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

Logic mastery strengthens comprehension and improve home, work & study habits.
Logic 5 Chapters Arithmetic 10 Steps Algebra 12 Starter Steps & 5 Advanced Steps
Work & Study 23 Tips Geometry 15 Steps Calculus 70 Lessons

Ages 15+: Why study slopes Polynomials Quadratics Why factor polynomials Logarithms Functions
What is similarity Euclidean geometry leanly Coordinates + complex no.s Vectors DC Electric Circuits

Ages 12+: Prime factorization Written work formats Decimal place value Extend arithmetic skills orally
What is a variable 5. Fraction Operations by Raising Terms Solving Linear Equations: Take I Take II


Online Volumes: 1 - Elements of Reason, 2 - 3 Skills For Algebra, 3 - Why Slopes and
More Math
, 1A - Pattern Based Reason, 1B - Skill Development Principles + Troubles
Forewords + leading chapters give original reasons, still valid, for site content & growth.

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

Teachers & Tutors: This December 2011, 5-phase framework offers a context for mathematics & logic education. Phases 1 to 3 may focus on skills with actual or potential local value for adult & daily life. College-oriented phases 5 & 4 focus on calculus & preparation for it. Phases 1 to 4 may also serve trades & professions not dependent on calculus. Reform: look before you leap - plan all in detail first.

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

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  1.    wt: 6:   Volume 1B Mathematics Curriculum Notes/
  2.    wt: 3:   PreSchool and Primary Mathematics or Quantitative Skills/
  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 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:   Mathematics Skill Development Framework/

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66 matches:

  1.    wt: 3:   18 Primary School Mathematics
  2.    wt: 2:   Appendix 2 primary school Arithmetic 01
  3.    wt: 2:   Appendix 1 primary and preschool mathematic
  4.    wt: 2:   mathematics curriculum shifts
  5.    wt: 2:   04 29 New Mathematics Curriculum
  6.    wt: 2:   need for a mixed mathematics curriculum
  7.    wt: 2:   Leaner mathematics curriculum
  8.    wt: 2:   22 Student Centered Highschool Mathematics
  9.    wt: 2:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  10.    wt: 2:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  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:   key notes and themes
  16.    wt: 1:   Mathematics Education Professors
  17.    wt: 1:   mathematics in context
  18.    wt: 1:   Secondary Three Mathematics
  19.    wt: 1:   Secondary Two Mathematics
  20.    wt: 1:   Secondary One Mathematics
  21.    wt: 1:   three goals for Mathematics Education
  22.    wt: 1:   02 20 mathematics education references
  23.    wt: 1:   three aims for mathematics students
  24.    wt: 1:   mathematics instruction in general
  25.    wt: 1:   Education in mathematics science and technology
  26.    wt: 1:   three kinds of reason in mathematics
  27.    wt: 1:   words for mathematics instructor
  28.    wt: 1:   Home Tutoring and Home Schooling
  29.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  30.    wt: 1:   19 Extending the Oral Dimension of 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:   8 Notes for instructors or tutors
  35.    wt: 1:   12 From Applied To Pure Mathematics
  36.    wt: 1:   Skill Development Notes
  37.    wt: 1:   11 Volume of Sphere
  38.    wt: 1:   10 Volume of Pyramid
  39.    wt: 1:   9 Volume of Cone
  40.    wt: 1:   5 Box Volume Formula Example
  41.    wt: 1:   7 Calculator Usage Notes and Cautions
  42.    wt: 1:   015 School and work day counting tables
  43.    wt: 1:   2 Time and Date Matters in School
  44.    wt: 1:   Example 2 volume of a cone
  45.    wt: 1:   Example 1 volume of a pyramid
  46.    wt: 1:   Volume of Solid by Cross Sections Lesson
  47.    wt: 1:   A Related Material in Volume 3
  48.    wt: 1:   A Related lessons in Volume 3
  49.    wt: 1:   Appendix E. How To Study Mathematics and Why
  50.    wt: 1:   Appendix D. What to do in School and Why
  51.    wt: 1:   Postscript B Mathematics Education References
  52.    wt: 1:   Chapter 6 Rule Based Reason in Mathematics
  53.    wt: 1:   Chapter 2 For and Against Mathematics
  54.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  55.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  56.    wt: 1:   R Why Learn Mathematics Skills
  57.    wt: 1:   O On Learning Mathematics and Science
  58.    wt: 1:   N Mathematics Prepare for College Studies
  59.    wt: 1:   Primary and Secondary Skills and Practices with Take Home Value
  60.    wt: 1:   Helping the Blind in Logic and Mathematics
  61.    wt: 1:   Mathematics Education References
  62.    wt: 1:   Mathematics Education References
  63.    wt: 1:   Multiple Ways to Improve Mathematics Skill Development
  64.    wt: 1:   Implementation Notes
  65.    wt: 1:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  66.    wt: 1:   Mathematics Teacher Certification Best Practices

Extended Search

342 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: 4:   Primary and Secondary Skills and Practices with Take Home Value
  18.    wt: 3:   Appendix 2 primary school Arithmetic 01
  19.    wt: 3:   Appendix 1 primary and preschool mathematic
  20.    wt: 3:   mathematics curriculum shifts
  21.    wt: 3:   04 29 New Mathematics Curriculum
  22.    wt: 3:   need for a mixed mathematics curriculum
  23.    wt: 3:   Leaner mathematics curriculum
  24.    wt: 3:   18 Primary School Mathematics
  25.    wt: 3:   7 Games and Activities for Instruction
  26.    wt: 3:   6 Measuring via counting or arithmetic the role of fractions
  27.    wt: 3:   5 Interpreting and Drawing Maps and Plans.
  28.    wt: 3:   4 Money Matters Saving Earning Buying Selling and Budgets
  29.    wt: 3:   3 Telling Tracking Time Temporal and More Place Sense
  30.    wt: 3:   2 Identifying Size and Position Place and Spatial Sense
  31.    wt: 3:   1 From Number Recognition and Counting to Arithmetic B
  32.    wt: 3:   1 From Number Recognition and Counting to Arithmetic A
  33.    wt: 2:   E LAMP Introduction Modern Mathematics
  34.    wt: 2:   C LAMP Introduction Culture in Mathematics Education
  35.    wt: 2:   B LAMP Introduction Curriculum Development Standards
  36.    wt: 2:   11 pure mathematics
  37.    wt: 2:   key notes and themes
  38.    wt: 2:   Mathematics Education Professors
  39.    wt: 2:   mathematics in context
  40.    wt: 2:   Secondary Three Mathematics
  41.    wt: 2:   Secondary Two Mathematics
  42.    wt: 2:   Secondary One Mathematics
  43.    wt: 2:   three goals for Mathematics Education
  44.    wt: 2:   02 20 mathematics education references
  45.    wt: 2:   three aims for mathematics students
  46.    wt: 2:   mathematics instruction in general
  47.    wt: 2:   Education in mathematics science and technology
  48.    wt: 2:   three kinds of reason in mathematics
  49.    wt: 2:   words for mathematics instructor
  50.    wt: 2:   22 Student Centered Highschool Mathematics
  51.    wt: 2:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  52.    wt: 2:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  53.    wt: 2:   Example 2 volume of a cone
  54.    wt: 2:   Example 1 volume of a pyramid
  55.    wt: 2:   Volume of Solid by Cross Sections Lesson
  56.    wt: 2:   Appendix E. How To Study Mathematics and Why
  57.    wt: 2:   Appendix D. What to do in School and Why
  58.    wt: 2:   Chapter 14 Deductive and Empirical Views of Mathematics
  59.    wt: 2:   Helping the Blind in Logic and Mathematics
  60.    wt: 2:   Mathematics Education References
  61.    wt: 2:   Mathematics Education References
  62.    wt: 2:   Multiple Ways to Improve Mathematics Skill Development
  63.    wt: 2:   Implementation Notes
  64.    wt: 2:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  65.    wt: 1:   K LAMP Musings Science Education
  66.    wt: 1:   J LAMP Introduction Extrinsic Origins
  67.    wt: 1:   I LAMP Introduction Study Habits
  68.    wt: 1:   H LAMP Introduction Instructional Concepts
  69.    wt: 1:   G LAMP Introduction Problem Solving Skills
  70.    wt: 1:   F LAMP Introduction Prerequisites
  71.    wt: 1:   A Introduction Objectives
  72.    wt: 1:   Skills Chapter 5 Calculus
  73.    wt: 1:   Skills Chapter 4 Logic
  74.    wt: 1:   Ramblings Extrinsic numbers theory
  75.    wt: 1:   Ramblings Introduction Algebra Essay
  76.    wt: 1:   Skills Chapter 3 Algebra
  77.    wt: 1:   Skills Chapter 2 Geometry
  78.    wt: 1:   Skills Chapter 1 Arithmetic
  79.    wt: 1:   Skills Chapter 0 Introduction
  80.    wt: 1:   10 statistics
  81.    wt: 1:   9 combinatorics probability sets
  82.    wt: 1:   8 analytic geometry etc
  83.    wt: 1:   7 logic review and decimals an odd combination
  84.    wt: 1:   6 polynomials etc
  85.    wt: 1:   5 logarithms and exponentials etc
  86.    wt: 1:   4 algebra
  87.    wt: 1:   3 Euclidean Geometry Leanly
  88.    wt: 1:   2 arithmetic with signed numbers
  89.    wt: 1:   1 arithmetic with unsigned numbers
  90.    wt: 1:   What is POMME
  91.    wt: 1:   why bother
  92.    wt: 1:   which way to go
  93.    wt: 1:   website reviews
  94.    wt: 1:   three goals to set for students
  95.    wt: 1:   Teach the teachers plus goals
  96.    wt: 1:   permissions for teachers
  97.    wt: 1:   Math Ed if it must be short make it lean effective
  98.    wt: 1:   Applied Maths Program14092009 POMME variant
  99.    wt: 1:   activities for students
  100.    wt: 1:   links Education Resources online
  101.    wt: 1:   site origins
  102.    wt: 1:   site eurekas
  103.    wt: 1:   About site lesson plans
  104.    wt: 1:   teacher certification
  105.    wt: 1:   modern education
  106.    wt: 1:   learning takes time
  107.    wt: 1:   grouping students according to ability
  108.    wt: 1:   what should be learnt and When
  109.    wt: 1:   Postscript 2007 01 10
  110.    wt: 1:   Education Reform Inconsistencies
  111.    wt: 1:   five decades make a difference
  112.    wt: 1:   Maps Plans Drawings
  113.    wt: 1:   how letters appear
  114.    wt: 1:   talk the algebra talk
  115.    wt: 1:   three difficulties
  116.    wt: 1:   teaching tips
  117.    wt: 1:   What to Tell Students
  118.    wt: 1:   geometric implications for algebra
  119.    wt: 1:   teaching tutoring algebraic reason
  120.    wt: 1:   Lessening Algebra Difficulties
  121.    wt: 1:   the trouble with algebra
  122.    wt: 1:   05 13 OldSiteEntrancePage
  123.    wt: 1:   04 25 when to stop or suspend mathemat
  124.    wt: 1:   02 21 words for teachers
  125.    wt: 1:   standards for course material
  126.    wt: 1:   Operational Viewpoint to Value
  127.    wt: 1:   formal or informal peer review
  128.    wt: 1:   Theory of Knowledge
  129.    wt: 1:   Different Kinds of Reasoning in maths
  130.    wt: 1:   cultivating intelligence
  131.    wt: 1:   Four ways to improve education reform
  132.    wt: 1:   How to be a better instructor
  133.    wt: 1:   Motivation and Context Problem
  134.    wt: 1:   Prequel In For A Penny In For A Pound
  135.    wt: 1:   education an empirical art
  136.    wt: 1:   fairness and inductive principles for instruction
  137.    wt: 1:   chapitre 12 00 les iles et division
  138.    wt: 1:   chapitre 07 01 principle D induction mathematique
  139.    wt: 1:   chapitre 07 00 Des chaines plus longues de la raison
  140.    wt: 1:   chapitre 06 00 Chaines de la raison
  141.    wt: 1:   chapitre 05 00 Deception
  142.    wt: 1:   chapitre 04 10 Etapes pour une meilleur raison
  143.    wt: 1:   chapitre 04 09 Regles accidentelles
  144.    wt: 1:   chapitre 04 08 Limitations et benefices
  145.    wt: 1:   chapitre 04 07 RepetablesEtReproductibles
  146.    wt: 1:   chapitre 04 06 engagements
  147.    wt: 1:   chapitre 04 05 Implication versus suggestion
  148.    wt: 1:   chapitre 04 04 Parlons de la logique
  149.    wt: 1:   chapitre 04 03 Unidirectionnel versus bidirectionnel
  150.    wt: 1:   chapitre 04 02 Deuxieme enigme
  151.    wt: 1:   chapitre 04 01 Premiere enigme
  152.    wt: 1:   chapitre 04 00 Les regles d implication
  153.    wt: 1:   chapitre 03 A Propos Des Prochains Chapitre
  154.    wt: 1:   chapitre 02 00 La Communication des idees
  155.    wt: 1:   chapitre 01 00 Introduction
  156.    wt: 1:   Home Tutoring and Home Schooling
  157.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  158.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  159.    wt: 1:   16 Secondary Mathematics Tips
  160.    wt: 1:   12 Goals and Objectives For Mathematics
  161.    wt: 1:   Ages 12 to 14 Skills with take home value
  162.    wt: 1:   Ages 12 to 14 Geometry
  163.    wt: 1:   Ages 12 to 14 Arithmetic
  164.    wt: 1:   Ages 10 to 12 Geometry
  165.    wt: 1:   Ages 10 to 12 Arithmetic
  166.    wt: 1:   Ages 9 to 10
  167.    wt: 1:   Ages 8 to 9
  168.    wt: 1:   Ages 7 to 8
  169.    wt: 1:   Ages 6 to 7
  170.    wt: 1:   Ages 4 plus to 5 plus
  171.    wt: 1:   Ages 3 plus to 4 plus
  172.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  173.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  174.    wt: 1:   4 Function notation in and beyond mathematics
  175.    wt: 1:   8 Notes for instructors or tutors
  176.    wt: 1:   12 From Applied To Pure Mathematics
  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:   7 Calculator Usage Notes and Cautions
  183.    wt: 1:   015 School and work day counting tables
  184.    wt: 1:   2 Time and Date Matters in School
  185.    wt: 1:   Example 1. Area Between x and x squared
  186.    wt: 1:   Area Between Crossing Curves Lesson Take 2
  187.    wt: 1:   Area Between Crossing Curves Lesson Take 1
  188.    wt: 1:   Example 4 with x function of y
  189.    wt: 1:   Example 3
  190.    wt: 1:   Example 2
  191.    wt: 1:   Example 1
  192.    wt: 1:   Area Between Curves Lesson Take 2
  193.    wt: 1:   Area Between Curves Lesson Take 1
  194.    wt: 1:   Summary
  195.    wt: 1:   A Related Material in Volume 3
  196.    wt: 1:   A Related lessons in Volume 3
  197.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  198.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  199.    wt: 1:   G.1 First Fundamental Theorem of Calculus
  200.    wt: 1:   G.6 Bounded Derivatives implies Lipshitz Continuity
  201.    wt: 1:   G.5 Motions With Bounded Velocities
  202.    wt: 1:   G.4 Lipschitz Continuity implies EquiContinuity
  203.    wt: 1:   G.3 Constant Difference Theorem Proof
  204.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  205.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  206.    wt: 1:   F.5b Extreme Value Theorem
  207.    wt: 1:   F.5a Equicontinuity Theorems
  208.    wt: 1:   F.4 Finite Covering Theorem
  209.    wt: 1:   F.3 Intermediate Value Theorem
  210.    wt: 1:   F.2 Closed Range Theorem
  211.    wt: 1:   F.1 What Functions are Continuous
  212.    wt: 1:   E2 Algebraic Properties of Limits
  213.    wt: 1:   E1 Error Control Inequalities
  214.    wt: 1:   D2 Limits of Monotone Sequences
  215.    wt: 1:   D1 Sets and Sequences GLBs and LGBs
  216.    wt: 1:   C Triangle Inequalities
  217.    wt: 1:   B3 Bolzano Weierstrass Theorem
  218.    wt: 1:   B1 Pigeon Hole Principles from combinatorics
  219.    wt: 1:   PostScript For and Against Decimal Perspectives
  220.    wt: 1:   A1. Introduction
  221.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  222.    wt: 1:   Postscript Pythagorean Theorem yet another proof
  223.    wt: 1:   Chapter 24 Logarithms Powers and Exponentials
  224.    wt: 1:   Chapter 23 Links To Trigonometry
  225.    wt: 1:   Chapter 22 Complex Numbers
  226.    wt: 1:   Chapter 21 Arrow Addition
  227.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  228.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  229.    wt: 1:   Chapter 18. Slopes Areas Integration
  230.    wt: 1:   Chapter 17. Area Approximation
  231.    wt: 1:   Chapter 16. Velocity Approximation
  232.    wt: 1:   Chapter 15. Slope Approximation
  233.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  234.    wt: 1:   Chapter 14 Limits and Continuity with and sans Decimals
  235.    wt: 1:   Chapter 13. Acceleration
  236.    wt: 1:   Chapter 12. Units and Slopes
  237.    wt: 1:   Chapter 11. Graphing Slope versus Position
  238.    wt: 1:   Chapter 10 Slopes and Units
  239.    wt: 1:   Chapter 9 About First Courses in Calculus
  240.    wt: 1:   Chapter 8. Slope Interpretation
  241.    wt: 1:   Chapter 7 Slopes and Velocity
  242.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  243.    wt: 1:   Chapter 5. Slope Sign Tests
  244.    wt: 1:   Chapter 4. More Slope Sign Analysis
  245.    wt: 1:   Chapter 3. Slope Sign Analysis
  246.    wt: 1:   Chapter 2. Slopes and Ski Trails
  247.    wt: 1:   Chapter 1.Introduction
  248.    wt: 1:   Fall 1983 Calculus Appetizer
  249.    wt: 1:   Foreword
  250.    wt: 1:   Postscript More on Better Performance
  251.    wt: 1:   Postscript For Better Performance
  252.    wt: 1:   Appendix C. How to Read
  253.    wt: 1:   Appendix B. How To Learn
  254.    wt: 1:   Appendix A. Reading Guide For Next Appendices
  255.    wt: 1:   Chapter 31 Direct and Indirect Reason
  256.    wt: 1:   Chapter 30 Truth Tables
  257.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  258.    wt: 1:   Chapter 28 Occurrence Tables
  259.    wt: 1:   Chapter 27 Shorthand Symbols as Pronouns
  260.    wt: 1:   Chapter 26 What is in chapters 27 to 31
  261.    wt: 1:   Chapter 25. Mathematical Induction Examples
  262.    wt: 1:   Chapter 24. Personal Investment and Pension EGS
  263.    wt: 1:   Chapter 23. Notation For Sums
  264.    wt: 1:   Chapter 22. Geometric Sums and Sequences
  265.    wt: 1:   Chapter 21. Third Reading Guide
  266.    wt: 1:   Chapter 20. Degrees and Radians
  267.    wt: 1:   Chapter 19. Functions and Sets
  268.    wt: 1:   Chapter 18. Rules for Algebra
  269.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  270.    wt: 1:   Chapter 16. Painless Theorem Proving
  271.    wt: 1:   Chapter 15. Solving Linear Equations
  272.    wt: 1:   Chapter 14. Forward and Backward Use of a Formula
  273.    wt: 1:   Postscript Unifying Theme A Fourth Skill For Algebra
  274.    wt: 1:   Chapter 13. Second Reading Guide
  275.    wt: 1:   Chapter 12. Shorthand Usage Guide
  276.    wt: 1:   Chapter 11. Why Shorthand
  277.    wt: 1:   Chapter 10 Describing and Changing Calculations
  278.    wt: 1:   Postscript What is a Variable
  279.    wt: 1:   Chapter 9 Talking about Numbers or Quantities
  280.    wt: 1:   Chapter 8 Three Skills For Algebra
  281.    wt: 1:   Solutions For Arithmetic Exercises
  282.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  283.    wt: 1:   Chapter 6 Change of Language
  284.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  285.    wt: 1:   Chapter 4 Longer Chains of Reason
  286.    wt: 1:   Chapter 3 Chains of Reason
  287.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  288.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  289.    wt: 1:   Foreword
  290.    wt: 1:   Postscript D Reflections on Law of the Excluded Middle
  291.    wt: 1:   Postscript C Consistency as a Tool for Reason
  292.    wt: 1:   Postscript B More on Story Telling and Reason
  293.    wt: 1:   Postscript A Story Telling
  294.    wt: 1:   Chapter 24 Direct and Indirect Reason
  295.    wt: 1:   Chapter 23 Truth Tables
  296.    wt: 1:   Chapter 22 Contrapositive and Vacuously True Implications
  297.    wt: 1:   Chapter 21 Occurrence Tables
  298.    wt: 1:   Chapter 20 Shorthand Symbols as Pronouns
  299.    wt: 1:   Chapter 19 What is in chapters 20 to 24
  300.    wt: 1:   Chapter 18 Sense and Knowledge
  301.    wt: 1:   Chapter 17 Objective Ways Trial and Error Discovery
  302.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  303.    wt: 1:   Chapter 15 Objective Processes
  304.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  305.    wt: 1:   Chapter 12 Islands and Divisions of Knowledge
  306.    wt: 1:   Chapter 11 Accidental Patterns
  307.    wt: 1:   Chapter 10 Responsibility
  308.    wt: 1:   Chapter 9 What is in Chapters 10 to 18
  309.    wt: 1:   Chapter 8 Change of Language
  310.    wt: 1:   Chapter 7 Longer Chains of Reason
  311.    wt: 1:   Chapter 6 Chains of Reason
  312.    wt: 1:   Chapter 5 Deception
  313.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  314.    wt: 1:   Chapter 3 What is in chapters 4 to 8
  315.    wt: 1:   Chapter 2 Skill Development
  316.    wt: 1:   Chapter 1 Introduction
  317.    wt: 1:   Three Remarks
  318.    wt: 1:   Foreword
  319.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  320.    wt: 1:   R Why Learn Mathematics Skills
  321.    wt: 1:   O On Learning Mathematics and Science
  322.    wt: 1:   N Mathematics Prepare for College Studies
  323.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  324.    wt: 1:   Chapter 8 Skipped Topics and Why
  325.    wt: 1:   Chapter 7 Calculus Previews and Calculus Lightly
  326.    wt: 1:   Chapter 6 More Algebra and Geometry
  327.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  328.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  329.    wt: 1:   Chapter 3 Algebra Starter Lessons
  330.    wt: 1:   Chapter 2 Why Sets
  331.    wt: 1:   Chapter 1 Arithmetic
  332.    wt: 1:   Ends Values Methods For Skill Development Framework Prequel
  333.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  334.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  335.    wt: 1:   More Algebra and Slope based Calculus Preview
  336.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  337.    wt: 1:   Systematic Algebra Skill Development Missing Links
  338.    wt: 1:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  339.    wt: 1:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  340.    wt: 1:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  341.    wt: 1:   Which Way To Go
  342.    wt: 1:   Mathematics Teacher Certification Best Practices

Road Safety Messages and Questions: When and why should you face traffic when walking along a road or cycle path? Is it a good idea to hang limbs outside of cars etc? What gives more protection in a crash: a car, motorbike or bicylce?

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

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

May 2012, Composition Starting: Pre-School and Primary Mathematics - Quantitative Skills, An Intellectual View, Feedback Welcome:

The 8 Most Popular Site Inlinks

20 Times Table - the most popular site page - popular pages - unexpected.
Fractions & Ratios - with lesson on raising terms to introduce & justify times, division & comparison as well addition & subtraction
Parent Center - See below
Volume 1, Elements of Reason - Intro to all site books.
What is a Variable - best for ages 13+
Written work formats for Arithmetic and Algebra - a skill method and standard!
Complex Numbers Visually - best for ages 13+
Natural Logs, Exponentials, Powers, Roots

Division of Labour: This site offers advice and directions with pointers to resources elsewhere, if known, when they help or lessen the need to write more.

Parent Center: Help your child or teen learn:

Parent-friendly Work Booklets for ages 3+ to 13 Use these or others to check or build skills. Other booklets are available but these booklets allow parents unsure of themselves in mathematics to help their children. The selection acquired in Canada is published in the USA. So it has a US orientation. In retrospect, the selection shows parents what to check with the booklets or by other ways, the choice is theirs. But in retrospect, the selection does not cover integral and fractions liquid weights and measures - ask the publishers to correct that! For ages 9 to 12 say, parents may compensate by showing boys and girls how to use weights or mass, and further measures in food preparation. Beyond that children may be shown how to measure and calculate angles, lengths and areas [proportional amounts too] directly or by using maps and plans drawns to scale. Learning how to gather and measure all the ingredients, pots and pans for a dish or a meal, along with cleaning up sets the stage for like activities or experiments in science courses, and in developing organizational skills, gives boys and girls a head start. Good luck. At the other extreme, more comprehensive than light, if your motto is McCainian: drill, drill, drill then Toronto mathematician and actor John Mighton's jump math organization has jump math workbooks for at least grades 3 to 8 for at-home and in-school use - training sessions for teachers available. Jump math has been expanding to cover older students. Jump Math Samples: plus Fractions for Grades 3-4 & Grades 5-6 [Read] Free Resources grades 1 to 8 [unread - likely to be good]. and

Mathematics Skills For Ages 3 to 14 - technical!

Skills with take home value - A few ideas

Basic skills include time-date-calendar Matters; money matters; map, plan and scale diagram matters;counting, measuring and figuring; decision making with logic and likelyhood; being careful and being aware of the domino effect of mistakes; reading and writing with precision.

Is your child able to add, subtract and multiply amounts of money, work with fractions, work with clocks and calendars, work with maps and plans, and measure length, weight-mass and volume? Schools may promote your son or daughter without providing basic skills in reading, writing and arithmetic.

Arithmetic and Number Theory Skills

Algebra Starter Lessons

1 Working With Sets
2 Formula Forward Use - Evaluation
3 Solving Linear Equations - Skip first step with students able to solve 1 eqn in 1 unknown.
4 Computation Rules and Function Notation
5 Real Numbers
6 More Less Greater Than Inequalities and Comparison
7 Axioms Logic and Equivalent Equations
8 Unifying Theme For Algebra
9 Proportionality Backwards and Forwards
10 Examples of Algebraic Reasoning
A Origins of Counting and Figuring Methods
B Real Numbers Extrinsic Development


Site coverage of formuala evaluation format, of computation rules and axioms, and of the forward and backward use of formulas and proportionality relations lessens the amount of natural talent needed to understand and explain algebra.

Geometry - maps plans trigonometry vectors

1 Maps Plans Measurement
2 Euclidean Geometry - Constructions + extras
3 Cartesian and Polar Coordinates
4 Lines and Slopes Take 1
5 What is Similarity
6 Trigonometry first steps
7 Complex Numbers
8 Unit-Circle Trigonometry
9 Lines and Slopes Take 2 with tangent function
10 Intersecting Straight Lines and Transversals
11 Parallel Straight Lines and Transversals
12 Function Translating and Rescaling
13 Vectors
14 Degrees to Radians and Radians to Degrees
15 Arc or Inverse Trigonometric Function

Pre-Teen and young teen mastery of skills and practices which should be common with map-plans-diagrams drawn to scale, contour interpretation included, has actual or potential take-home value for daily- and adult-life in solving routine problems. Elevating some practices to principles, axioms or postualates, provides a base for analytic and Euclidean geometry, an analytic view of similarity, and an efficient mastery of trigonometry and complex numbers. Right triangle trigonometry provide an analytic alternative to solving geometric problems by drawing diagrams to scale.

More Algebra

Natural-Logarithms Exponentials Powers Roots
Five Polynomial Operations
Quadratics Geometrically
Functions
5 Factored Polynomial Sign Analysis Examples
Rewriting algebraic substitution as function substitutions

The first topic leads to a full high school level theory for the forward and backward mastery of growth and decay models and for definition, range and domains of radicals, roots and powers. The next two topics make quadratics and polynomials easier to learn and teach. Site coverage of functions turns vertical and horizontal line rules into computation methods for evaluating functions.

70 Calculus Starter Lessons

Calculus Lessons Elsewhere:

  1. How to Ace Calculus: Street Wise Guide - Mostly Text.

  2. Flash Video for Calculus Phobics

They cover basic topics in ways likely to complement your notes, your textbooks and site material. When Goldilocks trespassed in the house of the three bears, she found three bowls of porridge, two not to her liking, and one just right. Different bears have different tastes. As invited guest here and elsewhere, if one or more explanations is not to liking, try another. It may be better or just right.

Unsolicited Advice

Learning to do and high marks if it comes to easy is often deceptive - light rather than deep. For that reason, students with learning difficulties determined not to let it get in their way may go deeper and farther than those with none. High marks, if the come easy, may be deceptive - provide a too light and not a deep mastery. That could have been your problem in secondary school, one that leads to comprehension shock or difficulties in calculus and more generally in the first year of college. Bon Appetite.


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Logic-Reason for all
Careful Thinking
Chains of Reason
Mathematical Induction
Responsibility
Bodies-of-Knowledge

Arithmetic - Ages 10+
1. Deciml Place Value - fun
2. Decimals for Tutors
3. Prime Factors - quickly
4. Fractions + Ratios
5. Arith with units - science

Geometry
1 Maps + Plans Use
2 Euclidean Geometry
3 Rct +Polr Coordinates
4 Lines-Slopes [I]
5. What is Similarity
Algebra Starters - the base
1. Better Work Format
2. Solve Linear Eqns
3. Computation Rules
4. Axioms, Item 3 Viewpnt
5. Formulas Backwards
More Algebra
Logarithms-ax & m/nth roots
Five Polynomial Operations
Quadratics Geometrically
Functions || Vectors too
Arith. Skill Check+Answers
Calculus Prep/Preview
What is a Variable
Why study slopes
Why factor polynomials
Complex Numbers
Limits + Continuity

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