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/
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  4.    wt: 1:   Mathematics Education Essays/
  5.    wt: 1:   Volume 1A Regles et modeles/
  6.    wt: 1:   Mathematics Skills Year by Year/
  7.    wt: 1:   2 Euclidean Geometry Constructions Theory extras/
  8.    wt: 1:   12 Webvideo Lessons on Area and Volume Calculation/
  9.    wt: 1:   Advanced Calculus Volume 3 Appendices/
  10.    wt: 1:   Volume 3 Why Slopes A Calculus Intro Etc/
  11.    wt: 1:   Volume 2 Three Skills For Algebra/
  12.    wt: 1:   Volume 1A Pattern Based Reason/
  13.    wt: 1:   Volume 1 Elements of Reason/
  14.    wt: 1:   Mathematics 506 Lessons/
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  1.    wt: 2:   mathematics curriculum shifts
  2.    wt: 2:   04 29 New Mathematics Curriculum
  3.    wt: 2:   need for a mixed mathematics curriculum
  4.    wt: 2:   Leaner mathematics curriculum
  5.    wt: 1:   E LAMP Introduction Modern Mathematics
  6.    wt: 1:   C LAMP Introduction Culture in Mathematics Education
  7.    wt: 1:   B LAMP Introduction Curriculum Development Standards
  8.    wt: 1:   11 pure mathematics
  9.    wt: 1:   3 Euclidean Geometry Leanly
  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:   12 Goals and Objectives For Mathematics
  31.    wt: 1:   4 Function notation in and beyond mathematics
  32.    wt: 1:   8 Notes for instructors or tutors
  33.    wt: 1:   12 From Applied To Pure Mathematics
  34.    wt: 1:   Euclidean Geometry Elsewhere LINKS
  35.    wt: 1:   Short Course on Euclidean Geometry
  36.    wt: 1:   Skill Development Notes
  37.    wt: 1:   11 Volume of Sphere
  38.    wt: 1:   10 Volume of Pyramid
  39.    wt: 1:   9 Volume of Cone
  40.    wt: 1:   5 Box Volume Formula Example
  41.    wt: 1:   8 GCD from Euclidean Algorithm
  42.    wt: 1:   7 Calculator Usage Notes and Cautions
  43.    wt: 1:   6 Multiplication Commutes Order Not Important
  44.    wt: 1:   Example 2 volume of a cone
  45.    wt: 1:   Example 1 volume of a pyramid
  46.    wt: 1:   Volume of Solid by Cross Sections Lesson
  47.    wt: 1:   A Related Material in Volume 3
  48.    wt: 1:   A Related lessons in Volume 3
  49.    wt: 1:   Appendix E. How To Study Mathematics and Why
  50.    wt: 1:   Postscript B Mathematics Education References
  51.    wt: 1:   Chapter 6 Rule Based Reason in Mathematics
  52.    wt: 1:   Chapter 2 For and Against Mathematics
  53.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  54.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  55.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  56.    wt: 1:   R Why Learn Mathematics Skills
  57.    wt: 1:   O On Learning Mathematics and Science
  58.    wt: 1:   N Mathematics Prepare for College Studies
  59.    wt: 1:   Helping the Blind in Logic and Mathematics
  60.    wt: 1:   Mathematics Education References
  61.    wt: 1:   Mathematics Education References
  62.    wt: 1:   Multiple Ways to Improve Mathematics Skill Development
  63.    wt: 1:   Implementation Notes
  64.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  65.    wt: 1:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  66.    wt: 1:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years

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