Original Site Title: Appetizers and Lessons for Mathematics and Reason, June 1995 to April 2012. New site title:
Logic and Mathematics Skill & Concept Building Site Map || Français: 26 pages
for college students, gifted teens, home-tutoring and K1-12 schooling, with chapters on Logic
and Pattern Based Reason to inform and amuse thinkers and avid readers, studying or not. Enjoy.

Logic mastery strengthens comprehension and improve home, work & study habits.
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
Forewords + leading chapters give original reasons, still valid, for site content & growth.

About: Site material shows how common troubles stem from steps too large or missing. Site material may develop critical thinking, improve reading and writing, and build mathematics and pattern based reasoning skills. Online Volumes 1, 1A and 2 give avid readers in school and out the best places to begin. If one site element is not to your liking, try another. Each is different. Many are unique

Teachers & Tutors: This December 2011, 5-phase framework offers a context for mathematics & logic education. Phases 1 to 3 may focus on skills with actual or potential local 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. Reform: look before you leap - plan all in detail first.

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:   Mathematics 506 Lessons/
  14.    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: 1:   E LAMP Introduction Modern Mathematics
  6.    wt: 1:   C LAMP Introduction Culture in Mathematics Education
  7.    wt: 1:   B LAMP Introduction Curriculum Development Standards
  8.    wt: 1:   11 pure mathematics
  9.    wt: 1:   key notes and themes
  10.    wt: 1:   Mathematics Education Professors
  11.    wt: 1:   mathematics in context
  12.    wt: 1:   Secondary Three Mathematics
  13.    wt: 1:   Secondary Two Mathematics
  14.    wt: 1:   Secondary One Mathematics
  15.    wt: 1:   three goals for Mathematics Education
  16.    wt: 1:   02 20 mathematics education references
  17.    wt: 1:   three aims for mathematics students
  18.    wt: 1:   mathematics instruction in general
  19.    wt: 1:   Education in mathematics science and technology
  20.    wt: 1:   three kinds of reason in mathematics
  21.    wt: 1:   words for mathematics instructor
  22.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  23.    wt: 1:   22 Student Centered Highschool Mathematics
  24.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  25.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  26.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  27.    wt: 1:   18 Primary School Mathematics
  28.    wt: 1:   16 Secondary Mathematics Tips
  29.    wt: 1:   12 Goals and Objectives For Mathematics
  30.    wt: 1:   4 Function notation in and beyond mathematics
  31.    wt: 1:   8 Notes for instructors or tutors
  32.    wt: 1:   12 From Applied To Pure Mathematics
  33.    wt: 1:   Skill Development Notes
  34.    wt: 1:   11 Volume of Sphere
  35.    wt: 1:   10 Volume of Pyramid
  36.    wt: 1:   9 Volume of Cone
  37.    wt: 1:   5 Box Volume Formula Example
  38.    wt: 1:   7 Calculator Usage Notes and Cautions
  39.    wt: 1:   Example 2 volume of a cone
  40.    wt: 1:   Example 1 volume of a pyramid
  41.    wt: 1:   Volume of Solid by Cross Sections Lesson
  42.    wt: 1:   A Related Material in Volume 3
  43.    wt: 1:   A Related lessons in Volume 3
  44.    wt: 1:   Appendix E. How To Study Mathematics and Why
  45.    wt: 1:   Postscript B Mathematics Education References
  46.    wt: 1:   Chapter 6 Rule Based Reason in Mathematics
  47.    wt: 1:   Chapter 2 For and Against Mathematics
  48.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  49.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  50.    wt: 1:   R Why Learn Mathematics Skills
  51.    wt: 1:   O On Learning Mathematics and Science
  52.    wt: 1:   N Mathematics Prepare for College Studies
  53.    wt: 1:   Helping the Blind in Logic and Mathematics
  54.    wt: 1:   Mathematics Education References
  55.    wt: 1:   Mathematics Education References
  56.    wt: 1:   Multiple Ways to Improve Mathematics Skill Development
  57.    wt: 1:   Implementation Notes
  58.    wt: 1:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  59.    wt: 1:   Mathematics Teacher Certification Best Practices

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

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 bicylce?

Death Penalty: How Texas sent an innocent man to his death - The wrong Carlos.

For home-tutoring or -schooling, or for schools or colleges with course content control: Secondary Mathematics for Ages 11+, A Practical Approach.

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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