wt: 1:   PostScript For and Against Decimal Perspectives
  407.    wt: 1:   A1. Introduction
  408.    wt: 1:   Chapter 24 Logarithms Powers and Exponentials
  409.    wt: 1:   Chapter 23 Links To Trigonometry
  410.    wt: 1:   Chapter 22 Complex Numbers
  411.    wt: 1:   Chapter 21 Arrow Addition
  412.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  413.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  414.    wt: 1:   Chapter 18. Slopes Areas Integration
  415.    wt: 1:   Chapter 17. Area Approximation
  416.    wt: 1:   Chapter 16. Velocity Approximation
  417.    wt: 1:   Chapter 15. Slope Approximation
  418.    wt: 1:   Chapter 14 Limits and Continuity with and sans Decimals
  419.    wt: 1:   Chapter 13. Acceleration
  420.    wt: 1:   Chapter 12. Units and Slopes
  421.    wt: 1:   Chapter 11. Graphing Slope versus Position
  422.    wt: 1:   Chapter 10 Slopes and Units
  423.    wt: 1:   Chapter 9 About First Courses in Calculus
  424.    wt: 1:   Chapter 8. Slope Interpretation
  425.    wt: 1:   Chapter 7 Slopes and Velocity
  426.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  427.    wt: 1:   Chapter 5. Slope Sign Tests
  428.    wt: 1:   Chapter 4. More Slope Sign Analysis
  429.    wt: 1:   Chapter 3. Slope Sign Analysis
  430.    wt: 1:   Chapter 2. Slopes and Ski Trails
  431.    wt: 1:   Chapter 1.Introduction
  432.    wt: 1:   Fall 1983 Calculus Appetizer
  433.    wt: 1:   Foreword
  434.    wt: 1:   Postscript More on Better Performance
  435.    wt: 1:   Postscript For Better Performance
  436.    wt: 1:   Appendix D. What to do in School and Why
  437.    wt: 1:   Appendix C. How to Read
  438.    wt: 1:   Appendix B. How To Learn
  439.    wt: 1:   Appendix A. Reading Guide For Next Appendices
  440.    wt: 1:   Chapter 30 Truth Tables
  441.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  442.    wt: 1:   Chapter 28 Occurrence Tables
  443.    wt: 1:   Chapter 27 Shorthand Symbols as Pronouns
  444.    wt: 1:   Chapter 26 What is in chapters 27 to 31
  445.    wt: 1:   Chapter 24. Personal Investment and Pension EGS
  446.    wt: 1:   Chapter 23. Notation For Sums
  447.    wt: 1:   Chapter 22. Geometric Sums and Sequences
  448.    wt: 1:   Chapter 21. Third Reading Guide
  449.    wt: 1:   Chapter 20. Degrees and Radians
  450.    wt: 1:   Chapter 19. Functions and Sets
  451.    wt: 1:   Chapter 18. Rules for Algebra
  452.    wt: 1:   Chapter 16. Painless Theorem Proving
  453.    wt: 1:   Chapter 15. Solving Linear Equations
  454.    wt: 1:   Postscript Unifying Theme A Fourth Skill For Algebra
  455.    wt: 1:   Chapter 13. Second Reading Guide
  456.    wt: 1:   Chapter 12. Shorthand Usage Guide
  457.    wt: 1:   Chapter 11. Why Shorthand
  458.    wt: 1:   Chapter 10 Describing and Changing Calculations
  459.    wt: 1:   Postscript What is a Variable
  460.    wt: 1:   Chapter 9 Talking about Numbers or Quantities
  461.    wt: 1:   Chapter 8 Three Skills For Algebra
  462.    wt: 1:   Solutions For Arithmetic Exercises
  463.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  464.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  465.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  466.    wt: 1:   Foreword
  467.    wt: 1:   R Why Learn Mathematics Skills
  468.    wt: 1:   Q How Logic and Proofs extend Show Work Practices
  469.    wt: 1:   N Mathematics Prepare for College Studies
  470.    wt: 1:   C. Domino effect of being careful
  471.    wt: 1:   B. Domino effect of errors
  472.    wt: 1:   Chapter 8 Skipped Topics and Why
  473.    wt: 1:   Chapter 7 Calculus Previews and Calculus Lightly
  474.    wt: 1:   Chapter 6 More Algebra and Geometry
  475.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  476.    wt: 1:   Chapter 3 Algebra Starter Lessons
  477.    wt: 1:   Chapter 2 Why Sets
  478.    wt: 1:   Chapter 1 Arithmetic
  479.    wt: 1:   Primary and Secondary Skills and Practices with Take Home Value
  480.    wt: 1:   7 Games and Activities for Instruction
  481.    wt: 1:   5 Interpreting and Drawing Maps and Plans.
  482.    wt: 1:   4 Money Matters Saving Earning Buying Selling and Budgets
  483.    wt: 1:   3 Telling Tracking Time Temporal and More Place Sense
  484.    wt: 1:   2 Identifying Size and Position Place and Spatial Sense
  485.    wt: 1:   1 From Number Recognition and Counting to Arithmetic B
  486.    wt: 1:   1 From Number Recognition and Counting to Arithmetic A
  487.    wt: 1:   Ends Values Methods For Skill Development Framework Prequel
  488.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  489.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  490.    wt: 1:   Implementation Notes
  491.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  492.    wt: 1:   Systematic Algebra Skill Development Missing Links
  493.    wt: 1:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  494.    wt: 1:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  495.    wt: 1:   Which Way To Go
  496.    wt: 1:   The Math Forum and Site Content

Teachers & Tutors: Site pages offer better or best practices for providing skills - simpler than expected & comprehensive but for exercises. For your charges, your duty is to study them alone or in groups and develop skill building exercises & activities to share. Start now. The effort here is the best I can do. Others are welcome to refine or exceed it. Please do.

Secondary Mathematics for Ages 11+, A Practical Approach for home-tutoring or -schooling, or for schools & colleges with local curriculum control. Study how to include site content - its skill development how-TOs and innovations into present or future lesson plans - some reading required.

Road Safety Messages and Questions: When and why should you face traffic when walking along a road or cycle path? Is it a good idea to hang limbs outside of cars etc? What gives more protection in a crash: a car, motorbike or bicycle? See too, the BBC-Belgium story Texting and Driving - texting & the impossible test - the article links to a gruesome utube video on the subject

The Logic of Injustice: How Texas sent an innocent man to his death - The wrong Carlos. Some judgments are irreversible. Procescution: Where and when prosectors play to win rather than for justice, guilt beyond a reasonable doubt goes unrespected due to prosecutors who putting winning first, those innocence before the law may be convicted. Some procescutors offices in continuing to accuse after a pardon due to reasonable doubt or innocent being shown, may sucessfully oppose compensaton for false convictions by asserting a pardon individual is still under suspicion. Then the pardoned individual or the latter's estate is not compensation for years or decade of improper or false imprisonment, or for execution. Site chapters on Logic
and some in Pattern Based Reason may slowly lead to greater precision in reading, applying and writing laws.

May 2012, Composition Starting: Pre-School and Primary Mathematics - Quantitative Skills, An Intellectual View, Feedback Welcome:

The 8 Most Popular Site Inlinks

20 Times Table - the most popular site page - popular pages - unexpected.
Fractions & Ratios - with lesson on raising terms to introduce & justify times, division & comparison as well addition & subtraction
Parent Center - See below
Volume 1, Elements of Reason - Intro to all site books.
What is a Variable - best for ages 13+
Written work formats for Arithmetic and Algebra - a skill method and standard!
Complex Numbers Visually - best for ages 13+
Natural Logs, Exponentials, Powers, Roots

Division of Labour: This site offers advice and directions with pointers to resources elsewhere, if known, when they help or lessen the need to write more.

Parent Center: Help your child or teen learn:

Parent-friendly Work Booklets for ages 3+ to 13 Use these or others to check or build skills. Other booklets are available but these booklets allow parents unsure of themselves in mathematics to help their children. The selection acquired in Canada is published in the USA. So it has a US orientation. In retrospect, the selection shows parents what to check with the booklets or by other ways, the choice is theirs. But in retrospect, the selection does not cover integral and fractions liquid weights and measures - ask the publishers to correct that! For ages 9 to 12 say, parents may compensate by showing boys and girls how to use weights or mass, and further measures in food preparation. Beyond that children may be shown how to measure and calculate angles, lengths and areas [proportional amounts too] directly or by using maps and plans drawns to scale. Learning how to gather and measure all the ingredients, pots and pans for a dish or a meal, along with cleaning up sets the stage for like activities or experiments in science courses, and in developing organizational skills, gives boys and girls a head start. Good luck. At the other extreme, more comprehensive than light, if your motto is McCainian: drill, drill, drill then Toronto mathematician and actor John Mighton's jump math organization has jump math workbooks for at least grades 3 to 8 for at-home and in-school use - training sessions for teachers available. Jump math has been expanding to cover older students. Jump Math Samples: plus Fractions for Grades 3-4 & Grades 5-6 [Read] Free Resources grades 1 to 8 [unread - likely to be good]. and

Mathematics Skills For Ages 3 to 14 - technical!

Skills with take home value - A few ideas

Basic skills include time-date-calendar Matters; money matters; map, plan and scale diagram matters;counting, measuring and figuring; decision making with logic and likelyhood; being careful and being aware of the domino effect of mistakes; reading and writing with precision.

Is your child able to add, subtract and multiply amounts of money, work with fractions, work with clocks and calendars, work with maps and plans, and measure length, weight-mass and volume? Schools may promote your son or daughter without providing basic skills in reading, writing and arithmetic.

Arithmetic and Number Theory Skills

Algebra Starter Lessons

1 Working With Sets
2 Formula Forward Use - Evaluation
3 Solving Linear Equations - Skip first step with students able to solve 1 eqn in 1 unknown.
4 Computation Rules and Function Notation
5 Real Numbers
6 More Less Greater Than Inequalities and Comparison
7 Axioms Logic and Equivalent Equations
8 Unifying Theme For Algebra
9 Proportionality Backwards and Forwards
10 Examples of Algebraic Reasoning
A Origins of Counting and Figuring Methods
B Real Numbers Extrinsic Development


Site coverage of formuala evaluation format, of computation rules and axioms, and of the forward and backward use of formulas and proportionality relations lessens the amount of natural talent needed to understand and explain algebra.

Geometry - maps plans trigonometry vectors

1 Maps Plans Measurement
2 Euclidean Geometry - Constructions + extras
3 Cartesian and Polar Coordinates
4 Lines and Slopes Take 1
5 What is Similarity
6 Trigonometry first steps
7 Complex Numbers
8 Unit-Circle Trigonometry
9 Lines and Slopes Take 2 with tangent function
10 Intersecting Straight Lines and Transversals
11 Parallel Straight Lines and Transversals
12 Function Translating and Rescaling
13 Vectors
14 Degrees to Radians and Radians to Degrees
15 Arc or Inverse Trigonometric Function

Pre-Teen and young teen mastery of skills and practices which should be common with map-plans-diagrams drawn to scale, contour interpretation included, has actual or potential take-home value for daily- and adult-life in solving routine problems. Elevating some practices to principles, axioms or postualates, provides a base for analytic and Euclidean geometry, an analytic view of similarity, and an efficient mastery of trigonometry and complex numbers. Right triangle trigonometry provide an analytic alternative to solving geometric problems by drawing diagrams to scale.

More Algebra

Natural-Logarithms Exponentials Powers Roots
Five Polynomial Operations
Quadratics Geometrically
Functions
5 Factored Polynomial Sign Analysis Examples
Rewriting algebraic substitution as function substitutions

The first topic leads to a full high school level theory for the forward and backward mastery of growth and decay models and for definition, range and domains of radicals, roots and powers. The next two topics make quadratics and polynomials easier to learn and teach. Site coverage of functions turns vertical and horizontal line rules into computation methods for evaluating functions.

70 Calculus Starter Lessons

Calculus Lessons Elsewhere:

  1. How to Ace Calculus: Street Wise Guide - Mostly Text.

  2. Flash Video for Calculus Phobics

They cover basic topics in ways likely to complement your notes, your textbooks and site material. When Goldilocks trespassed in the house of the three bears, she found three bowls of porridge, two not to her liking, and one just right. Different bears have different tastes. As invited guest here and elsewhere, if one or more explanations is not to liking, try another. It may be better or just right.

Unsolicited Advice

Learning to do and high marks if it comes to easy is often deceptive - light rather than deep. For that reason, students with learning difficulties determined not to let it get in their way may go deeper and farther than those with none. High marks, if the come easy, may be deceptive - provide a too light and not a deep mastery. That could have been your problem in secondary school, one that leads to comprehension shock or difficulties in calculus and more generally in the first year of college. Bon Appetite.

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Logic-Reason for all
Careful Thinking
Chains of Reason
Mathematical Induction
Responsibility
Bodies-of-Knowledge

Arithmetic - Ages 10+
1. Deciml Place Value - fun
2. Decimals for Tutors
3. Prime Factors - quickly
4. Fractions + Ratios
5. Arith with units - science

Geometry
1 Maps + Plans Use
2 Euclidean Geometry
3 Rct +Polr Coordinates
4 Lines-Slopes [I]
5. What is Similarity 		Algebra Starters - the base
1. Better Work Format
2. Solve Linear Eqns
3. Computation Rules
4. Axioms, Item 3 Viewpnt
5. Formulas Backwards 		More Algebra
Logarithms-ax & m/nth roots
Five Polynomial Operations
Quadratics Geometrically
Functions || Vectors too
Arith. Skill Check+Answers 		Calculus Prep/Preview
What is a Variable
Why study slopes
Why factor polynomials
Complex Numbers
Limits + Continuity

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