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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16 matches:

  1.    wt: 6:   Volume 1B Mathematics Curriculum Notes/
  2.    wt: 2:   Volume 2 Three Skills For Algebra/
  3.    wt: 1:   LAMP Lean Applied Mathematics Program/
  4.    wt: 1:   Progressive Observable Motivated Mathematics Education/
  5.    wt: 1:   Mathematics Education Essays/
  6.    wt: 1:   Volume 1A Regles et modeles/
  7.    wt: 1:   Mathematics Skills Year by Year/
  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 1A Pattern Based Reason/
  12.    wt: 1:   Volume 1 Elements of Reason/
  13.    wt: 1:   Mathematics 506 Lessons/
  14.    wt: 1:   Secondary Mathematics A Practical Approach/
  15.    wt: 1:   PreSchool and Primary Mathematics or Quantitative Skills/
  16.    wt: 1:   Mathematics Skill Development Framework/

Web Page Search

81 matches:

  1.    wt: 2:   Secondary Three Mathematics
  2.    wt: 2:   mathematics curriculum shifts
  3.    wt: 2:   three goals for Mathematics Education
  4.    wt: 2:   04 29 New Mathematics Curriculum
  5.    wt: 2:   three aims for mathematics students
  6.    wt: 2:   three kinds of reason in mathematics
  7.    wt: 2:   need for a mixed mathematics curriculum
  8.    wt: 2:   Leaner mathematics curriculum
  9.    wt: 2:   Postscript A Three Remarks
  10.    wt: 2:   Three Remarks
  11.    wt: 1:   E LAMP Introduction Modern Mathematics
  12.    wt: 1:   C LAMP Introduction Culture in Mathematics Education
  13.    wt: 1:   B LAMP Introduction Curriculum Development Standards
  14.    wt: 1:   11 pure mathematics
  15.    wt: 1:   three goals to set for students
  16.    wt: 1:   key notes and themes
  17.    wt: 1:   Mathematics Education Professors
  18.    wt: 1:   mathematics in context
  19.    wt: 1:   Secondary Two Mathematics
  20.    wt: 1:   Secondary One Mathematics
  21.    wt: 1:   three difficulties
  22.    wt: 1:   02 20 mathematics education references
  23.    wt: 1:   mathematics instruction in general
  24.    wt: 1:   Education in mathematics science and technology
  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:   8 The Effect of Negative Remarks
  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:   4 Equations for lines three forms
  39.    wt: 1:   C Three Decimal Subtraction Methods
  40.    wt: 1:   2 Essentially one exercises three with solution
  41.    wt: 1:   2 Three Examples
  42.    wt: 1:   Skill Development Notes
  43.    wt: 1:   9 Three Examples
  44.    wt: 1:   6 Three Examples
  45.    wt: 1:   5 Three Examples
  46.    wt: 1:   2 Three Examples
  47.    wt: 1:   11 Volume of Sphere
  48.    wt: 1:   10 Volume of Pyramid
  49.    wt: 1:   9 Volume of Cone
  50.    wt: 1:   5 Box Volume Formula Example
  51.    wt: 1:   6 Three Notions of What is a Variable
  52.    wt: 1:   1 Three Skills For Algebra
  53.    wt: 1:   D Three Term Ratios
  54.    wt: 1:   7 Calculator Usage Notes and Cautions
  55.    wt: 1:   4 Two and Three Digit Multipliers
  56.    wt: 1:   Appendix 2 Three Decimal Subtraction Methods
  57.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  58.    wt: 1:   1 Place Value in Three Digit Whole Numbers
  59.    wt: 1:   Example 2 volume of a cone
  60.    wt: 1:   Example 1 volume of a pyramid
  61.    wt: 1:   Volume of Solid by Cross Sections Lesson
  62.    wt: 1:   A Related Material in Volume 3
  63.    wt: 1:   A Related lessons in Volume 3
  64.    wt: 1:   11 Limits at infinity Three Examples
  65.    wt: 1:   10 Three one sided limits with infinite values
  66.    wt: 1:   Appendix E. How To Study Mathematics and Why
  67.    wt: 1:   Chapter 8 Three Skills For Algebra
  68.    wt: 1:   Postscript B Mathematics Education References
  69.    wt: 1:   Chapter 6 Rule Based Reason in Mathematics
  70.    wt: 1:   Chapter 2 For and Against Mathematics
  71.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  72.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  73.    wt: 1:   R Why Learn Mathematics Skills
  74.    wt: 1:   O On Learning Mathematics and Science
  75.    wt: 1:   N Mathematics Prepare for College Studies
  76.    wt: 1:   Helping the Blind in Logic and Mathematics
  77.    wt: 1:   Mathematics Education References
  78.    wt: 1:   Mathematics Education References
  79.    wt: 1:   Multiple Ways to Improve Mathematics Skill Development
  80.    wt: 1:   Implementation Notes
  81.    wt: 1:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years

Extended Search

356 matches:

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