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

Logic 5 Chapters Arithmetic 10 Steps Algebra 12 Starter Steps & 5 Advanced Steps
Work & Study 23 Tips Geometry 15 Steps Calculus 70 Lessons

Ages 15+: Why study slopes Polynomials Quadratics Why factor polynomials Logarithms Functions
What is similarity Euclidean geometry leanly Coordinates + complex no.s Vectors DC Electric Circuits
Ages 12+: Prime factorization Written work formats Decimal place value Extend arithmetic skills orally
What is a variable 5. Fraction Operations by Raising Terms Solving Linear Equations: Take I Take II


Online Volumes: 1 - Elements of Reason, 2 - 3 Skills For Algebra, 3 - Why Slopes and
More Math
, 1A - Pattern Based Reason, 1B - Skill Development Principles + Troubles

Welcome: Site content may develop critical thinking, improve reading and writing, and build mathematics skills. See online chapters on on logic and pattern based reason.

Teachers: This December 2011, 5-phase framework offers a context for mathematics & logic instruction. Phases 1 to 3 focus on skills with actual or potential value for adult & daily life. College-oriented phases 5 & 4 focus on calculus & preparation for it. Phases 1 to 4 may also serve trades & professions not dependent on calculus.

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

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  1.    wt: 6:   Volume 1B Mathematics Curriculum Notes/
  2.    wt: 1:   LAMP Lean Applied Mathematics Program/
  3.    wt: 1:   Progressive Observable Motivated Mathematics Education/
  4.    wt: 1:   Mathematics Education Essays/
  5.    wt: 1:   Volume 1A Regles et modeles/
  6.    wt: 1:   Mathematics Skills Year by Year/
  7.    wt: 1:   4 Computation Rules and Function Notation/
  8.    wt: 1:   12 Webvideo Lessons on Area and Volume Calculation/
  9.    wt: 1:   Advanced Calculus Volume 3 Appendices/
  10.    wt: 1:   Volume 3 Why Slopes A Calculus Intro Etc/
  11.    wt: 1:   Volume 2 Three Skills For Algebra/
  12.    wt: 1:   Volume 1A Pattern Based Reason/
  13.    wt: 1:   Volume 1 Elements of Reason/
  14.    wt: 1:   Mathematics 506 Lessons/
  15.    wt: 1:   Secondary Mathematics A Practical Approach/
  16.    wt: 1:   PreSchool and Primary Mathematics or Quantitative Skills/
  17.    wt: 1:   Mathematics Skill Development Framework/

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70 matches:

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

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352 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:   4 Function notation in and beyond mathematics
  39.    wt: 2:   3 Geometric Formulas and Function Notation
  40.    wt: 2:   1 Formulas Dependence and Function Notation
  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 23. Notation For Sums
  46.    wt: 2:   Chapter 14 Deductive and Empirical Views of Mathematics
  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:   H LAMP Introduction Instructional Concepts
  59.    wt: 1:   G LAMP Introduction Problem Solving Skills
  60.    wt: 1:   F LAMP Introduction Prerequisites
  61.    wt: 1:   A Introduction Objectives
  62.    wt: 1:   Skills Chapter 5 Calculus
  63.    wt: 1:   Skills Chapter 4 Logic
  64.    wt: 1:   Ramblings Extrinsic numbers theory
  65.    wt: 1:   Ramblings Introduction Algebra Essay
  66.    wt: 1:   Skills Chapter 3 Algebra
  67.    wt: 1:   Skills Chapter 2 Geometry
  68.    wt: 1:   Skills Chapter 1 Arithmetic
  69.    wt: 1:   Skills Chapter 0 Introduction
  70.    wt: 1:   10 statistics
  71.    wt: 1:   9 combinatorics probability sets
  72.    wt: 1:   8 analytic geometry etc
  73.    wt: 1:   7 logic review and decimals an odd combination
  74.    wt: 1:   6 polynomials etc
  75.    wt: 1:   5 logarithms and exponentials etc
  76.    wt: 1:   4 algebra
  77.    wt: 1:   3 Euclidean Geometry Leanly
  78.    wt: 1:   2 arithmetic with signed numbers
  79.    wt: 1:   1 arithmetic with unsigned numbers
  80.    wt: 1:   What is POMME
  81.    wt: 1:   why bother
  82.    wt: 1:   which way to go
  83.    wt: 1:   website reviews
  84.    wt: 1:   three goals to set for students
  85.    wt: 1:   Teach the teachers plus goals
  86.    wt: 1:   permissions for teachers
  87.    wt: 1:   Math Ed if it must be short make it lean effective
  88.    wt: 1:   Applied Maths Program14092009 POMME variant
  89.    wt: 1:   activities for students
  90.    wt: 1:   links Education Resources online
  91.    wt: 1:   site origins
  92.    wt: 1:   site eurekas
  93.    wt: 1:   About site lesson plans
  94.    wt: 1:   teacher certification
  95.    wt: 1:   modern education
  96.    wt: 1:   learning takes time
  97.    wt: 1:   grouping students according to ability
  98.    wt: 1:   what should be learnt and When
  99.    wt: 1:   Postscript 2007 01 10
  100.    wt: 1:   Education Reform Inconsistencies
  101.    wt: 1:   five decades make a difference
  102.    wt: 1:   Maps Plans Drawings
  103.    wt: 1:   how letters appear
  104.    wt: 1:   talk the algebra talk
  105.    wt: 1:   three difficulties
  106.    wt: 1:   teaching tips
  107.    wt: 1:   What to Tell Students
  108.    wt: 1:   geometric implications for algebra
  109.    wt: 1:   teaching tutoring algebraic reason
  110.    wt: 1:   Lessening Algebra Difficulties
  111.    wt: 1:   the trouble with algebra
  112.    wt: 1:   05 13 OldSiteEntrancePage
  113.    wt: 1:   04 25 when to stop or suspend mathemat
  114.    wt: 1:   02 21 words for teachers
  115.    wt: 1:   standards for course material
  116.    wt: 1:   Operational Viewpoint to Value
  117.    wt: 1:   formal or informal peer review
  118.    wt: 1:   Theory of Knowledge
  119.    wt: 1:   Different Kinds of Reasoning in maths
  120.    wt: 1:   cultivating intelligence
  121.    wt: 1:   Four ways to improve education reform
  122.    wt: 1:   How to be a better instructor
  123.    wt: 1:   Motivation and Context Problem
  124.    wt: 1:   Prequel In For A Penny In For A Pound
  125.    wt: 1:   education an empirical art
  126.    wt: 1:   fairness and inductive principles for instruction
  127.    wt: 1:   chapitre 12 00 les iles et division
  128.    wt: 1:   chapitre 07 01 principle D induction mathematique
  129.    wt: 1:   chapitre 07 00 Des chaines plus longues de la raison
  130.    wt: 1:   chapitre 06 00 Chaines de la raison
  131.    wt: 1:   chapitre 05 00 Deception
  132.    wt: 1:   chapitre 04 10 Etapes pour une meilleur raison
  133.    wt: 1:   chapitre 04 09 Regles accidentelles
  134.    wt: 1:   chapitre 04 08 Limitations et benefices
  135.    wt: 1:   chapitre 04 07 RepetablesEtReproductibles
  136.    wt: 1:   chapitre 04 06 engagements
  137.    wt: 1:   chapitre 04 05 Implication versus suggestion
  138.    wt: 1:   chapitre 04 04 Parlons de la logique
  139.    wt: 1:   chapitre 04 03 Unidirectionnel versus bidirectionnel
  140.    wt: 1:   chapitre 04 02 Deuxieme enigme
  141.    wt: 1:   chapitre 04 01 Premiere enigme
  142.    wt: 1:   chapitre 04 00 Les regles d implication
  143.    wt: 1:   chapitre 03 A Propos Des Prochains Chapitre
  144.    wt: 1:   chapitre 02 00 La Communication des idees
  145.    wt: 1:   chapitre 01 00 Introduction
  146.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  147.    wt: 1:   22 Student Centered Highschool Mathematics
  148.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  149.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  150.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  151.    wt: 1:   18 Primary School Mathematics
  152.    wt: 1:   16 Secondary Mathematics Tips
  153.    wt: 1:   12 Goals and Objectives For Mathematics
  154.    wt: 1:   Ages 12 to 14 Skills with take home value
  155.    wt: 1:   Ages 12 to 14 Geometry
  156.    wt: 1:   Ages 12 to 14 Arithmetic
  157.    wt: 1:   Ages 10 to 12 Geometry
  158.    wt: 1:   Ages 10 to 12 Arithmetic
  159.    wt: 1:   Ages 9 to 10
  160.    wt: 1:   Ages 8 to 9
  161.    wt: 1:   Ages 7 to 8
  162.    wt: 1:   Ages 6 to 7
  163.    wt: 1:   Ages 4 plus to 5 plus
  164.    wt: 1:   Ages 3 plus to 4 plus
  165.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  166.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  167.    wt: 1:   10 Interval Notation
  168.    wt: 1:   6 Set Existence Formation and Notation
  169.    wt: 1:   5 Function notation for geometric transformations
  170.    wt: 1:   2 Algebraic use of function notation
  171.    wt: 1:   1 Geometric Introduction of Function Notation
  172.    wt: 1:   8 Notes for instructors or tutors
  173.    wt: 1:   12 From Applied To Pure Mathematics
  174.    wt: 1:   5 Independent versus Dependent Variables
  175.    wt: 1:   4 Changing Letters
  176.    wt: 1:   2 Computation Rules Evaluation
  177.    wt: 1:   Skill Development Notes
  178.    wt: 1:   11 Volume of Sphere
  179.    wt: 1:   10 Volume of Pyramid
  180.    wt: 1:   9 Volume of Cone
  181.    wt: 1:   5 Box Volume Formula Example
  182.    wt: 1:   6 Power Set Notation
  183.    wt: 1:   5 Product Builder Notation
  184.    wt: 1:   4 Subset Builder Notation
  185.    wt: 1:   7 Calculator Usage Notes and Cautions
  186.    wt: 1:   Video Power Notation in Decimal Expansion
  187.    wt: 1:   Example 1. Area Between x and x squared
  188.    wt: 1:   Area Between Crossing Curves Lesson Take 2
  189.    wt: 1:   Area Between Crossing Curves Lesson Take 1
  190.    wt: 1:   Example 4 with x function of y
  191.    wt: 1:   Example 3
  192.    wt: 1:   Example 2
  193.    wt: 1:   Example 1
  194.    wt: 1:   Area Between Curves Lesson Take 2
  195.    wt: 1:   Area Between Curves Lesson Take 1
  196.    wt: 1:   Summary
  197.    wt: 1:   A Related Material in Volume 3
  198.    wt: 1:   A Related lessons in Volume 3
  199.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  200.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  201.    wt: 1:   G.1 First Fundamental Theorem of Calculus
  202.    wt: 1:   G.6 Bounded Derivatives implies Lipshitz Continuity
  203.    wt: 1:   G.5 Motions With Bounded Velocities
  204.    wt: 1:   G.4 Lipschitz Continuity implies EquiContinuity
  205.    wt: 1:   G.3 Constant Difference Theorem Proof
  206.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  207.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  208.    wt: 1:   F.5b Extreme Value Theorem
  209.    wt: 1:   F.5a Equicontinuity Theorems
  210.    wt: 1:   F.4 Finite Covering Theorem
  211.    wt: 1:   F.3 Intermediate Value Theorem
  212.    wt: 1:   F.2 Closed Range Theorem
  213.    wt: 1:   F.1 What Functions are Continuous
  214.    wt: 1:   E2 Algebraic Properties of Limits
  215.    wt: 1:   E1 Error Control Inequalities
  216.    wt: 1:   D2 Limits of Monotone Sequences
  217.    wt: 1:   D1 Sets and Sequences GLBs and LGBs
  218.    wt: 1:   C Triangle Inequalities
  219.    wt: 1:   B3 Bolzano Weierstrass Theorem
  220.    wt: 1:   B1 Pigeon Hole Principles from combinatorics
  221.    wt: 1:   PostScript For and Against Decimal Perspectives
  222.    wt: 1:   A1. Introduction
  223.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  224.    wt: 1:   Postscript Pythagorean Theorem yet another proof
  225.    wt: 1:   Chapter 24 Logarithms Powers and Exponentials
  226.    wt: 1:   Chapter 23 Links To Trigonometry
  227.    wt: 1:   Chapter 22 Complex Numbers
  228.    wt: 1:   Chapter 21 Arrow Addition
  229.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  230.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  231.    wt: 1:   Chapter 18. Slopes Areas Integration
  232.    wt: 1:   Chapter 17. Area Approximation
  233.    wt: 1:   Chapter 16. Velocity Approximation
  234.    wt: 1:   Chapter 15. Slope Approximation
  235.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  236.    wt: 1:   Chapter 14 Limits and Continuity with and sans Decimals
  237.    wt: 1:   Chapter 13. Acceleration
  238.    wt: 1:   Chapter 12. Units and Slopes
  239.    wt: 1:   Chapter 11. Graphing Slope versus Position
  240.    wt: 1:   Chapter 10 Slopes and Units
  241.    wt: 1:   Chapter 9 About First Courses in Calculus
  242.    wt: 1:   Chapter 8. Slope Interpretation
  243.    wt: 1:   Chapter 7 Slopes and Velocity
  244.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  245.    wt: 1:   Chapter 5. Slope Sign Tests
  246.    wt: 1:   Chapter 4. More Slope Sign Analysis
  247.    wt: 1:   Chapter 3. Slope Sign Analysis
  248.    wt: 1:   Chapter 2. Slopes and Ski Trails
  249.    wt: 1:   Chapter 1.Introduction
  250.    wt: 1:   Fall 1983 Calculus Appetizer
  251.    wt: 1:   Foreword
  252.    wt: 1:   Postscript More on Better Performance
  253.    wt: 1:   Postscript For Better Performance
  254.    wt: 1:   Appendix D. What to do in School and Why
  255.    wt: 1:   Appendix C. How to Read
  256.    wt: 1:   Appendix B. How To Learn
  257.    wt: 1:   Appendix A. Reading Guide For Next Appendices
  258.    wt: 1:   Chapter 31 Direct and Indirect Reason
  259.    wt: 1:   Chapter 30 Truth Tables
  260.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  261.    wt: 1:   Chapter 28 Occurrence Tables
  262.    wt: 1:   Chapter 27 Shorthand Symbols as Pronouns
  263.    wt: 1:   Chapter 26 What is in chapters 27 to 31
  264.    wt: 1:   Chapter 25. Mathematical Induction Examples
  265.    wt: 1:   Chapter 24. Personal Investment and Pension EGS
  266.    wt: 1:   Chapter 22. Geometric Sums and Sequences
  267.    wt: 1:   Chapter 21. Third Reading Guide
  268.    wt: 1:   Chapter 20. Degrees and Radians
  269.    wt: 1:   Chapter 19. Functions and Sets
  270.    wt: 1:   Chapter 18. Rules for Algebra
  271.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  272.    wt: 1:   Chapter 16. Painless Theorem Proving
  273.    wt: 1:   Chapter 15. Solving Linear Equations
  274.    wt: 1:   Chapter 14. Forward and Backward Use of a Formula
  275.    wt: 1:   Postscript Unifying Theme A Fourth Skill For Algebra
  276.    wt: 1:   Chapter 13. Second Reading Guide
  277.    wt: 1:   Chapter 12. Shorthand Usage Guide
  278.    wt: 1:   Chapter 11. Why Shorthand
  279.    wt: 1:   Chapter 10 Describing and Changing Calculations
  280.    wt: 1:   Postscript What is a Variable
  281.    wt: 1:   Chapter 9 Talking about Numbers or Quantities
  282.    wt: 1:   Chapter 8 Three Skills For Algebra
  283.    wt: 1:   Solutions For Arithmetic Exercises
  284.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  285.    wt: 1:   Chapter 6 Change of Language
  286.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  287.    wt: 1:   Chapter 4 Longer Chains of Reason
  288.    wt: 1:   Chapter 3 Chains of Reason
  289.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  290.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  291.    wt: 1:   Foreword
  292.    wt: 1:   Postscript D Reflections on Law of the Excluded Middle
  293.    wt: 1:   Postscript C Consistency as a Tool for Reason
  294.    wt: 1:   Postscript B More on Story Telling and Reason
  295.    wt: 1:   Postscript A Story Telling
  296.    wt: 1:   Chapter 24 Direct and Indirect Reason
  297.    wt: 1:   Chapter 23 Truth Tables
  298.    wt: 1:   Chapter 22 Contrapositive and Vacuously True Implications
  299.    wt: 1:   Chapter 21 Occurrence Tables
  300.    wt: 1:   Chapter 20 Shorthand Symbols as Pronouns
  301.    wt: 1:   Chapter 19 What is in chapters 20 to 24
  302.    wt: 1:   Chapter 18 Sense and Knowledge
  303.    wt: 1:   Chapter 17 Objective Ways Trial and Error Discovery
  304.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  305.    wt: 1:   Chapter 15 Objective Processes
  306.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  307.    wt: 1:   Chapter 12 Islands and Divisions of Knowledge
  308.    wt: 1:   Chapter 11 Accidental Patterns
  309.    wt: 1:   Chapter 10 Responsibility
  310.    wt: 1:   Chapter 9 What is in Chapters 10 to 18
  311.    wt: 1:   Chapter 8 Change of Language
  312.    wt: 1:   Chapter 7 Longer Chains of Reason
  313.    wt: 1:   Chapter 6 Chains of Reason
  314.    wt: 1:   Chapter 5 Deception
  315.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  316.    wt: 1:   Chapter 3 What is in chapters 4 to 8
  317.    wt: 1:   Chapter 2 Skill Development
  318.    wt: 1:   Chapter 1 Introduction
  319.    wt: 1:   Three Remarks
  320.    wt: 1:   Foreword
  321.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  322.    wt: 1:   R Why Learn Mathematics Skills
  323.    wt: 1:   O On Learning Mathematics and Science
  324.    wt: 1:   N Mathematics Prepare for College Studies
  325.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  326.    wt: 1:   Chapter 8 Skipped Topics and Why
  327.    wt: 1:   Chapter 7 Calculus Previews and Calculus Lightly
  328.    wt: 1:   Chapter 6 More Algebra and Geometry
  329.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  330.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  331.    wt: 1:   Chapter 3 Algebra Starter Lessons
  332.    wt: 1:   Chapter 2 Why Sets
  333.    wt: 1:   Chapter 1 Arithmetic
  334.    wt: 1:   Primary and Secondary Skills and Practices with Take Home Value
  335.    wt: 1:   7 Games and Activities for Instruction
  336.    wt: 1:   6 Measuring via counting or arithmetic the role of fractions
  337.    wt: 1:   5 Interpreting and Drawing Maps and Plans.
  338.    wt: 1:   4 Money Matters Saving Earning Buying Selling and Budgets
  339.    wt: 1:   3 Telling Tracking Time Temporal and More Place Sense
  340.    wt: 1:   2 Identifying Size and Position Place and Spatial Sense
  341.    wt: 1:   1 From Number Recognition and Counting to Arithmetic B
  342.    wt: 1:   1 From Number Recognition and Counting to Arithmetic A
  343.    wt: 1:   Ends Values Methods For Skill Development Framework Prequel
  344.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  345.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  346.    wt: 1:   More Algebra and Slope based Calculus Preview
  347.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  348.    wt: 1:   Systematic Algebra Skill Development Missing Links
  349.    wt: 1:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  350.    wt: 1:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  351.    wt: 1:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  352.    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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