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

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340 matches:

  1.    wt: 8:   Chapter 8 Modern Instruction
  2.    wt: 7:   Postscript B Mathematics Education References
  3.    wt: 7:   Chapter 11 Elementary Instruction
  4.    wt: 7:   Chapter 6 Rule Based Reason in Mathematics
  5.    wt: 7:   Chapter 2 For and Against Mathematics
  6.    wt: 6:   Annotated Links to Material Elsehwere
  7.    wt: 6:   Postscript A Three Remarks
  8.    wt: 6:   Chapter 12 Four Phases
  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: 3:   E LAMP Introduction Modern Mathematics
  18.    wt: 3:   mathematics curriculum shifts
  19.    wt: 3:   04 29 New Mathematics Curriculum
  20.    wt: 3:   mathematics instruction in general
  21.    wt: 3:   need for a mixed mathematics curriculum
  22.    wt: 3:   Leaner mathematics curriculum
  23.    wt: 2:   H LAMP Introduction Instructional Concepts
  24.    wt: 2:   C LAMP Introduction Culture in Mathematics Education
  25.    wt: 2:   B LAMP Introduction Curriculum Development Standards
  26.    wt: 2:   11 pure mathematics
  27.    wt: 2:   key notes and themes
  28.    wt: 2:   Mathematics Education Professors
  29.    wt: 2:   modern education
  30.    wt: 2:   mathematics in context
  31.    wt: 2:   Secondary Three Mathematics
  32.    wt: 2:   Secondary Two Mathematics
  33.    wt: 2:   Secondary One Mathematics
  34.    wt: 2:   three goals for Mathematics Education
  35.    wt: 2:   02 20 mathematics education references
  36.    wt: 2:   three aims for mathematics students
  37.    wt: 2:   Education in mathematics science and technology
  38.    wt: 2:   three kinds of reason in mathematics
  39.    wt: 2:   fairness and inductive principles for instruction
  40.    wt: 2:   words for mathematics instructor
  41.    wt: 2:   Example 2 volume of a cone
  42.    wt: 2:   Example 1 volume of a pyramid
  43.    wt: 2:   Volume of Solid by Cross Sections Lesson
  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:   7 Games and Activities for Instruction
  47.    wt: 2:   Helping the Blind in Logic and Mathematics
  48.    wt: 2:   Mathematics Education References
  49.    wt: 2:   Mathematics Education References
  50.    wt: 2:   Multiple Ways to Improve Mathematics Skill Development
  51.    wt: 2:   Implementation Notes
  52.    wt: 2:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  53.    wt: 1:   Appendix 2 primary school Arithmetic 01
  54.    wt: 1:   Appendix 1 primary and preschool mathematic
  55.    wt: 1:   K LAMP Musings Science Education
  56.    wt: 1:   J LAMP Introduction Extrinsic Origins
  57.    wt: 1:   I LAMP Introduction Study Habits
  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:   links Education Resources online
  90.    wt: 1:   site origins
  91.    wt: 1:   site eurekas
  92.    wt: 1:   About site lesson plans
  93.    wt: 1:   teacher certification
  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:   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:   25 Mathematics Education Leaving A Good Impression
  144.    wt: 1:   22 Student Centered Highschool Mathematics
  145.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  146.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  147.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  148.    wt: 1:   18 Primary School Mathematics
  149.    wt: 1:   16 Secondary Mathematics Tips
  150.    wt: 1:   12 Goals and Objectives For Mathematics
  151.    wt: 1:   10 Ends values for work study instruction
  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:   12 From Applied To Pure Mathematics
  168.    wt: 1:   Skill Development Notes
  169.    wt: 1:   11 Volume of Sphere
  170.    wt: 1:   10 Volume of Pyramid
  171.    wt: 1:   9 Volume of Cone
  172.    wt: 1:   5 Box Volume Formula Example
  173.    wt: 1:   7 Calculator Usage Notes and Cautions
  174.    wt: 1:   Example 1. Area Between x and x squared
  175.    wt: 1:   Area Between Crossing Curves Lesson Take 2
  176.    wt: 1:   Area Between Crossing Curves Lesson Take 1
  177.    wt: 1:   Example 4 with x function of y
  178.    wt: 1:   Example 3
  179.    wt: 1:   Example 2
  180.    wt: 1:   Example 1
  181.    wt: 1:   Area Between Curves Lesson Take 2
  182.    wt: 1:   Area Between Curves Lesson Take 1
  183.    wt: 1:   Summary
  184.    wt: 1:   A Related Material in Volume 3
  185.    wt: 1:   A Related lessons in Volume 3
  186.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  187.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  188.    wt: 1:   G.1 First Fundamental Theorem of Calculus
  189.    wt: 1:   G.6 Bounded Derivatives implies Lipshitz Continuity
  190.    wt: 1:   G.5 Motions With Bounded Velocities
  191.    wt: 1:   G.4 Lipschitz Continuity implies EquiContinuity
  192.    wt: 1:   G.3 Constant Difference Theorem Proof
  193.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  194.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  195.    wt: 1:   F.5b Extreme Value Theorem
  196.    wt: 1:   F.5a Equicontinuity Theorems
  197.    wt: 1:   F.4 Finite Covering Theorem
  198.    wt: 1:   F.3 Intermediate Value Theorem
  199.    wt: 1:   F.2 Closed Range Theorem
  200.    wt: 1:   F.1 What Functions are Continuous
  201.    wt: 1:   E2 Algebraic Properties of Limits
  202.    wt: 1:   E1 Error Control Inequalities
  203.    wt: 1:   D2 Limits of Monotone Sequences
  204.    wt: 1:   D1 Sets and Sequences GLBs and LGBs
  205.    wt: 1:   C Triangle Inequalities
  206.    wt: 1:   B3 Bolzano Weierstrass Theorem
  207.    wt: 1:   B1 Pigeon Hole Principles from combinatorics
  208.    wt: 1:   PostScript For and Against Decimal Perspectives
  209.    wt: 1:   A1. Introduction
  210.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  211.    wt: 1:   Postscript Pythagorean Theorem yet another proof
  212.    wt: 1:   Chapter 24 Logarithms Powers and Exponentials
  213.    wt: 1:   Chapter 23 Links To Trigonometry
  214.    wt: 1:   Chapter 22 Complex Numbers
  215.    wt: 1:   Chapter 21 Arrow Addition
  216.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  217.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  218.    wt: 1:   Chapter 18. Slopes Areas Integration
  219.    wt: 1:   Chapter 17. Area Approximation
  220.    wt: 1:   Chapter 16. Velocity Approximation
  221.    wt: 1:   Chapter 15. Slope Approximation
  222.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  223.    wt: 1:   Chapter 14 Limits and Continuity with and sans Decimals
  224.    wt: 1:   Chapter 13. Acceleration
  225.    wt: 1:   Chapter 12. Units and Slopes
  226.    wt: 1:   Chapter 11. Graphing Slope versus Position
  227.    wt: 1:   Chapter 10 Slopes and Units
  228.    wt: 1:   Chapter 9 About First Courses in Calculus
  229.    wt: 1:   Chapter 8. Slope Interpretation
  230.    wt: 1:   Chapter 7 Slopes and Velocity
  231.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  232.    wt: 1:   Chapter 5. Slope Sign Tests
  233.    wt: 1:   Chapter 4. More Slope Sign Analysis
  234.    wt: 1:   Chapter 3. Slope Sign Analysis
  235.    wt: 1:   Chapter 2. Slopes and Ski Trails
  236.    wt: 1:   Chapter 1.Introduction
  237.    wt: 1:   Fall 1983 Calculus Appetizer
  238.    wt: 1:   Foreword
  239.    wt: 1:   Postscript More on Better Performance
  240.    wt: 1:   Postscript For Better Performance
  241.    wt: 1:   Appendix D. What to do in School and Why
  242.    wt: 1:   Appendix C. How to Read
  243.    wt: 1:   Appendix B. How To Learn
  244.    wt: 1:   Appendix A. Reading Guide For Next Appendices
  245.    wt: 1:   Chapter 31 Direct and Indirect Reason
  246.    wt: 1:   Chapter 30 Truth Tables
  247.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  248.    wt: 1:   Chapter 28 Occurrence Tables
  249.    wt: 1:   Chapter 27 Shorthand Symbols as Pronouns
  250.    wt: 1:   Chapter 26 What is in chapters 27 to 31
  251.    wt: 1:   Chapter 25. Mathematical Induction Examples
  252.    wt: 1:   Chapter 24. Personal Investment and Pension EGS
  253.    wt: 1:   Chapter 23. Notation For Sums
  254.    wt: 1:   Chapter 22. Geometric Sums and Sequences
  255.    wt: 1:   Chapter 21. Third Reading Guide
  256.    wt: 1:   Chapter 20. Degrees and Radians
  257.    wt: 1:   Chapter 19. Functions and Sets
  258.    wt: 1:   Chapter 18. Rules for Algebra
  259.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  260.    wt: 1:   Chapter 16. Painless Theorem Proving
  261.    wt: 1:   Chapter 15. Solving Linear Equations
  262.    wt: 1:   Chapter 14. Forward and Backward Use of a Formula
  263.    wt: 1:   Postscript Unifying Theme A Fourth Skill For Algebra
  264.    wt: 1:   Chapter 13. Second Reading Guide
  265.    wt: 1:   Chapter 12. Shorthand Usage Guide
  266.    wt: 1:   Chapter 11. Why Shorthand
  267.    wt: 1:   Chapter 10 Describing and Changing Calculations
  268.    wt: 1:   Postscript What is a Variable
  269.    wt: 1:   Chapter 9 Talking about Numbers or Quantities
  270.    wt: 1:   Chapter 8 Three Skills For Algebra
  271.    wt: 1:   Solutions For Arithmetic Exercises
  272.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  273.    wt: 1:   Chapter 6 Change of Language
  274.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  275.    wt: 1:   Chapter 4 Longer Chains of Reason
  276.    wt: 1:   Chapter 3 Chains of Reason
  277.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  278.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  279.    wt: 1:   Foreword
  280.    wt: 1:   Postscript D Reflections on Law of the Excluded Middle
  281.    wt: 1:   Postscript C Consistency as a Tool for Reason
  282.    wt: 1:   Postscript B More on Story Telling and Reason
  283.    wt: 1:   Postscript A Story Telling
  284.    wt: 1:   Chapter 24 Direct and Indirect Reason
  285.    wt: 1:   Chapter 23 Truth Tables
  286.    wt: 1:   Chapter 22 Contrapositive and Vacuously True Implications
  287.    wt: 1:   Chapter 21 Occurrence Tables
  288.    wt: 1:   Chapter 20 Shorthand Symbols as Pronouns
  289.    wt: 1:   Chapter 19 What is in chapters 20 to 24
  290.    wt: 1:   Chapter 18 Sense and Knowledge
  291.    wt: 1:   Chapter 17 Objective Ways Trial and Error Discovery
  292.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  293.    wt: 1:   Chapter 15 Objective Processes
  294.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  295.    wt: 1:   Chapter 12 Islands and Divisions of Knowledge
  296.    wt: 1:   Chapter 11 Accidental Patterns
  297.    wt: 1:   Chapter 10 Responsibility
  298.    wt: 1:   Chapter 9 What is in Chapters 10 to 18
  299.    wt: 1:   Chapter 8 Change of Language
  300.    wt: 1:   Chapter 7 Longer Chains of Reason
  301.    wt: 1:   Chapter 6 Chains of Reason
  302.    wt: 1:   Chapter 5 Deception
  303.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  304.    wt: 1:   Chapter 3 What is in chapters 4 to 8
  305.    wt: 1:   Chapter 2 Skill Development
  306.    wt: 1:   Chapter 1 Introduction
  307.    wt: 1:   Three Remarks
  308.    wt: 1:   Foreword
  309.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  310.    wt: 1:   R Why Learn Mathematics Skills
  311.    wt: 1:   O On Learning Mathematics and Science
  312.    wt: 1:   N Mathematics Prepare for College Studies
  313.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  314.    wt: 1:   Chapter 8 Skipped Topics and Why
  315.    wt: 1:   Chapter 7 Calculus Previews and Calculus Lightly
  316.    wt: 1:   Chapter 6 More Algebra and Geometry
  317.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  318.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  319.    wt: 1:   Chapter 3 Algebra Starter Lessons
  320.    wt: 1:   Chapter 2 Why Sets
  321.    wt: 1:   Chapter 1 Arithmetic
  322.    wt: 1:   Primary and Secondary Skills and Practices with Take Home Value
  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
  340.    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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