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:   10 Examples of Algebraic Reasoning/
  8.    wt: 1:   Step 2 Algebraic solutions for one unknown/
  9.    wt: 1:   12 Webvideo Lessons on Area and Volume Calculation/
  10.    wt: 1:   Advanced Calculus Volume 3 Appendices/
  11.    wt: 1:   Volume 3 Why Slopes A Calculus Intro Etc/
  12.    wt: 1:   Volume 2 Three Skills For Algebra/
  13.    wt: 1:   Volume 1A Pattern Based Reason/
  14.    wt: 1:   Volume 1 Elements of Reason/
  15.    wt: 1:   Mathematics 506 Lessons/
  16.    wt: 1:   Secondary Mathematics A Practical Approach/
  17.    wt: 1:   PreSchool and Primary Mathematics or Quantitative Skills/
  18.    wt: 1:   Mathematics Skill Development Framework/

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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 difficulties
  16.    wt: 1:   teaching tutoring algebraic reason
  17.    wt: 1:   Lessening Algebra Difficulties
  18.    wt: 1:   three goals for Mathematics Education
  19.    wt: 1:   02 20 mathematics education references
  20.    wt: 1:   three aims for mathematics students
  21.    wt: 1:   mathematics instruction in general
  22.    wt: 1:   Education in mathematics science and technology
  23.    wt: 1:   three kinds of reason in mathematics
  24.    wt: 1:   words for mathematics instructor
  25.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  26.    wt: 1:   22 Student Centered Highschool Mathematics
  27.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  28.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  29.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  30.    wt: 1:   18 Primary School Mathematics
  31.    wt: 1:   16 Secondary Mathematics Tips
  32.    wt: 1:   12 Goals and Objectives For Mathematics
  33.    wt: 1:   4 Function notation in and beyond mathematics
  34.    wt: 1:   2 Algebraic use of function notation
  35.    wt: 1:   8 Notes for instructors or tutors
  36.    wt: 1:   Rewriting algebraic substitution as function substitutions
  37.    wt: 1:   12 From Applied To Pure Mathematics
  38.    wt: 1:   5 Algebraic View of Slopes
  39.    wt: 1:   3 Inequalities Algebraically
  40.    wt: 1:   2 Algebraic View
  41.    wt: 1:   6 Algebraic Solution Example
  42.    wt: 1:   5 Algebraic Solutions Introduction
  43.    wt: 1:   Skill Development Notes
  44.    wt: 1:   11 Volume of Sphere
  45.    wt: 1:   10 Volume of Pyramid
  46.    wt: 1:   9 Volume of Cone
  47.    wt: 1:   5 Box Volume Formula Example
  48.    wt: 1:   13 Fraction Comparison Algebraic View
  49.    wt: 1:   11 Simplification an Algebraic View
  50.    wt: 1:   6 Multiplication Algebraically Take II
  51.    wt: 1:   7 Calculator Usage Notes and Cautions
  52.    wt: 1:   Example 2 volume of a cone
  53.    wt: 1:   Example 1 volume of a pyramid
  54.    wt: 1:   Volume of Solid by Cross Sections Lesson
  55.    wt: 1:   A Related Material in Volume 3
  56.    wt: 1:   A Related lessons in Volume 3
  57.    wt: 1:   2 Algebraic codification
  58.    wt: 1:   E2 Algebraic Properties of Limits
  59.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  60.    wt: 1:   Appendix E. How To Study Mathematics and Why
  61.    wt: 1:   Postscript B Mathematics Education References
  62.    wt: 1:   Chapter 6 Rule Based Reason in Mathematics
  63.    wt: 1:   Chapter 3 Algebra Difficulties
  64.    wt: 1:   Chapter 2 For and Against Mathematics
  65.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  66.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  67.    wt: 1:   R Why Learn Mathematics Skills
  68.    wt: 1:   O On Learning Mathematics and Science
  69.    wt: 1:   N Mathematics Prepare for College Studies
  70.    wt: 1:   Helping the Blind in Logic and Mathematics
  71.    wt: 1:   Mathematics Education References
  72.    wt: 1:   Mathematics Education References
  73.    wt: 1:   Multiple Ways to Improve Mathematics Skill Development
  74.    wt: 1:   Implementation Notes
  75.    wt: 1:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years

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357 matches:

  1.    wt: 7:   Postscript B Mathematics Education References
  2.    wt: 7:   Chapter 6 Rule Based Reason in Mathematics
  3.    wt: 7:   Chapter 3 Algebra Difficulties
  4.    wt: 7:   Chapter 2 For and Against Mathematics
  5.    wt: 6:   Annotated Links to Material Elsehwere
  6.    wt: 6:   Postscript A Three Remarks
  7.    wt: 6:   Chapter 12 Four Phases
  8.    wt: 6:   Chapter 11 Elementary Instruction
  9.    wt: 6:   Chapter 10 Transition
  10.    wt: 6:   Chapter 9 The Two Ends
  11.    wt: 6:   Chapter 8 Modern Instruction
  12.    wt: 6:   Chapter 7 Two Treatments of Geometry
  13.    wt: 6:   Chapter 5 Four References
  14.    wt: 6:   Chapter 4 Complex Numbers and Why Slopes
  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 difficulties
  32.    wt: 2:   teaching tutoring algebraic reason
  33.    wt: 2:   Lessening Algebra Difficulties
  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:   mathematics instruction in general
  38.    wt: 2:   Education in mathematics science and technology
  39.    wt: 2:   three kinds of reason in mathematics
  40.    wt: 2:   words for mathematics instructor
  41.    wt: 2:   3 Inequalities Algebraically
  42.    wt: 2:   6 Algebraic Solution Example
  43.    wt: 2:   5 Algebraic Solutions Introduction
  44.    wt: 2:   Example 2 volume of a cone
  45.    wt: 2:   Example 1 volume of a pyramid
  46.    wt: 2:   Volume of Solid by Cross Sections Lesson
  47.    wt: 2:   E2 Algebraic Properties of Limits
  48.    wt: 2:   Chapter 15. Algebraic Evaluation of Limits
  49.    wt: 2:   Appendix E. How To Study Mathematics and Why
  50.    wt: 2:   Chapter 14 Deductive and Empirical Views of Mathematics
  51.    wt: 2:   Helping the Blind in Logic and Mathematics
  52.    wt: 2:   Mathematics Education References
  53.    wt: 2:   Mathematics Education References
  54.    wt: 2:   Multiple Ways to Improve Mathematics Skill Development
  55.    wt: 2:   Implementation Notes
  56.    wt: 2:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  57.    wt: 1:   Appendix 2 primary school Arithmetic 01
  58.    wt: 1:   Appendix 1 primary and preschool mathematic
  59.    wt: 1:   K LAMP Musings Science Education
  60.    wt: 1:   J LAMP Introduction Extrinsic Origins
  61.    wt: 1:   I LAMP Introduction Study Habits
  62.    wt: 1:   H LAMP Introduction Instructional Concepts
  63.    wt: 1:   G LAMP Introduction Problem Solving Skills
  64.    wt: 1:   F LAMP Introduction Prerequisites
  65.    wt: 1:   A Introduction Objectives
  66.    wt: 1:   Skills Chapter 5 Calculus
  67.    wt: 1:   Skills Chapter 4 Logic
  68.    wt: 1:   Ramblings Extrinsic numbers theory
  69.    wt: 1:   Ramblings Introduction Algebra Essay
  70.    wt: 1:   Skills Chapter 3 Algebra
  71.    wt: 1:   Skills Chapter 2 Geometry
  72.    wt: 1:   Skills Chapter 1 Arithmetic
  73.    wt: 1:   Skills Chapter 0 Introduction
  74.    wt: 1:   10 statistics
  75.    wt: 1:   9 combinatorics probability sets
  76.    wt: 1:   8 analytic geometry etc
  77.    wt: 1:   7 logic review and decimals an odd combination
  78.    wt: 1:   6 polynomials etc
  79.    wt: 1:   5 logarithms and exponentials etc
  80.    wt: 1:   4 algebra
  81.    wt: 1:   3 Euclidean Geometry Leanly
  82.    wt: 1:   2 arithmetic with signed numbers
  83.    wt: 1:   1 arithmetic with unsigned numbers
  84.    wt: 1:   What is POMME
  85.    wt: 1:   why bother
  86.    wt: 1:   which way to go
  87.    wt: 1:   website reviews
  88.    wt: 1:   three goals to set for students
  89.    wt: 1:   Teach the teachers plus goals
  90.    wt: 1:   permissions for teachers
  91.    wt: 1:   Math Ed if it must be short make it lean effective
  92.    wt: 1:   Applied Maths Program14092009 POMME variant
  93.    wt: 1:   activities for students
  94.    wt: 1:   links Education Resources online
  95.    wt: 1:   site origins
  96.    wt: 1:   site eurekas
  97.    wt: 1:   About site lesson plans
  98.    wt: 1:   teacher certification
  99.    wt: 1:   modern education
  100.    wt: 1:   learning takes time
  101.    wt: 1:   grouping students according to ability
  102.    wt: 1:   what should be learnt and When
  103.    wt: 1:   Postscript 2007 01 10
  104.    wt: 1:   Education Reform Inconsistencies
  105.    wt: 1:   five decades make a difference
  106.    wt: 1:   Maps Plans Drawings
  107.    wt: 1:   how letters appear
  108.    wt: 1:   talk the algebra talk
  109.    wt: 1:   teaching tips
  110.    wt: 1:   What to Tell Students
  111.    wt: 1:   geometric implications for algebra
  112.    wt: 1:   the trouble with algebra
  113.    wt: 1:   05 13 OldSiteEntrancePage
  114.    wt: 1:   04 25 when to stop or suspend mathemat
  115.    wt: 1:   02 21 words for teachers
  116.    wt: 1:   standards for course material
  117.    wt: 1:   Operational Viewpoint to Value
  118.    wt: 1:   formal or informal peer review
  119.    wt: 1:   Theory of Knowledge
  120.    wt: 1:   Different Kinds of Reasoning in maths
  121.    wt: 1:   cultivating intelligence
  122.    wt: 1:   Four ways to improve education reform
  123.    wt: 1:   How to be a better instructor
  124.    wt: 1:   Motivation and Context Problem
  125.    wt: 1:   Prequel In For A Penny In For A Pound
  126.    wt: 1:   education an empirical art
  127.    wt: 1:   fairness and inductive principles for instruction
  128.    wt: 1:   chapitre 12 00 les iles et division
  129.    wt: 1:   chapitre 07 01 principle D induction mathematique
  130.    wt: 1:   chapitre 07 00 Des chaines plus longues de la raison
  131.    wt: 1:   chapitre 06 00 Chaines de la raison
  132.    wt: 1:   chapitre 05 00 Deception
  133.    wt: 1:   chapitre 04 10 Etapes pour une meilleur raison
  134.    wt: 1:   chapitre 04 09 Regles accidentelles
  135.    wt: 1:   chapitre 04 08 Limitations et benefices
  136.    wt: 1:   chapitre 04 07 RepetablesEtReproductibles
  137.    wt: 1:   chapitre 04 06 engagements
  138.    wt: 1:   chapitre 04 05 Implication versus suggestion
  139.    wt: 1:   chapitre 04 04 Parlons de la logique
  140.    wt: 1:   chapitre 04 03 Unidirectionnel versus bidirectionnel
  141.    wt: 1:   chapitre 04 02 Deuxieme enigme
  142.    wt: 1:   chapitre 04 01 Premiere enigme
  143.    wt: 1:   chapitre 04 00 Les regles d implication
  144.    wt: 1:   chapitre 03 A Propos Des Prochains Chapitre
  145.    wt: 1:   chapitre 02 00 La Communication des idees
  146.    wt: 1:   chapitre 01 00 Introduction
  147.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  148.    wt: 1:   22 Student Centered Highschool Mathematics
  149.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  150.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  151.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  152.    wt: 1:   18 Primary School Mathematics
  153.    wt: 1:   16 Secondary Mathematics Tips
  154.    wt: 1:   12 Goals and Objectives For Mathematics
  155.    wt: 1:   Ages 12 to 14 Skills with take home value
  156.    wt: 1:   Ages 12 to 14 Geometry
  157.    wt: 1:   Ages 12 to 14 Arithmetic
  158.    wt: 1:   Ages 10 to 12 Geometry
  159.    wt: 1:   Ages 10 to 12 Arithmetic
  160.    wt: 1:   Ages 9 to 10
  161.    wt: 1:   Ages 8 to 9
  162.    wt: 1:   Ages 7 to 8
  163.    wt: 1:   Ages 6 to 7
  164.    wt: 1:   Ages 4 plus to 5 plus
  165.    wt: 1:   Ages 3 plus to 4 plus
  166.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  167.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  168.    wt: 1:   4 Function notation in and beyond mathematics
  169.    wt: 1:   2 Algebraic use of function notation
  170.    wt: 1:   8 Notes for instructors or tutors
  171.    wt: 1:   Rewriting algebraic substitution as function substitutions
  172.    wt: 1:   12 From Applied To Pure Mathematics
  173.    wt: 1:   5 Algebraic View of Slopes
  174.    wt: 1:   5 Areas of Rectangles Revisited
  175.    wt: 1:   4 Fraction Operations Axiomatic Development
  176.    wt: 1:   2 Fraction Operations Physical Development
  177.    wt: 1:   1 Decimals Modular and Remainder Arithmetic
  178.    wt: 1:   2 Algebraic View
  179.    wt: 1:   4 Four Examples Fractional Coefficients
  180.    wt: 1:   3 Four Examples
  181.    wt: 1:   2 Three Examples
  182.    wt: 1:   1 Proper Equal Sign Usage
  183.    wt: 1:   Skill Development Notes
  184.    wt: 1:   11 Volume of Sphere
  185.    wt: 1:   10 Volume of Pyramid
  186.    wt: 1:   9 Volume of Cone
  187.    wt: 1:   5 Box Volume Formula Example
  188.    wt: 1:   13 Fraction Comparison Algebraic View
  189.    wt: 1:   11 Simplification an Algebraic View
  190.    wt: 1:   6 Multiplication Algebraically Take II
  191.    wt: 1:   7 Calculator Usage Notes and Cautions
  192.    wt: 1:   Example 1. Area Between x and x squared
  193.    wt: 1:   Area Between Crossing Curves Lesson Take 2
  194.    wt: 1:   Area Between Crossing Curves Lesson Take 1
  195.    wt: 1:   Example 4 with x function of y
  196.    wt: 1:   Example 3
  197.    wt: 1:   Example 2
  198.    wt: 1:   Example 1
  199.    wt: 1:   Area Between Curves Lesson Take 2
  200.    wt: 1:   Area Between Curves Lesson Take 1
  201.    wt: 1:   Summary
  202.    wt: 1:   A Related Material in Volume 3
  203.    wt: 1:   A Related lessons in Volume 3
  204.    wt: 1:   2 Algebraic codification
  205.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  206.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  207.    wt: 1:   G.1 First Fundamental Theorem of Calculus
  208.    wt: 1:   G.6 Bounded Derivatives implies Lipshitz Continuity
  209.    wt: 1:   G.5 Motions With Bounded Velocities
  210.    wt: 1:   G.4 Lipschitz Continuity implies EquiContinuity
  211.    wt: 1:   G.3 Constant Difference Theorem Proof
  212.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  213.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  214.    wt: 1:   F.5b Extreme Value Theorem
  215.    wt: 1:   F.5a Equicontinuity Theorems
  216.    wt: 1:   F.4 Finite Covering Theorem
  217.    wt: 1:   F.3 Intermediate Value Theorem
  218.    wt: 1:   F.2 Closed Range Theorem
  219.    wt: 1:   F.1 What Functions are Continuous
  220.    wt: 1:   E1 Error Control Inequalities
  221.    wt: 1:   D2 Limits of Monotone Sequences
  222.    wt: 1:   D1 Sets and Sequences GLBs and LGBs
  223.    wt: 1:   C Triangle Inequalities
  224.    wt: 1:   B3 Bolzano Weierstrass Theorem
  225.    wt: 1:   B1 Pigeon Hole Principles from combinatorics
  226.    wt: 1:   PostScript For and Against Decimal Perspectives
  227.    wt: 1:   A1. Introduction
  228.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  229.    wt: 1:   Postscript Pythagorean Theorem yet another proof
  230.    wt: 1:   Chapter 24 Logarithms Powers and Exponentials
  231.    wt: 1:   Chapter 23 Links To Trigonometry
  232.    wt: 1:   Chapter 22 Complex Numbers
  233.    wt: 1:   Chapter 21 Arrow Addition
  234.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  235.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  236.    wt: 1:   Chapter 18. Slopes Areas Integration
  237.    wt: 1:   Chapter 17. Area Approximation
  238.    wt: 1:   Chapter 16. Velocity Approximation
  239.    wt: 1:   Chapter 15. Slope Approximation
  240.    wt: 1:   Chapter 14 Limits and Continuity with and sans Decimals
  241.    wt: 1:   Chapter 13. Acceleration
  242.    wt: 1:   Chapter 12. Units and Slopes
  243.    wt: 1:   Chapter 11. Graphing Slope versus Position
  244.    wt: 1:   Chapter 10 Slopes and Units
  245.    wt: 1:   Chapter 9 About First Courses in Calculus
  246.    wt: 1:   Chapter 8. Slope Interpretation
  247.    wt: 1:   Chapter 7 Slopes and Velocity
  248.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  249.    wt: 1:   Chapter 5. Slope Sign Tests
  250.    wt: 1:   Chapter 4. More Slope Sign Analysis
  251.    wt: 1:   Chapter 3. Slope Sign Analysis
  252.    wt: 1:   Chapter 2. Slopes and Ski Trails
  253.    wt: 1:   Chapter 1.Introduction
  254.    wt: 1:   Fall 1983 Calculus Appetizer
  255.    wt: 1:   Foreword
  256.    wt: 1:   Postscript More on Better Performance
  257.    wt: 1:   Postscript For Better Performance
  258.    wt: 1:   Appendix D. What to do in School and Why
  259.    wt: 1:   Appendix C. How to Read
  260.    wt: 1:   Appendix B. How To Learn
  261.    wt: 1:   Appendix A. Reading Guide For Next Appendices
  262.    wt: 1:   Chapter 31 Direct and Indirect Reason
  263.    wt: 1:   Chapter 30 Truth Tables
  264.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  265.    wt: 1:   Chapter 28 Occurrence Tables
  266.    wt: 1:   Chapter 27 Shorthand Symbols as Pronouns
  267.    wt: 1:   Chapter 26 What is in chapters 27 to 31
  268.    wt: 1:   Chapter 25. Mathematical Induction Examples
  269.    wt: 1:   Chapter 24. Personal Investment and Pension EGS
  270.    wt: 1:   Chapter 23. Notation For Sums
  271.    wt: 1:   Chapter 22. Geometric Sums and Sequences
  272.    wt: 1:   Chapter 21. Third Reading Guide
  273.    wt: 1:   Chapter 20. Degrees and Radians
  274.    wt: 1:   Chapter 19. Functions and Sets
  275.    wt: 1:   Chapter 18. Rules for Algebra
  276.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  277.    wt: 1:   Chapter 16. Painless Theorem Proving
  278.    wt: 1:   Chapter 15. Solving Linear Equations
  279.    wt: 1:   Chapter 14. Forward and Backward Use of a Formula
  280.    wt: 1:   Postscript Unifying Theme A Fourth Skill For Algebra
  281.    wt: 1:   Chapter 13. Second Reading Guide
  282.    wt: 1:   Chapter 12. Shorthand Usage Guide
  283.    wt: 1:   Chapter 11. Why Shorthand
  284.    wt: 1:   Chapter 10 Describing and Changing Calculations
  285.    wt: 1:   Postscript What is a Variable
  286.    wt: 1:   Chapter 9 Talking about Numbers or Quantities
  287.    wt: 1:   Chapter 8 Three Skills For Algebra
  288.    wt: 1:   Solutions For Arithmetic Exercises
  289.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  290.    wt: 1:   Chapter 6 Change of Language
  291.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  292.    wt: 1:   Chapter 4 Longer Chains of Reason
  293.    wt: 1:   Chapter 3 Chains of Reason
  294.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  295.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  296.    wt: 1:   Foreword
  297.    wt: 1:   Postscript D Reflections on Law of the Excluded Middle
  298.    wt: 1:   Postscript C Consistency as a Tool for Reason
  299.    wt: 1:   Postscript B More on Story Telling and Reason
  300.    wt: 1:   Postscript A Story Telling
  301.    wt: 1:   Chapter 24 Direct and Indirect Reason
  302.    wt: 1:   Chapter 23 Truth Tables
  303.    wt: 1:   Chapter 22 Contrapositive and Vacuously True Implications
  304.    wt: 1:   Chapter 21 Occurrence Tables
  305.    wt: 1:   Chapter 20 Shorthand Symbols as Pronouns
  306.    wt: 1:   Chapter 19 What is in chapters 20 to 24
  307.    wt: 1:   Chapter 18 Sense and Knowledge
  308.    wt: 1:   Chapter 17 Objective Ways Trial and Error Discovery
  309.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  310.    wt: 1:   Chapter 15 Objective Processes
  311.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  312.    wt: 1:   Chapter 12 Islands and Divisions of Knowledge
  313.    wt: 1:   Chapter 11 Accidental Patterns
  314.    wt: 1:   Chapter 10 Responsibility
  315.    wt: 1:   Chapter 9 What is in Chapters 10 to 18
  316.    wt: 1:   Chapter 8 Change of Language
  317.    wt: 1:   Chapter 7 Longer Chains of Reason
  318.    wt: 1:   Chapter 6 Chains of Reason
  319.    wt: 1:   Chapter 5 Deception
  320.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  321.    wt: 1:   Chapter 3 What is in chapters 4 to 8
  322.    wt: 1:   Chapter 2 Skill Development
  323.    wt: 1:   Chapter 1 Introduction
  324.    wt: 1:   Three Remarks
  325.    wt: 1:   Foreword
  326.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  327.    wt: 1:   R Why Learn Mathematics Skills
  328.    wt: 1:   O On Learning Mathematics and Science
  329.    wt: 1:   N Mathematics Prepare for College Studies
  330.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  331.    wt: 1:   Chapter 8 Skipped Topics and Why
  332.    wt: 1:   Chapter 7 Calculus Previews and Calculus Lightly
  333.    wt: 1:   Chapter 6 More Algebra and Geometry
  334.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  335.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  336.    wt: 1:   Chapter 3 Algebra Starter Lessons
  337.    wt: 1:   Chapter 2 Why Sets
  338.    wt: 1:   Chapter 1 Arithmetic
  339.    wt: 1:   Primary and Secondary Skills and Practices with Take Home Value
  340.    wt: 1:   7 Games and Activities for Instruction
  341.    wt: 1:   6 Measuring via counting or arithmetic the role of fractions
  342.    wt: 1:   5 Interpreting and Drawing Maps and Plans.
  343.    wt: 1:   4 Money Matters Saving Earning Buying Selling and Budgets
  344.    wt: 1:   3 Telling Tracking Time Temporal and More Place Sense
  345.    wt: 1:   2 Identifying Size and Position Place and Spatial Sense
  346.    wt: 1:   1 From Number Recognition and Counting to Arithmetic B
  347.    wt: 1:   1 From Number Recognition and Counting to Arithmetic A
  348.    wt: 1:   Ends Values Methods For Skill Development Framework Prequel
  349.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  350.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  351.    wt: 1:   More Algebra and Slope based Calculus Preview
  352.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  353.    wt: 1:   Systematic Algebra Skill Development Missing Links
  354.    wt: 1:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  355.    wt: 1:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  356.    wt: 1:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  357.    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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