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Logic and Mathematics Skill & Concept Development How-TOs Français: 26 pages
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Logic 5 Chapters Arithmetic 10 Steps Algebra 12 Starter Steps & 5 Advanced Steps
Work & Study 23 Tips Geometry 15 Steps Calculus 70 Lessons

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.

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  1.    wt: 6:   Advanced Calculus Volume 3 Appendices/
  2.    wt: 3:   Step 3 Easy systems in 2 or more unknowns/
  3.    wt: 3:   Volume 3 Why Slopes A Calculus Intro Etc/
  4.    wt: 2:   3 Quadratics Geometrically/
  5.    wt: 2:   13 Vectors/
  6.    wt: 2:   3 Cartesian and Polar Coordinates/
  7.    wt: 2:   3 Prime Factorization Skills/
  8.    wt: 2:   12 Webvideo Lessons on Area and Volume Calculation/
  9.    wt: 2:   4 Lessons on Using Derivatives/
  10.    wt: 2:   38 Lessons on Calculating Derivatives/
  11.    wt: 2:   13 Lessons on Limits and Continuity/
  12.    wt: 1:   LAMP Lean Applied Mathematics Program/
  13.    wt: 1:   Volume 1A Regles et modeles/
  14.    wt: 1:   4 Functions/
  15.    wt: 1:   Step 4 Gaussian Elimination/
  16.    wt: 1:   Step 2 Algebraic solutions for one unknown/
  17.    wt: 1:   Step 1 Stick diagram and fractions/
  18.    wt: 1:   3 Solving Linear Equations/
  19.    wt: 1:   C Decimal Multiplication Methods/
  20.    wt: 1:   5 Lessons on Integration/
  21.    wt: 1:   70 Calculus Starter Lessons/
  22.    wt: 1:   Volume 2 Three Skills For Algebra/
  23.    wt: 1:   Volume 1B Mathematics Curriculum Notes/
  24.    wt: 1:   Volume 1A Pattern Based Reason/
  25.    wt: 1:   Volume 1 Elements of Reason/
  26.    wt: 1:   Mathematics Skill Development Framework/

Web Page Search

185 matches:

  1.    wt: 3:   33 sines and cosines of 2A 3A 4A 5A
  2.    wt: 2:   23 Inverse Functions
  3.    wt: 2:   35 sines and cosines of 2A 3A 4A 5A
  4.    wt: 2:   34 sines and cosines of 2A 3A 4A 5A
  5.    wt: 2:   30 unit circle calculation of six trigonometric functions
  6.    wt: 2:   3 Gaussian Elimination 3 unknowns first example
  7.    wt: 2:   3 More on Groups of 3 Multi Digit Place Value
  8.    wt: 2:   A Related Material in Volume 3
  9.    wt: 2:   A Related lessons in Volume 3
  10.    wt: 2:   33 Chain Rule Real Player video examples
  11.    wt: 2:   31 Derivatives of inverse functions
  12.    wt: 2:   F.1 What Functions are Continuous
  13.    wt: 2:   Fall 1983 Calculus Appetizer
  14.    wt: 2:   Chapter 7 Calculus Previews and Calculus Lightly
  15.    wt: 1:   Skills Chapter 5 Calculus
  16.    wt: 1:   Skills Chapter 3 Algebra
  17.    wt: 1:   3 Euclidean Geometry Leanly
  18.    wt: 1:   05 13 OldSiteEntrancePage
  19.    wt: 1:   chapitre 04 03 Unidirectionnel versus bidirectionnel
  20.    wt: 1:   chapitre 03 A Propos Des Prochains Chapitre
  21.    wt: 1:   3 Energy Power Heat08
  22.    wt: 1:   C Energy Power03
  23.    wt: 1:   E Wire Resistance Calculation03
  24.    wt: 1:   3 Like resistors in parallel
  25.    wt: 1:   23 Modularized Skill Development Modularized Rigor Take IV
  26.    wt: 1:   23 Modularized Skill Development Modularized Rigor Take III
  27.    wt: 1:   23 Modularized Skill Development Modularized Rigor Take II
  28.    wt: 1:   23 Modularized Skill Development Modularized Rigor
  29.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  30.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  31.    wt: 1:   13 Addition and Addition Tables
  32.    wt: 1:   3 Preparing for Science Studies
  33.    wt: 1:   Ages 3 plus to 4 plus
  34.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  35.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  36.    wt: 1:   sign monoticity analysis example 3
  37.    wt: 1:   25 Absolute Value greatest integer and saw tooth functions
  38.    wt: 1:   24 Monotoncity Injectivity and Inverse Functions
  39.    wt: 1:   21 Graphs of functions given by Horizontal Line Method
  40.    wt: 1:   15 Sign analysis of functions
  41.    wt: 1:   13 From one to one to many to one
  42.    wt: 1:   8 Set view of relations and functions
  43.    wt: 1:   7 Functions with finite domains
  44.    wt: 1:   3 Formula or function graphing exercise
  45.    wt: 1:   3 quadratics factoring by inspection
  46.    wt: 1:   3 Natural Logarithms and Exponentials Basic Properties
  47.    wt: 1:   3 Polynomials Multiplication Addition
  48.    wt: 1:   13 cosecant function Definition Graph and Inverse
  49.    wt: 1:   3 Left Inverse of cosine arccos definition
  50.    wt: 1:   3 Circle Arclengh Proportional to Central Angle
  51.    wt: 1:   13 Velocity Vectors in Physics
  52.    wt: 1:   3 Navigation with Arrows or Vectors
  53.    wt: 1:   3 graphing y=f(x c) plus K
  54.    wt: 1:   13 Straight Lines Finding Equations from 2 points
  55.    wt: 1:   3 Straight Lines Slope as Tangent of Inclination Angle
  56.    wt: 1:   32 seven rows of pascals triangle
  57.    wt: 1:   31 basic secant cosecant cotangent trig identities
  58.    wt: 1:   23 sine and cosine of 180 plus 22.5 degrees
  59.    wt: 1:   19 Pythagorean Identity For sine and cosine functions
  60.    wt: 1:   13 Graph of tangent function many periods
  61.    wt: 1:   6 sines and cosines for reference angle 30 degrees
  62.    wt: 1:   3 sines and cosines for reference angle 90 degrees
  63.    wt: 1:   13 Trig Formulas for dot and cross Products
  64.    wt: 1:   3 Addition Properties
  65.    wt: 1:   3 Trigonometric Ratios sine and cosine
  66.    wt: 1:   13 Navigation Location from Angles to 2 Landmarks
  67.    wt: 1:   3 Similarity by Design with coordinates
  68.    wt: 1:   3 Slope product for perpendicular lines
  69.    wt: 1:   13 Pythagorean spatial distance formulas
  70.    wt: 1:   3 Rectangular Coordinates Review
  71.    wt: 1:   13 Angle Side Angle Failure
  72.    wt: 1:   3 Isometry of Triangles Congruence
  73.    wt: 1:   3 Lengths and Areas on Maps and Plans
  74.    wt: 1:   23 Distributive Law Two Derivations
  75.    wt: 1:   13 Arrows and Vectors in a Plane
  76.    wt: 1:   3 Location of Point in Decimal Multiplication
  77.    wt: 1:   3 Multiplicative Counting Skills Principles
  78.    wt: 1:   3 Inequalities Algebraically
  79.    wt: 1:   3 Proportionality Examples
  80.    wt: 1:   3 Linear Equation Literal Solution More
  81.    wt: 1:   3 Product Axioms Two Forms
  82.    wt: 1:   3 More and Less Than with Unlike Signs
  83.    wt: 1:   13 Real Number Subtraction
  84.    wt: 1:   3 Fractions
  85.    wt: 1:   3 Geometric Formulas and Function Notation
  86.    wt: 1:   5 Gaussian Elimination for 3 unknowns 2nd example
  87.    wt: 1:   3 GE III Equation Addition and Multiplication
  88.    wt: 1:   3 Solving triangular system example
  89.    wt: 1:   3 Four Examples
  90.    wt: 1:   3 Two Examples
  91.    wt: 1:   13 Naming Identifying Formulas with Words
  92.    wt: 1:   11 Volume of Sphere
  93.    wt: 1:   10 Volume of Pyramid
  94.    wt: 1:   9 Volume of Cone
  95.    wt: 1:   5 Box Volume Formula Example
  96.    wt: 1:   3 Triangle Area Formula Example
  97.    wt: 1:   3 Counting with Sets etc
  98.    wt: 1:   3 Adding Words To Arithmetic
  99.    wt: 1:   3 Comparison of Negative Numbers
  100.    wt: 1:   3 Properties of Square Roots with example
  101.    wt: 1:   13 GCD from given Prime Factorization
  102.    wt: 1:   9 GCD of 360 110 via Primes and Euclid Algorithm
  103.    wt: 1:   3 Counting with Tables and Trees II
  104.    wt: 1:   3 signed coordinates for maps and planes
  105.    wt: 1:   3 Multiplying Units and Numbers
  106.    wt: 1:   13 Fraction Comparison Algebraic View
  107.    wt: 1:   3 Unit fraction of a fraction
  108.    wt: 1:   13 Subtraction with Additive Inverse
  109.    wt: 1:   3 Adding Movements with same direction
  110.    wt: 1:   27 Divisibility by 2 3 6 5 9 10 Example
  111.    wt: 1:   26 Divisibility by 2 3 5 Example
  112.    wt: 1:   25 Divisibility Tests for 2 3 5 9 10 Example
  113.    wt: 1:   24 Divisibility Tests for 2 3 5 9 10
  114.    wt: 1:   23 Remainder Arithmetic Modulo 2
  115.    wt: 1:   22 Remainder Arithmetic Modulo 3 more
  116.    wt: 1:   21 Remainder Arithmetic Modulo 3
  117.    wt: 1:   13 Remainder Arithmetic Modulo 5 Example
  118.    wt: 1:   3 Remainder Arithmetic Modulos 10 more still
  119.    wt: 1:   13 video Factors of 24 using prime
  120.    wt: 1:   10 video Prime Factorization upto 23 squared
  121.    wt: 1:   3 video Primes and Composites from 9 times table
  122.    wt: 1:   Long Division forwards and backwards Example 3
  123.    wt: 1:   3 Division Single Digit Divisor Example
  124.    wt: 1:   3 More One Digit Multipliers
  125.    wt: 1:   1 Why 3 times 5 gives 15
  126.    wt: 1:   3 Harder Cases Convert to Compare and Subtract
  127.    wt: 1:   3. How to add with decimals A sans conversions
  128.    wt: 1:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  129.    wt: 1:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  130.    wt: 1:   5 More on Groups of 3 Place Value in Decimal Fractions
  131.    wt: 1:   4 Groups of 3 Place Value in Decimal Fractions
  132.    wt: 1:   013 Travel Time Tables
  133.    wt: 1:   3 Units and Lengths of Time
  134.    wt: 1:   Example 2 volume of a cone
  135.    wt: 1:   Example 1 volume of a pyramid
  136.    wt: 1:   Volume of Solid by Cross Sections Lesson
  137.    wt: 1:   Example 3
  138.    wt: 1:   3 Two Chain Rule Method Exercises
  139.    wt: 1:   3 Second derivative test
  140.    wt: 1:   38 Formulas and derivatives for powers and roots
  141.    wt: 1:   36 Cube root derivative animated
  142.    wt: 1:   34 Derivative of exponential function
  143.    wt: 1:   30Chain Rule A Proof
  144.    wt: 1:   27 Chain Rule sinusoidal outer inner functions EGS
  145.    wt: 1:   26 Chain Rule Recognising outer inner functions
  146.    wt: 1:   23 Chain Rule in general
  147.    wt: 1:   19 Chain Rule for linear functions
  148.    wt: 1:   15 sine and cosine derivatives 3rd step
  149.    wt: 1:   13 sine and cosine derivatives 1st step
  150.    wt: 1:   3 Motivation for Limit Definition Take 2
  151.    wt: 1:   1 Fall 1983 Why Slopes Appetizer
  152.    wt: 1:   13 Limits with Parameters and Derivatives Take II
  153.    wt: 1:   3 Decimal insights for limits continuity convergence
  154.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  155.    wt: 1:   G.1 First Fundamental Theorem of Calculus
  156.    wt: 1:   G.3 Constant Difference Theorem Proof
  157.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  158.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  159.    wt: 1:   F.3 Intermediate Value Theorem
  160.    wt: 1:   B3 Bolzano Weierstrass Theorem
  161.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  162.    wt: 1:   Chapter 23 Links To Trigonometry
  163.    wt: 1:   Chapter 13. Acceleration
  164.    wt: 1:   Chapter 9 About First Courses in Calculus
  165.    wt: 1:   Chapter 3. Slope Sign Analysis
  166.    wt: 1:   Appendix A. Reading Guide For Next Appendices
  167.    wt: 1:   Chapter 31 Direct and Indirect Reason
  168.    wt: 1:   Chapter 30 Truth Tables
  169.    wt: 1:   Chapter 26 What is in chapters 27 to 31
  170.    wt: 1:   Chapter 23. Notation For Sums
  171.    wt: 1:   Chapter 19. Functions and Sets
  172.    wt: 1:   Chapter 13. Second Reading Guide
  173.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  174.    wt: 1:   Chapter 3 Chains of Reason
  175.    wt: 1:   Chapter 3 Algebra Difficulties
  176.    wt: 1:   Chapter 23 Truth Tables
  177.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  178.    wt: 1:   Chapter 3 What is in chapters 4 to 8
  179.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  180.    wt: 1:   Chapter 3 Algebra Starter Lessons
  181.    wt: 1:   3 Telling Tracking Time Temporal and More Place Sense
  182.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  183.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  184.    wt: 1:   More Algebra and Slope based Calculus Preview
  185.    wt: 1:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years

Extended Search

555 matches:

  1.    wt: 8:   F.1 What Functions are Continuous
  2.    wt: 8:   B3 Bolzano Weierstrass Theorem
  3.    wt: 7:   G.2 Lipshitz Conditions Integration Calculus Reform
  4.    wt: 7:   G.1 First Fundamental Theorem of Calculus
  5.    wt: 7:   G.3 Constant Difference Theorem Proof
  6.    wt: 7:   G.2 Differentiable Functions Mean Value Theorem
  7.    wt: 7:   G.1 Differentiable Functions Rolles Theorem
  8.    wt: 7:   F.5a Equicontinuity Theorems
  9.    wt: 7:   F.3 Intermediate Value Theorem
  10.    wt: 7:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  11.    wt: 6:   Postscript One Sided and Intermediate Value Theorems
  12.    wt: 6:   G.6 Bounded Derivatives implies Lipshitz Continuity
  13.    wt: 6:   G.5 Motions With Bounded Velocities
  14.    wt: 6:   G.4 Lipschitz Continuity implies EquiContinuity
  15.    wt: 6:   F.5b Extreme Value Theorem
  16.    wt: 6:   F.4 Finite Covering Theorem
  17.    wt: 6:   F.2 Closed Range Theorem
  18.    wt: 6:   E2 Algebraic Properties of Limits
  19.    wt: 6:   E1 Error Control Inequalities
  20.    wt: 6:   D2 Limits of Monotone Sequences
  21.    wt: 6:   D1 Sets and Sequences GLBs and LGBs
  22.    wt: 6:   C Triangle Inequalities
  23.    wt: 6:   B1 Pigeon Hole Principles from combinatorics
  24.    wt: 6:   PostScript For and Against Decimal Perspectives
  25.    wt: 6:   A1. Introduction
  26.    wt: 5:   3 Solving triangular system example
  27.    wt: 5:   31 Derivatives of inverse functions
  28.    wt: 5:   Chapter 23 Links To Trigonometry
  29.    wt: 5:   Chapter 13. Acceleration
  30.    wt: 5:   Chapter 3. Slope Sign Analysis
  31.    wt: 5:   Fall 1983 Calculus Appetizer
  32.    wt: 4:   23 Inverse Functions
  33.    wt: 4:   13 Velocity Vectors in Physics
  34.    wt: 4:   3 Navigation with Arrows or Vectors
  35.    wt: 4:   34 sines and cosines of 2A 3A 4A 5A
  36.    wt: 4:   33 sines and cosines of 2A 3A 4A 5A
  37.    wt: 4:   13 Pythagorean spatial distance formulas
  38.    wt: 4:   3 Rectangular Coordinates Review
  39.    wt: 4:   3 Gaussian Elimination 3 unknowns first example
  40.    wt: 4:   13 video Factors of 24 using prime
  41.    wt: 4:   3 video Primes and Composites from 9 times table
  42.    wt: 4:   Example 3
  43.    wt: 4:   A Related lessons in Volume 3
  44.    wt: 4:   33 Chain Rule Real Player video examples
  45.    wt: 4:   Chapter 9 About First Courses in Calculus
  46.    wt: 3:   Skills Chapter 3 Algebra
  47.    wt: 3:   13 From one to one to many to one
  48.    wt: 3:   3 Formula or function graphing exercise
  49.    wt: 3:   3 quadratics factoring by inspection
  50.    wt: 3:   35 sines and cosines of 2A 3A 4A 5A
  51.    wt: 3:   3 GE III Equation Addition and Multiplication
  52.    wt: 3:   4 Solving a triangular system exercise
  53.    wt: 3:   2 Essentially one exercises three with solution
  54.    wt: 3:   1 Essentially One Unknown
  55.    wt: 3:   3 Four Examples
  56.    wt: 3:   3 Two Examples
  57.    wt: 3:   10 video Prime Factorization upto 23 squared
  58.    wt: 3:   3 More One Digit Multipliers
  59.    wt: 3:   3 More on Groups of 3 Multi Digit Place Value
  60.    wt: 3:   Example 2 volume of a cone
  61.    wt: 3:   Example 1 volume of a pyramid
  62.    wt: 3:   Volume of Solid by Cross Sections Lesson
  63.    wt: 3:   Example 4 with x function of y
  64.    wt: 3:   Example 2
  65.    wt: 3:   Example 1
  66.    wt: 3:   A Related Material in Volume 3
  67.    wt: 3:   3 Second derivative test
  68.    wt: 3:   2 Second derivative test prequel
  69.    wt: 3:   38 Formulas and derivatives for powers and roots
  70.    wt: 3:   36 Cube root derivative animated
  71.    wt: 3:   34 Derivative of exponential function
  72.    wt: 3:   30Chain Rule A Proof
  73.    wt: 3:   27 Chain Rule sinusoidal outer inner functions EGS
  74.    wt: 3:   26 Chain Rule Recognising outer inner functions
  75.    wt: 3:   23 Chain Rule in general
  76.    wt: 3:   22 Chain Rule for polynomials
  77.    wt: 3:   19 Chain Rule for linear functions
  78.    wt: 3:   15 sine and cosine derivatives 3rd step
  79.    wt: 3:   13 sine and cosine derivatives 1st step
  80.    wt: 3:   12 Quotient rule examples
  81.    wt: 3:   5 Product Rule
  82.    wt: 3:   3 Motivation for Limit Definition Take 2
  83.    wt: 3:   1 Fall 1983 Why Slopes Appetizer
  84.    wt: 3:   13 Limits with Parameters and Derivatives Take II
  85.    wt: 3:   4 Numerical properties
  86.    wt: 3:   3 Decimal insights for limits continuity convergence
  87.    wt: 3:   Postscript Pythagorean Theorem yet another proof
  88.    wt: 3:   Chapter 24 Logarithms Powers and Exponentials
  89.    wt: 3:   Chapter 22 Complex Numbers
  90.    wt: 3:   Chapter 21 Arrow Addition
  91.    wt: 3:   Chapter 20 Vectors and Complex Numbers
  92.    wt: 3:   Chapter 19. Exponentials and Natural Logarithms
  93.    wt: 3:   Chapter 18. Slopes Areas Integration
  94.    wt: 3:   Chapter 17. Area Approximation
  95.    wt: 3:   Chapter 16. Velocity Approximation
  96.    wt: 3:   Chapter 15. Slope Approximation
  97.    wt: 3:   Chapter 15. Algebraic Evaluation of Limits
  98.    wt: 3:   Chapter 14 Limits and Continuity with and sans Decimals
  99.    wt: 3:   Chapter 12. Units and Slopes
  100.    wt: 3:   Chapter 11. Graphing Slope versus Position
  101.    wt: 3:   Chapter 10 Slopes and Units
  102.    wt: 3:   Chapter 8. Slope Interpretation
  103.    wt: 3:   Chapter 7 Slopes and Velocity
  104.    wt: 3:   Chapter 6. Slopes and Vertical Shifts
  105.    wt: 3:   Chapter 5. Slope Sign Tests
  106.    wt: 3:   Chapter 4. More Slope Sign Analysis
  107.    wt: 3:   Chapter 2. Slopes and Ski Trails
  108.    wt: 3:   Chapter 1.Introduction
  109.    wt: 3:   Foreword
  110.    wt: 3:   Chapter 31 Direct and Indirect Reason
  111.    wt: 3:   Chapter 30 Truth Tables
  112.    wt: 3:   Chapter 23. Notation For Sums
  113.    wt: 3:   Chapter 13. Second Reading Guide
  114.    wt: 3:   Chapter 3 Chains of Reason
  115.    wt: 3:   Chapter 3 Algebra Difficulties
  116.    wt: 3:   Chapter 23 Truth Tables
  117.    wt: 3:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  118.    wt: 3:   Chapter 3 What is in chapters 4 to 8
  119.    wt: 3:   More Algebra and Slope based Calculus Preview
  120.    wt: 3:   Systematic Algebra Skill Development Missing Links
  121.    wt: 3:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  122.    wt: 2:   Skills Chapter 5 Calculus
  123.    wt: 2:   Ramblings Extrinsic numbers theory
  124.    wt: 2:   Ramblings Introduction Algebra Essay
  125.    wt: 2:   3 Euclidean Geometry Leanly
  126.    wt: 2:   Education Reform Inconsistencies
  127.    wt: 2:   chapitre 04 03 Unidirectionnel versus bidirectionnel
  128.    wt: 2:   chapitre 03 A Propos Des Prochains Chapitre
  129.    wt: 2:   C Energy Power03
  130.    wt: 2:   23 Modularized Skill Development Modularized Rigor Take IV
  131.    wt: 2:   23 Modularized Skill Development Modularized Rigor Take III
  132.    wt: 2:   23 Modularized Skill Development Modularized Rigor Take II
  133.    wt: 2:   23 Modularized Skill Development Modularized Rigor
  134.    wt: 2:   13 Addition and Addition Tables
  135.    wt: 2:   3 Preparing for Science Studies
  136.    wt: 2:   Ages 3 plus to 4 plus
  137.    wt: 2:   sign monoticity analysis example 3
  138.    wt: 2:   25 Absolute Value greatest integer and saw tooth functions
  139.    wt: 2:   24 Monotoncity Injectivity and Inverse Functions
  140.    wt: 2:   21 Graphs of functions given by Horizontal Line Method
  141.    wt: 2:   15 Sign analysis of functions
  142.    wt: 2:   8 Set view of relations and functions
  143.    wt: 2:   7 Functions with finite domains
  144.    wt: 2:   A Quadratics Summary
  145.    wt: 2:   10 quadratic exercises
  146.    wt: 2:   9 quadratics physical and further context
  147.    wt: 2:   8 quadratics backward use of various formulas
  148.    wt: 2:   7 quadratic formulla derivation
  149.    wt: 2:   6 quadratics numerical approach
  150.    wt: 2:   5 quadratics completing the square
  151.    wt: 2:   4 quadratics difference of two squares
  152.    wt: 2:   2 quadratics graphing in general
  153.    wt: 2:   1 quadratics graphing exercises
  154.    wt: 2:   Quadratics in 10 steps
  155.    wt: 2:   3 Natural Logarithms and Exponentials Basic Properties
  156.    wt: 2:   3 Circle Arclengh Proportional to Central Angle
  157.    wt: 2:   A Global Time and Navigation
  158.    wt: 2:   15 Dot and Cross Product
  159.    wt: 2:   14 Why Scalar Multiplication Distributes Physical Argument
  160.    wt: 2:   12 From Applied To Pure Mathematics
  161.    wt: 2:   11 Component Method
  162.    wt: 2:   10 Parallelogram Addition Method
  163.    wt: 2:   9 Head to Tail Coordinate View
  164.    wt: 2:   8 Parallel Vectors
  165.    wt: 2:   7 Coordinate Addition and Scalar Multiplication
  166.    wt: 2:   6 Vectors with Coordinates
  167.    wt: 2:   5 Head To Tail Arrow Addition
  168.    wt: 2:   4 Resultant of a Sum of Movements
  169.    wt: 2:   2 Signed Coordinates
  170.    wt: 2:   1 Unsigned Coordinates
  171.    wt: 2:   Vector and Complex Number Applet
  172.    wt: 2:   13 Straight Lines Finding Equations from 2 points
  173.    wt: 2:   12 Straight Lines Graphing mx plus b
  174.    wt: 2:   32 seven rows of pascals triangle
  175.    wt: 2:   31 basic secant cosecant cotangent trig identities
  176.    wt: 2:   30 unit circle calculation of six trigonometric functions
  177.    wt: 2:   6 sines and cosines for reference angle 30 degrees
  178.    wt: 2:   13 Trig Formulas for dot and cross Products
  179.    wt: 2:   3 Addition Properties
  180.    wt: 2:   13 Navigation Location from Angles to 2 Landmarks
  181.    wt: 2:   3 Similarity by Design with coordinates
  182.    wt: 2:   3 Slope product for perpendicular lines
  183.    wt: 2:   12 Spatial Coordinates
  184.    wt: 2:   11 Triangle Inequality
  185.    wt: 2:   10 Pythagorean plane distance formula
  186.    wt: 2:   9 Pythagorean Theorem Chinese Square Proof
  187.    wt: 2:   8 Distance Between Points on a Line
  188.    wt: 2:   7 Complex Numbers Appetizer
  189.    wt: 2:   6 Polar Multiplication and Rotation
  190.    wt: 2:   5 Cartesian Addition and Translation
  191.    wt: 2:   4 Polar Coordinates to and from
  192.    wt: 2:   2 Cartesian Coordinates with signs
  193.    wt: 2:   1 Cartesian Coordinates sans signs
  194.    wt: 2:   13 Angle Side Angle Failure
  195.    wt: 2:   3 Isometry of Triangles Congruence
  196.    wt: 2:   23 Distributive Law Two Derivations
  197.    wt: 2:   3 Multiplicative Counting Skills Principles
  198.    wt: 2:   3 Proportionality Examples
  199.    wt: 2:   5 Gaussian Elimination for 3 unknowns 2nd example
  200.    wt: 2:   3 Comparison of Negative Numbers
  201.    wt: 2:   9 GCD of 360 110 via Primes and Euclid Algorithm
  202.    wt: 2:   3 Unit fraction of a fraction
  203.    wt: 2:   3 Adding Movements with same direction
  204.    wt: 2:   13 Remainder Arithmetic Modulo 5 Example
  205.    wt: 2:   9 Remainder Arithmetic Divisibility by 5
  206.    wt: 2:   20 Uniqueness of Prime Factorization
  207.    wt: 2:   19 video Prime Factorization Unique
  208.    wt: 2:   18 video Count Factors given Prime Factorization
  209.    wt: 2:   17 Identify and Count Factors using Primes
  210.    wt: 2:   16 video Factors of 980 using prime
  211.    wt: 2:   15 video Factors of 20 using Prime Factorization
  212.    wt: 2:   14 video Factors of 24 Take II
  213.    wt: 2:   12 LCD GCD and LCM using Primes
  214.    wt: 2:   11 Efficient Square Rule Use
  215.    wt: 2:   9 video Prime Factorization upto 19 squared
  216.    wt: 2:   8 video Prime Factorization upto 19
  217.    wt: 2:   7 Calculator Usage Notes and Cautions
  218.    wt: 2:   6 Sieve of Eratosthenes and Square Rule
  219.    wt: 2:   5 Prime Factorization and a Square Rule
  220.    wt: 2:   4 video Prime Factorization Introduction
  221.    wt: 2:   2 Prime and Composites less than 16
  222.    wt: 2:   1 video how Products are bigger than factor
  223.    wt: 2:   3 Division Single Digit Divisor Example
  224.    wt: 2:   Video Decimal Multiplication Geometric View Example 2
  225.    wt: 2:   1 Why 3 times 5 gives 15
  226.    wt: 2:   3 Harder Cases Convert to Compare and Subtract
  227.    wt: 2:   3. How to add with decimals A sans conversions
  228.    wt: 2:   Example 1. Area Between x and x squared
  229.    wt: 2:   Area Between Crossing Curves Lesson Take 2
  230.    wt: 2:   Area Between Crossing Curves Lesson Take 1
  231.    wt: 2:   Area Between Curves Lesson Take 2
  232.    wt: 2:   Area Between Curves Lesson Take 1
  233.    wt: 2:   Summary
  234.    wt: 2:   3 Two Chain Rule Method Exercises
  235.    wt: 2:   4 Second derivative test exercise example
  236.    wt: 2:   1 Two cubic sketching exercises with 1st derivative
  237.    wt: 2:   A Chain Rule Real Player video examples
  238.    wt: 2:   29 Chain Rule Optional Reading
  239.    wt: 2:   28 Chain Rule Preparation for a Proof
  240.    wt: 2:   25 Chain Rule Animated Examples Continued
  241.    wt: 2:   24 Chain Rule Animated Examples
  242.    wt: 2:   21 Chain Rule for powers
  243.    wt: 2:   20 Chain Rule for Pulley Systems
  244.    wt: 2:   18 Chain Rule Introduction
  245.    wt: 2:   17 Derivatives of quotients of sine and cosine
  246.    wt: 2:   16 Derivatives of reciprocals of sine and cosine
  247.    wt: 2:   14 sine and cosine derivatives 2nd step
  248.    wt: 2:   11 Quotient rule
  249.    wt: 2:   10 Power rule for negative integers
  250.    wt: 2:   9 Reciprocal rule
  251.    wt: 2:   8 Differentiation of polynomials
  252.    wt: 2:   7 Animated Differentiation Examples
  253.    wt: 2:   6 Power rule from product rule
  254.    wt: 2:   4 Sum Rule
  255.    wt: 2:   2 Motivation for Limit Definition Take 1
  256.    wt: 2:   12 Limits with Parameters and Derivatives Take I
  257.    wt: 2:   11 Limits at infinity Three Examples
  258.    wt: 2:   10 Three one sided limits with infinite values
  259.    wt: 2:   9 Limits Continuity and Composition
  260.    wt: 2:   8 Four Animated Examples
  261.    wt: 2:   7 Evaluation by immediate or delayed substitution
  262.    wt: 2:   6 Continuity at a point
  263.    wt: 2:   5 Jumps and absence of unlimited error control
  264.    wt: 2:   2 Algebraic codification
  265.    wt: 2:   1 Numerical introduction
  266.    wt: 2:   Appendix C. How to Read
  267.    wt: 2:   Appendix A. Reading Guide For Next Appendices
  268.    wt: 2:   Chapter 26 What is in chapters 27 to 31
  269.    wt: 2:   Chapter 19. Functions and Sets
  270.    wt: 2:   Postscript Unifying Theme A Fourth Skill For Algebra
  271.    wt: 2:   Chapter 7 Prep for Calculus Arithmetic Exercises
  272.    wt: 2:   Postscript A Three Remarks
  273.    wt: 2:   Chapter 7 Calculus Previews and Calculus Lightly
  274.    wt: 2:   Chapter 3 Algebra Starter Lessons
  275.    wt: 2:   3 Telling Tracking Time Temporal and More Place Sense
  276.    wt: 2:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  277.    wt: 2:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  278.    wt: 2:   Implementation Notes
  279.    wt: 2:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  280.    wt: 2:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  281.    wt: 1:   Appendix 2 primary school Arithmetic 01
  282.    wt: 1:   Appendix 1 primary and preschool mathematic
  283.    wt: 1:   K LAMP Musings Science Education
  284.    wt: 1:   J LAMP Introduction Extrinsic Origins
  285.    wt: 1:   I LAMP Introduction Study Habits
  286.    wt: 1:   H LAMP Introduction Instructional Concepts
  287.    wt: 1:   G LAMP Introduction Problem Solving Skills
  288.    wt: 1:   F LAMP Introduction Prerequisites
  289.    wt: 1:   E LAMP Introduction Modern Mathematics
  290.    wt: 1:   C LAMP Introduction Culture in Mathematics Education
  291.    wt: 1:   B LAMP Introduction Curriculum Development Standards
  292.    wt: 1:   A Introduction Objectives
  293.    wt: 1:   Skills Chapter 4 Logic
  294.    wt: 1:   Skills Chapter 2 Geometry
  295.    wt: 1:   Skills Chapter 1 Arithmetic
  296.    wt: 1:   Skills Chapter 0 Introduction
  297.    wt: 1:   permissions for teachers
  298.    wt: 1:   Math Ed if it must be short make it lean effective
  299.    wt: 1:   modern education
  300.    wt: 1:   learning takes time
  301.    wt: 1:   grouping students according to ability
  302.    wt: 1:   what should be learnt and When
  303.    wt: 1:   mathematics in context
  304.    wt: 1:   Postscript 2007 01 10
  305.    wt: 1:   five decades make a difference
  306.    wt: 1:   teaching tutoring algebraic reason
  307.    wt: 1:   the trouble with algebra
  308.    wt: 1:   05 13 OldSiteEntrancePage
  309.    wt: 1:   Theory of Knowledge
  310.    wt: 1:   Different Kinds of Reasoning in maths
  311.    wt: 1:   chapitre 12 00 les iles et division
  312.    wt: 1:   chapitre 07 01 principle D induction mathematique
  313.    wt: 1:   chapitre 07 00 Des chaines plus longues de la raison
  314.    wt: 1:   chapitre 06 00 Chaines de la raison
  315.    wt: 1:   chapitre 05 00 Deception
  316.    wt: 1:   chapitre 04 10 Etapes pour une meilleur raison
  317.    wt: 1:   chapitre 04 09 Regles accidentelles
  318.    wt: 1:   chapitre 04 08 Limitations et benefices
  319.    wt: 1:   chapitre 04 07 RepetablesEtReproductibles
  320.    wt: 1:   chapitre 04 06 engagements
  321.    wt: 1:   chapitre 04 05 Implication versus suggestion
  322.    wt: 1:   chapitre 04 04 Parlons de la logique
  323.    wt: 1:   chapitre 04 02 Deuxieme enigme
  324.    wt: 1:   chapitre 04 01 Premiere enigme
  325.    wt: 1:   chapitre 04 00 Les regles d implication
  326.    wt: 1:   chapitre 02 00 La Communication des idees
  327.    wt: 1:   chapitre 01 00 Introduction
  328.    wt: 1:   liens
  329.    wt: 1:   3 Energy Power Heat08
  330.    wt: 1:   E Wire Resistance Calculation03
  331.    wt: 1:   A Wire Resistance Qualitative01
  332.    wt: 1:   3 Like resistors in parallel
  333.    wt: 1:   B Electromotive force conventional current01
  334.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  335.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  336.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  337.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  338.    wt: 1:   26 Function definitions done and coming
  339.    wt: 1:   22 Square Root function graphically
  340.    wt: 1:   20 Interchanging coordinates a reflection
  341.    wt: 1:   19 Horizontal line rule and method
  342.    wt: 1:   18 Vertical Line Rule and Method
  343.    wt: 1:   17 Function maxima minima and their location
  344.    wt: 1:   16 Increasing or decreasing on intervals
  345.    wt: 1:   14 Surjections Injections Bijections
  346.    wt: 1:   12 Function Domain Recognition Exercises
  347.    wt: 1:   11 Function Domain Range Source and Targets
  348.    wt: 1:   10 Interval Notation
  349.    wt: 1:   9 Set theory term relation possible origins
  350.    wt: 1:   6 Set Existence Formation and Notation
  351.    wt: 1:   5 Function notation for geometric transformations
  352.    wt: 1:   4 Function notation in and beyond mathematics
  353.    wt: 1:   2 Algebraic use of function notation
  354.    wt: 1:   1 Geometric Introduction of Function Notation
  355.    wt: 1:   Introduction Reading Guide
  356.    wt: 1:   3 Polynomials Multiplication Addition
  357.    wt: 1:   13 cosecant function Definition Graph and Inverse
  358.    wt: 1:   3 Left Inverse of cosine arccos definition
  359.    wt: 1:   3 graphing y=f(x c) plus K
  360.    wt: 1:   Parallel Lines and Alternating Corresponding Angles
  361.    wt: 1:   Straight Lines Intersection of
  362.    wt: 1:   14 Straight Lines Equations General Case
  363.    wt: 1:   11 Straight Lines Graphing y=mx
  364.    wt: 1:   10 Straight Lines through Origin Equations More
  365.    wt: 1:   9 Straight Lines through Origin Equations
  366.    wt: 1:   3 Straight Lines Slope as Tangent of Inclination Angle
  367.    wt: 1:   24 tangent Angle Difference Formula
  368.    wt: 1:   23 sine and cosine of 180 plus 22.5 degrees
  369.    wt: 1:   19 Pythagorean Identity For sine and cosine functions
  370.    wt: 1:   15 sine cosine Complementary Angle Relations
  371.    wt: 1:   13 Graph of tangent function many periods
  372.    wt: 1:   3 sines and cosines for reference angle 90 degrees
  373.    wt: 1:   3 Trigonometric Ratios sine and cosine
  374.    wt: 1:   6 Geometric Diagrams in Class
  375.    wt: 1:   Euclidean Geometry Elsewhere LINKS
  376.    wt: 1:   PS C Similarity Use Recognize it in Trigonometry
  377.    wt: 1:   3 Lengths and Areas on Maps and Plans
  378.    wt: 1:   26 More Less Greater Than Comparison
  379.    wt: 1:   25 Mid way Convergence to Axiomatic Approach
  380.    wt: 1:   24 Signed Numbers Arithmmetic Properties
  381.    wt: 1:   22 Multiplication of Signed Numbers
  382.    wt: 1:   13 Arrows and Vectors in a Plane
  383.    wt: 1:   3 Location of Point in Decimal Multiplication
  384.    wt: 1:   3 Inequalities Algebraically
  385.    wt: 1:   3 Linear Equation Literal Solution More
  386.    wt: 1:   3 Product Axioms Two Forms
  387.    wt: 1:   3 More and Less Than with Unlike Signs
  388.    wt: 1:   13 Real Number Subtraction
  389.    wt: 1:   3 Fractions
  390.    wt: 1:   3 Geometric Formulas and Function Notation
  391.    wt: 1:   More Exercises
  392.    wt: 1:   Simple Exercises
  393.    wt: 1:   4 GE III Animated Examples
  394.    wt: 1:   2 GE II Comparison
  395.    wt: 1:   1 GE Substitution four examples
  396.    wt: 1:   6 Algebraic Solution Example
  397.    wt: 1:   5 Algebraic Solutions Introduction
  398.    wt: 1:   4 Four Examples Fractional Coefficients
  399.    wt: 1:   2 Three Examples
  400.    wt: 1:   1 Proper Equal Sign Usage
  401.    wt: 1:   Skill Development Notes
  402.    wt: 1:   10 One Example
  403.    wt: 1:   9 Three Examples
  404.    wt: 1:   8 One Example
  405.    wt: 1:   7 Two Examples
  406.    wt: 1:   6 Three Examples
  407.    wt: 1:   5 Three Examples
  408.    wt: 1:   4 Two Examples
  409.    wt: 1:   2 Three Examples
  410.    wt: 1:   Using Letters for Physical Quantities
  411.    wt: 1:   Formula Usage Show Work Format
  412.    wt: 1:   13 Naming Identifying Formulas with Words
  413.    wt: 1:   11 Volume of Sphere
  414.    wt: 1:   10 Volume of Pyramid
  415.    wt: 1:   9 Volume of Cone
  416.    wt: 1:   5 Box Volume Formula Example
  417.    wt: 1:   3 Triangle Area Formula Example
  418.    wt: 1:   3 Counting with Sets etc
  419.    wt: 1:   3 Adding Words To Arithmetic
  420.    wt: 1:   3 Properties of Square Roots with example
  421.    wt: 1:   17 GCD LCM of 85 and 60 via Prime
  422.    wt: 1:   13 GCD from given Prime Factorization
  423.    wt: 1:   LCM 60 45 Avoid List Method Use Prime
  424.    wt: 1:   2 Least Common Multiple LCM intro via list method
  425.    wt: 1:   3 Counting with Tables and Trees II
  426.    wt: 1:   3 signed coordinates for maps and planes
  427.    wt: 1:   3 Multiplying Units and Numbers
  428.    wt: 1:   13 Fraction Comparison Algebraic View
  429.    wt: 1:   A Associative Law Theorectical Note
  430.    wt: 1:   13 Subtraction with Additive Inverse
  431.    wt: 1:   A Decimals Modular and Remainder Arithmetic
  432.    wt: 1:   27 Divisibility by 2 3 6 5 9 10 Example
  433.    wt: 1:   26 Divisibility by 2 3 5 Example
  434.    wt: 1:   25 Divisibility Tests for 2 3 5 9 10 Example
  435.    wt: 1:   24 Divisibility Tests for 2 3 5 9 10
  436.    wt: 1:   23 Remainder Arithmetic Modulo 2
  437.    wt: 1:   22 Remainder Arithmetic Modulo 3 more
  438.    wt: 1:   21 Remainder Arithmetic Modulo 3
  439.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  440.    wt: 1:   15 Remainder Arithmetic Modulo 9 Example
  441.    wt: 1:   14 Remainder Arithmetic Modulo 9 Example
  442.    wt: 1:   12 Remainder Arithmetic Modulo 10 Example
  443.    wt: 1:   11 Remainder Arithmetic Long Division by 5 Quickly more
  444.    wt: 1:   10 Remainder Arithmetic Long Division by 5 Quickly
  445.    wt: 1:   8 Remainder Arithmetic Morulo 5 Examples II
  446.    wt: 1:   7 Remainder Arithmetic Modulo 5 Examples I
  447.    wt: 1:   6 Remainder Arithmetic Modulo 5 Propertie
  448.    wt: 1:   3 Remainder Arithmetic Modulos 10 more still
  449.    wt: 1:   Long Division Backward
  450.    wt: 1:   Long Division forwards and backwards Example 3
  451.    wt: 1:   D Decimal Multiplication Methods Derived
  452.    wt: 1:   C Counting Areas with Powers of Ten
  453.    wt: 1:   B Powers of Ten
  454.    wt: 1:   A Elementary Basis for Multiplication Methods
  455.    wt: 1:   6 Multiplication Commutes Order Not Important
  456.    wt: 1:   5 Decimal Fraction Multiplication
  457.    wt: 1:   4 Two and Three Digit Multipliers
  458.    wt: 1:   2 One Digit Multipliers
  459.    wt: 1:   Video Decimal Multiplication Geometric View Example 2
  460.    wt: 1:   Video Power Notation in Decimal Expansion
  461.    wt: 1:   Subtraction Another Video Lesson
  462.    wt: 1:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  463.    wt: 1:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  464.    wt: 1:   5 More on Groups of 3 Place Value in Decimal Fractions
  465.    wt: 1:   4 Groups of 3 Place Value in Decimal Fractions
  466.    wt: 1:   Expression Evaluation how to show work
  467.    wt: 1:   013 Travel Time Tables
  468.    wt: 1:   3 Units and Lengths of Time
  469.    wt: 1:   5 Area Under Curve Exercise
  470.    wt: 1:   4 Definite Integrals Evaluation Exercises
  471.    wt: 1:   2 Indefinite Integrals Exercises
  472.    wt: 1:   1 Chain Rule in Reverse Integration Method
  473.    wt: 1:   Postscript More on Better Performance
  474.    wt: 1:   Postscript For Better Performance
  475.    wt: 1:   Appendix E. How To Study Mathematics and Why
  476.    wt: 1:   Appendix D. What to do in School and Why
  477.    wt: 1:   Appendix B. How To Learn
  478.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  479.    wt: 1:   Chapter 28 Occurrence Tables
  480.    wt: 1:   Chapter 27 Shorthand Symbols as Pronouns
  481.    wt: 1:   Chapter 25. Mathematical Induction Examples
  482.    wt: 1:   Chapter 24. Personal Investment and Pension EGS
  483.    wt: 1:   Chapter 22. Geometric Sums and Sequences
  484.    wt: 1:   Chapter 21. Third Reading Guide
  485.    wt: 1:   Chapter 20. Degrees and Radians
  486.    wt: 1:   Chapter 18. Rules for Algebra
  487.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  488.    wt: 1:   Chapter 16. Painless Theorem Proving
  489.    wt: 1:   Chapter 15. Solving Linear Equations
  490.    wt: 1:   Chapter 14. Forward and Backward Use of a Formula
  491.    wt: 1:   Chapter 12. Shorthand Usage Guide
  492.    wt: 1:   Chapter 11. Why Shorthand
  493.    wt: 1:   Chapter 10 Describing and Changing Calculations
  494.    wt: 1:   Postscript What is a Variable
  495.    wt: 1:   Chapter 9 Talking about Numbers or Quantities
  496.    wt: 1:   Chapter 8 Three Skills For Algebra
  497.    wt: 1:   Solutions For Arithmetic Exercises
  498.    wt: 1:   Chapter 6 Change of Language
  499.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  500.    wt: 1:   Chapter 4 Longer Chains of Reason
  501.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  502.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  503.    wt: 1:   Foreword
  504.    wt: 1:   Annotated Links to Material Elsehwere
  505.    wt: 1:   Postscript B Mathematics Education References
  506.    wt: 1:   Chapter 12 Four Phases
  507.    wt: 1:   Chapter 11 Elementary Instruction
  508.    wt: 1:   Chapter 10 Transition
  509.    wt: 1:   Chapter 9 The Two Ends
  510.    wt: 1:   Chapter 8 Modern Instruction
  511.    wt: 1:   Chapter 7 Two Treatments of Geometry
  512.    wt: 1:   Chapter 6 Rule Based Reason in Mathematics
  513.    wt: 1:   Chapter 5 Four References
  514.    wt: 1:   Chapter 4 Complex Numbers and Why Slopes
  515.    wt: 1:   Chapter 2 For and Against Mathematics
  516.    wt: 1:   Chapter 1 Introduction
  517.    wt: 1:   Foreword
  518.    wt: 1:   Postscript D Reflections on Law of the Excluded Middle
  519.    wt: 1:   Postscript C Consistency as a Tool for Reason
  520.    wt: 1:   Postscript B More on Story Telling and Reason
  521.    wt: 1:   Postscript A Story Telling
  522.    wt: 1:   Chapter 24 Direct and Indirect Reason
  523.    wt: 1:   Chapter 22 Contrapositive and Vacuously True Implications
  524.    wt: 1:   Chapter 21 Occurrence Tables
  525.    wt: 1:   Chapter 20 Shorthand Symbols as Pronouns
  526.    wt: 1:   Chapter 19 What is in chapters 20 to 24
  527.    wt: 1:   Chapter 18 Sense and Knowledge
  528.    wt: 1:   Chapter 17 Objective Ways Trial and Error Discovery
  529.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  530.    wt: 1:   Chapter 15 Objective Processes
  531.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  532.    wt: 1:   Chapter 12 Islands and Divisions of Knowledge
  533.    wt: 1:   Chapter 11 Accidental Patterns
  534.    wt: 1:   Chapter 10 Responsibility
  535.    wt: 1:   Chapter 9 What is in Chapters 10 to 18
  536.    wt: 1:   Chapter 8 Change of Language
  537.    wt: 1:   Chapter 7 Longer Chains of Reason
  538.    wt: 1:   Chapter 6 Chains of Reason
  539.    wt: 1:   Chapter 5 Deception
  540.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  541.    wt: 1:   Chapter 2 Skill Development
  542.    wt: 1:   Chapter 1 Introduction
  543.    wt: 1:   Three Remarks
  544.    wt: 1:   Foreword
  545.    wt: 1:   M Words to extend arithmetic
  546.    wt: 1:   C. Domino effect of being careful
  547.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  548.    wt: 1:   Helping the Blind in Logic and Mathematics
  549.    wt: 1:   Mathematics Education References
  550.    wt: 1:   Mathematics Education References
  551.    wt: 1:   Ends Values Methods For Skill Development Framework Prequel
  552.    wt: 1:   Multiple Ways to Improve Mathematics Skill Development
  553.    wt: 1:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  554.    wt: 1:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  555.    wt: 1:   Which Way To Go

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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