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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

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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:   Step 4 Gaussian Elimination/
  15.    wt: 1:   Step 2 Algebraic solutions for one unknown/
  16.    wt: 1:   Step 1 Stick diagram and fractions/
  17.    wt: 1:   3 Solving Linear Equations/
  18.    wt: 1:   C Decimal Multiplication Methods/
  19.    wt: 1:   5 Lessons on Integration/
  20.    wt: 1:   70 Calculus Starter Lessons/
  21.    wt: 1:   Volume 2 Three Skills For Algebra/
  22.    wt: 1:   Volume 1B Mathematics Curriculum Notes/
  23.    wt: 1:   Volume 1A Pattern Based Reason/
  24.    wt: 1:   Volume 1 Elements of Reason/
  25.    wt: 1:   Mathematics Skill Development Framework/

Web Page Search

188 matches:

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

Extended Search

535 matches:

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