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: 2:   Progressive Observable Motivated Mathematics Education/
  3.    wt: 2:   Mathematics Education Essays/
  4.    wt: 1:   LAMP Lean Applied Mathematics Program/
  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:   Mathematics 506 Lessons/
  14.    wt: 1:   Secondary Mathematics A Practical Approach/
  15.    wt: 1:   PreSchool and Primary Mathematics or Quantitative Skills/
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66 matches:

  1.    wt: 2:   E LAMP Introduction Modern Mathematics
  2.    wt: 2:   C LAMP Introduction Culture in Mathematics Education
  3.    wt: 2:   Mathematics Education Professors
  4.    wt: 2:   modern education
  5.    wt: 2:   mathematics curriculum shifts
  6.    wt: 2:   three goals for Mathematics Education
  7.    wt: 2:   04 29 New Mathematics Curriculum
  8.    wt: 2:   02 20 mathematics education references
  9.    wt: 2:   Education in mathematics science and technology
  10.    wt: 2:   need for a mixed mathematics curriculum
  11.    wt: 2:   Leaner mathematics curriculum
  12.    wt: 2:   25 Mathematics Education Leaving A Good Impression
  13.    wt: 2:   Postscript B Mathematics Education References
  14.    wt: 2:   Mathematics Education References
  15.    wt: 2:   Mathematics Education References
  16.    wt: 1:   K LAMP Musings Science Education
  17.    wt: 1:   B LAMP Introduction Curriculum Development Standards
  18.    wt: 1:   11 pure mathematics
  19.    wt: 1:   links Education Resources online
  20.    wt: 1:   key notes and themes
  21.    wt: 1:   mathematics in context
  22.    wt: 1:   Education Reform Inconsistencies
  23.    wt: 1:   Secondary Three Mathematics
  24.    wt: 1:   Secondary Two Mathematics
  25.    wt: 1:   Secondary One Mathematics
  26.    wt: 1:   three aims for mathematics students
  27.    wt: 1:   mathematics instruction in general
  28.    wt: 1:   three kinds of reason in mathematics
  29.    wt: 1:   Four ways to improve education reform
  30.    wt: 1:   education an empirical art
  31.    wt: 1:   words for mathematics instructor
  32.    wt: 1:   22 Student Centered Highschool Mathematics
  33.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  34.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  35.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  36.    wt: 1:   18 Primary School Mathematics
  37.    wt: 1:   16 Secondary Mathematics Tips
  38.    wt: 1:   12 Goals and Objectives For Mathematics
  39.    wt: 1:   11 Help and Defend Your Child or Teens Education
  40.    wt: 1:   4 Function notation in and beyond mathematics
  41.    wt: 1:   8 Notes for instructors or tutors
  42.    wt: 1:   12 From Applied To Pure Mathematics
  43.    wt: 1:   Skill Development Notes
  44.    wt: 1:   11 Volume of Sphere
  45.    wt: 1:   10 Volume of Pyramid
  46.    wt: 1:   9 Volume of Cone
  47.    wt: 1:   5 Box Volume Formula Example
  48.    wt: 1:   7 Calculator Usage Notes and Cautions
  49.    wt: 1:   Example 2 volume of a cone
  50.    wt: 1:   Example 1 volume of a pyramid
  51.    wt: 1:   Volume of Solid by Cross Sections Lesson
  52.    wt: 1:   A Related Material in Volume 3
  53.    wt: 1:   A Related lessons in Volume 3
  54.    wt: 1:   Appendix E. How To Study Mathematics and Why
  55.    wt: 1:   Chapter 8 Modern Instruction
  56.    wt: 1:   Chapter 6 Rule Based Reason in Mathematics
  57.    wt: 1:   Chapter 2 For and Against Mathematics
  58.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  59.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  60.    wt: 1:   R Why Learn Mathematics Skills
  61.    wt: 1:   O On Learning Mathematics and Science
  62.    wt: 1:   N Mathematics Prepare for College Studies
  63.    wt: 1:   Helping the Blind in Logic and Mathematics
  64.    wt: 1:   Multiple Ways to Improve Mathematics Skill Development
  65.    wt: 1:   Implementation Notes
  66.    wt: 1:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years

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339 matches:

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