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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  1.    wt: 6:   Volume 1B Mathematics Curriculum Notes/
  2.    wt: 1:   LAMP Lean Applied Mathematics Program/
  3.    wt: 1:   Progressive Observable Motivated Mathematics Education/
  4.    wt: 1:   Mathematics Education Essays/
  5.    wt: 1:   Volume 1A Regles et modeles/
  6.    wt: 1:   Mathematics Skills Year by Year/
  7.    wt: 1:   12 Webvideo Lessons on Area and Volume Calculation/
  8.    wt: 1:   Advanced Calculus Volume 3 Appendices/
  9.    wt: 1:   Volume 3 Why Slopes A Calculus Intro Etc/
  10.    wt: 1:   Volume 2 Three Skills For Algebra/
  11.    wt: 1:   Volume 1A Pattern Based Reason/
  12.    wt: 1:   Volume 1 Elements of Reason/
  13.    wt: 1:   Resources and Reciprocal Links/
  14.    wt: 1:   Mathematics 506 Lessons/
  15.    wt: 1:   Secondary Mathematics A Practical Approach/
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  1.    wt: 2:   mathematics curriculum shifts
  2.    wt: 2:   04 29 New Mathematics Curriculum
  3.    wt: 2:   need for a mixed mathematics curriculum
  4.    wt: 2:   Leaner mathematics curriculum
  5.    wt: 2:   Systematic Algebra Skill Development Missing Links
  6.    wt: 1:   E LAMP Introduction Modern Mathematics
  7.    wt: 1:   C LAMP Introduction Culture in Mathematics Education
  8.    wt: 1:   B LAMP Introduction Curriculum Development Standards
  9.    wt: 1:   11 pure mathematics
  10.    wt: 1:   links Education Resources online
  11.    wt: 1:   key notes and themes
  12.    wt: 1:   Mathematics Education Professors
  13.    wt: 1:   mathematics in context
  14.    wt: 1:   Secondary Three Mathematics
  15.    wt: 1:   Secondary Two Mathematics
  16.    wt: 1:   Secondary One Mathematics
  17.    wt: 1:   three goals for Mathematics Education
  18.    wt: 1:   02 20 mathematics education references
  19.    wt: 1:   three aims for mathematics students
  20.    wt: 1:   mathematics instruction in general
  21.    wt: 1:   Education in mathematics science and technology
  22.    wt: 1:   three kinds of reason in mathematics
  23.    wt: 1:   words for mathematics instructor
  24.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  25.    wt: 1:   22 Student Centered Highschool Mathematics
  26.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  27.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  28.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  29.    wt: 1:   18 Primary School Mathematics
  30.    wt: 1:   16 Secondary Mathematics Tips
  31.    wt: 1:   12 Goals and Objectives For Mathematics
  32.    wt: 1:   4 Function notation in and beyond mathematics
  33.    wt: 1:   8 Notes for instructors or tutors
  34.    wt: 1:   7 Links Lessons Elsewhere
  35.    wt: 1:   12 From Applied To Pure Mathematics
  36.    wt: 1:   11 Triangle Similarity Missing Side Problem
  37.    wt: 1:   12 Links Lessons elsewhere
  38.    wt: 1:   Euclidean Geometry Elsewhere LINKS
  39.    wt: 1:   Skill Development Notes
  40.    wt: 1:   11 Volume of Sphere
  41.    wt: 1:   10 Volume of Pyramid
  42.    wt: 1:   9 Volume of Cone
  43.    wt: 1:   5 Box Volume Formula Example
  44.    wt: 1:   7 Calculator Usage Notes and Cautions
  45.    wt: 1:   Example 2 volume of a cone
  46.    wt: 1:   Example 1 volume of a pyramid
  47.    wt: 1:   Volume of Solid by Cross Sections Lesson
  48.    wt: 1:   A Related Material in Volume 3
  49.    wt: 1:   A Related lessons in Volume 3
  50.    wt: 1:   Chapter 23 Links To Trigonometry
  51.    wt: 1:   Appendix E. How To Study Mathematics and Why
  52.    wt: 1:   Annotated Links to Material Elsehwere
  53.    wt: 1:   Postscript B Mathematics Education References
  54.    wt: 1:   Chapter 6 Rule Based Reason in Mathematics
  55.    wt: 1:   Chapter 2 For and Against Mathematics
  56.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  57.    wt: 1:   1 Links to Online Resources Elsewhere Take 1
  58.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  59.    wt: 1:   R Why Learn Mathematics Skills
  60.    wt: 1:   O On Learning Mathematics and Science
  61.    wt: 1:   N Mathematics Prepare for College Studies
  62.    wt: 1:   Helping the Blind in Logic and Mathematics
  63.    wt: 1:   Mathematics Education References
  64.    wt: 1:   Mathematics Education References
  65.    wt: 1:   Multiple Ways to Improve Mathematics Skill Development
  66.    wt: 1:   Implementation Notes
  67.    wt: 1:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years

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343 matches:

  1.    wt: 7:   Annotated Links to Material Elsehwere
  2.    wt: 7:   Postscript B Mathematics Education References
  3.    wt: 7:   Chapter 6 Rule Based Reason in Mathematics
  4.    wt: 7:   Chapter 2 For and Against Mathematics
  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:   mathematics curriculum shifts
  18.    wt: 3:   04 29 New Mathematics Curriculum
  19.    wt: 3:   need for a mixed mathematics curriculum
  20.    wt: 3:   Leaner mathematics curriculum
  21.    wt: 3:   Systematic Algebra Skill Development Missing Links
  22.    wt: 2:   E LAMP Introduction Modern Mathematics
  23.    wt: 2:   C LAMP Introduction Culture in Mathematics Education
  24.    wt: 2:   B LAMP Introduction Curriculum Development Standards
  25.    wt: 2:   11 pure mathematics
  26.    wt: 2:   links Education Resources online
  27.    wt: 2:   key notes and themes
  28.    wt: 2:   Mathematics Education Professors
  29.    wt: 2:   mathematics in context
  30.    wt: 2:   Secondary Three Mathematics
  31.    wt: 2:   Secondary Two Mathematics
  32.    wt: 2:   Secondary One Mathematics
  33.    wt: 2:   three goals for Mathematics Education
  34.    wt: 2:   02 20 mathematics education references
  35.    wt: 2:   three aims for mathematics students
  36.    wt: 2:   mathematics instruction in general
  37.    wt: 2:   Education in mathematics science and technology
  38.    wt: 2:   three kinds of reason in mathematics
  39.    wt: 2:   words for mathematics instructor
  40.    wt: 2:   Example 2 volume of a cone
  41.    wt: 2:   Example 1 volume of a pyramid
  42.    wt: 2:   Volume of Solid by Cross Sections Lesson
  43.    wt: 2:   Chapter 23 Links To Trigonometry
  44.    wt: 2:   Appendix E. How To Study Mathematics and Why
  45.    wt: 2:   Chapter 14 Deductive and Empirical Views of Mathematics
  46.    wt: 2:   Helping the Blind in Logic and Mathematics
  47.    wt: 2:   Mathematics Education References
  48.    wt: 2:   Mathematics Education References
  49.    wt: 2:   Multiple Ways to Improve Mathematics Skill Development
  50.    wt: 2:   Implementation Notes
  51.    wt: 2:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  52.    wt: 1:   Appendix 2 primary school Arithmetic 01
  53.    wt: 1:   Appendix 1 primary and preschool mathematic
  54.    wt: 1:   K LAMP Musings Science Education
  55.    wt: 1:   J LAMP Introduction Extrinsic Origins
  56.    wt: 1:   I LAMP Introduction Study Habits
  57.    wt: 1:   H LAMP Introduction Instructional Concepts
  58.    wt: 1:   G LAMP Introduction Problem Solving Skills
  59.    wt: 1:   F LAMP Introduction Prerequisites
  60.    wt: 1:   A Introduction Objectives
  61.    wt: 1:   Skills Chapter 5 Calculus
  62.    wt: 1:   Skills Chapter 4 Logic
  63.    wt: 1:   Ramblings Extrinsic numbers theory
  64.    wt: 1:   Ramblings Introduction Algebra Essay
  65.    wt: 1:   Skills Chapter 3 Algebra
  66.    wt: 1:   Skills Chapter 2 Geometry
  67.    wt: 1:   Skills Chapter 1 Arithmetic
  68.    wt: 1:   Skills Chapter 0 Introduction
  69.    wt: 1:   10 statistics
  70.    wt: 1:   9 combinatorics probability sets
  71.    wt: 1:   8 analytic geometry etc
  72.    wt: 1:   7 logic review and decimals an odd combination
  73.    wt: 1:   6 polynomials etc
  74.    wt: 1:   5 logarithms and exponentials etc
  75.    wt: 1:   4 algebra
  76.    wt: 1:   3 Euclidean Geometry Leanly
  77.    wt: 1:   2 arithmetic with signed numbers
  78.    wt: 1:   1 arithmetic with unsigned numbers
  79.    wt: 1:   What is POMME
  80.    wt: 1:   why bother
  81.    wt: 1:   which way to go
  82.    wt: 1:   website reviews
  83.    wt: 1:   three goals to set for students
  84.    wt: 1:   Teach the teachers plus goals
  85.    wt: 1:   permissions for teachers
  86.    wt: 1:   Math Ed if it must be short make it lean effective
  87.    wt: 1:   Applied Maths Program14092009 POMME variant
  88.    wt: 1:   activities for students
  89.    wt: 1:   site origins
  90.    wt: 1:   site eurekas
  91.    wt: 1:   About site lesson plans
  92.    wt: 1:   teacher certification
  93.    wt: 1:   modern education
  94.    wt: 1:   learning takes time
  95.    wt: 1:   grouping students according to ability
  96.    wt: 1:   what should be learnt and When
  97.    wt: 1:   Postscript 2007 01 10
  98.    wt: 1:   Education Reform Inconsistencies
  99.    wt: 1:   five decades make a difference
  100.    wt: 1:   Maps Plans Drawings
  101.    wt: 1:   how letters appear
  102.    wt: 1:   talk the algebra talk
  103.    wt: 1:   three difficulties
  104.    wt: 1:   teaching tips
  105.    wt: 1:   What to Tell Students
  106.    wt: 1:   geometric implications for algebra
  107.    wt: 1:   teaching tutoring algebraic reason
  108.    wt: 1:   Lessening Algebra Difficulties
  109.    wt: 1:   the trouble with algebra
  110.    wt: 1:   05 13 OldSiteEntrancePage
  111.    wt: 1:   04 25 when to stop or suspend mathemat
  112.    wt: 1:   02 21 words for teachers
  113.    wt: 1:   standards for course material
  114.    wt: 1:   Operational Viewpoint to Value
  115.    wt: 1:   formal or informal peer review
  116.    wt: 1:   Theory of Knowledge
  117.    wt: 1:   Different Kinds of Reasoning in maths
  118.    wt: 1:   cultivating intelligence
  119.    wt: 1:   Four ways to improve education reform
  120.    wt: 1:   How to be a better instructor
  121.    wt: 1:   Motivation and Context Problem
  122.    wt: 1:   Prequel In For A Penny In For A Pound
  123.    wt: 1:   education an empirical art
  124.    wt: 1:   fairness and inductive principles for instruction
  125.    wt: 1:   chapitre 12 00 les iles et division
  126.    wt: 1:   chapitre 07 01 principle D induction mathematique
  127.    wt: 1:   chapitre 07 00 Des chaines plus longues de la raison
  128.    wt: 1:   chapitre 06 00 Chaines de la raison
  129.    wt: 1:   chapitre 05 00 Deception
  130.    wt: 1:   chapitre 04 10 Etapes pour une meilleur raison
  131.    wt: 1:   chapitre 04 09 Regles accidentelles
  132.    wt: 1:   chapitre 04 08 Limitations et benefices
  133.    wt: 1:   chapitre 04 07 RepetablesEtReproductibles
  134.    wt: 1:   chapitre 04 06 engagements
  135.    wt: 1:   chapitre 04 05 Implication versus suggestion
  136.    wt: 1:   chapitre 04 04 Parlons de la logique
  137.    wt: 1:   chapitre 04 03 Unidirectionnel versus bidirectionnel
  138.    wt: 1:   chapitre 04 02 Deuxieme enigme
  139.    wt: 1:   chapitre 04 01 Premiere enigme
  140.    wt: 1:   chapitre 04 00 Les regles d implication
  141.    wt: 1:   chapitre 03 A Propos Des Prochains Chapitre
  142.    wt: 1:   chapitre 02 00 La Communication des idees
  143.    wt: 1:   chapitre 01 00 Introduction
  144.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  145.    wt: 1:   22 Student Centered Highschool Mathematics
  146.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  147.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  148.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  149.    wt: 1:   18 Primary School Mathematics
  150.    wt: 1:   16 Secondary Mathematics Tips
  151.    wt: 1:   12 Goals and Objectives For Mathematics
  152.    wt: 1:   Ages 12 to 14 Skills with take home value
  153.    wt: 1:   Ages 12 to 14 Geometry
  154.    wt: 1:   Ages 12 to 14 Arithmetic
  155.    wt: 1:   Ages 10 to 12 Geometry
  156.    wt: 1:   Ages 10 to 12 Arithmetic
  157.    wt: 1:   Ages 9 to 10
  158.    wt: 1:   Ages 8 to 9
  159.    wt: 1:   Ages 7 to 8
  160.    wt: 1:   Ages 6 to 7
  161.    wt: 1:   Ages 4 plus to 5 plus
  162.    wt: 1:   Ages 3 plus to 4 plus
  163.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  164.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  165.    wt: 1:   4 Function notation in and beyond mathematics
  166.    wt: 1:   8 Notes for instructors or tutors
  167.    wt: 1:   7 Links Lessons Elsewhere
  168.    wt: 1:   12 From Applied To Pure Mathematics
  169.    wt: 1:   11 Triangle Similarity Missing Side Problem
  170.    wt: 1:   12 Links Lessons elsewhere
  171.    wt: 1:   Euclidean Geometry Elsewhere LINKS
  172.    wt: 1:   Skill Development Notes
  173.    wt: 1:   11 Volume of Sphere
  174.    wt: 1:   10 Volume of Pyramid
  175.    wt: 1:   9 Volume of Cone
  176.    wt: 1:   5 Box Volume Formula Example
  177.    wt: 1:   7 Calculator Usage Notes and Cautions
  178.    wt: 1:   Example 1. Area Between x and x squared
  179.    wt: 1:   Area Between Crossing Curves Lesson Take 2
  180.    wt: 1:   Area Between Crossing Curves Lesson Take 1
  181.    wt: 1:   Example 4 with x function of y
  182.    wt: 1:   Example 3
  183.    wt: 1:   Example 2
  184.    wt: 1:   Example 1
  185.    wt: 1:   Area Between Curves Lesson Take 2
  186.    wt: 1:   Area Between Curves Lesson Take 1
  187.    wt: 1:   Summary
  188.    wt: 1:   A Related Material in Volume 3
  189.    wt: 1:   A Related lessons in Volume 3
  190.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  191.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  192.    wt: 1:   G.1 First Fundamental Theorem of Calculus
  193.    wt: 1:   G.6 Bounded Derivatives implies Lipshitz Continuity
  194.    wt: 1:   G.5 Motions With Bounded Velocities
  195.    wt: 1:   G.4 Lipschitz Continuity implies EquiContinuity
  196.    wt: 1:   G.3 Constant Difference Theorem Proof
  197.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  198.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  199.    wt: 1:   F.5b Extreme Value Theorem
  200.    wt: 1:   F.5a Equicontinuity Theorems
  201.    wt: 1:   F.4 Finite Covering Theorem
  202.    wt: 1:   F.3 Intermediate Value Theorem
  203.    wt: 1:   F.2 Closed Range Theorem
  204.    wt: 1:   F.1 What Functions are Continuous
  205.    wt: 1:   E2 Algebraic Properties of Limits
  206.    wt: 1:   E1 Error Control Inequalities
  207.    wt: 1:   D2 Limits of Monotone Sequences
  208.    wt: 1:   D1 Sets and Sequences GLBs and LGBs
  209.    wt: 1:   C Triangle Inequalities
  210.    wt: 1:   B3 Bolzano Weierstrass Theorem
  211.    wt: 1:   B1 Pigeon Hole Principles from combinatorics
  212.    wt: 1:   PostScript For and Against Decimal Perspectives
  213.    wt: 1:   A1. Introduction
  214.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  215.    wt: 1:   Postscript Pythagorean Theorem yet another proof
  216.    wt: 1:   Chapter 24 Logarithms Powers and Exponentials
  217.    wt: 1:   Chapter 22 Complex Numbers
  218.    wt: 1:   Chapter 21 Arrow Addition
  219.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  220.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  221.    wt: 1:   Chapter 18. Slopes Areas Integration
  222.    wt: 1:   Chapter 17. Area Approximation
  223.    wt: 1:   Chapter 16. Velocity Approximation
  224.    wt: 1:   Chapter 15. Slope Approximation
  225.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  226.    wt: 1:   Chapter 14 Limits and Continuity with and sans Decimals
  227.    wt: 1:   Chapter 13. Acceleration
  228.    wt: 1:   Chapter 12. Units and Slopes
  229.    wt: 1:   Chapter 11. Graphing Slope versus Position
  230.    wt: 1:   Chapter 10 Slopes and Units
  231.    wt: 1:   Chapter 9 About First Courses in Calculus
  232.    wt: 1:   Chapter 8. Slope Interpretation
  233.    wt: 1:   Chapter 7 Slopes and Velocity
  234.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  235.    wt: 1:   Chapter 5. Slope Sign Tests
  236.    wt: 1:   Chapter 4. More Slope Sign Analysis
  237.    wt: 1:   Chapter 3. Slope Sign Analysis
  238.    wt: 1:   Chapter 2. Slopes and Ski Trails
  239.    wt: 1:   Chapter 1.Introduction
  240.    wt: 1:   Fall 1983 Calculus Appetizer
  241.    wt: 1:   Foreword
  242.    wt: 1:   Postscript More on Better Performance
  243.    wt: 1:   Postscript For Better Performance
  244.    wt: 1:   Appendix D. What to do in School and Why
  245.    wt: 1:   Appendix C. How to Read
  246.    wt: 1:   Appendix B. How To Learn
  247.    wt: 1:   Appendix A. Reading Guide For Next Appendices
  248.    wt: 1:   Chapter 31 Direct and Indirect Reason
  249.    wt: 1:   Chapter 30 Truth Tables
  250.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  251.    wt: 1:   Chapter 28 Occurrence Tables
  252.    wt: 1:   Chapter 27 Shorthand Symbols as Pronouns
  253.    wt: 1:   Chapter 26 What is in chapters 27 to 31
  254.    wt: 1:   Chapter 25. Mathematical Induction Examples
  255.    wt: 1:   Chapter 24. Personal Investment and Pension EGS
  256.    wt: 1:   Chapter 23. Notation For Sums
  257.    wt: 1:   Chapter 22. Geometric Sums and Sequences
  258.    wt: 1:   Chapter 21. Third Reading Guide
  259.    wt: 1:   Chapter 20. Degrees and Radians
  260.    wt: 1:   Chapter 19. Functions and Sets
  261.    wt: 1:   Chapter 18. Rules for Algebra
  262.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  263.    wt: 1:   Chapter 16. Painless Theorem Proving
  264.    wt: 1:   Chapter 15. Solving Linear Equations
  265.    wt: 1:   Chapter 14. Forward and Backward Use of a Formula
  266.    wt: 1:   Postscript Unifying Theme A Fourth Skill For Algebra
  267.    wt: 1:   Chapter 13. Second Reading Guide
  268.    wt: 1:   Chapter 12. Shorthand Usage Guide
  269.    wt: 1:   Chapter 11. Why Shorthand
  270.    wt: 1:   Chapter 10 Describing and Changing Calculations
  271.    wt: 1:   Postscript What is a Variable
  272.    wt: 1:   Chapter 9 Talking about Numbers or Quantities
  273.    wt: 1:   Chapter 8 Three Skills For Algebra
  274.    wt: 1:   Solutions For Arithmetic Exercises
  275.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  276.    wt: 1:   Chapter 6 Change of Language
  277.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  278.    wt: 1:   Chapter 4 Longer Chains of Reason
  279.    wt: 1:   Chapter 3 Chains of Reason
  280.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  281.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  282.    wt: 1:   Foreword
  283.    wt: 1:   Postscript D Reflections on Law of the Excluded Middle
  284.    wt: 1:   Postscript C Consistency as a Tool for Reason
  285.    wt: 1:   Postscript B More on Story Telling and Reason
  286.    wt: 1:   Postscript A Story Telling
  287.    wt: 1:   Chapter 24 Direct and Indirect Reason
  288.    wt: 1:   Chapter 23 Truth Tables
  289.    wt: 1:   Chapter 22 Contrapositive and Vacuously True Implications
  290.    wt: 1:   Chapter 21 Occurrence Tables
  291.    wt: 1:   Chapter 20 Shorthand Symbols as Pronouns
  292.    wt: 1:   Chapter 19 What is in chapters 20 to 24
  293.    wt: 1:   Chapter 18 Sense and Knowledge
  294.    wt: 1:   Chapter 17 Objective Ways Trial and Error Discovery
  295.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  296.    wt: 1:   Chapter 15 Objective Processes
  297.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  298.    wt: 1:   Chapter 12 Islands and Divisions of Knowledge
  299.    wt: 1:   Chapter 11 Accidental Patterns
  300.    wt: 1:   Chapter 10 Responsibility
  301.    wt: 1:   Chapter 9 What is in Chapters 10 to 18
  302.    wt: 1:   Chapter 8 Change of Language
  303.    wt: 1:   Chapter 7 Longer Chains of Reason
  304.    wt: 1:   Chapter 6 Chains of Reason
  305.    wt: 1:   Chapter 5 Deception
  306.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  307.    wt: 1:   Chapter 3 What is in chapters 4 to 8
  308.    wt: 1:   Chapter 2 Skill Development
  309.    wt: 1:   Chapter 1 Introduction
  310.    wt: 1:   Three Remarks
  311.    wt: 1:   Foreword
  312.    wt: 1:   1 Links to Online Resources Elsewhere Take 1
  313.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  314.    wt: 1:   R Why Learn Mathematics Skills
  315.    wt: 1:   O On Learning Mathematics and Science
  316.    wt: 1:   N Mathematics Prepare for College Studies
  317.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  318.    wt: 1:   Chapter 8 Skipped Topics and Why
  319.    wt: 1:   Chapter 7 Calculus Previews and Calculus Lightly
  320.    wt: 1:   Chapter 6 More Algebra and Geometry
  321.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  322.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  323.    wt: 1:   Chapter 3 Algebra Starter Lessons
  324.    wt: 1:   Chapter 2 Why Sets
  325.    wt: 1:   Chapter 1 Arithmetic
  326.    wt: 1:   Primary and Secondary Skills and Practices with Take Home Value
  327.    wt: 1:   7 Games and Activities for Instruction
  328.    wt: 1:   6 Measuring via counting or arithmetic the role of fractions
  329.    wt: 1:   5 Interpreting and Drawing Maps and Plans.
  330.    wt: 1:   4 Money Matters Saving Earning Buying Selling and Budgets
  331.    wt: 1:   3 Telling Tracking Time Temporal and More Place Sense
  332.    wt: 1:   2 Identifying Size and Position Place and Spatial Sense
  333.    wt: 1:   1 From Number Recognition and Counting to Arithmetic B
  334.    wt: 1:   1 From Number Recognition and Counting to Arithmetic A
  335.    wt: 1:   Ends Values Methods For Skill Development Framework Prequel
  336.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  337.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  338.    wt: 1:   More Algebra and Slope based Calculus Preview
  339.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  340.    wt: 1:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  341.    wt: 1:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  342.    wt: 1:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  343.    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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