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

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68 matches:

  1.    wt: 2:   mathematics curriculum shifts
  2.    wt: 2:   04 29 New Mathematics Curriculum
  3.    wt: 2:   need for a mixed mathematics curriculum
  4.    wt: 2:   Leaner mathematics curriculum
  5.    wt: 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 goals for Mathematics Education
  16.    wt: 1:   02 20 mathematics education references
  17.    wt: 1:   three aims for mathematics students
  18.    wt: 1:   mathematics instruction in general
  19.    wt: 1:   Education in mathematics science and technology
  20.    wt: 1:   three kinds of reason in mathematics
  21.    wt: 1:   words for mathematics instructor
  22.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  23.    wt: 1:   22 Student Centered Highschool Mathematics
  24.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  25.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  26.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  27.    wt: 1:   18 Primary School Mathematics
  28.    wt: 1:   16 Secondary Mathematics Tips
  29.    wt: 1:   12 Goals and Objectives For Mathematics
  30.    wt: 1:   4 Function notation in and beyond mathematics
  31.    wt: 1:   2 Algebraic use of function notation
  32.    wt: 1:   8 quadratics backward use of various formulas
  33.    wt: 1:   8 Notes for instructors or tutors
  34.    wt: 1:   12 From Applied To Pure Mathematics
  35.    wt: 1:   27 Logarithmic use of products of sines and cosines
  36.    wt: 1:   PS C Similarity Use Recognize it in Trigonometry
  37.    wt: 1:   A Measurement with Ruler Proper Use
  38.    wt: 1:   8 More Use of Maps Not Drawn to Scale
  39.    wt: 1:   Skill Development Notes
  40.    wt: 1:   11 Volume of Sphere
  41.    wt: 1:   10 Volume of Pyramid
  42.    wt: 1:   9 Volume of Cone
  43.    wt: 1:   6 Pythagorean Hypotenuse Calculation Example
  44.    wt: 1:   5 Box Volume Formula Example
  45.    wt: 1:   LCM 60 45 Avoid List Method Use Prime
  46.    wt: 1:   11 Efficient Square Rule Use
  47.    wt: 1:   7 Calculator Usage Notes and Cautions
  48.    wt: 1:   Example 2 volume of a cone
  49.    wt: 1:   Example 1 volume of a pyramid
  50.    wt: 1:   Volume of Solid by Cross Sections Lesson
  51.    wt: 1:   A Related Material in Volume 3
  52.    wt: 1:   A Related lessons in Volume 3
  53.    wt: 1:   Appendix E. How To Study Mathematics and Why
  54.    wt: 1:   Chapter 14. Forward and Backward Use of a Formula
  55.    wt: 1:   Postscript B Mathematics Education References
  56.    wt: 1:   Chapter 6 Rule Based Reason in Mathematics
  57.    wt: 1:   Chapter 2 For and Against Mathematics
  58.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  59.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  60.    wt: 1:   R Why Learn Mathematics Skills
  61.    wt: 1:   O On Learning Mathematics and Science
  62.    wt: 1:   N Mathematics Prepare for College Studies
  63.    wt: 1:   Helping the Blind in Logic and Mathematics
  64.    wt: 1:   Mathematics Education References
  65.    wt: 1:   Mathematics Education References
  66.    wt: 1:   Multiple Ways to Improve Mathematics Skill Development
  67.    wt: 1:   Implementation Notes
  68.    wt: 1:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years

Extended Search

355 matches:

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