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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21 matches:

  1.    wt: 6:   Volume 1B Mathematics Curriculum Notes/
  2.    wt: 2:   12 Webvideo Lessons on Area and Volume Calculation/
  3.    wt: 2:   Advanced Calculus Volume 3 Appendices/
  4.    wt: 2:   Volume 3 Why Slopes A Calculus Intro Etc/
  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:   Volume 1A Regles et modeles/
  9.    wt: 1:   Mathematics Skills Year by Year/
  10.    wt: 1:   5 Lessons on Integration/
  11.    wt: 1:   4 Lessons on Using Derivatives/
  12.    wt: 1:   38 Lessons on Calculating Derivatives/
  13.    wt: 1:   13 Lessons on Limits and Continuity/
  14.    wt: 1:   70 Calculus Starter Lessons/
  15.    wt: 1:   Volume 2 Three Skills For Algebra/
  16.    wt: 1:   Volume 1A Pattern Based Reason/
  17.    wt: 1:   Volume 1 Elements of Reason/
  18.    wt: 1:   Mathematics 506 Lessons/
  19.    wt: 1:   Secondary Mathematics A Practical Approach/
  20.    wt: 1:   PreSchool and Primary Mathematics or Quantitative Skills/
  21.    wt: 1:   Mathematics Skill Development Framework/

Web Page Search

74 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:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  6.    wt: 2:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  7.    wt: 2:   16 Increasing or decreasing on intervals
  8.    wt: 2:   Chapter 7 Calculus Previews and Calculus Lightly
  9.    wt: 1:   E LAMP Introduction Modern Mathematics
  10.    wt: 1:   C LAMP Introduction Culture in Mathematics Education
  11.    wt: 1:   B LAMP Introduction Curriculum Development Standards
  12.    wt: 1:   Skills Chapter 5 Calculus
  13.    wt: 1:   11 pure mathematics
  14.    wt: 1:   key notes and themes
  15.    wt: 1:   Mathematics Education Professors
  16.    wt: 1:   mathematics in context
  17.    wt: 1:   Secondary Three Mathematics
  18.    wt: 1:   Secondary Two Mathematics
  19.    wt: 1:   Secondary One Mathematics
  20.    wt: 1:   three difficulties
  21.    wt: 1:   Lessening Algebra Difficulties
  22.    wt: 1:   three goals for Mathematics Education
  23.    wt: 1:   02 20 mathematics education references
  24.    wt: 1:   three aims for mathematics students
  25.    wt: 1:   mathematics instruction in general
  26.    wt: 1:   Education in mathematics science and technology
  27.    wt: 1:   three kinds of reason in mathematics
  28.    wt: 1:   words for mathematics instructor
  29.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  30.    wt: 1:   22 Student Centered Highschool Mathematics
  31.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  32.    wt: 1:   18 Primary School Mathematics
  33.    wt: 1:   16 Secondary Mathematics Tips
  34.    wt: 1:   12 Goals and Objectives For Mathematics
  35.    wt: 1:   4 Function notation in and beyond mathematics
  36.    wt: 1:   8 Notes for instructors or tutors
  37.    wt: 1:   12 From Applied To Pure Mathematics
  38.    wt: 1:   Skill Development Notes
  39.    wt: 1:   11 Volume of Sphere
  40.    wt: 1:   10 Volume of Pyramid
  41.    wt: 1:   9 Volume of Cone
  42.    wt: 1:   5 Box Volume Formula Example
  43.    wt: 1:   7 Calculator Usage Notes and Cautions
  44.    wt: 1:   Example 2 volume of a cone
  45.    wt: 1:   Example 1 volume of a pyramid
  46.    wt: 1:   Volume of Solid by Cross Sections Lesson
  47.    wt: 1:   A Related Material in Volume 3
  48.    wt: 1:   A Related lessons in Volume 3
  49.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  50.    wt: 1:   G.1 First Fundamental Theorem of Calculus
  51.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  52.    wt: 1:   Chapter 9 About First Courses in Calculus
  53.    wt: 1:   Fall 1983 Calculus Appetizer
  54.    wt: 1:   Appendix E. How To Study Mathematics and Why
  55.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  56.    wt: 1:   Postscript B Mathematics Education References
  57.    wt: 1:   Chapter 6 Rule Based Reason in Mathematics
  58.    wt: 1:   Chapter 3 Algebra Difficulties
  59.    wt: 1:   Chapter 2 For and Against Mathematics
  60.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  61.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  62.    wt: 1:   R Why Learn Mathematics Skills
  63.    wt: 1:   O On Learning Mathematics and Science
  64.    wt: 1:   N Mathematics Prepare for College Studies
  65.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  66.    wt: 1:   Helping the Blind in Logic and Mathematics
  67.    wt: 1:   Mathematics Education References
  68.    wt: 1:   Mathematics Education References
  69.    wt: 1:   Multiple Ways to Improve Mathematics Skill Development
  70.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  71.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  72.    wt: 1:   Implementation Notes
  73.    wt: 1:   More Algebra and Slope based Calculus Preview
  74.    wt: 1:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years

Extended Search

397 matches:

  1.    wt: 7:   Postscript B Mathematics Education References
  2.    wt: 7:   Chapter 6 Rule Based Reason in Mathematics
  3.    wt: 7:   Chapter 3 Algebra Difficulties
  4.    wt: 7:   Chapter 2 For and Against Mathematics
  5.    wt: 6:   Annotated Links to Material Elsehwere
  6.    wt: 6:   Postscript A Three Remarks
  7.    wt: 6:   Chapter 12 Four Phases
  8.    wt: 6:   Chapter 11 Elementary Instruction
  9.    wt: 6:   Chapter 10 Transition
  10.    wt: 6:   Chapter 9 The Two Ends
  11.    wt: 6:   Chapter 8 Modern Instruction
  12.    wt: 6:   Chapter 7 Two Treatments of Geometry
  13.    wt: 6:   Chapter 5 Four References
  14.    wt: 6:   Chapter 4 Complex Numbers and Why Slopes
  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: 3:   Example 2 volume of a cone
  22.    wt: 3:   Example 1 volume of a pyramid
  23.    wt: 3:   Volume of Solid by Cross Sections Lesson
  24.    wt: 3:   G.2 Lipshitz Conditions Integration Calculus Reform
  25.    wt: 3:   G.1 First Fundamental Theorem of Calculus
  26.    wt: 3:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  27.    wt: 3:   Chapter 9 About First Courses in Calculus
  28.    wt: 3:   Fall 1983 Calculus Appetizer
  29.    wt: 3:   Chapter 7 Calculus Previews and Calculus Lightly
  30.    wt: 2:   E LAMP Introduction Modern Mathematics
  31.    wt: 2:   C LAMP Introduction Culture in Mathematics Education
  32.    wt: 2:   B LAMP Introduction Curriculum Development Standards
  33.    wt: 2:   Skills Chapter 5 Calculus
  34.    wt: 2:   11 pure mathematics
  35.    wt: 2:   key notes and themes
  36.    wt: 2:   Mathematics Education Professors
  37.    wt: 2:   mathematics in context
  38.    wt: 2:   Secondary Three Mathematics
  39.    wt: 2:   Secondary Two Mathematics
  40.    wt: 2:   Secondary One Mathematics
  41.    wt: 2:   three difficulties
  42.    wt: 2:   Lessening Algebra Difficulties
  43.    wt: 2:   three goals for Mathematics Education
  44.    wt: 2:   02 20 mathematics education references
  45.    wt: 2:   three aims for mathematics students
  46.    wt: 2:   mathematics instruction in general
  47.    wt: 2:   Education in mathematics science and technology
  48.    wt: 2:   three kinds of reason in mathematics
  49.    wt: 2:   words for mathematics instructor
  50.    wt: 2:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  51.    wt: 2:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  52.    wt: 2:   16 Increasing or decreasing on intervals
  53.    wt: 2:   Example 1. Area Between x and x squared
  54.    wt: 2:   Area Between Crossing Curves Lesson Take 2
  55.    wt: 2:   Area Between Crossing Curves Lesson Take 1
  56.    wt: 2:   Example 4 with x function of y
  57.    wt: 2:   Example 3
  58.    wt: 2:   Example 2
  59.    wt: 2:   Example 1
  60.    wt: 2:   Area Between Curves Lesson Take 2
  61.    wt: 2:   Area Between Curves Lesson Take 1
  62.    wt: 2:   Summary
  63.    wt: 2:   A Related Material in Volume 3
  64.    wt: 2:   A Related lessons in Volume 3
  65.    wt: 2:   Postscript One Sided and Intermediate Value Theorems
  66.    wt: 2:   G.6 Bounded Derivatives implies Lipshitz Continuity
  67.    wt: 2:   G.5 Motions With Bounded Velocities
  68.    wt: 2:   G.4 Lipschitz Continuity implies EquiContinuity
  69.    wt: 2:   G.3 Constant Difference Theorem Proof
  70.    wt: 2:   G.2 Differentiable Functions Mean Value Theorem
  71.    wt: 2:   G.1 Differentiable Functions Rolles Theorem
  72.    wt: 2:   F.5b Extreme Value Theorem
  73.    wt: 2:   F.5a Equicontinuity Theorems
  74.    wt: 2:   F.4 Finite Covering Theorem
  75.    wt: 2:   F.3 Intermediate Value Theorem
  76.    wt: 2:   F.2 Closed Range Theorem
  77.    wt: 2:   F.1 What Functions are Continuous
  78.    wt: 2:   E2 Algebraic Properties of Limits
  79.    wt: 2:   E1 Error Control Inequalities
  80.    wt: 2:   D2 Limits of Monotone Sequences
  81.    wt: 2:   D1 Sets and Sequences GLBs and LGBs
  82.    wt: 2:   C Triangle Inequalities
  83.    wt: 2:   B3 Bolzano Weierstrass Theorem
  84.    wt: 2:   B1 Pigeon Hole Principles from combinatorics
  85.    wt: 2:   PostScript For and Against Decimal Perspectives
  86.    wt: 2:   A1. Introduction
  87.    wt: 2:   Postscript Pythagorean Theorem yet another proof
  88.    wt: 2:   Chapter 24 Logarithms Powers and Exponentials
  89.    wt: 2:   Chapter 23 Links To Trigonometry
  90.    wt: 2:   Chapter 22 Complex Numbers
  91.    wt: 2:   Chapter 21 Arrow Addition
  92.    wt: 2:   Chapter 20 Vectors and Complex Numbers
  93.    wt: 2:   Chapter 19. Exponentials and Natural Logarithms
  94.    wt: 2:   Chapter 18. Slopes Areas Integration
  95.    wt: 2:   Chapter 17. Area Approximation
  96.    wt: 2:   Chapter 16. Velocity Approximation
  97.    wt: 2:   Chapter 15. Slope Approximation
  98.    wt: 2:   Chapter 15. Algebraic Evaluation of Limits
  99.    wt: 2:   Chapter 14 Limits and Continuity with and sans Decimals
  100.    wt: 2:   Chapter 13. Acceleration
  101.    wt: 2:   Chapter 12. Units and Slopes
  102.    wt: 2:   Chapter 11. Graphing Slope versus Position
  103.    wt: 2:   Chapter 10 Slopes and Units
  104.    wt: 2:   Chapter 8. Slope Interpretation
  105.    wt: 2:   Chapter 7 Slopes and Velocity
  106.    wt: 2:   Chapter 6. Slopes and Vertical Shifts
  107.    wt: 2:   Chapter 5. Slope Sign Tests
  108.    wt: 2:   Chapter 4. More Slope Sign Analysis
  109.    wt: 2:   Chapter 3. Slope Sign Analysis
  110.    wt: 2:   Chapter 2. Slopes and Ski Trails
  111.    wt: 2:   Chapter 1.Introduction
  112.    wt: 2:   Foreword
  113.    wt: 2:   Appendix E. How To Study Mathematics and Why
  114.    wt: 2:   Chapter 7 Prep for Calculus Arithmetic Exercises
  115.    wt: 2:   Chapter 14 Deductive and Empirical Views of Mathematics
  116.    wt: 2:   Appendix A Calculus with Proofs for Keen or Gifted
  117.    wt: 2:   Helping the Blind in Logic and Mathematics
  118.    wt: 2:   Mathematics Education References
  119.    wt: 2:   Mathematics Education References
  120.    wt: 2:   Multiple Ways to Improve Mathematics Skill Development
  121.    wt: 2:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  122.    wt: 2:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  123.    wt: 2:   Implementation Notes
  124.    wt: 2:   More Algebra and Slope based Calculus Preview
  125.    wt: 2:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  126.    wt: 1:   Appendix 2 primary school Arithmetic 01
  127.    wt: 1:   Appendix 1 primary and preschool mathematic
  128.    wt: 1:   K LAMP Musings Science Education
  129.    wt: 1:   J LAMP Introduction Extrinsic Origins
  130.    wt: 1:   I LAMP Introduction Study Habits
  131.    wt: 1:   H LAMP Introduction Instructional Concepts
  132.    wt: 1:   G LAMP Introduction Problem Solving Skills
  133.    wt: 1:   F LAMP Introduction Prerequisites
  134.    wt: 1:   A Introduction Objectives
  135.    wt: 1:   Skills Chapter 4 Logic
  136.    wt: 1:   Ramblings Extrinsic numbers theory
  137.    wt: 1:   Ramblings Introduction Algebra Essay
  138.    wt: 1:   Skills Chapter 3 Algebra
  139.    wt: 1:   Skills Chapter 2 Geometry
  140.    wt: 1:   Skills Chapter 1 Arithmetic
  141.    wt: 1:   Skills Chapter 0 Introduction
  142.    wt: 1:   10 statistics
  143.    wt: 1:   9 combinatorics probability sets
  144.    wt: 1:   8 analytic geometry etc
  145.    wt: 1:   7 logic review and decimals an odd combination
  146.    wt: 1:   6 polynomials etc
  147.    wt: 1:   5 logarithms and exponentials etc
  148.    wt: 1:   4 algebra
  149.    wt: 1:   3 Euclidean Geometry Leanly
  150.    wt: 1:   2 arithmetic with signed numbers
  151.    wt: 1:   1 arithmetic with unsigned numbers
  152.    wt: 1:   What is POMME
  153.    wt: 1:   why bother
  154.    wt: 1:   which way to go
  155.    wt: 1:   website reviews
  156.    wt: 1:   three goals to set for students
  157.    wt: 1:   Teach the teachers plus goals
  158.    wt: 1:   permissions for teachers
  159.    wt: 1:   Math Ed if it must be short make it lean effective
  160.    wt: 1:   Applied Maths Program14092009 POMME variant
  161.    wt: 1:   activities for students
  162.    wt: 1:   links Education Resources online
  163.    wt: 1:   site origins
  164.    wt: 1:   site eurekas
  165.    wt: 1:   About site lesson plans
  166.    wt: 1:   teacher certification
  167.    wt: 1:   modern education
  168.    wt: 1:   learning takes time
  169.    wt: 1:   grouping students according to ability
  170.    wt: 1:   what should be learnt and When
  171.    wt: 1:   Postscript 2007 01 10
  172.    wt: 1:   Education Reform Inconsistencies
  173.    wt: 1:   five decades make a difference
  174.    wt: 1:   Maps Plans Drawings
  175.    wt: 1:   how letters appear
  176.    wt: 1:   talk the algebra talk
  177.    wt: 1:   teaching tips
  178.    wt: 1:   What to Tell Students
  179.    wt: 1:   geometric implications for algebra
  180.    wt: 1:   teaching tutoring algebraic reason
  181.    wt: 1:   the trouble with algebra
  182.    wt: 1:   05 13 OldSiteEntrancePage
  183.    wt: 1:   04 25 when to stop or suspend mathemat
  184.    wt: 1:   02 21 words for teachers
  185.    wt: 1:   standards for course material
  186.    wt: 1:   Operational Viewpoint to Value
  187.    wt: 1:   formal or informal peer review
  188.    wt: 1:   Theory of Knowledge
  189.    wt: 1:   Different Kinds of Reasoning in maths
  190.    wt: 1:   cultivating intelligence
  191.    wt: 1:   Four ways to improve education reform
  192.    wt: 1:   How to be a better instructor
  193.    wt: 1:   Motivation and Context Problem
  194.    wt: 1:   Prequel In For A Penny In For A Pound
  195.    wt: 1:   education an empirical art
  196.    wt: 1:   fairness and inductive principles for instruction
  197.    wt: 1:   chapitre 12 00 les iles et division
  198.    wt: 1:   chapitre 07 01 principle D induction mathematique
  199.    wt: 1:   chapitre 07 00 Des chaines plus longues de la raison
  200.    wt: 1:   chapitre 06 00 Chaines de la raison
  201.    wt: 1:   chapitre 05 00 Deception
  202.    wt: 1:   chapitre 04 10 Etapes pour une meilleur raison
  203.    wt: 1:   chapitre 04 09 Regles accidentelles
  204.    wt: 1:   chapitre 04 08 Limitations et benefices
  205.    wt: 1:   chapitre 04 07 RepetablesEtReproductibles
  206.    wt: 1:   chapitre 04 06 engagements
  207.    wt: 1:   chapitre 04 05 Implication versus suggestion
  208.    wt: 1:   chapitre 04 04 Parlons de la logique
  209.    wt: 1:   chapitre 04 03 Unidirectionnel versus bidirectionnel
  210.    wt: 1:   chapitre 04 02 Deuxieme enigme
  211.    wt: 1:   chapitre 04 01 Premiere enigme
  212.    wt: 1:   chapitre 04 00 Les regles d implication
  213.    wt: 1:   chapitre 03 A Propos Des Prochains Chapitre
  214.    wt: 1:   chapitre 02 00 La Communication des idees
  215.    wt: 1:   chapitre 01 00 Introduction
  216.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  217.    wt: 1:   22 Student Centered Highschool Mathematics
  218.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  219.    wt: 1:   18 Primary School Mathematics
  220.    wt: 1:   16 Secondary Mathematics Tips
  221.    wt: 1:   12 Goals and Objectives For Mathematics
  222.    wt: 1:   Ages 12 to 14 Skills with take home value
  223.    wt: 1:   Ages 12 to 14 Geometry
  224.    wt: 1:   Ages 12 to 14 Arithmetic
  225.    wt: 1:   Ages 10 to 12 Geometry
  226.    wt: 1:   Ages 10 to 12 Arithmetic
  227.    wt: 1:   Ages 9 to 10
  228.    wt: 1:   Ages 8 to 9
  229.    wt: 1:   Ages 7 to 8
  230.    wt: 1:   Ages 6 to 7
  231.    wt: 1:   Ages 4 plus to 5 plus
  232.    wt: 1:   Ages 3 plus to 4 plus
  233.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  234.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  235.    wt: 1:   4 Function notation in and beyond mathematics
  236.    wt: 1:   8 Notes for instructors or tutors
  237.    wt: 1:   12 From Applied To Pure Mathematics
  238.    wt: 1:   Skill Development Notes
  239.    wt: 1:   11 Volume of Sphere
  240.    wt: 1:   10 Volume of Pyramid
  241.    wt: 1:   9 Volume of Cone
  242.    wt: 1:   5 Box Volume Formula Example
  243.    wt: 1:   7 Calculator Usage Notes and Cautions
  244.    wt: 1:   5 Area Under Curve Exercise
  245.    wt: 1:   4 Definite Integrals Evaluation Exercises
  246.    wt: 1:   3 Two Chain Rule Method Exercises
  247.    wt: 1:   2 Indefinite Integrals Exercises
  248.    wt: 1:   1 Chain Rule in Reverse Integration Method
  249.    wt: 1:   4 Second derivative test exercise example
  250.    wt: 1:   3 Second derivative test
  251.    wt: 1:   2 Second derivative test prequel
  252.    wt: 1:   1 Two cubic sketching exercises with 1st derivative
  253.    wt: 1:   A Chain Rule Real Player video examples
  254.    wt: 1:   38 Formulas and derivatives for powers and roots
  255.    wt: 1:   36 Cube root derivative animated
  256.    wt: 1:   34 Derivative of exponential function
  257.    wt: 1:   33 Chain Rule Real Player video examples
  258.    wt: 1:   31 Derivatives of inverse functions
  259.    wt: 1:   30Chain Rule A Proof
  260.    wt: 1:   29 Chain Rule Optional Reading
  261.    wt: 1:   28 Chain Rule Preparation for a Proof
  262.    wt: 1:   27 Chain Rule sinusoidal outer inner functions EGS
  263.    wt: 1:   26 Chain Rule Recognising outer inner functions
  264.    wt: 1:   25 Chain Rule Animated Examples Continued
  265.    wt: 1:   24 Chain Rule Animated Examples
  266.    wt: 1:   23 Chain Rule in general
  267.    wt: 1:   22 Chain Rule for polynomials
  268.    wt: 1:   21 Chain Rule for powers
  269.    wt: 1:   20 Chain Rule for Pulley Systems
  270.    wt: 1:   19 Chain Rule for linear functions
  271.    wt: 1:   18 Chain Rule Introduction
  272.    wt: 1:   17 Derivatives of quotients of sine and cosine
  273.    wt: 1:   16 Derivatives of reciprocals of sine and cosine
  274.    wt: 1:   15 sine and cosine derivatives 3rd step
  275.    wt: 1:   14 sine and cosine derivatives 2nd step
  276.    wt: 1:   13 sine and cosine derivatives 1st step
  277.    wt: 1:   12 Quotient rule examples
  278.    wt: 1:   11 Quotient rule
  279.    wt: 1:   10 Power rule for negative integers
  280.    wt: 1:   9 Reciprocal rule
  281.    wt: 1:   8 Differentiation of polynomials
  282.    wt: 1:   7 Animated Differentiation Examples
  283.    wt: 1:   6 Power rule from product rule
  284.    wt: 1:   5 Product Rule
  285.    wt: 1:   4 Sum Rule
  286.    wt: 1:   3 Motivation for Limit Definition Take 2
  287.    wt: 1:   2 Motivation for Limit Definition Take 1
  288.    wt: 1:   1 Fall 1983 Why Slopes Appetizer
  289.    wt: 1:   13 Limits with Parameters and Derivatives Take II
  290.    wt: 1:   12 Limits with Parameters and Derivatives Take I
  291.    wt: 1:   11 Limits at infinity Three Examples
  292.    wt: 1:   10 Three one sided limits with infinite values
  293.    wt: 1:   9 Limits Continuity and Composition
  294.    wt: 1:   8 Four Animated Examples
  295.    wt: 1:   7 Evaluation by immediate or delayed substitution
  296.    wt: 1:   6 Continuity at a point
  297.    wt: 1:   5 Jumps and absence of unlimited error control
  298.    wt: 1:   4 Numerical properties
  299.    wt: 1:   3 Decimal insights for limits continuity convergence
  300.    wt: 1:   2 Algebraic codification
  301.    wt: 1:   1 Numerical introduction
  302.    wt: 1:   Postscript More on Better Performance
  303.    wt: 1:   Postscript For Better Performance
  304.    wt: 1:   Appendix D. What to do in School and Why
  305.    wt: 1:   Appendix C. How to Read
  306.    wt: 1:   Appendix B. How To Learn
  307.    wt: 1:   Appendix A. Reading Guide For Next Appendices
  308.    wt: 1:   Chapter 31 Direct and Indirect Reason
  309.    wt: 1:   Chapter 30 Truth Tables
  310.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  311.    wt: 1:   Chapter 28 Occurrence Tables
  312.    wt: 1:   Chapter 27 Shorthand Symbols as Pronouns
  313.    wt: 1:   Chapter 26 What is in chapters 27 to 31
  314.    wt: 1:   Chapter 25. Mathematical Induction Examples
  315.    wt: 1:   Chapter 24. Personal Investment and Pension EGS
  316.    wt: 1:   Chapter 23. Notation For Sums
  317.    wt: 1:   Chapter 22. Geometric Sums and Sequences
  318.    wt: 1:   Chapter 21. Third Reading Guide
  319.    wt: 1:   Chapter 20. Degrees and Radians
  320.    wt: 1:   Chapter 19. Functions and Sets
  321.    wt: 1:   Chapter 18. Rules for Algebra
  322.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  323.    wt: 1:   Chapter 16. Painless Theorem Proving
  324.    wt: 1:   Chapter 15. Solving Linear Equations
  325.    wt: 1:   Chapter 14. Forward and Backward Use of a Formula
  326.    wt: 1:   Postscript Unifying Theme A Fourth Skill For Algebra
  327.    wt: 1:   Chapter 13. Second Reading Guide
  328.    wt: 1:   Chapter 12. Shorthand Usage Guide
  329.    wt: 1:   Chapter 11. Why Shorthand
  330.    wt: 1:   Chapter 10 Describing and Changing Calculations
  331.    wt: 1:   Postscript What is a Variable
  332.    wt: 1:   Chapter 9 Talking about Numbers or Quantities
  333.    wt: 1:   Chapter 8 Three Skills For Algebra
  334.    wt: 1:   Solutions For Arithmetic Exercises
  335.    wt: 1:   Chapter 6 Change of Language
  336.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  337.    wt: 1:   Chapter 4 Longer Chains of Reason
  338.    wt: 1:   Chapter 3 Chains of Reason
  339.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  340.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  341.    wt: 1:   Foreword
  342.    wt: 1:   Postscript D Reflections on Law of the Excluded Middle
  343.    wt: 1:   Postscript C Consistency as a Tool for Reason
  344.    wt: 1:   Postscript B More on Story Telling and Reason
  345.    wt: 1:   Postscript A Story Telling
  346.    wt: 1:   Chapter 24 Direct and Indirect Reason
  347.    wt: 1:   Chapter 23 Truth Tables
  348.    wt: 1:   Chapter 22 Contrapositive and Vacuously True Implications
  349.    wt: 1:   Chapter 21 Occurrence Tables
  350.    wt: 1:   Chapter 20 Shorthand Symbols as Pronouns
  351.    wt: 1:   Chapter 19 What is in chapters 20 to 24
  352.    wt: 1:   Chapter 18 Sense and Knowledge
  353.    wt: 1:   Chapter 17 Objective Ways Trial and Error Discovery
  354.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  355.    wt: 1:   Chapter 15 Objective Processes
  356.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  357.    wt: 1:   Chapter 12 Islands and Divisions of Knowledge
  358.    wt: 1:   Chapter 11 Accidental Patterns
  359.    wt: 1:   Chapter 10 Responsibility
  360.    wt: 1:   Chapter 9 What is in Chapters 10 to 18
  361.    wt: 1:   Chapter 8 Change of Language
  362.    wt: 1:   Chapter 7 Longer Chains of Reason
  363.    wt: 1:   Chapter 6 Chains of Reason
  364.    wt: 1:   Chapter 5 Deception
  365.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  366.    wt: 1:   Chapter 3 What is in chapters 4 to 8
  367.    wt: 1:   Chapter 2 Skill Development
  368.    wt: 1:   Chapter 1 Introduction
  369.    wt: 1:   Three Remarks
  370.    wt: 1:   Foreword
  371.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  372.    wt: 1:   R Why Learn Mathematics Skills
  373.    wt: 1:   O On Learning Mathematics and Science
  374.    wt: 1:   N Mathematics Prepare for College Studies
  375.    wt: 1:   Chapter 8 Skipped Topics and Why
  376.    wt: 1:   Chapter 6 More Algebra and Geometry
  377.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  378.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  379.    wt: 1:   Chapter 3 Algebra Starter Lessons
  380.    wt: 1:   Chapter 2 Why Sets
  381.    wt: 1:   Chapter 1 Arithmetic
  382.    wt: 1:   Primary and Secondary Skills and Practices with Take Home Value
  383.    wt: 1:   7 Games and Activities for Instruction
  384.    wt: 1:   6 Measuring via counting or arithmetic the role of fractions
  385.    wt: 1:   5 Interpreting and Drawing Maps and Plans.
  386.    wt: 1:   4 Money Matters Saving Earning Buying Selling and Budgets
  387.    wt: 1:   3 Telling Tracking Time Temporal and More Place Sense
  388.    wt: 1:   2 Identifying Size and Position Place and Spatial Sense
  389.    wt: 1:   1 From Number Recognition and Counting to Arithmetic B
  390.    wt: 1:   1 From Number Recognition and Counting to Arithmetic A
  391.    wt: 1:   Ends Values Methods For Skill Development Framework Prequel
  392.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  393.    wt: 1:   Systematic Algebra Skill Development Missing Links
  394.    wt: 1:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  395.    wt: 1:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  396.    wt: 1:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  397.    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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