Original Site Title: Appetizers and Lessons for Mathematics and Reason, June 1995 to April 2012. New site title:
Logic and Mathematics Skill & Concept Development How-TOs Français: 26 pages
for college students, gifted teens, home-tutoring and K1-12 schooling; and for avid readers not in school. See Site Map

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.

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

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25 matches:

  1.    wt: 6:   Volume 1B Mathematics Curriculum Notes/
  2.    wt: 2:   Volume 1A Regles et modeles/
  3.    wt: 2:   5 What is Similarity/
  4.    wt: 1:   LAMP Lean Applied Mathematics Program/
  5.    wt: 1:   Progressive Observable Motivated Mathematics Education/
  6.    wt: 1:   Mathematics Education Essays/
  7.    wt: 1:   francais/
  8.    wt: 1:   Mathematics Skills Year by Year/
  9.    wt: 1:   5 Factored Polynomial Sign Analysis Examples/
  10.    wt: 1:   10 Examples of Algebraic Reasoning/
  11.    wt: 1:   6 More Less Greater Than Inequalities and Comparison/
  12.    wt: 1:   Step 2 Algebraic solutions for one unknown/
  13.    wt: 1:   12 Comparison of Unsigned and Signed Numbers/
  14.    wt: 1:   4 Remainder Arithmetic and Divisibility/
  15.    wt: 1:   D Decimal Long Division Methods/
  16.    wt: 1:   12 Webvideo Lessons on Area and Volume Calculation/
  17.    wt: 1:   Advanced Calculus Volume 3 Appendices/
  18.    wt: 1:   Volume 3 Why Slopes A Calculus Intro Etc/
  19.    wt: 1:   Volume 2 Three Skills For Algebra/
  20.    wt: 1:   Volume 1A Pattern Based Reason/
  21.    wt: 1:   Volume 1 Elements of Reason/
  22.    wt: 1:   Mathematics 506 Lessons/
  23.    wt: 1:   Secondary Mathematics A Practical Approach/
  24.    wt: 1:   PreSchool and Primary Mathematics or Quantitative Skills/
  25.    wt: 1:   Mathematics Skill Development Framework/

Web Page Search

241 matches:

  1.    wt: 3:   What is and is not here
  2.    wt: 2:   What is POMME
  3.    wt: 2:   mathematics curriculum shifts
  4.    wt: 2:   04 29 New Mathematics Curriculum
  5.    wt: 2:   need for a mixed mathematics curriculum
  6.    wt: 2:   Leaner mathematics curriculum
  7.    wt: 2:   6 Discipline Who is in Charge Conserving Authority
  8.    wt: 2:   5 Polynomials Long division Nonlinear divisor
  9.    wt: 2:   4 Polynomials Long division linear divisor
  10.    wt: 2:   7 Tangent Function is odd on this domain
  11.    wt: 2:   1 What is Proportionality
  12.    wt: 2:   6 Three Notions of What is a Variable
  13.    wt: 2:   2 What is a Variable
  14.    wt: 2:   13 Fraction Comparison Algebraic View
  15.    wt: 2:   1 What is a fraction Take II
  16.    wt: 2:   1 What is a fraction
  17.    wt: 2:   7 Long Divison Mistake Catching
  18.    wt: 2:   3 Division Single Digit Divisor Example
  19.    wt: 2:   2 Division with Single Digit Divisors
  20.    wt: 2:   Chapter 26 What is in chapters 27 to 31
  21.    wt: 2:   Postscript What is a Variable
  22.    wt: 2:   Chapter 5 Islands and Divisions of Knowledge
  23.    wt: 2:   Chapter 19 What is in chapters 20 to 24
  24.    wt: 2:   Chapter 12 Islands and Divisions of Knowledge
  25.    wt: 2:   Chapter 9 What is in Chapters 10 to 18
  26.    wt: 2:   Chapter 3 What is in chapters 4 to 8
  27.    wt: 1:   F LAMP Introduction Prerequisites
  28.    wt: 1:   E LAMP Introduction Modern Mathematics
  29.    wt: 1:   C LAMP Introduction Culture in Mathematics Education
  30.    wt: 1:   B LAMP Introduction Curriculum Development Standards
  31.    wt: 1:   11 pure mathematics
  32.    wt: 1:   10 statistics
  33.    wt: 1:   permissions for teachers
  34.    wt: 1:   key notes and themes
  35.    wt: 1:   Mathematics Education Professors
  36.    wt: 1:   what should be learnt and When
  37.    wt: 1:   mathematics in context
  38.    wt: 1:   Education Reform Inconsistencies
  39.    wt: 1:   Secondary Three Mathematics
  40.    wt: 1:   Secondary Two Mathematics
  41.    wt: 1:   Secondary One Mathematics
  42.    wt: 1:   What to Tell Students
  43.    wt: 1:   teaching tutoring algebraic reason
  44.    wt: 1:   three goals for Mathematics Education
  45.    wt: 1:   02 20 mathematics education references
  46.    wt: 1:   three aims for mathematics students
  47.    wt: 1:   mathematics instruction in general
  48.    wt: 1:   Education in mathematics science and technology
  49.    wt: 1:   three kinds of reason in mathematics
  50.    wt: 1:   words for mathematics instructor
  51.    wt: 1:   chapitre 12 00 les iles et division
  52.    wt: 1:   chapitre 07 00 Des chaines plus longues de la raison
  53.    wt: 1:   chapitre 06 00 Chaines de la raison
  54.    wt: 1:   chapitre 04 10 Etapes pour une meilleur raison
  55.    wt: 1:   Quebec cahiers d apprentissage en mathematiques pour 4 16
  56.    wt: 1:   Trois Notions qui menent a algebre
  57.    wt: 1:   2 Conductance Resistance Duality02
  58.    wt: 1:   1 Conductance Resistance Duality01
  59.    wt: 1:   F Wire Resistance Calculation04
  60.    wt: 1:   E Wire Resistance Calculation03
  61.    wt: 1:   D Wire Resistance Calculation02
  62.    wt: 1:   C Wire Resistance Calculation01
  63.    wt: 1:   B Wire Resistance Qualitative02
  64.    wt: 1:   A Wire Resistance Qualitative01
  65.    wt: 1:   3 Like resistors in parallel
  66.    wt: 1:   2 Unlike resistors in parallel01
  67.    wt: 1:   1 Like resistors in series
  68.    wt: 1:   F Unlike Resistors in Series
  69.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  70.    wt: 1:   22 Student Centered Highschool Mathematics
  71.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  72.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  73.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  74.    wt: 1:   18 Primary School Mathematics
  75.    wt: 1:   16 Secondary Mathematics Tips
  76.    wt: 1:   12 Goals and Objectives For Mathematics
  77.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  78.    wt: 1:   sign monoticity analysis example 4
  79.    wt: 1:   sign monoticity analysis example 3
  80.    wt: 1:   sign monoticity analysis example 2
  81.    wt: 1:   sign monoticity analysis example 1
  82.    wt: 1:   15 Sign analysis of functions
  83.    wt: 1:   12 Function Domain Recognition Exercises
  84.    wt: 1:   6 Set Existence Formation and Notation
  85.    wt: 1:   4 Function notation in and beyond mathematics
  86.    wt: 1:   3 Formula or function graphing exercise
  87.    wt: 1:   2 Algebraic use of function notation
  88.    wt: 1:   10 quadratic exercises
  89.    wt: 1:   1 quadratics graphing exercises
  90.    wt: 1:   5 Natural Logarithm Calculator Exercises
  91.    wt: 1:   1 Calculator Starter Exercises
  92.    wt: 1:   8 Notes for instructors or tutors
  93.    wt: 1:   1 Polynomials Distributive Law
  94.    wt: 1:   Rewriting algebraic substitution as function substitutions
  95.    wt: 1:   5 Swapping Coordinates is a reflection
  96.    wt: 1:   14 Why Scalar Multiplication Distributes Physical Argument
  97.    wt: 1:   12 From Applied To Pure Mathematics
  98.    wt: 1:   Construction Methods and Criteria for Isometric and Similar Triangles
  99.    wt: 1:   SAS Method For Isometric Or Proportional Triangle Construction
  100.    wt: 1:   2 Straight Lines Slopes As Rise Over Run
  101.    wt: 1:   17D cis formulas for sine cosines and tangent
  102.    wt: 1:   17B sine cosine Angle Sum Formulas via cis
  103.    wt: 1:   17A The complex number valued trig function cis
  104.    wt: 1:   12 cis formulas for sine cosines and tangent
  105.    wt: 1:   10 sine cosine Angle Sum Formulas via cis
  106.    wt: 1:   9 The complex number valued trig function cis
  107.    wt: 1:   5 An Easy Proof of the Distributive Law
  108.    wt: 1:   11 Triangle Similarity Missing Side Problem
  109.    wt: 1:   Four Simple Exercises
  110.    wt: 1:   7 Exercises to test skill and concept mastery
  111.    wt: 1:   5 Algebraic View of Slopes
  112.    wt: 1:   13 Pythagorean spatial distance formulas
  113.    wt: 1:   10 Pythagorean plane distance formula
  114.    wt: 1:   8 Distance Between Points on a Line
  115.    wt: 1:   PS H Distributive Law For Complex Numbers
  116.    wt: 1:   PS G Rotation Distributes over Addition
  117.    wt: 1:   PS F Scalar Multiplication Distributes over Addition
  118.    wt: 1:   17 Right Bisectors of Triangle Sides
  119.    wt: 1:   15 Triangle Angle Sum is 180 degrees
  120.    wt: 1:   9 Construction of a right bisector
  121.    wt: 1:   8 Isoceles Triangles
  122.    wt: 1:   6 Ruler and compass Angle Bisection
  123.    wt: 1:   3 Isometry of Triangles Congruence
  124.    wt: 1:   5 Drawing to Scale Avoids Angle Distortions
  125.    wt: 1:   musings do not puiblish real numbers
  126.    wt: 1:   26 More Less Greater Than Comparison
  127.    wt: 1:   23 Distributive Law Two Derivations
  128.    wt: 1:   9 Division with Digits after Decimal Point
  129.    wt: 1:   8 Division and Mulplication of Compound Fractions
  130.    wt: 1:   E Long Division Methods more
  131.    wt: 1:   D Long Division Methods
  132.    wt: 1:   B Decimal Comparison and Subtraction
  133.    wt: 1:   5 Distributive Law for Whole Numbers
  134.    wt: 1:   5 Areas of Rectangles Revisited
  135.    wt: 1:   3 Inequalities Algebraically
  136.    wt: 1:   2 Algebraic View
  137.    wt: 1:   4 Subtraction and Division Axioms
  138.    wt: 1:   4 Comparison of Negative Numbers
  139.    wt: 1:   1 Real Numbers Comparison
  140.    wt: 1:   16 Real Numbers Comparison
  141.    wt: 1:   15 Real Number Division
  142.    wt: 1:   More Exercises
  143.    wt: 1:   Simple Exercises
  144.    wt: 1:   2 GE II Comparison
  145.    wt: 1:   4 Solving a triangular system exercise
  146.    wt: 1:   2 Essentially one exercises three with solution
  147.    wt: 1:   6 Algebraic Solution Example
  148.    wt: 1:   5 Algebraic Solutions Introduction
  149.    wt: 1:   Skill Development Notes
  150.    wt: 1:   11 Volume of Sphere
  151.    wt: 1:   10 Volume of Pyramid
  152.    wt: 1:   9 Volume of Cone
  153.    wt: 1:   5 Box Volume Formula Example
  154.    wt: 1:   9 Sets in Probability and Statistics
  155.    wt: 1:   3 Comparison of Negative Numbers
  156.    wt: 1:   5 Common Divisors 60 45 via Prime
  157.    wt: 1:   LCM 60 45 Avoid List Method Use Prime
  158.    wt: 1:   2 Least Common Multiple LCM intro via list method
  159.    wt: 1:   11 What are real lengths and numbers
  160.    wt: 1:   5 Reciprocals and Division for Fractions with Units
  161.    wt: 1:   16 Addition Subtraction Comparision Compared
  162.    wt: 1:   12 Fraction Comparison
  163.    wt: 1:   11 Simplification an Algebraic View
  164.    wt: 1:   6 Multiplication Algebraically Take II
  165.    wt: 1:   Fraction Operations by Raising Terms A Simple Innovation
  166.    wt: 1:   C Divisibility by 11 Integer Recognition Method
  167.    wt: 1:   B Integer Long Division Multiple Choices
  168.    wt: 1:   27 Divisibility by 2 3 6 5 9 10 Example
  169.    wt: 1:   26 Divisibility by 2 3 5 Example
  170.    wt: 1:   25 Divisibility Tests for 2 3 5 9 10 Example
  171.    wt: 1:   24 Divisibility Tests for 2 3 5 9 10
  172.    wt: 1:   11 Remainder Arithmetic Long Division by 5 Quickly more
  173.    wt: 1:   10 Remainder Arithmetic Long Division by 5 Quickly
  174.    wt: 1:   9 Remainder Arithmetic Divisibility by 5
  175.    wt: 1:   7 Calculator Usage Notes and Cautions
  176.    wt: 1:   Long Division Backwards more
  177.    wt: 1:   Long Division Backward
  178.    wt: 1:   Division with Counts and Length
  179.    wt: 1:   Long Division forwards and backwards Example 3
  180.    wt: 1:   Long Division forwards and backwards Example 2
  181.    wt: 1:   Long Division forwards and backwards Example 1
  182.    wt: 1:   12 Why Long Division Works Take III
  183.    wt: 1:   11 Another Single Digit Divisor Example
  184.    wt: 1:   10 Division by Five Long and Short Ways
  185.    wt: 1:   9 Why Long Division Works Take II
  186.    wt: 1:   8 Correcting the Mistake
  187.    wt: 1:   6 Why Decimal Long Division Methods Works Take I
  188.    wt: 1:   5 Long Division Include Zeroes or not
  189.    wt: 1:   4 Division with 2 Digit Divsors
  190.    wt: 1:   A Elementary Basis for Multiplication Methods
  191.    wt: 1:   Appendix 1 Decimals Comparison Method Take II
  192.    wt: 1:   7 Subtraction for Decimal Fractions with Exercises
  193.    wt: 1:   6 Subtraction with Conversion Example with Exercises
  194.    wt: 1:   1 Comparison and Subtraction Easy Direct Cases
  195.    wt: 1:   Appendix 1 Counting Revisited 15 minute video
  196.    wt: 1:   8 What skills and work habits to require
  197.    wt: 1:   Quick history of numbers and algebra
  198.    wt: 1:   The 12 Times Table Visually
  199.    wt: 1:   012 Division of Time Intervals by Time Intervals
  200.    wt: 1:   011 Division of Time Intervals By Numbers
  201.    wt: 1:   9 Comparison and Subtraction of Time Intervals
  202.    wt: 1:   6 How long is a million seconds
  203.    wt: 1:   Example 2 volume of a cone
  204.    wt: 1:   Example 1 volume of a pyramid
  205.    wt: 1:   Volume of Solid by Cross Sections Lesson
  206.    wt: 1:   A Related Material in Volume 3
  207.    wt: 1:   5 Area Under Curve Exercise
  208.    wt: 1:   4 Definite Integrals Evaluation Exercises
  209.    wt: 1:   3 Two Chain Rule Method Exercises
  210.    wt: 1:   2 Indefinite Integrals Exercises
  211.    wt: 1:   A Related lessons in Volume 3
  212.    wt: 1:   4 Second derivative test exercise example
  213.    wt: 1:   1 Two cubic sketching exercises with 1st derivative
  214.    wt: 1:   26 Chain Rule Recognising outer inner functions
  215.    wt: 1:   2 Algebraic codification
  216.    wt: 1:   F.1 What Functions are Continuous
  217.    wt: 1:   E2 Algebraic Properties of Limits
  218.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  219.    wt: 1:   Chapter 4. More Slope Sign Analysis
  220.    wt: 1:   Chapter 3. Slope Sign Analysis
  221.    wt: 1:   Appendix E. How To Study Mathematics and Why
  222.    wt: 1:   Appendix D. What to do in School and Why
  223.    wt: 1:   Solutions For Arithmetic Exercises
  224.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  225.    wt: 1:   Postscript B Mathematics Education References
  226.    wt: 1:   Chapter 6 Rule Based Reason in Mathematics
  227.    wt: 1:   Chapter 2 For and Against Mathematics
  228.    wt: 1:   Postscript C Consistency as a Tool for Reason
  229.    wt: 1:   Chapter 17 Objective Ways Trial and Error Discovery
  230.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  231.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  232.    wt: 1:   R Why Learn Mathematics Skills
  233.    wt: 1:   O On Learning Mathematics and Science
  234.    wt: 1:   N Mathematics Prepare for College Studies
  235.    wt: 1:   Helping the Blind in Logic and Mathematics
  236.    wt: 1:   Mathematics Education References
  237.    wt: 1:   Mathematics Education References
  238.    wt: 1:   Multiple Ways to Improve Mathematics Skill Development
  239.    wt: 1:   Implementation Notes
  240.    wt: 1:   Systematic Algebra Skill Development Missing Links
  241.    wt: 1:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years

Extended Search

542 matches:

  1.    wt: 7:   Postscript B Mathematics Education References
  2.    wt: 7:   Chapter 6 Rule Based Reason in Mathematics
  3.    wt: 7:   Chapter 2 For and Against Mathematics
  4.    wt: 6:   Annotated Links to Material Elsehwere
  5.    wt: 6:   Postscript A Three Remarks
  6.    wt: 6:   Chapter 12 Four Phases
  7.    wt: 6:   Chapter 11 Elementary Instruction
  8.    wt: 6:   Chapter 10 Transition
  9.    wt: 6:   Chapter 9 The Two Ends
  10.    wt: 6:   Chapter 8 Modern Instruction
  11.    wt: 6:   Chapter 7 Two Treatments of Geometry
  12.    wt: 6:   Chapter 5 Four References
  13.    wt: 6:   Chapter 4 Complex Numbers and Why Slopes
  14.    wt: 6:   Chapter 3 Algebra Difficulties
  15.    wt: 6:   Chapter 1 Introduction
  16.    wt: 6:   Foreword
  17.    wt: 3:   What is POMME
  18.    wt: 3:   mathematics curriculum shifts
  19.    wt: 3:   04 29 New Mathematics Curriculum
  20.    wt: 3:   need for a mixed mathematics curriculum
  21.    wt: 3:   Leaner mathematics curriculum
  22.    wt: 3:   chapitre 12 00 les iles et division
  23.    wt: 3:   chapitre 07 00 Des chaines plus longues de la raison
  24.    wt: 3:   chapitre 06 00 Chaines de la raison
  25.    wt: 3:   chapitre 04 10 Etapes pour une meilleur raison
  26.    wt: 3:   11 Triangle Similarity Missing Side Problem
  27.    wt: 3:   What is and is not here
  28.    wt: 3:   7 Long Divison Mistake Catching
  29.    wt: 3:   3 Division Single Digit Divisor Example
  30.    wt: 3:   2 Division with Single Digit Divisors
  31.    wt: 3:   Chapter 26 What is in chapters 27 to 31
  32.    wt: 3:   Postscript What is a Variable
  33.    wt: 3:   Chapter 5 Islands and Divisions of Knowledge
  34.    wt: 3:   Chapter 19 What is in chapters 20 to 24
  35.    wt: 3:   Chapter 12 Islands and Divisions of Knowledge
  36.    wt: 3:   Chapter 9 What is in Chapters 10 to 18
  37.    wt: 3:   Chapter 3 What is in chapters 4 to 8
  38.    wt: 2:   F LAMP Introduction Prerequisites
  39.    wt: 2:   E LAMP Introduction Modern Mathematics
  40.    wt: 2:   C LAMP Introduction Culture in Mathematics Education
  41.    wt: 2:   B LAMP Introduction Curriculum Development Standards
  42.    wt: 2:   11 pure mathematics
  43.    wt: 2:   10 statistics
  44.    wt: 2:   permissions for teachers
  45.    wt: 2:   key notes and themes
  46.    wt: 2:   Mathematics Education Professors
  47.    wt: 2:   what should be learnt and When
  48.    wt: 2:   mathematics in context
  49.    wt: 2:   Education Reform Inconsistencies
  50.    wt: 2:   Secondary Three Mathematics
  51.    wt: 2:   Secondary Two Mathematics
  52.    wt: 2:   Secondary One Mathematics
  53.    wt: 2:   What to Tell Students
  54.    wt: 2:   teaching tutoring algebraic reason
  55.    wt: 2:   three goals for Mathematics Education
  56.    wt: 2:   02 20 mathematics education references
  57.    wt: 2:   three aims for mathematics students
  58.    wt: 2:   mathematics instruction in general
  59.    wt: 2:   Education in mathematics science and technology
  60.    wt: 2:   three kinds of reason in mathematics
  61.    wt: 2:   words for mathematics instructor
  62.    wt: 2:   chapitre 07 01 principle D induction mathematique
  63.    wt: 2:   chapitre 05 00 Deception
  64.    wt: 2:   chapitre 04 09 Regles accidentelles
  65.    wt: 2:   chapitre 04 08 Limitations et benefices
  66.    wt: 2:   chapitre 04 07 RepetablesEtReproductibles
  67.    wt: 2:   chapitre 04 06 engagements
  68.    wt: 2:   chapitre 04 05 Implication versus suggestion
  69.    wt: 2:   chapitre 04 04 Parlons de la logique
  70.    wt: 2:   chapitre 04 03 Unidirectionnel versus bidirectionnel
  71.    wt: 2:   chapitre 04 02 Deuxieme enigme
  72.    wt: 2:   chapitre 04 01 Premiere enigme
  73.    wt: 2:   chapitre 04 00 Les regles d implication
  74.    wt: 2:   chapitre 03 A Propos Des Prochains Chapitre
  75.    wt: 2:   chapitre 02 00 La Communication des idees
  76.    wt: 2:   chapitre 01 00 Introduction
  77.    wt: 2:   Quebec cahiers d apprentissage en mathematiques pour 4 16
  78.    wt: 2:   Trois Notions qui menent a algebre
  79.    wt: 2:   6 Discipline Who is in Charge Conserving Authority
  80.    wt: 2:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  81.    wt: 2:   sign monoticity analysis example 4
  82.    wt: 2:   sign monoticity analysis example 3
  83.    wt: 2:   sign monoticity analysis example 2
  84.    wt: 2:   sign monoticity analysis example 1
  85.    wt: 2:   5 Polynomials Long division Nonlinear divisor
  86.    wt: 2:   4 Polynomials Long division linear divisor
  87.    wt: 2:   7 Tangent Function is odd on this domain
  88.    wt: 2:   13 Navigation Location from Angles to 2 Landmarks
  89.    wt: 2:   12 Triangles Similarity More Problems
  90.    wt: 2:   10 Similarity of Triangles Equivalent of Two Criteria
  91.    wt: 2:   9 Similarity of Triangles Usual Criteria
  92.    wt: 2:   8 Similarity of Triangles and Polygons
  93.    wt: 2:   7 Translations Rotations Reflections Dilatations
  94.    wt: 2:   6 Geometric Diagrams in Class
  95.    wt: 2:   5 Similarity of Circles Squares and Rectangles
  96.    wt: 2:   4 Similarity Definition with Coordinate
  97.    wt: 2:   3 Similarity by Design with coordinates
  98.    wt: 2:   2 Similarity By Design
  99.    wt: 2:   1 Early Concept of Like or Similar Shapes
  100.    wt: 2:   5 Areas of Rectangles Revisited
  101.    wt: 2:   3 Inequalities Algebraically
  102.    wt: 2:   1 What is Proportionality
  103.    wt: 2:   4 Comparison of Negative Numbers
  104.    wt: 2:   1 Real Numbers Comparison
  105.    wt: 2:   6 Algebraic Solution Example
  106.    wt: 2:   5 Algebraic Solutions Introduction
  107.    wt: 2:   6 Three Notions of What is a Variable
  108.    wt: 2:   2 What is a Variable
  109.    wt: 2:   3 Comparison of Negative Numbers
  110.    wt: 2:   13 Fraction Comparison Algebraic View
  111.    wt: 2:   1 What is a fraction Take II
  112.    wt: 2:   1 What is a fraction
  113.    wt: 2:   27 Divisibility by 2 3 6 5 9 10 Example
  114.    wt: 2:   26 Divisibility by 2 3 5 Example
  115.    wt: 2:   25 Divisibility Tests for 2 3 5 9 10 Example
  116.    wt: 2:   24 Divisibility Tests for 2 3 5 9 10
  117.    wt: 2:   11 Remainder Arithmetic Long Division by 5 Quickly more
  118.    wt: 2:   10 Remainder Arithmetic Long Division by 5 Quickly
  119.    wt: 2:   9 Remainder Arithmetic Divisibility by 5
  120.    wt: 2:   Long Division Backwards more
  121.    wt: 2:   Long Division Backward
  122.    wt: 2:   Division with Counts and Length
  123.    wt: 2:   Long Division forwards and backwards Example 3
  124.    wt: 2:   Long Division forwards and backwards Example 2
  125.    wt: 2:   Long Division forwards and backwards Example 1
  126.    wt: 2:   12 Why Long Division Works Take III
  127.    wt: 2:   11 Another Single Digit Divisor Example
  128.    wt: 2:   10 Division by Five Long and Short Ways
  129.    wt: 2:   9 Why Long Division Works Take II
  130.    wt: 2:   8 Correcting the Mistake
  131.    wt: 2:   6 Why Decimal Long Division Methods Works Take I
  132.    wt: 2:   5 Long Division Include Zeroes or not
  133.    wt: 2:   4 Division with 2 Digit Divsors
  134.    wt: 2:   Example 2 volume of a cone
  135.    wt: 2:   Example 1 volume of a pyramid
  136.    wt: 2:   Volume of Solid by Cross Sections Lesson
  137.    wt: 2:   F.1 What Functions are Continuous
  138.    wt: 2:   E2 Algebraic Properties of Limits
  139.    wt: 2:   Chapter 15. Algebraic Evaluation of Limits
  140.    wt: 2:   Chapter 4. More Slope Sign Analysis
  141.    wt: 2:   Chapter 3. Slope Sign Analysis
  142.    wt: 2:   Appendix E. How To Study Mathematics and Why
  143.    wt: 2:   Appendix D. What to do in School and Why
  144.    wt: 2:   Solutions For Arithmetic Exercises
  145.    wt: 2:   Chapter 7 Prep for Calculus Arithmetic Exercises
  146.    wt: 2:   Postscript C Consistency as a Tool for Reason
  147.    wt: 2:   Chapter 17 Objective Ways Trial and Error Discovery
  148.    wt: 2:   Chapter 14 Deductive and Empirical Views of Mathematics
  149.    wt: 2:   Helping the Blind in Logic and Mathematics
  150.    wt: 2:   Mathematics Education References
  151.    wt: 2:   Mathematics Education References
  152.    wt: 2:   Multiple Ways to Improve Mathematics Skill Development
  153.    wt: 2:   Implementation Notes
  154.    wt: 2:   Systematic Algebra Skill Development Missing Links
  155.    wt: 2:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  156.    wt: 1:   Appendix 2 primary school Arithmetic 01
  157.    wt: 1:   Appendix 1 primary and preschool mathematic
  158.    wt: 1:   K LAMP Musings Science Education
  159.    wt: 1:   J LAMP Introduction Extrinsic Origins
  160.    wt: 1:   I LAMP Introduction Study Habits
  161.    wt: 1:   H LAMP Introduction Instructional Concepts
  162.    wt: 1:   G LAMP Introduction Problem Solving Skills
  163.    wt: 1:   A Introduction Objectives
  164.    wt: 1:   Skills Chapter 5 Calculus
  165.    wt: 1:   Skills Chapter 4 Logic
  166.    wt: 1:   Ramblings Extrinsic numbers theory
  167.    wt: 1:   Ramblings Introduction Algebra Essay
  168.    wt: 1:   Skills Chapter 3 Algebra
  169.    wt: 1:   Skills Chapter 2 Geometry
  170.    wt: 1:   Skills Chapter 1 Arithmetic
  171.    wt: 1:   Skills Chapter 0 Introduction
  172.    wt: 1:   9 combinatorics probability sets
  173.    wt: 1:   8 analytic geometry etc
  174.    wt: 1:   7 logic review and decimals an odd combination
  175.    wt: 1:   6 polynomials etc
  176.    wt: 1:   5 logarithms and exponentials etc
  177.    wt: 1:   4 algebra
  178.    wt: 1:   3 Euclidean Geometry Leanly
  179.    wt: 1:   2 arithmetic with signed numbers
  180.    wt: 1:   1 arithmetic with unsigned numbers
  181.    wt: 1:   why bother
  182.    wt: 1:   which way to go
  183.    wt: 1:   website reviews
  184.    wt: 1:   three goals to set for students
  185.    wt: 1:   Teach the teachers plus goals
  186.    wt: 1:   Math Ed if it must be short make it lean effective
  187.    wt: 1:   Applied Maths Program14092009 POMME variant
  188.    wt: 1:   activities for students
  189.    wt: 1:   links Education Resources online
  190.    wt: 1:   site origins
  191.    wt: 1:   site eurekas
  192.    wt: 1:   About site lesson plans
  193.    wt: 1:   teacher certification
  194.    wt: 1:   modern education
  195.    wt: 1:   learning takes time
  196.    wt: 1:   grouping students according to ability
  197.    wt: 1:   Postscript 2007 01 10
  198.    wt: 1:   five decades make a difference
  199.    wt: 1:   Maps Plans Drawings
  200.    wt: 1:   how letters appear
  201.    wt: 1:   talk the algebra talk
  202.    wt: 1:   three difficulties
  203.    wt: 1:   teaching tips
  204.    wt: 1:   geometric implications for algebra
  205.    wt: 1:   Lessening Algebra Difficulties
  206.    wt: 1:   the trouble with algebra
  207.    wt: 1:   05 13 OldSiteEntrancePage
  208.    wt: 1:   04 25 when to stop or suspend mathemat
  209.    wt: 1:   02 21 words for teachers
  210.    wt: 1:   standards for course material
  211.    wt: 1:   Operational Viewpoint to Value
  212.    wt: 1:   formal or informal peer review
  213.    wt: 1:   Theory of Knowledge
  214.    wt: 1:   Different Kinds of Reasoning in maths
  215.    wt: 1:   cultivating intelligence
  216.    wt: 1:   Four ways to improve education reform
  217.    wt: 1:   How to be a better instructor
  218.    wt: 1:   Motivation and Context Problem
  219.    wt: 1:   Prequel In For A Penny In For A Pound
  220.    wt: 1:   education an empirical art
  221.    wt: 1:   fairness and inductive principles for instruction
  222.    wt: 1:   liens
  223.    wt: 1:   problemes responses
  224.    wt: 1:   problemes algebre et arithmetique
  225.    wt: 1:   deux definitions pour variable
  226.    wt: 1:   logique deux enigme
  227.    wt: 1:   2 Conductance Resistance Duality02
  228.    wt: 1:   1 Conductance Resistance Duality01
  229.    wt: 1:   F Wire Resistance Calculation04
  230.    wt: 1:   E Wire Resistance Calculation03
  231.    wt: 1:   D Wire Resistance Calculation02
  232.    wt: 1:   C Wire Resistance Calculation01
  233.    wt: 1:   B Wire Resistance Qualitative02
  234.    wt: 1:   A Wire Resistance Qualitative01
  235.    wt: 1:   3 Like resistors in parallel
  236.    wt: 1:   2 Unlike resistors in parallel01
  237.    wt: 1:   1 Like resistors in series
  238.    wt: 1:   F Unlike Resistors in Series
  239.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  240.    wt: 1:   22 Student Centered Highschool Mathematics
  241.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  242.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  243.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  244.    wt: 1:   18 Primary School Mathematics
  245.    wt: 1:   16 Secondary Mathematics Tips
  246.    wt: 1:   12 Goals and Objectives For Mathematics
  247.    wt: 1:   Ages 12 to 14 Skills with take home value
  248.    wt: 1:   Ages 12 to 14 Geometry
  249.    wt: 1:   Ages 12 to 14 Arithmetic
  250.    wt: 1:   Ages 10 to 12 Geometry
  251.    wt: 1:   Ages 10 to 12 Arithmetic
  252.    wt: 1:   Ages 9 to 10
  253.    wt: 1:   Ages 8 to 9
  254.    wt: 1:   Ages 7 to 8
  255.    wt: 1:   Ages 6 to 7
  256.    wt: 1:   Ages 4 plus to 5 plus
  257.    wt: 1:   Ages 3 plus to 4 plus
  258.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  259.    wt: 1:   15 Sign analysis of functions
  260.    wt: 1:   12 Function Domain Recognition Exercises
  261.    wt: 1:   6 Set Existence Formation and Notation
  262.    wt: 1:   4 Function notation in and beyond mathematics
  263.    wt: 1:   3 Formula or function graphing exercise
  264.    wt: 1:   2 Algebraic use of function notation
  265.    wt: 1:   10 quadratic exercises
  266.    wt: 1:   1 quadratics graphing exercises
  267.    wt: 1:   5 Natural Logarithm Calculator Exercises
  268.    wt: 1:   1 Calculator Starter Exercises
  269.    wt: 1:   8 Notes for instructors or tutors
  270.    wt: 1:   1 Polynomials Distributive Law
  271.    wt: 1:   Rewriting algebraic substitution as function substitutions
  272.    wt: 1:   5 Swapping Coordinates is a reflection
  273.    wt: 1:   14 Why Scalar Multiplication Distributes Physical Argument
  274.    wt: 1:   12 From Applied To Pure Mathematics
  275.    wt: 1:   Construction Methods and Criteria for Isometric and Similar Triangles
  276.    wt: 1:   SAS Method For Isometric Or Proportional Triangle Construction
  277.    wt: 1:   2 Straight Lines Slopes As Rise Over Run
  278.    wt: 1:   17D cis formulas for sine cosines and tangent
  279.    wt: 1:   17B sine cosine Angle Sum Formulas via cis
  280.    wt: 1:   17A The complex number valued trig function cis
  281.    wt: 1:   12 cis formulas for sine cosines and tangent
  282.    wt: 1:   10 sine cosine Angle Sum Formulas via cis
  283.    wt: 1:   9 The complex number valued trig function cis
  284.    wt: 1:   5 An Easy Proof of the Distributive Law
  285.    wt: 1:   Four Simple Exercises
  286.    wt: 1:   7 Exercises to test skill and concept mastery
  287.    wt: 1:   5 Algebraic View of Slopes
  288.    wt: 1:   13 Pythagorean spatial distance formulas
  289.    wt: 1:   10 Pythagorean plane distance formula
  290.    wt: 1:   8 Distance Between Points on a Line
  291.    wt: 1:   PS H Distributive Law For Complex Numbers
  292.    wt: 1:   PS G Rotation Distributes over Addition
  293.    wt: 1:   PS F Scalar Multiplication Distributes over Addition
  294.    wt: 1:   17 Right Bisectors of Triangle Sides
  295.    wt: 1:   15 Triangle Angle Sum is 180 degrees
  296.    wt: 1:   9 Construction of a right bisector
  297.    wt: 1:   8 Isoceles Triangles
  298.    wt: 1:   6 Ruler and compass Angle Bisection
  299.    wt: 1:   3 Isometry of Triangles Congruence
  300.    wt: 1:   5 Drawing to Scale Avoids Angle Distortions
  301.    wt: 1:   musings do not puiblish real numbers
  302.    wt: 1:   26 More Less Greater Than Comparison
  303.    wt: 1:   23 Distributive Law Two Derivations
  304.    wt: 1:   9 Division with Digits after Decimal Point
  305.    wt: 1:   8 Division and Mulplication of Compound Fractions
  306.    wt: 1:   E Long Division Methods more
  307.    wt: 1:   D Long Division Methods
  308.    wt: 1:   B Decimal Comparison and Subtraction
  309.    wt: 1:   5 Distributive Law for Whole Numbers
  310.    wt: 1:   4 Fraction Operations Axiomatic Development
  311.    wt: 1:   2 Fraction Operations Physical Development
  312.    wt: 1:   1 Decimals Modular and Remainder Arithmetic
  313.    wt: 1:   2 Algebraic View
  314.    wt: 1:   4 Subtraction and Division Axioms
  315.    wt: 1:   5 Greater More Less Than Signs in General
  316.    wt: 1:   3 More and Less Than with Unlike Signs
  317.    wt: 1:   2 More and Less Than for Counts and Measures
  318.    wt: 1:   16 Real Numbers Comparison
  319.    wt: 1:   15 Real Number Division
  320.    wt: 1:   More Exercises
  321.    wt: 1:   Simple Exercises
  322.    wt: 1:   2 GE II Comparison
  323.    wt: 1:   4 Solving a triangular system exercise
  324.    wt: 1:   2 Essentially one exercises three with solution
  325.    wt: 1:   4 Four Examples Fractional Coefficients
  326.    wt: 1:   3 Four Examples
  327.    wt: 1:   2 Three Examples
  328.    wt: 1:   1 Proper Equal Sign Usage
  329.    wt: 1:   Skill Development Notes
  330.    wt: 1:   11 Volume of Sphere
  331.    wt: 1:   10 Volume of Pyramid
  332.    wt: 1:   9 Volume of Cone
  333.    wt: 1:   5 Box Volume Formula Example
  334.    wt: 1:   9 Sets in Probability and Statistics
  335.    wt: 1:   4 Greater More Less Than Signs in General
  336.    wt: 1:   2 More and Less Than with Unlike Signs
  337.    wt: 1:   1 More and Less Than for Counts and Measures
  338.    wt: 1:   5 Common Divisors 60 45 via Prime
  339.    wt: 1:   LCM 60 45 Avoid List Method Use Prime
  340.    wt: 1:   2 Least Common Multiple LCM intro via list method
  341.    wt: 1:   11 What are real lengths and numbers
  342.    wt: 1:   5 Reciprocals and Division for Fractions with Units
  343.    wt: 1:   16 Addition Subtraction Comparision Compared
  344.    wt: 1:   12 Fraction Comparison
  345.    wt: 1:   11 Simplification an Algebraic View
  346.    wt: 1:   6 Multiplication Algebraically Take II
  347.    wt: 1:   Fraction Operations by Raising Terms A Simple Innovation
  348.    wt: 1:   C Divisibility by 11 Integer Recognition Method
  349.    wt: 1:   B Integer Long Division Multiple Choices
  350.    wt: 1:   A Decimals Modular and Remainder Arithmetic
  351.    wt: 1:   23 Remainder Arithmetic Modulo 2
  352.    wt: 1:   22 Remainder Arithmetic Modulo 3 more
  353.    wt: 1:   21 Remainder Arithmetic Modulo 3
  354.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  355.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  356.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  357.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  358.    wt: 1:   16 Remainder Arithmetic Modulo 9 Example 2
  359.    wt: 1:   15 Remainder Arithmetic Modulo 9 Example
  360.    wt: 1:   14 Remainder Arithmetic Modulo 9 Example
  361.    wt: 1:   13 Remainder Arithmetic Modulo 5 Example
  362.    wt: 1:   12 Remainder Arithmetic Modulo 10 Example
  363.    wt: 1:   8 Remainder Arithmetic Morulo 5 Examples II
  364.    wt: 1:   7 Remainder Arithmetic Modulo 5 Examples I
  365.    wt: 1:   6 Remainder Arithmetic Modulo 5 Propertie
  366.    wt: 1:   5 Remainder Arithmetic Modulo 5
  367.    wt: 1:   4 Remainder Arithmetic Modulo 10 in general
  368.    wt: 1:   3 Remainder Arithmetic Modulos 10 more still
  369.    wt: 1:   2 Remainder Arithmetic Modulo 10 more
  370.    wt: 1:   1 Remainder Arithmetic Modulo 10
  371.    wt: 1:   7 Calculator Usage Notes and Cautions
  372.    wt: 1:   1 Divsion Physical Examples
  373.    wt: 1:   A Elementary Basis for Multiplication Methods
  374.    wt: 1:   Appendix 1 Decimals Comparison Method Take II
  375.    wt: 1:   7 Subtraction for Decimal Fractions with Exercises
  376.    wt: 1:   6 Subtraction with Conversion Example with Exercises
  377.    wt: 1:   1 Comparison and Subtraction Easy Direct Cases
  378.    wt: 1:   Appendix 1 Counting Revisited 15 minute video
  379.    wt: 1:   8 What skills and work habits to require
  380.    wt: 1:   Quick history of numbers and algebra
  381.    wt: 1:   The 12 Times Table Visually
  382.    wt: 1:   012 Division of Time Intervals by Time Intervals
  383.    wt: 1:   011 Division of Time Intervals By Numbers
  384.    wt: 1:   9 Comparison and Subtraction of Time Intervals
  385.    wt: 1:   6 How long is a million seconds
  386.    wt: 1:   Example 1. Area Between x and x squared
  387.    wt: 1:   Area Between Crossing Curves Lesson Take 2
  388.    wt: 1:   Area Between Crossing Curves Lesson Take 1
  389.    wt: 1:   Example 4 with x function of y
  390.    wt: 1:   Example 3
  391.    wt: 1:   Example 2
  392.    wt: 1:   Example 1
  393.    wt: 1:   Area Between Curves Lesson Take 2
  394.    wt: 1:   Area Between Curves Lesson Take 1
  395.    wt: 1:   Summary
  396.    wt: 1:   A Related Material in Volume 3
  397.    wt: 1:   5 Area Under Curve Exercise
  398.    wt: 1:   4 Definite Integrals Evaluation Exercises
  399.    wt: 1:   3 Two Chain Rule Method Exercises
  400.    wt: 1:   2 Indefinite Integrals Exercises
  401.    wt: 1:   A Related lessons in Volume 3
  402.    wt: 1:   4 Second derivative test exercise example
  403.    wt: 1:   1 Two cubic sketching exercises with 1st derivative
  404.    wt: 1:   26 Chain Rule Recognising outer inner functions
  405.    wt: 1:   2 Algebraic codification
  406.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  407.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  408.    wt: 1:   G.1 First Fundamental Theorem of Calculus
  409.    wt: 1:   G.6 Bounded Derivatives implies Lipshitz Continuity
  410.    wt: 1:   G.5 Motions With Bounded Velocities
  411.    wt: 1:   G.4 Lipschitz Continuity implies EquiContinuity
  412.    wt: 1:   G.3 Constant Difference Theorem Proof
  413.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  414.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  415.    wt: 1:   F.5b Extreme Value Theorem
  416.    wt: 1:   F.5a Equicontinuity Theorems
  417.    wt: 1:   F.4 Finite Covering Theorem
  418.    wt: 1:   F.3 Intermediate Value Theorem
  419.    wt: 1:   F.2 Closed Range Theorem
  420.    wt: 1:   E1 Error Control Inequalities
  421.    wt: 1:   D2 Limits of Monotone Sequences
  422.    wt: 1:   D1 Sets and Sequences GLBs and LGBs
  423.    wt: 1:   C Triangle Inequalities
  424.    wt: 1:   B3 Bolzano Weierstrass Theorem
  425.    wt: 1:   B1 Pigeon Hole Principles from combinatorics
  426.    wt: 1:   PostScript For and Against Decimal Perspectives
  427.    wt: 1:   A1. Introduction
  428.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  429.    wt: 1:   Postscript Pythagorean Theorem yet another proof
  430.    wt: 1:   Chapter 24 Logarithms Powers and Exponentials
  431.    wt: 1:   Chapter 23 Links To Trigonometry
  432.    wt: 1:   Chapter 22 Complex Numbers
  433.    wt: 1:   Chapter 21 Arrow Addition
  434.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  435.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  436.    wt: 1:   Chapter 18. Slopes Areas Integration
  437.    wt: 1:   Chapter 17. Area Approximation
  438.    wt: 1:   Chapter 16. Velocity Approximation
  439.    wt: 1:   Chapter 15. Slope Approximation
  440.    wt: 1:   Chapter 14 Limits and Continuity with and sans Decimals
  441.    wt: 1:   Chapter 13. Acceleration
  442.    wt: 1:   Chapter 12. Units and Slopes
  443.    wt: 1:   Chapter 11. Graphing Slope versus Position
  444.    wt: 1:   Chapter 10 Slopes and Units
  445.    wt: 1:   Chapter 9 About First Courses in Calculus
  446.    wt: 1:   Chapter 8. Slope Interpretation
  447.    wt: 1:   Chapter 7 Slopes and Velocity
  448.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  449.    wt: 1:   Chapter 5. Slope Sign Tests
  450.    wt: 1:   Chapter 2. Slopes and Ski Trails
  451.    wt: 1:   Chapter 1.Introduction
  452.    wt: 1:   Fall 1983 Calculus Appetizer
  453.    wt: 1:   Foreword
  454.    wt: 1:   Postscript More on Better Performance
  455.    wt: 1:   Postscript For Better Performance
  456.    wt: 1:   Appendix C. How to Read
  457.    wt: 1:   Appendix B. How To Learn
  458.    wt: 1:   Appendix A. Reading Guide For Next Appendices
  459.    wt: 1:   Chapter 31 Direct and Indirect Reason
  460.    wt: 1:   Chapter 30 Truth Tables
  461.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  462.    wt: 1:   Chapter 28 Occurrence Tables
  463.    wt: 1:   Chapter 27 Shorthand Symbols as Pronouns
  464.    wt: 1:   Chapter 25. Mathematical Induction Examples
  465.    wt: 1:   Chapter 24. Personal Investment and Pension EGS
  466.    wt: 1:   Chapter 23. Notation For Sums
  467.    wt: 1:   Chapter 22. Geometric Sums and Sequences
  468.    wt: 1:   Chapter 21. Third Reading Guide
  469.    wt: 1:   Chapter 20. Degrees and Radians
  470.    wt: 1:   Chapter 19. Functions and Sets
  471.    wt: 1:   Chapter 18. Rules for Algebra
  472.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  473.    wt: 1:   Chapter 16. Painless Theorem Proving
  474.    wt: 1:   Chapter 15. Solving Linear Equations
  475.    wt: 1:   Chapter 14. Forward and Backward Use of a Formula
  476.    wt: 1:   Postscript Unifying Theme A Fourth Skill For Algebra
  477.    wt: 1:   Chapter 13. Second Reading Guide
  478.    wt: 1:   Chapter 12. Shorthand Usage Guide
  479.    wt: 1:   Chapter 11. Why Shorthand
  480.    wt: 1:   Chapter 10 Describing and Changing Calculations
  481.    wt: 1:   Chapter 9 Talking about Numbers or Quantities
  482.    wt: 1:   Chapter 8 Three Skills For Algebra
  483.    wt: 1:   Chapter 6 Change of Language
  484.    wt: 1:   Chapter 4 Longer Chains of Reason
  485.    wt: 1:   Chapter 3 Chains of Reason
  486.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  487.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  488.    wt: 1:   Foreword
  489.    wt: 1:   Postscript D Reflections on Law of the Excluded Middle
  490.    wt: 1:   Postscript B More on Story Telling and Reason
  491.    wt: 1:   Postscript A Story Telling
  492.    wt: 1:   Chapter 24 Direct and Indirect Reason
  493.    wt: 1:   Chapter 23 Truth Tables
  494.    wt: 1:   Chapter 22 Contrapositive and Vacuously True Implications
  495.    wt: 1:   Chapter 21 Occurrence Tables
  496.    wt: 1:   Chapter 20 Shorthand Symbols as Pronouns
  497.    wt: 1:   Chapter 18 Sense and Knowledge
  498.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  499.    wt: 1:   Chapter 15 Objective Processes
  500.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  501.    wt: 1:   Chapter 11 Accidental Patterns
  502.    wt: 1:   Chapter 10 Responsibility
  503.    wt: 1:   Chapter 8 Change of Language
  504.    wt: 1:   Chapter 7 Longer Chains of Reason
  505.    wt: 1:   Chapter 6 Chains of Reason
  506.    wt: 1:   Chapter 5 Deception
  507.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  508.    wt: 1:   Chapter 2 Skill Development
  509.    wt: 1:   Chapter 1 Introduction
  510.    wt: 1:   Three Remarks
  511.    wt: 1:   Foreword
  512.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  513.    wt: 1:   R Why Learn Mathematics Skills
  514.    wt: 1:   O On Learning Mathematics and Science
  515.    wt: 1:   N Mathematics Prepare for College Studies
  516.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  517.    wt: 1:   Chapter 8 Skipped Topics and Why
  518.    wt: 1:   Chapter 7 Calculus Previews and Calculus Lightly
  519.    wt: 1:   Chapter 6 More Algebra and Geometry
  520.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  521.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  522.    wt: 1:   Chapter 3 Algebra Starter Lessons
  523.    wt: 1:   Chapter 2 Why Sets
  524.    wt: 1:   Chapter 1 Arithmetic
  525.    wt: 1:   Primary and Secondary Skills and Practices with Take Home Value
  526.    wt: 1:   7 Games and Activities for Instruction
  527.    wt: 1:   6 Measuring via counting or arithmetic the role of fractions
  528.    wt: 1:   5 Interpreting and Drawing Maps and Plans.
  529.    wt: 1:   4 Money Matters Saving Earning Buying Selling and Budgets
  530.    wt: 1:   3 Telling Tracking Time Temporal and More Place Sense
  531.    wt: 1:   2 Identifying Size and Position Place and Spatial Sense
  532.    wt: 1:   1 From Number Recognition and Counting to Arithmetic B
  533.    wt: 1:   1 From Number Recognition and Counting to Arithmetic A
  534.    wt: 1:   Ends Values Methods For Skill Development Framework Prequel
  535.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  536.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  537.    wt: 1:   More Algebra and Slope based Calculus Preview
  538.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  539.    wt: 1:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  540.    wt: 1:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  541.    wt: 1:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  542.    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:

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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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