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

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78 matches:

  1.    wt: 2:   mathematics curriculum shifts
  2.    wt: 2:   04 29 New Mathematics Curriculum
  3.    wt: 2:   need for a mixed mathematics curriculum
  4.    wt: 2:   Leaner mathematics curriculum
  5.    wt: 2:   1 Counting and Counting Methods I
  6.    wt: 1:   E LAMP Introduction Modern Mathematics
  7.    wt: 1:   C LAMP Introduction Culture in Mathematics Education
  8.    wt: 1:   B LAMP Introduction Curriculum Development Standards
  9.    wt: 1:   11 pure mathematics
  10.    wt: 1:   key notes and themes
  11.    wt: 1:   Mathematics Education Professors
  12.    wt: 1:   mathematics in context
  13.    wt: 1:   Secondary Three Mathematics
  14.    wt: 1:   Secondary Two Mathematics
  15.    wt: 1:   Secondary One Mathematics
  16.    wt: 1:   three goals for Mathematics Education
  17.    wt: 1:   02 20 mathematics education references
  18.    wt: 1:   three aims for mathematics students
  19.    wt: 1:   mathematics instruction in general
  20.    wt: 1:   Education in mathematics science and technology
  21.    wt: 1:   three kinds of reason in mathematics
  22.    wt: 1:   words for mathematics instructor
  23.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  24.    wt: 1:   22 Student Centered Highschool Mathematics
  25.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  26.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  27.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  28.    wt: 1:   18 Primary School Mathematics
  29.    wt: 1:   16 Secondary Mathematics Tips
  30.    wt: 1:   15 Counting For Parents
  31.    wt: 1:   12 Goals and Objectives For Mathematics
  32.    wt: 1:   4 Function notation in and beyond mathematics
  33.    wt: 1:   8 Notes for instructors or tutors
  34.    wt: 1:   12 From Applied To Pure Mathematics
  35.    wt: 1:   2 Counting Digits in Decimal Multiplication
  36.    wt: 1:   4 Commutative Law Groups Counting Form
  37.    wt: 1:   3 Multiplicative Counting Skills Principles
  38.    wt: 1:   1 The Counting Origins of Numbers
  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:   5 Box Volume Formula Example
  44.    wt: 1:   3 Counting with Sets etc
  45.    wt: 1:   5 Counting with Tables Trees Product Rule Take II
  46.    wt: 1:   4 Counting with Trees Product Rule Take I
  47.    wt: 1:   3 Counting with Tables and Trees II
  48.    wt: 1:   2 Counting with Tables and Trees I
  49.    wt: 1:   7 Calculator Usage Notes and Cautions
  50.    wt: 1:   C Counting Areas with Powers of Ten
  51.    wt: 1:   Appendix 1 Counting Revisited 15 minute video
  52.    wt: 1:   6. Counting and adding units and mixed units
  53.    wt: 1:   2 Decimal Counting Practices
  54.    wt: 1:   015 School and work day counting tables
  55.    wt: 1:   014 Counting Days with Calendars
  56.    wt: 1:   Example 2 volume of a cone
  57.    wt: 1:   Example 1 volume of a pyramid
  58.    wt: 1:   Volume of Solid by Cross Sections Lesson
  59.    wt: 1:   A Related Material in Volume 3
  60.    wt: 1:   A Related lessons in Volume 3
  61.    wt: 1:   Appendix E. How To Study Mathematics and Why
  62.    wt: 1:   Postscript B Mathematics Education References
  63.    wt: 1:   Chapter 6 Rule Based Reason in Mathematics
  64.    wt: 1:   Chapter 2 For and Against Mathematics
  65.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  66.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  67.    wt: 1:   R Why Learn Mathematics Skills
  68.    wt: 1:   O On Learning Mathematics and Science
  69.    wt: 1:   N Mathematics Prepare for College Studies
  70.    wt: 1:   6 Measuring via counting or arithmetic the role of fractions
  71.    wt: 1:   1 From Number Recognition and Counting to Arithmetic B
  72.    wt: 1:   1 From Number Recognition and Counting to Arithmetic A
  73.    wt: 1:   Helping the Blind in Logic and Mathematics
  74.    wt: 1:   Mathematics Education References
  75.    wt: 1:   Mathematics Education References
  76.    wt: 1:   Multiple Ways to Improve Mathematics Skill Development
  77.    wt: 1:   Implementation Notes
  78.    wt: 1:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years

Extended Search

371 matches:

  1.    wt: 7:   Postscript B Mathematics Education References
  2.    wt: 7:   Chapter 6 Rule Based Reason in Mathematics
  3.    wt: 7:   Chapter 2 For and Against Mathematics
  4.    wt: 6:   Annotated Links to Material Elsehwere
  5.    wt: 6:   Postscript A Three Remarks
  6.    wt: 6:   Chapter 12 Four Phases
  7.    wt: 6:   Chapter 11 Elementary Instruction
  8.    wt: 6:   Chapter 10 Transition
  9.    wt: 6:   Chapter 9 The Two Ends
  10.    wt: 6:   Chapter 8 Modern Instruction
  11.    wt: 6:   Chapter 7 Two Treatments of Geometry
  12.    wt: 6:   Chapter 5 Four References
  13.    wt: 6:   Chapter 4 Complex Numbers and Why Slopes
  14.    wt: 6:   Chapter 3 Algebra Difficulties
  15.    wt: 6:   Chapter 1 Introduction
  16.    wt: 6:   Foreword
  17.    wt: 3:   mathematics curriculum shifts
  18.    wt: 3:   04 29 New Mathematics Curriculum
  19.    wt: 3:   need for a mixed mathematics curriculum
  20.    wt: 3:   Leaner mathematics curriculum
  21.    wt: 2:   E LAMP Introduction Modern Mathematics
  22.    wt: 2:   C LAMP Introduction Culture in Mathematics Education
  23.    wt: 2:   B LAMP Introduction Curriculum Development Standards
  24.    wt: 2:   11 pure mathematics
  25.    wt: 2:   key notes and themes
  26.    wt: 2:   Mathematics Education Professors
  27.    wt: 2:   mathematics in context
  28.    wt: 2:   Secondary Three Mathematics
  29.    wt: 2:   Secondary Two Mathematics
  30.    wt: 2:   Secondary One Mathematics
  31.    wt: 2:   three goals for Mathematics Education
  32.    wt: 2:   02 20 mathematics education references
  33.    wt: 2:   three aims for mathematics students
  34.    wt: 2:   mathematics instruction in general
  35.    wt: 2:   Education in mathematics science and technology
  36.    wt: 2:   three kinds of reason in mathematics
  37.    wt: 2:   words for mathematics instructor
  38.    wt: 2:   4 Commutative Law Groups Counting Form
  39.    wt: 2:   3 Multiplicative Counting Skills Principles
  40.    wt: 2:   1 The Counting Origins of Numbers
  41.    wt: 2:   1 Counting and Counting Methods I
  42.    wt: 2:   Appendix 1 Counting Revisited 15 minute video
  43.    wt: 2:   6. Counting and adding units and mixed units
  44.    wt: 2:   2 Decimal Counting Practices
  45.    wt: 2:   Example 2 volume of a cone
  46.    wt: 2:   Example 1 volume of a pyramid
  47.    wt: 2:   Volume of Solid by Cross Sections Lesson
  48.    wt: 2:   Appendix E. How To Study Mathematics and Why
  49.    wt: 2:   Chapter 14 Deductive and Empirical Views of Mathematics
  50.    wt: 2:   6 Measuring via counting or arithmetic the role of fractions
  51.    wt: 2:   1 From Number Recognition and Counting to Arithmetic B
  52.    wt: 2:   1 From Number Recognition and Counting to Arithmetic A
  53.    wt: 2:   Helping the Blind in Logic and Mathematics
  54.    wt: 2:   Mathematics Education References
  55.    wt: 2:   Mathematics Education References
  56.    wt: 2:   Multiple Ways to Improve Mathematics Skill Development
  57.    wt: 2:   Implementation Notes
  58.    wt: 2:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  59.    wt: 1:   Appendix 2 primary school Arithmetic 01
  60.    wt: 1:   Appendix 1 primary and preschool mathematic
  61.    wt: 1:   K LAMP Musings Science Education
  62.    wt: 1:   J LAMP Introduction Extrinsic Origins
  63.    wt: 1:   I LAMP Introduction Study Habits
  64.    wt: 1:   H LAMP Introduction Instructional Concepts
  65.    wt: 1:   G LAMP Introduction Problem Solving Skills
  66.    wt: 1:   F LAMP Introduction Prerequisites
  67.    wt: 1:   A Introduction Objectives
  68.    wt: 1:   Skills Chapter 5 Calculus
  69.    wt: 1:   Skills Chapter 4 Logic
  70.    wt: 1:   Ramblings Extrinsic numbers theory
  71.    wt: 1:   Ramblings Introduction Algebra Essay
  72.    wt: 1:   Skills Chapter 3 Algebra
  73.    wt: 1:   Skills Chapter 2 Geometry
  74.    wt: 1:   Skills Chapter 1 Arithmetic
  75.    wt: 1:   Skills Chapter 0 Introduction
  76.    wt: 1:   10 statistics
  77.    wt: 1:   9 combinatorics probability sets
  78.    wt: 1:   8 analytic geometry etc
  79.    wt: 1:   7 logic review and decimals an odd combination
  80.    wt: 1:   6 polynomials etc
  81.    wt: 1:   5 logarithms and exponentials etc
  82.    wt: 1:   4 algebra
  83.    wt: 1:   3 Euclidean Geometry Leanly
  84.    wt: 1:   2 arithmetic with signed numbers
  85.    wt: 1:   1 arithmetic with unsigned numbers
  86.    wt: 1:   What is POMME
  87.    wt: 1:   why bother
  88.    wt: 1:   which way to go
  89.    wt: 1:   website reviews
  90.    wt: 1:   three goals to set for students
  91.    wt: 1:   Teach the teachers plus goals
  92.    wt: 1:   permissions for teachers
  93.    wt: 1:   Math Ed if it must be short make it lean effective
  94.    wt: 1:   Applied Maths Program14092009 POMME variant
  95.    wt: 1:   activities for students
  96.    wt: 1:   links Education Resources online
  97.    wt: 1:   site origins
  98.    wt: 1:   site eurekas
  99.    wt: 1:   About site lesson plans
  100.    wt: 1:   teacher certification
  101.    wt: 1:   modern education
  102.    wt: 1:   learning takes time
  103.    wt: 1:   grouping students according to ability
  104.    wt: 1:   what should be learnt and When
  105.    wt: 1:   Postscript 2007 01 10
  106.    wt: 1:   Education Reform Inconsistencies
  107.    wt: 1:   five decades make a difference
  108.    wt: 1:   Maps Plans Drawings
  109.    wt: 1:   how letters appear
  110.    wt: 1:   talk the algebra talk
  111.    wt: 1:   three difficulties
  112.    wt: 1:   teaching tips
  113.    wt: 1:   What to Tell Students
  114.    wt: 1:   geometric implications for algebra
  115.    wt: 1:   teaching tutoring algebraic reason
  116.    wt: 1:   Lessening Algebra Difficulties
  117.    wt: 1:   the trouble with algebra
  118.    wt: 1:   05 13 OldSiteEntrancePage
  119.    wt: 1:   04 25 when to stop or suspend mathemat
  120.    wt: 1:   02 21 words for teachers
  121.    wt: 1:   standards for course material
  122.    wt: 1:   Operational Viewpoint to Value
  123.    wt: 1:   formal or informal peer review
  124.    wt: 1:   Theory of Knowledge
  125.    wt: 1:   Different Kinds of Reasoning in maths
  126.    wt: 1:   cultivating intelligence
  127.    wt: 1:   Four ways to improve education reform
  128.    wt: 1:   How to be a better instructor
  129.    wt: 1:   Motivation and Context Problem
  130.    wt: 1:   Prequel In For A Penny In For A Pound
  131.    wt: 1:   education an empirical art
  132.    wt: 1:   fairness and inductive principles for instruction
  133.    wt: 1:   chapitre 12 00 les iles et division
  134.    wt: 1:   chapitre 07 01 principle D induction mathematique
  135.    wt: 1:   chapitre 07 00 Des chaines plus longues de la raison
  136.    wt: 1:   chapitre 06 00 Chaines de la raison
  137.    wt: 1:   chapitre 05 00 Deception
  138.    wt: 1:   chapitre 04 10 Etapes pour une meilleur raison
  139.    wt: 1:   chapitre 04 09 Regles accidentelles
  140.    wt: 1:   chapitre 04 08 Limitations et benefices
  141.    wt: 1:   chapitre 04 07 RepetablesEtReproductibles
  142.    wt: 1:   chapitre 04 06 engagements
  143.    wt: 1:   chapitre 04 05 Implication versus suggestion
  144.    wt: 1:   chapitre 04 04 Parlons de la logique
  145.    wt: 1:   chapitre 04 03 Unidirectionnel versus bidirectionnel
  146.    wt: 1:   chapitre 04 02 Deuxieme enigme
  147.    wt: 1:   chapitre 04 01 Premiere enigme
  148.    wt: 1:   chapitre 04 00 Les regles d implication
  149.    wt: 1:   chapitre 03 A Propos Des Prochains Chapitre
  150.    wt: 1:   chapitre 02 00 La Communication des idees
  151.    wt: 1:   chapitre 01 00 Introduction
  152.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  153.    wt: 1:   22 Student Centered Highschool Mathematics
  154.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  155.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  156.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  157.    wt: 1:   18 Primary School Mathematics
  158.    wt: 1:   16 Secondary Mathematics Tips
  159.    wt: 1:   15 Counting For Parents
  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:   2 Counting Digits in Decimal Multiplication
  178.    wt: 1:   E Long Division Methods more
  179.    wt: 1:   D Long Division Methods
  180.    wt: 1:   C Three Decimal Subtraction Methods
  181.    wt: 1:   B Decimal Comparison and Subtraction
  182.    wt: 1:   A Decimal Addition Columm Methods
  183.    wt: 1:   8 Column Multiplication Methods in General
  184.    wt: 1:   7 Decimals Multiplication Methods Examples
  185.    wt: 1:   6 Column Methods for Decimal Multiplication
  186.    wt: 1:   5 Distributive Law for Whole Numbers
  187.    wt: 1:   2 Combing Counts Addition Skills and Principles
  188.    wt: 1:   Skill Development Notes
  189.    wt: 1:   11 Volume of Sphere
  190.    wt: 1:   10 Volume of Pyramid
  191.    wt: 1:   9 Volume of Cone
  192.    wt: 1:   5 Box Volume Formula Example
  193.    wt: 1:   3 Counting with Sets etc
  194.    wt: 1:   5 Counting with Tables Trees Product Rule Take II
  195.    wt: 1:   4 Counting with Trees Product Rule Take I
  196.    wt: 1:   3 Counting with Tables and Trees II
  197.    wt: 1:   2 Counting with Tables and Trees I
  198.    wt: 1:   7 Calculator Usage Notes and Cautions
  199.    wt: 1:   C Counting Areas with Powers of Ten
  200.    wt: 1:   8 What skills and work habits to require
  201.    wt: 1:   7 Adding decimal fractions using decimal point
  202.    wt: 1:   5. How to add decimals C. Examples
  203.    wt: 1:   4. How to add with decimals B with conversions
  204.    wt: 1:   3. How to add with decimals A sans conversions
  205.    wt: 1:   1. Explaining Addition Table
  206.    wt: 1:   015 School and work day counting tables
  207.    wt: 1:   014 Counting Days with Calendars
  208.    wt: 1:   Example 1. Area Between x and x squared
  209.    wt: 1:   Area Between Crossing Curves Lesson Take 2
  210.    wt: 1:   Area Between Crossing Curves Lesson Take 1
  211.    wt: 1:   Example 4 with x function of y
  212.    wt: 1:   Example 3
  213.    wt: 1:   Example 2
  214.    wt: 1:   Example 1
  215.    wt: 1:   Area Between Curves Lesson Take 2
  216.    wt: 1:   Area Between Curves Lesson Take 1
  217.    wt: 1:   Summary
  218.    wt: 1:   A Related Material in Volume 3
  219.    wt: 1:   A Related lessons in Volume 3
  220.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  221.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  222.    wt: 1:   G.1 First Fundamental Theorem of Calculus
  223.    wt: 1:   G.6 Bounded Derivatives implies Lipshitz Continuity
  224.    wt: 1:   G.5 Motions With Bounded Velocities
  225.    wt: 1:   G.4 Lipschitz Continuity implies EquiContinuity
  226.    wt: 1:   G.3 Constant Difference Theorem Proof
  227.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  228.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  229.    wt: 1:   F.5b Extreme Value Theorem
  230.    wt: 1:   F.5a Equicontinuity Theorems
  231.    wt: 1:   F.4 Finite Covering Theorem
  232.    wt: 1:   F.3 Intermediate Value Theorem
  233.    wt: 1:   F.2 Closed Range Theorem
  234.    wt: 1:   F.1 What Functions are Continuous
  235.    wt: 1:   E2 Algebraic Properties of Limits
  236.    wt: 1:   E1 Error Control Inequalities
  237.    wt: 1:   D2 Limits of Monotone Sequences
  238.    wt: 1:   D1 Sets and Sequences GLBs and LGBs
  239.    wt: 1:   C Triangle Inequalities
  240.    wt: 1:   B3 Bolzano Weierstrass Theorem
  241.    wt: 1:   B1 Pigeon Hole Principles from combinatorics
  242.    wt: 1:   PostScript For and Against Decimal Perspectives
  243.    wt: 1:   A1. Introduction
  244.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  245.    wt: 1:   Postscript Pythagorean Theorem yet another proof
  246.    wt: 1:   Chapter 24 Logarithms Powers and Exponentials
  247.    wt: 1:   Chapter 23 Links To Trigonometry
  248.    wt: 1:   Chapter 22 Complex Numbers
  249.    wt: 1:   Chapter 21 Arrow Addition
  250.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  251.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  252.    wt: 1:   Chapter 18. Slopes Areas Integration
  253.    wt: 1:   Chapter 17. Area Approximation
  254.    wt: 1:   Chapter 16. Velocity Approximation
  255.    wt: 1:   Chapter 15. Slope Approximation
  256.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  257.    wt: 1:   Chapter 14 Limits and Continuity with and sans Decimals
  258.    wt: 1:   Chapter 13. Acceleration
  259.    wt: 1:   Chapter 12. Units and Slopes
  260.    wt: 1:   Chapter 11. Graphing Slope versus Position
  261.    wt: 1:   Chapter 10 Slopes and Units
  262.    wt: 1:   Chapter 9 About First Courses in Calculus
  263.    wt: 1:   Chapter 8. Slope Interpretation
  264.    wt: 1:   Chapter 7 Slopes and Velocity
  265.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  266.    wt: 1:   Chapter 5. Slope Sign Tests
  267.    wt: 1:   Chapter 4. More Slope Sign Analysis
  268.    wt: 1:   Chapter 3. Slope Sign Analysis
  269.    wt: 1:   Chapter 2. Slopes and Ski Trails
  270.    wt: 1:   Chapter 1.Introduction
  271.    wt: 1:   Fall 1983 Calculus Appetizer
  272.    wt: 1:   Foreword
  273.    wt: 1:   Postscript More on Better Performance
  274.    wt: 1:   Postscript For Better Performance
  275.    wt: 1:   Appendix D. What to do in School and Why
  276.    wt: 1:   Appendix C. How to Read
  277.    wt: 1:   Appendix B. How To Learn
  278.    wt: 1:   Appendix A. Reading Guide For Next Appendices
  279.    wt: 1:   Chapter 31 Direct and Indirect Reason
  280.    wt: 1:   Chapter 30 Truth Tables
  281.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  282.    wt: 1:   Chapter 28 Occurrence Tables
  283.    wt: 1:   Chapter 27 Shorthand Symbols as Pronouns
  284.    wt: 1:   Chapter 26 What is in chapters 27 to 31
  285.    wt: 1:   Chapter 25. Mathematical Induction Examples
  286.    wt: 1:   Chapter 24. Personal Investment and Pension EGS
  287.    wt: 1:   Chapter 23. Notation For Sums
  288.    wt: 1:   Chapter 22. Geometric Sums and Sequences
  289.    wt: 1:   Chapter 21. Third Reading Guide
  290.    wt: 1:   Chapter 20. Degrees and Radians
  291.    wt: 1:   Chapter 19. Functions and Sets
  292.    wt: 1:   Chapter 18. Rules for Algebra
  293.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  294.    wt: 1:   Chapter 16. Painless Theorem Proving
  295.    wt: 1:   Chapter 15. Solving Linear Equations
  296.    wt: 1:   Chapter 14. Forward and Backward Use of a Formula
  297.    wt: 1:   Postscript Unifying Theme A Fourth Skill For Algebra
  298.    wt: 1:   Chapter 13. Second Reading Guide
  299.    wt: 1:   Chapter 12. Shorthand Usage Guide
  300.    wt: 1:   Chapter 11. Why Shorthand
  301.    wt: 1:   Chapter 10 Describing and Changing Calculations
  302.    wt: 1:   Postscript What is a Variable
  303.    wt: 1:   Chapter 9 Talking about Numbers or Quantities
  304.    wt: 1:   Chapter 8 Three Skills For Algebra
  305.    wt: 1:   Solutions For Arithmetic Exercises
  306.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  307.    wt: 1:   Chapter 6 Change of Language
  308.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  309.    wt: 1:   Chapter 4 Longer Chains of Reason
  310.    wt: 1:   Chapter 3 Chains of Reason
  311.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  312.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  313.    wt: 1:   Foreword
  314.    wt: 1:   Postscript D Reflections on Law of the Excluded Middle
  315.    wt: 1:   Postscript C Consistency as a Tool for Reason
  316.    wt: 1:   Postscript B More on Story Telling and Reason
  317.    wt: 1:   Postscript A Story Telling
  318.    wt: 1:   Chapter 24 Direct and Indirect Reason
  319.    wt: 1:   Chapter 23 Truth Tables
  320.    wt: 1:   Chapter 22 Contrapositive and Vacuously True Implications
  321.    wt: 1:   Chapter 21 Occurrence Tables
  322.    wt: 1:   Chapter 20 Shorthand Symbols as Pronouns
  323.    wt: 1:   Chapter 19 What is in chapters 20 to 24
  324.    wt: 1:   Chapter 18 Sense and Knowledge
  325.    wt: 1:   Chapter 17 Objective Ways Trial and Error Discovery
  326.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  327.    wt: 1:   Chapter 15 Objective Processes
  328.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  329.    wt: 1:   Chapter 12 Islands and Divisions of Knowledge
  330.    wt: 1:   Chapter 11 Accidental Patterns
  331.    wt: 1:   Chapter 10 Responsibility
  332.    wt: 1:   Chapter 9 What is in Chapters 10 to 18
  333.    wt: 1:   Chapter 8 Change of Language
  334.    wt: 1:   Chapter 7 Longer Chains of Reason
  335.    wt: 1:   Chapter 6 Chains of Reason
  336.    wt: 1:   Chapter 5 Deception
  337.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  338.    wt: 1:   Chapter 3 What is in chapters 4 to 8
  339.    wt: 1:   Chapter 2 Skill Development
  340.    wt: 1:   Chapter 1 Introduction
  341.    wt: 1:   Three Remarks
  342.    wt: 1:   Foreword
  343.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  344.    wt: 1:   R Why Learn Mathematics Skills
  345.    wt: 1:   O On Learning Mathematics and Science
  346.    wt: 1:   N Mathematics Prepare for College Studies
  347.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  348.    wt: 1:   Chapter 8 Skipped Topics and Why
  349.    wt: 1:   Chapter 7 Calculus Previews and Calculus Lightly
  350.    wt: 1:   Chapter 6 More Algebra and Geometry
  351.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  352.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  353.    wt: 1:   Chapter 3 Algebra Starter Lessons
  354.    wt: 1:   Chapter 2 Why Sets
  355.    wt: 1:   Chapter 1 Arithmetic
  356.    wt: 1:   Primary and Secondary Skills and Practices with Take Home Value
  357.    wt: 1:   7 Games and Activities for Instruction
  358.    wt: 1:   5 Interpreting and Drawing Maps and Plans.
  359.    wt: 1:   4 Money Matters Saving Earning Buying Selling and Budgets
  360.    wt: 1:   3 Telling Tracking Time Temporal and More Place Sense
  361.    wt: 1:   2 Identifying Size and Position Place and Spatial Sense
  362.    wt: 1:   Ends Values Methods For Skill Development Framework Prequel
  363.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  364.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  365.    wt: 1:   More Algebra and Slope based Calculus Preview
  366.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  367.    wt: 1:   Systematic Algebra Skill Development Missing Links
  368.    wt: 1:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  369.    wt: 1:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  370.    wt: 1:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  371.    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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