Original Site Title: Appetizers and Lessons for Mathematics and Reason, June 1995 to April 2012. New site title:
Logic and Mathematics Skill & Concept Development with How-TOs Français: 26 pages
for college students, gifted teens, home-tutoring and K1-12 schooling. Avid readers in school and out may like Site Volumes.

Logic 5 Chapters Arithmetic 10 Steps Algebra 12 Starter Steps & 5 Advanced Steps
Work & Study 23 Tips Geometry 15 Steps Calculus 70 Lessons. See Site Map

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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17 matches:

  1.    wt: 6:   Volume 1A Pattern Based Reason/
  2.    wt: 2:   Volume 1A Regles et modeles/
  3.    wt: 2:   Volume 1B Mathematics Curriculum Notes/
  4.    wt: 2:   Volume 1 Elements of Reason/
  5.    wt: 1:   LAMP Lean Applied Mathematics Program/
  6.    wt: 1:   Progressive Observable Motivated Mathematics Education/
  7.    wt: 1:   Mathematics Education Essays/
  8.    wt: 1:   Mathematics Skills Year by Year/
  9.    wt: 1:   10 Examples of Algebraic Reasoning/
  10.    wt: 1:   12 Webvideo Lessons on Area and Volume Calculation/
  11.    wt: 1:   Advanced Calculus Volume 3 Appendices/
  12.    wt: 1:   Volume 3 Why Slopes A Calculus Intro Etc/
  13.    wt: 1:   Volume 2 Three Skills For Algebra/
  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/

Web Page Search

70 matches:

  1.    wt: 3:   Chapter 6 Rule Based Reason in Mathematics
  2.    wt: 2:   E LAMP Introduction Modern Mathematics
  3.    wt: 2:   three kinds of reason in mathematics
  4.    wt: 2:   V Reasons and Motivations for Logic and Mathematics
  5.    wt: 1:   C LAMP Introduction Culture in Mathematics Education
  6.    wt: 1:   11 pure mathematics
  7.    wt: 1:   Mathematics Education Professors
  8.    wt: 1:   modern education
  9.    wt: 1:   mathematics in context
  10.    wt: 1:   Secondary Three Mathematics
  11.    wt: 1:   Secondary Two Mathematics
  12.    wt: 1:   Secondary One Mathematics
  13.    wt: 1:   mathematics curriculum shifts
  14.    wt: 1:   teaching tutoring algebraic reason
  15.    wt: 1:   three goals for Mathematics Education
  16.    wt: 1:   04 29 New Mathematics Curriculum
  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:   Different Kinds of Reasoning in maths
  22.    wt: 1:   need for a mixed mathematics curriculum
  23.    wt: 1:   Leaner mathematics curriculum
  24.    wt: 1:   words for mathematics instructor
  25.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  26.    wt: 1:   22 Student Centered Highschool Mathematics
  27.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  28.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  29.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  30.    wt: 1:   18 Primary School Mathematics
  31.    wt: 1:   16 Secondary Mathematics Tips
  32.    wt: 1:   12 Goals and Objectives For Mathematics
  33.    wt: 1:   4 Function notation in and beyond mathematics
  34.    wt: 1:   12 From Applied To Pure Mathematics
  35.    wt: 1:   11 Volume of Sphere
  36.    wt: 1:   10 Volume of Pyramid
  37.    wt: 1:   9 Volume of Cone
  38.    wt: 1:   5 Box Volume Formula Example
  39.    wt: 1:   Example 2 volume of a cone
  40.    wt: 1:   Example 1 volume of a pyramid
  41.    wt: 1:   Volume of Solid by Cross Sections Lesson
  42.    wt: 1:   A Related Material in Volume 3
  43.    wt: 1:   A Related lessons in Volume 3
  44.    wt: 1:   Appendix E. How To Study Mathematics and Why
  45.    wt: 1:   Chapter 31 Direct and Indirect Reason
  46.    wt: 1:   Chapter 4 Longer Chains of Reason
  47.    wt: 1:   Chapter 3 Chains of Reason
  48.    wt: 1:   Postscript B Mathematics Education References
  49.    wt: 1:   Chapter 8 Modern Instruction
  50.    wt: 1:   Chapter 2 For and Against Mathematics
  51.    wt: 1:   Postscript C Consistency as a Tool for Reason
  52.    wt: 1:   Postscript B More on Story Telling and Reason
  53.    wt: 1:   Chapter 24 Direct and Indirect Reason
  54.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  55.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  56.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  57.    wt: 1:   Chapter 11 Accidental Patterns
  58.    wt: 1:   Chapter 7 Longer Chains of Reason
  59.    wt: 1:   Chapter 6 Chains of Reason
  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:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  64.    wt: 1:   Helping the Blind in Logic and Mathematics
  65.    wt: 1:   Mathematics Education References
  66.    wt: 1:   Mathematics Education References
  67.    wt: 1:   Multiple Ways to Improve Mathematics Skill Development
  68.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  69.    wt: 1:   More Algebra and Slope based Calculus Preview
  70.    wt: 1:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years

Extended Search

340 matches:

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