Original Site Title: Appetizers and Lessons for Mathematics and Reason, June 1995 to April 2012. New site title:
Logic and Mathematics Skill & Concept Building Site Map || Français: 26 pages
for college students, gifted teens, home-tutoring and K1-12 schooling, with chapters on Logic and Pattern Based Reason to inform and amuse.

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 material may develop critical thinking, improve reading and writing, and build mathematics and pattern based reasoning skills. Online Volumes 1, 1A and 2 give avid readers in school and out the best places to begin.

Teachers & Tutors: This December 2011, 5-phase framework offers a context for mathematics & logic education. Phases 1 to 3 focus on skills with actual or potential local 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: 4:   Mathematics Education Essays/
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  5.    wt: 2:   Progressive Observable Motivated Mathematics Education/
  6.    wt: 2:   3 Quadratics Geometrically/
  7.    wt: 2:   10 Examples of Algebraic Reasoning/
  8.    wt: 2:   9 Proportionality Backwards and Forwards/
  9.    wt: 2:   Volume 2 Three Skills For Algebra/
  10.    wt: 1:   LAMP Lean Applied Mathematics Program/
  11.    wt: 1:   Archives/
  12.    wt: 1:   5 Factored Polynomial Sign Analysis Examples/
  13.    wt: 1:   4 Functions/
  14.    wt: 1:   2 Natural Logarithms Exponentials Powers Roots/
  15.    wt: 1:   1 Five Polynomial Operations/
  16.    wt: 1:   More Algebra/
  17.    wt: 1:   B Real Numbers Extrinsic Development/
  18.    wt: 1:   A Origins of Counting and Figuring Methods/
  19.    wt: 1:   7 Axioms Logic and Equivalent Equations/
  20.    wt: 1:   6 More Less Greater Than Inequalities and Comparison/
  21.    wt: 1:   5 Real Numbers/
  22.    wt: 1:   4 Computation Rules and Function Notation/
  23.    wt: 1:   Step 4 Gaussian Elimination/
  24.    wt: 1:   Step 3 Easy systems in 2 or more unknowns/
  25.    wt: 1:   Step 1 Stick diagram and fractions/
  26.    wt: 1:   3 Solving Linear Equations/
  27.    wt: 1:   1 Working With Sets/
  28.    wt: 1:   Algebra Starter Lessons/
  29.    wt: 1:   Volume 3 Why Slopes A Calculus Intro Etc/

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226 matches:

  1.    wt: 4:   geometric implications for algebra
  2.    wt: 3:   5 Function notation for geometric transformations
  3.    wt: 2:   Education Reform Inconsistencies
  4.    wt: 2:   three goals for Mathematics Education
  5.    wt: 2:   formal or informal peer review
  6.    wt: 2:   Four ways to improve education reform
  7.    wt: 2:   Prequel In For A Penny In For A Pound
  8.    wt: 2:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  9.    wt: 2:   9 Formulas for Real Exponents with Logarithms
  10.    wt: 2:   8 Formulas for Fractional Exponents with Logarithms
  11.    wt: 2:   7 Formulas for Roots with Logarithms Derivation
  12.    wt: 2:   6 Formulas for Even and Odd Roots with Logarithms
  13.    wt: 2:   26 Formulas for products of sines and cosines
  14.    wt: 2:   17E Trig Formulas for dot and cross Products
  15.    wt: 2:   17D cis formulas for sine cosines and tangent
  16.    wt: 2:   13 Trig Formulas for dot and cross Products
  17.    wt: 2:   12 cis formulas for sine cosines and tangent
  18.    wt: 2:   4 Equations for lines three forms
  19.    wt: 2:   9 Circle Area and Perimeter Formula Backwards Forwards
  20.    wt: 2:   3 Geometric Formulas and Function Notation
  21.    wt: 2:   Formula Usage Show Work Format
  22.    wt: 2:   1 Written work formats for developing and showing skill
  23.    wt: 2:   1 Three Skills For Algebra
  24.    wt: 2:   38 Formulas and derivatives for powers and roots
  25.    wt: 2:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  26.    wt: 2:   Postscript For Better Performance
  27.    wt: 2:   Chapter 18. Rules for Algebra
  28.    wt: 2:   Chapter 14. Forward and Backward Use of a Formula
  29.    wt: 2:   Postscript Unifying Theme A Fourth Skill For Algebra
  30.    wt: 2:   Chapter 8 Three Skills For Algebra
  31.    wt: 2:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  32.    wt: 2:   G. Written work formats for developing and showing skill
  33.    wt: 2:   Chapter 4 Logic for Reading Writing and Geometry etc
  34.    wt: 1:   K LAMP Musings Science Education
  35.    wt: 1:   C LAMP Introduction Culture in Mathematics Education
  36.    wt: 1:   Ramblings Introduction Algebra Essay
  37.    wt: 1:   Skills Chapter 3 Algebra
  38.    wt: 1:   8 analytic geometry etc
  39.    wt: 1:   6 polynomials etc
  40.    wt: 1:   5 logarithms and exponentials etc
  41.    wt: 1:   4 algebra
  42.    wt: 1:   three goals to set for students
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  47.    wt: 1:   modern education
  48.    wt: 1:   talk the algebra talk
  49.    wt: 1:   teaching tutoring algebraic reason
  50.    wt: 1:   Lessening Algebra Difficulties
  51.    wt: 1:   the trouble with algebra
  52.    wt: 1:   02 21 words for teachers
  53.    wt: 1:   02 20 mathematics education references
  54.    wt: 1:   three aims for mathematics students
  55.    wt: 1:   standards for course material
  56.    wt: 1:   Education in mathematics science and technology
  57.    wt: 1:   need for a mixed mathematics curriculum
  58.    wt: 1:   education an empirical art
  59.    wt: 1:   fairness and inductive principles for instruction
  60.    wt: 1:   words for mathematics instructor
  61.    wt: 1:   C Electromotive force conventional current02
  62.    wt: 1:   B Electromotive force conventional current01
  63.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  64.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  65.    wt: 1:   24 Standards For Skill Develoment Take II
  66.    wt: 1:   24 Standards For Skill Develoment
  67.    wt: 1:   17 Math Booklets for children and young teenagers
  68.    wt: 1:   15 Counting For Parents
  69.    wt: 1:   12 Goals and Objectives For Mathematics
  70.    wt: 1:   11 Help and Defend Your Child or Teens Education
  71.    wt: 1:   10 Ends values for work study instruction
  72.    wt: 1:   5 Patience Please for Yourself and Your Charges
  73.    wt: 1:   4 Learning Takes Time and Effort
  74.    wt: 1:   3 Preparing for Science Studies
  75.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  76.    wt: 1:   6 Set Existence Formation and Notation
  77.    wt: 1:   3 Formula or function graphing exercise
  78.    wt: 1:   2 Algebraic use of function notation
  79.    wt: 1:   1 Geometric Introduction of Function Notation
  80.    wt: 1:   8 quadratics backward use of various formulas
  81.    wt: 1:   7 quadratic formulla derivation
  82.    wt: 1:   8 Notes for instructors or tutors
  83.    wt: 1:   Rewriting algebraic substitution as function substitutions
  84.    wt: 1:   12 motivation for term arctan
  85.    wt: 1:   9 motivation for name arcsin
  86.    wt: 1:   4 possible motivation for term arccos
  87.    wt: 1:   Construction Methods and Criteria for Isometric and Similar Triangles
  88.    wt: 1:   SAS Method For Isometric Or Proportional Triangle Construction
  89.    wt: 1:   8 Straight Lines Equation for vertical
  90.    wt: 1:   17 tangent function angle sum formulas
  91.    wt: 1:   29 secant cosecant and cotangent for acute angles
  92.    wt: 1:   25 tangent double angle formula Slope connection
  93.    wt: 1:   24 tangent Angle Difference Formula
  94.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  95.    wt: 1:   21 sine and cosine Half Angle Formulas
  96.    wt: 1:   20 sine and cosine Double Angle Formulas
  97.    wt: 1:   19 Pythagorean Identity For sine and cosine functions
  98.    wt: 1:   17C sine and cosine double triple angle formulas
  99.    wt: 1:   17B sine cosine Angle Sum Formulas via cis
  100.    wt: 1:   12 Graph of tangent function for one period
  101.    wt: 1:   6 sines and cosines for reference angle 30 degrees
  102.    wt: 1:   5 sines and cosines for reference angle 60 degrees
  103.    wt: 1:   4 sines and cosines for reference angle 45 degrees
  104.    wt: 1:   3 sines and cosines for reference angle 90 degrees
  105.    wt: 1:   11 sine and cosine double triple angle formulas
  106.    wt: 1:   10 sine cosine Angle Sum Formulas via cis
  107.    wt: 1:   5 Trigonometric Ratios For Tangent and Special Triangles
  108.    wt: 1:   4 Trigonometric Ratios For Two Special Triangles
  109.    wt: 1:   6 Geometric Diagrams in Class
  110.    wt: 1:   8 Mid Point Formula
  111.    wt: 1:   5 Algebraic View of Slopes
  112.    wt: 1:   3 Slope product for perpendicular lines
  113.    wt: 1:   2 point slope equation for a line
  114.    wt: 1:   13 Pythagorean spatial distance formulas
  115.    wt: 1:   10 Pythagorean plane distance formula
  116.    wt: 1:   PS H Distributive Law For Complex Numbers
  117.    wt: 1:   18 Geometrically Why Vector Addition Commutes
  118.    wt: 1:   6 Column Methods for Decimal Multiplication
  119.    wt: 1:   5 Distributive Law for Whole Numbers
  120.    wt: 1:   4 Commutative Law Groups Counting Form
  121.    wt: 1:   3 Inequalities Algebraically
  122.    wt: 1:   2 Algebraic View
  123.    wt: 1:   8 Pythagorean Relation Forwards Backwards
  124.    wt: 1:   6 Compound Interest Forward and Backwards
  125.    wt: 1:   5 Triangle Area Formula Backwards
  126.    wt: 1:   4 Rectangle Area and Like Formulas Backwards
  127.    wt: 1:   5 Equality in Algebra
  128.    wt: 1:   3 Product Axioms Two Forms
  129.    wt: 1:   2 More and Less Than for Counts and Measures
  130.    wt: 1:   9 Coordinates for Regions in Space
  131.    wt: 1:   8 Coordinates for Maps and Planes
  132.    wt: 1:   1 Formulas Dependence and Function Notation
  133.    wt: 1:   5 Gaussian Elimination for 3 unknowns 2nd example
  134.    wt: 1:   6 Algebraic Solution Example
  135.    wt: 1:   5 Algebraic Solutions Introduction
  136.    wt: 1:   Using Letters for Physical Quantities
  137.    wt: 1:   13 Naming Identifying Formulas with Words
  138.    wt: 1:   8 Compound Interest Formula Evaluation
  139.    wt: 1:   7 Compound Interest Formula Introduction
  140.    wt: 1:   5 Box Volume Formula Example
  141.    wt: 1:   4 Circle Area Formula Example
  142.    wt: 1:   3 Triangle Area Formula Example
  143.    wt: 1:   2 Another Rectangle Area Formula Example
  144.    wt: 1:   3 Counting with Sets etc
  145.    wt: 1:   4 A Brief Story of numbers and algebra
  146.    wt: 1:   arithmetic videos Real Player Format
  147.    wt: 1:   1 More and Less Than for Counts and Measures
  148.    wt: 1:   4 signed coordinates for regions in space
  149.    wt: 1:   3 signed coordinates for maps and planes
  150.    wt: 1:   5 Reciprocals and Division for Fractions with Units
  151.    wt: 1:   C Equality for Fractions and Two Term Ratios and Fractions
  152.    wt: 1:   21 Reciprocals for Fractions and Wholes
  153.    wt: 1:   13 Fraction Comparison Algebraic View
  154.    wt: 1:   11 Simplification an Algebraic View
  155.    wt: 1:   6 Multiplication Algebraically Take II
  156.    wt: 1:   11 Adding Integers Formulas and Examples
  157.    wt: 1:   10 Integer Multiplication Formulas
  158.    wt: 1:   25 Divisibility Tests for 2 3 5 9 10 Example
  159.    wt: 1:   24 Divisibility Tests for 2 3 5 9 10
  160.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  161.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  162.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  163.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  164.    wt: 1:   Long Division forwards and backwards Example 3
  165.    wt: 1:   Long Division forwards and backwards Example 2
  166.    wt: 1:   Long Division forwards and backwards Example 1
  167.    wt: 1:   A Elementary Basis for Multiplication Methods
  168.    wt: 1:   Video Decimal Multiplication Geometric View Example 2
  169.    wt: 1:   Video Decimal Multiplication Geometric View Example 2
  170.    wt: 1:   7 Subtraction for Decimal Fractions with Exercises
  171.    wt: 1:   5 A Tip for Efficent Subtraction
  172.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  173.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  174.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  175.    wt: 1:   Quick history of numbers and algebra
  176.    wt: 1:   Formula Evaluation how to show work
  177.    wt: 1:   Practical Methods Ends and Values for Arithmetic
  178.    wt: 1:   1 Two cubic sketching exercises with 1st derivative
  179.    wt: 1:   28 Chain Rule Preparation for a Proof
  180.    wt: 1:   22 Chain Rule for polynomials
  181.    wt: 1:   21 Chain Rule for powers
  182.    wt: 1:   20 Chain Rule for Pulley Systems
  183.    wt: 1:   19 Chain Rule for linear functions
  184.    wt: 1:   10 Power rule for negative integers
  185.    wt: 1:   3 Motivation for Limit Definition Take 2
  186.    wt: 1:   2 Motivation for Limit Definition Take 1
  187.    wt: 1:   3 Decimal insights for limits continuity convergence
  188.    wt: 1:   2 Algebraic codification
  189.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  190.    wt: 1:   E2 Algebraic Properties of Limits
  191.    wt: 1:   PostScript For and Against Decimal Perspectives
  192.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  193.    wt: 1:   Foreword
  194.    wt: 1:   Postscript More on Better Performance
  195.    wt: 1:   Appendix A. Reading Guide For Next Appendices
  196.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  197.    wt: 1:   Chapter 23. Notation For Sums
  198.    wt: 1:   Chapter 22. Geometric Sums and Sequences
  199.    wt: 1:   Solutions For Arithmetic Exercises
  200.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  201.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  202.    wt: 1:   Foreword
  203.    wt: 1:   Postscript B Mathematics Education References
  204.    wt: 1:   Chapter 3 Algebra Difficulties
  205.    wt: 1:   Chapter 2 For and Against Mathematics
  206.    wt: 1:   Foreword
  207.    wt: 1:   Postscript C Consistency as a Tool for Reason
  208.    wt: 1:   Chapter 22 Contrapositive and Vacuously True Implications
  209.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  210.    wt: 1:   Foreword
  211.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  212.    wt: 1:   S Adding words to algebra
  213.    wt: 1:   N Mathematics Prepare for College Studies
  214.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  215.    wt: 1:   Chapter 6 More Algebra and Geometry
  216.    wt: 1:   Chapter 3 Algebra Starter Lessons
  217.    wt: 1:   7 Games and Activities for Instruction
  218.    wt: 1:   Mathematics Education References
  219.    wt: 1:   Mathematics Education References
  220.    wt: 1:   Ends Values Methods For Skill Development Framework Prequel
  221.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  222.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  223.    wt: 1:   More Algebra and Slope based Calculus Preview
  224.    wt: 1:   Systematic Algebra Skill Development Missing Links
  225.    wt: 1:   Talking pdf files for online lessons a webvideo alternative
  226.    wt: 1:   The Math Forum and Site Content

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510 matches:

  1.    wt: 8:   geometric implications for algebra
  2.    wt: 6:   Education Reform Inconsistencies
  3.    wt: 6:   three goals for Mathematics Education
  4.    wt: 6:   formal or informal peer review
  5.    wt: 6:   Four ways to improve education reform
  6.    wt: 6:   Prequel In For A Penny In For A Pound
  7.    wt: 5:   three goals to set for students
  8.    wt: 5:   permissions for teachers
  9.    wt: 5:   activities for students
  10.    wt: 5:   links Education Resources online
  11.    wt: 5:   Mathematics Education Professors
  12.    wt: 5:   modern education
  13.    wt: 5:   talk the algebra talk
  14.    wt: 5:   teaching tutoring algebraic reason
  15.    wt: 5:   Lessening Algebra Difficulties
  16.    wt: 5:   the trouble with algebra
  17.    wt: 5:   02 21 words for teachers
  18.    wt: 5:   02 20 mathematics education references
  19.    wt: 5:   three aims for mathematics students
  20.    wt: 5:   standards for course material
  21.    wt: 5:   Education in mathematics science and technology
  22.    wt: 5:   need for a mixed mathematics curriculum
  23.    wt: 5:   education an empirical art
  24.    wt: 5:   fairness and inductive principles for instruction
  25.    wt: 5:   words for mathematics instructor
  26.    wt: 5:   9 Circle Area and Perimeter Formula Backwards Forwards
  27.    wt: 5:   1 Written work formats for developing and showing skill
  28.    wt: 4:   why bother
  29.    wt: 4:   which way to go
  30.    wt: 4:   website reviews
  31.    wt: 4:   Teach the teachers plus goals
  32.    wt: 4:   Math Ed if it must be short make it lean effective
  33.    wt: 4:   Applied Maths Program14092009 POMME variant
  34.    wt: 4:   site origins
  35.    wt: 4:   site eurekas
  36.    wt: 4:   About site lesson plans
  37.    wt: 4:   key notes and themes
  38.    wt: 4:   teacher certification
  39.    wt: 4:   learning takes time
  40.    wt: 4:   grouping students according to ability
  41.    wt: 4:   what should be learnt and When
  42.    wt: 4:   mathematics in context
  43.    wt: 4:   Postscript 2007 01 10
  44.    wt: 4:   five decades make a difference
  45.    wt: 4:   Maps Plans Drawings
  46.    wt: 4:   how letters appear
  47.    wt: 4:   Secondary Three Mathematics
  48.    wt: 4:   Secondary Two Mathematics
  49.    wt: 4:   Secondary One Mathematics
  50.    wt: 4:   three difficulties
  51.    wt: 4:   teaching tips
  52.    wt: 4:   What to Tell Students
  53.    wt: 4:   mathematics curriculum shifts
  54.    wt: 4:   05 13 OldSiteEntrancePage
  55.    wt: 4:   04 29 New Mathematics Curriculum
  56.    wt: 4:   04 25 when to stop or suspend mathemat
  57.    wt: 4:   Operational Viewpoint to Value
  58.    wt: 4:   Theory of Knowledge
  59.    wt: 4:   mathematics instruction in general
  60.    wt: 4:   Different Kinds of Reasoning in maths
  61.    wt: 4:   three kinds of reason in mathematics
  62.    wt: 4:   cultivating intelligence
  63.    wt: 4:   How to be a better instructor
  64.    wt: 4:   Motivation and Context Problem
  65.    wt: 4:   Leaner mathematics curriculum
  66.    wt: 4:   5 Function notation for geometric transformations
  67.    wt: 4:   8 Pythagorean Relation Forwards Backwards
  68.    wt: 4:   6 Compound Interest Forward and Backwards
  69.    wt: 4:   5 Triangle Area Formula Backwards
  70.    wt: 4:   4 Rectangle Area and Like Formulas Backwards
  71.    wt: 4:   6 Algebraic Solution Example
  72.    wt: 4:   5 Algebraic Solutions Introduction
  73.    wt: 4:   13 Naming Identifying Formulas with Words
  74.    wt: 4:   8 Compound Interest Formula Evaluation
  75.    wt: 4:   7 Compound Interest Formula Introduction
  76.    wt: 4:   5 Box Volume Formula Example
  77.    wt: 4:   4 Circle Area Formula Example
  78.    wt: 4:   3 Triangle Area Formula Example
  79.    wt: 4:   2 Another Rectangle Area Formula Example
  80.    wt: 4:   Postscript For Better Performance
  81.    wt: 4:   Chapter 18. Rules for Algebra
  82.    wt: 4:   Chapter 14. Forward and Backward Use of a Formula
  83.    wt: 4:   Postscript Unifying Theme A Fourth Skill For Algebra
  84.    wt: 4:   Chapter 8 Three Skills For Algebra
  85.    wt: 3:   8 analytic geometry etc
  86.    wt: 3:   6 polynomials etc
  87.    wt: 3:   5 logarithms and exponentials etc
  88.    wt: 3:   4 algebra
  89.    wt: 3:   8 quadratics backward use of various formulas
  90.    wt: 3:   7 quadratic formulla derivation
  91.    wt: 3:   9 Formulas for Real Exponents with Logarithms
  92.    wt: 3:   8 Formulas for Fractional Exponents with Logarithms
  93.    wt: 3:   7 Formulas for Roots with Logarithms Derivation
  94.    wt: 3:   6 Formulas for Even and Odd Roots with Logarithms
  95.    wt: 3:   3 Inequalities Algebraically
  96.    wt: 3:   2 Algebraic View
  97.    wt: 3:   7 Pythagorean Theorem Chinese Square Proof
  98.    wt: 3:   3 Linear Equation Literal Solution More
  99.    wt: 3:   2 Linear Equation Literal Solution
  100.    wt: 3:   1 Changing Calculations
  101.    wt: 3:   3 Geometric Formulas and Function Notation
  102.    wt: 3:   4 Four Examples Fractional Coefficients
  103.    wt: 3:   3 Four Examples
  104.    wt: 3:   2 Three Examples
  105.    wt: 3:   1 Proper Equal Sign Usage
  106.    wt: 3:   Formula Usage Show Work Format
  107.    wt: 3:   12 Cone Cylinder Sphere Lesson Idea
  108.    wt: 3:   11 Volume of Sphere
  109.    wt: 3:   10 Volume of Pyramid
  110.    wt: 3:   9 Volume of Cone
  111.    wt: 3:   6 Pythagorean Hypotenuse Calculation Example
  112.    wt: 3:   1 Three Skills For Algebra
  113.    wt: 3:   Postscript More on Better Performance
  114.    wt: 3:   Appendix A. Reading Guide For Next Appendices
  115.    wt: 3:   Chapter 29 Contrapositive and Vacuously True Implications
  116.    wt: 3:   Chapter 23. Notation For Sums
  117.    wt: 3:   Chapter 22. Geometric Sums and Sequences
  118.    wt: 3:   Solutions For Arithmetic Exercises
  119.    wt: 3:   Chapter 7 Prep for Calculus Arithmetic Exercises
  120.    wt: 3:   Chapter 2 Implication Rules Forwards and Backwards
  121.    wt: 3:   Foreword
  122.    wt: 2:   K LAMP Musings Science Education
  123.    wt: 2:   C LAMP Introduction Culture in Mathematics Education
  124.    wt: 2:   Ramblings Introduction Algebra Essay
  125.    wt: 2:   Skills Chapter 3 Algebra
  126.    wt: 2:   11 pure mathematics
  127.    wt: 2:   10 statistics
  128.    wt: 2:   9 combinatorics probability sets
  129.    wt: 2:   7 logic review and decimals an odd combination
  130.    wt: 2:   3 Euclidean Geometry Leanly
  131.    wt: 2:   2 arithmetic with signed numbers
  132.    wt: 2:   1 arithmetic with unsigned numbers
  133.    wt: 2:   What is POMME
  134.    wt: 2:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  135.    wt: 2:   6 Set Existence Formation and Notation
  136.    wt: 2:   3 Formula or function graphing exercise
  137.    wt: 2:   2 Algebraic use of function notation
  138.    wt: 2:   1 Geometric Introduction of Function Notation
  139.    wt: 2:   A Quadratics Summary
  140.    wt: 2:   10 quadratic exercises
  141.    wt: 2:   9 quadratics physical and further context
  142.    wt: 2:   6 quadratics numerical approach
  143.    wt: 2:   5 quadratics completing the square
  144.    wt: 2:   4 quadratics difference of two squares
  145.    wt: 2:   3 quadratics factoring by inspection
  146.    wt: 2:   2 quadratics graphing in general
  147.    wt: 2:   1 quadratics graphing exercises
  148.    wt: 2:   Quadratics in 10 steps
  149.    wt: 2:   8 Notes for instructors or tutors
  150.    wt: 2:   Rewriting algebraic substitution as function substitutions
  151.    wt: 2:   26 Formulas for products of sines and cosines
  152.    wt: 2:   17E Trig Formulas for dot and cross Products
  153.    wt: 2:   17D cis formulas for sine cosines and tangent
  154.    wt: 2:   13 Trig Formulas for dot and cross Products
  155.    wt: 2:   12 cis formulas for sine cosines and tangent
  156.    wt: 2:   4 Equations for lines three forms
  157.    wt: 2:   18 Geometrically Why Vector Addition Commutes
  158.    wt: 2:   6 Column Methods for Decimal Multiplication
  159.    wt: 2:   5 Distributive Law for Whole Numbers
  160.    wt: 2:   4 Commutative Law Groups Counting Form
  161.    wt: 2:   5 Areas of Rectangles Revisited
  162.    wt: 2:   4 Fraction Operations Axiomatic Development
  163.    wt: 2:   2 Fraction Operations Physical Development
  164.    wt: 2:   1 Decimals Modular and Remainder Arithmetic
  165.    wt: 2:   5 Proportionality in Equivalent Fractions
  166.    wt: 2:   4 Rates Ratios and Proporitionality
  167.    wt: 2:   3 Proportionality Examples
  168.    wt: 2:   1 What is Proportionality
  169.    wt: 2:   5 Equality in Algebra
  170.    wt: 2:   3 Product Axioms Two Forms
  171.    wt: 2:   2 More and Less Than for Counts and Measures
  172.    wt: 2:   9 Coordinates for Regions in Space
  173.    wt: 2:   8 Coordinates for Maps and Planes
  174.    wt: 2:   1 Formulas Dependence and Function Notation
  175.    wt: 2:   5 Gaussian Elimination for 3 unknowns 2nd example
  176.    wt: 2:   Using Letters for Physical Quantities
  177.    wt: 2:   3 Counting with Sets etc
  178.    wt: 2:   4 A Brief Story of numbers and algebra
  179.    wt: 2:   38 Formulas and derivatives for powers and roots
  180.    wt: 2:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  181.    wt: 2:   Chapter 15. Algebraic Evaluation of Limits
  182.    wt: 2:   Foreword
  183.    wt: 2:   Appendix E. How To Study Mathematics and Why
  184.    wt: 2:   Appendix D. What to do in School and Why
  185.    wt: 2:   Appendix C. How to Read
  186.    wt: 2:   Appendix B. How To Learn
  187.    wt: 2:   Chapter 31 Direct and Indirect Reason
  188.    wt: 2:   Chapter 30 Truth Tables
  189.    wt: 2:   Chapter 28 Occurrence Tables
  190.    wt: 2:   Chapter 27 Shorthand Symbols as Pronouns
  191.    wt: 2:   Chapter 26 What is in chapters 27 to 31
  192.    wt: 2:   Chapter 25. Mathematical Induction Examples
  193.    wt: 2:   Chapter 24. Personal Investment and Pension EGS
  194.    wt: 2:   Chapter 21. Third Reading Guide
  195.    wt: 2:   Chapter 20. Degrees and Radians
  196.    wt: 2:   Chapter 19. Functions and Sets
  197.    wt: 2:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  198.    wt: 2:   Chapter 16. Painless Theorem Proving
  199.    wt: 2:   Chapter 15. Solving Linear Equations
  200.    wt: 2:   Chapter 13. Second Reading Guide
  201.    wt: 2:   Chapter 12. Shorthand Usage Guide
  202.    wt: 2:   Chapter 11. Why Shorthand
  203.    wt: 2:   Chapter 10 Describing and Changing Calculations
  204.    wt: 2:   Postscript What is a Variable
  205.    wt: 2:   Chapter 9 Talking about Numbers or Quantities
  206.    wt: 2:   Chapter 6 Change of Language
  207.    wt: 2:   Chapter 5 Islands and Divisions of Knowledge
  208.    wt: 2:   Chapter 4 Longer Chains of Reason
  209.    wt: 2:   Chapter 3 Chains of Reason
  210.    wt: 2:   Chapter 1 Introduction to Chapters 2 to 6
  211.    wt: 2:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  212.    wt: 2:   G. Written work formats for developing and showing skill
  213.    wt: 2:   Chapter 4 Logic for Reading Writing and Geometry etc
  214.    wt: 1:   Appendix 2 primary school Arithmetic 01
  215.    wt: 1:   Appendix 1 primary and preschool mathematic
  216.    wt: 1:   J LAMP Introduction Extrinsic Origins
  217.    wt: 1:   I LAMP Introduction Study Habits
  218.    wt: 1:   H LAMP Introduction Instructional Concepts
  219.    wt: 1:   G LAMP Introduction Problem Solving Skills
  220.    wt: 1:   F LAMP Introduction Prerequisites
  221.    wt: 1:   E LAMP Introduction Modern Mathematics
  222.    wt: 1:   B LAMP Introduction Curriculum Development Standards
  223.    wt: 1:   A Introduction Objectives
  224.    wt: 1:   Skills Chapter 5 Calculus
  225.    wt: 1:   Skills Chapter 4 Logic
  226.    wt: 1:   Ramblings Extrinsic numbers theory
  227.    wt: 1:   Skills Chapter 2 Geometry
  228.    wt: 1:   Skills Chapter 1 Arithmetic
  229.    wt: 1:   Skills Chapter 0 Introduction
  230.    wt: 1:   C Electromotive force conventional current02
  231.    wt: 1:   B Electromotive force conventional current01
  232.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  233.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  234.    wt: 1:   24 Standards For Skill Develoment Take II
  235.    wt: 1:   24 Standards For Skill Develoment
  236.    wt: 1:   17 Math Booklets for children and young teenagers
  237.    wt: 1:   15 Counting For Parents
  238.    wt: 1:   12 Goals and Objectives For Mathematics
  239.    wt: 1:   11 Help and Defend Your Child or Teens Education
  240.    wt: 1:   10 Ends values for work study instruction
  241.    wt: 1:   5 Patience Please for Yourself and Your Charges
  242.    wt: 1:   4 Learning Takes Time and Effort
  243.    wt: 1:   3 Preparing for Science Studies
  244.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  245.    wt: 1:   sign monoticity analysis example 4
  246.    wt: 1:   sign monoticity analysis example 3
  247.    wt: 1:   sign monoticity analysis example 2
  248.    wt: 1:   sign monoticity analysis example 1
  249.    wt: 1:   26 Function definitions done and coming
  250.    wt: 1:   25 Absolute Value greatest integer and saw tooth functions
  251.    wt: 1:   24 Monotoncity Injectivity and Inverse Functions
  252.    wt: 1:   23 Inverse Functions
  253.    wt: 1:   22 Square Root function graphically
  254.    wt: 1:   21 Graphs of functions given by Horizontal Line Method
  255.    wt: 1:   20 Interchanging coordinates a reflection
  256.    wt: 1:   19 Horizontal line rule and method
  257.    wt: 1:   18 Vertical Line Rule and Method
  258.    wt: 1:   17 Function maxima minima and their location
  259.    wt: 1:   16 Increasing or decreasing on intervals
  260.    wt: 1:   15 Sign analysis of functions
  261.    wt: 1:   14 Surjections Injections Bijections
  262.    wt: 1:   13 From one to one to many to one
  263.    wt: 1:   12 Function Domain Recognition Exercises
  264.    wt: 1:   11 Function Domain Range Source and Targets
  265.    wt: 1:   10 Interval Notation
  266.    wt: 1:   9 Set theory term relation possible origins
  267.    wt: 1:   8 Set view of relations and functions
  268.    wt: 1:   7 Functions with finite domains
  269.    wt: 1:   4 Function notation in and beyond mathematics
  270.    wt: 1:   Introduction Reading Guide
  271.    wt: 1:   11 Growth and Decay in Biology
  272.    wt: 1:   10 Exponential Growth and Decay Models
  273.    wt: 1:   5 Natural Logarithm Calculator Exercises
  274.    wt: 1:   3 Natural Logarithms and Exponentials Basic Properties
  275.    wt: 1:   2 Square Root Simplification a prequel
  276.    wt: 1:   1 Calculator Starter Exercises
  277.    wt: 1:   7 Links Lessons Elsewhere
  278.    wt: 1:   6 Polynomial Operations and Equivalent Computation Rules
  279.    wt: 1:   5 Polynomials Long division Nonlinear divisor
  280.    wt: 1:   4 Polynomials Long division linear divisor
  281.    wt: 1:   3 Polynomials Multiplication Addition
  282.    wt: 1:   2 Column Multiplication Method
  283.    wt: 1:   1 Polynomials Distributive Law
  284.    wt: 1:   12 motivation for term arctan
  285.    wt: 1:   9 motivation for name arcsin
  286.    wt: 1:   4 possible motivation for term arccos
  287.    wt: 1:   Construction Methods and Criteria for Isometric and Similar Triangles
  288.    wt: 1:   SAS Method For Isometric Or Proportional Triangle Construction
  289.    wt: 1:   8 Straight Lines Equation for vertical
  290.    wt: 1:   17 tangent function angle sum formulas
  291.    wt: 1:   29 secant cosecant and cotangent for acute angles
  292.    wt: 1:   25 tangent double angle formula Slope connection
  293.    wt: 1:   24 tangent Angle Difference Formula
  294.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  295.    wt: 1:   21 sine and cosine Half Angle Formulas
  296.    wt: 1:   20 sine and cosine Double Angle Formulas
  297.    wt: 1:   19 Pythagorean Identity For sine and cosine functions
  298.    wt: 1:   17C sine and cosine double triple angle formulas
  299.    wt: 1:   17B sine cosine Angle Sum Formulas via cis
  300.    wt: 1:   12 Graph of tangent function for one period
  301.    wt: 1:   6 sines and cosines for reference angle 30 degrees
  302.    wt: 1:   5 sines and cosines for reference angle 60 degrees
  303.    wt: 1:   4 sines and cosines for reference angle 45 degrees
  304.    wt: 1:   3 sines and cosines for reference angle 90 degrees
  305.    wt: 1:   11 sine and cosine double triple angle formulas
  306.    wt: 1:   10 sine cosine Angle Sum Formulas via cis
  307.    wt: 1:   5 Trigonometric Ratios For Tangent and Special Triangles
  308.    wt: 1:   4 Trigonometric Ratios For Two Special Triangles
  309.    wt: 1:   6 Geometric Diagrams in Class
  310.    wt: 1:   8 Mid Point Formula
  311.    wt: 1:   5 Algebraic View of Slopes
  312.    wt: 1:   3 Slope product for perpendicular lines
  313.    wt: 1:   2 point slope equation for a line
  314.    wt: 1:   13 Pythagorean spatial distance formulas
  315.    wt: 1:   10 Pythagorean plane distance formula
  316.    wt: 1:   PS H Distributive Law For Complex Numbers
  317.    wt: 1:   musings do not puiblish real numbers
  318.    wt: 1:   A Modular and Remainder Arithmetic
  319.    wt: 1:   A Signed Number Arithmetic Review
  320.    wt: 1:   26 More Less Greater Than Comparison
  321.    wt: 1:   25 Mid way Convergence to Axiomatic Approach
  322.    wt: 1:   24 Signed Numbers Arithmmetic Properties
  323.    wt: 1:   23 Distributive Law Two Derivations
  324.    wt: 1:   22 Multiplication of Signed Numbers
  325.    wt: 1:   21 Addition of Multiples of a Single Vector
  326.    wt: 1:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  327.    wt: 1:   19 Signed Multiples of Vectors
  328.    wt: 1:   17 Arrows Rotate to Reverse with Length Unchanged
  329.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  330.    wt: 1:   15 Head to Tails in place Addition Associative
  331.    wt: 1:   14 Vector Head to Tail Sums and Resultants
  332.    wt: 1:   13 Arrows and Vectors in a Plane
  333.    wt: 1:   12 Real Numbers Line Signed Coordinates
  334.    wt: 1:   11 Signed Number Addition and Addition Properties
  335.    wt: 1:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  336.    wt: 1:   9 Division with Digits after Decimal Point
  337.    wt: 1:   8 Division and Mulplication of Compound Fractions
  338.    wt: 1:   7 Arithmetic with Infinite Decimal Expansions
  339.    wt: 1:   6 Infinite Decimals Ending in 9 repeating
  340.    wt: 1:   5 Fractions with Infinite Decimal Expansions
  341.    wt: 1:   4 Location of Point in Decimal Addition
  342.    wt: 1:   3 Location of Point in Decimal Multiplication
  343.    wt: 1:   2 Counting Digits in Decimal Multiplication
  344.    wt: 1:   1 Fractions with Finite Decimal Expansions
  345.    wt: 1:   E Long Division Methods more
  346.    wt: 1:   D Long Division Methods
  347.    wt: 1:   C Three Decimal Subtraction Methods
  348.    wt: 1:   B Decimal Comparison and Subtraction
  349.    wt: 1:   A Decimal Addition Columm Methods
  350.    wt: 1:   8 Column Multiplication Methods in General
  351.    wt: 1:   7 Decimals Multiplication Methods Examples
  352.    wt: 1:   3 Multiplicative Counting Skills Principles
  353.    wt: 1:   2 Combing Counts Addition Skills and Principles
  354.    wt: 1:   1 The Counting Origins of Numbers
  355.    wt: 1:   6 Equations and Systems Equivalent or Implied
  356.    wt: 1:   4 Subtraction and Division Axioms
  357.    wt: 1:   2 Addition and Multiplication Axioms
  358.    wt: 1:   1 Equivalent Computation Rules
  359.    wt: 1:   5 Greater More Less Than Signs in General
  360.    wt: 1:   4 Comparison of Negative Numbers
  361.    wt: 1:   3 More and Less Than with Unlike Signs
  362.    wt: 1:   1 Real Numbers Comparison
  363.    wt: 1:   16 Real Numbers Comparison
  364.    wt: 1:   15 Real Number Division
  365.    wt: 1:   14 Real Number Multiplication
  366.    wt: 1:   13 Real Number Subtraction
  367.    wt: 1:   12 Real Number Additive Inverses or Negatives
  368.    wt: 1:   11 Real Number Addition
  369.    wt: 1:   10 Real Number Lengths and Signs
  370.    wt: 1:   7 Real Numbers as Line Cordinates
  371.    wt: 1:   6 Unsigned Real Numbers
  372.    wt: 1:   5 Rational Numbers More
  373.    wt: 1:   4 Rational Numbers
  374.    wt: 1:   3 Fractions
  375.    wt: 1:   2 Integers
  376.    wt: 1:   1 Whole and Natural Numbers
  377.    wt: 1:   5 Independent versus Dependent Variables
  378.    wt: 1:   4 Changing Letters
  379.    wt: 1:   2 Computation Rules Evaluation
  380.    wt: 1:   More Exercises
  381.    wt: 1:   Simple Exercises
  382.    wt: 1:   4 GE III Animated Examples
  383.    wt: 1:   3 Gaussian Elimination 3 unknowns first example
  384.    wt: 1:   3 GE III Equation Addition and Multiplication
  385.    wt: 1:   2 GE II Comparison
  386.    wt: 1:   1 GE Substitution four examples
  387.    wt: 1:   4 Solving a triangular system exercise
  388.    wt: 1:   3 Solving triangular system example
  389.    wt: 1:   2 Essentially one exercises three with solution
  390.    wt: 1:   1 Essentially One Unknown
  391.    wt: 1:   Skill Development Notes
  392.    wt: 1:   10 One Example
  393.    wt: 1:   9 Three Examples
  394.    wt: 1:   8 One Example
  395.    wt: 1:   7 Two Examples
  396.    wt: 1:   6 Three Examples
  397.    wt: 1:   5 Three Examples
  398.    wt: 1:   4 Two Examples
  399.    wt: 1:   3 Two Examples
  400.    wt: 1:   2 Three Examples
  401.    wt: 1:   10 Set View of Wordy Extensions To Arithmetic
  402.    wt: 1:   9 Sets in Probability and Statistics
  403.    wt: 1:   8 Sets of Numbers
  404.    wt: 1:   7 Cautious or Safe Set Construction
  405.    wt: 1:   6 Power Set Notation
  406.    wt: 1:   5 Product Builder Notation
  407.    wt: 1:   4 Subset Builder Notation
  408.    wt: 1:   2 Venn Diagrams
  409.    wt: 1:   1 Finite Sets
  410.    wt: 1:   6 Three Notions of What is a Variable
  411.    wt: 1:   5 Talking about Numbers and Quantities
  412.    wt: 1:   3 Adding Words To Arithmetic
  413.    wt: 1:   2 What is a Variable
  414.    wt: 1:   About Folder Contents
  415.    wt: 1:   arithmetic videos Real Player Format
  416.    wt: 1:   1 More and Less Than for Counts and Measures
  417.    wt: 1:   4 signed coordinates for regions in space
  418.    wt: 1:   3 signed coordinates for maps and planes
  419.    wt: 1:   5 Reciprocals and Division for Fractions with Units
  420.    wt: 1:   C Equality for Fractions and Two Term Ratios and Fractions
  421.    wt: 1:   21 Reciprocals for Fractions and Wholes
  422.    wt: 1:   13 Fraction Comparison Algebraic View
  423.    wt: 1:   11 Simplification an Algebraic View
  424.    wt: 1:   6 Multiplication Algebraically Take II
  425.    wt: 1:   11 Adding Integers Formulas and Examples
  426.    wt: 1:   10 Integer Multiplication Formulas
  427.    wt: 1:   25 Divisibility Tests for 2 3 5 9 10 Example
  428.    wt: 1:   24 Divisibility Tests for 2 3 5 9 10
  429.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  430.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  431.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  432.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  433.    wt: 1:   Long Division forwards and backwards Example 3
  434.    wt: 1:   Long Division forwards and backwards Example 2
  435.    wt: 1:   Long Division forwards and backwards Example 1
  436.    wt: 1:   A Elementary Basis for Multiplication Methods
  437.    wt: 1:   Video Decimal Multiplication Geometric View Example 2
  438.    wt: 1:   Video Decimal Multiplication Geometric View Example 2
  439.    wt: 1:   7 Subtraction for Decimal Fractions with Exercises
  440.    wt: 1:   5 A Tip for Efficent Subtraction
  441.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  442.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  443.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  444.    wt: 1:   Quick history of numbers and algebra
  445.    wt: 1:   Formula Evaluation how to show work
  446.    wt: 1:   Practical Methods Ends and Values for Arithmetic
  447.    wt: 1:   1 Two cubic sketching exercises with 1st derivative
  448.    wt: 1:   28 Chain Rule Preparation for a Proof
  449.    wt: 1:   22 Chain Rule for polynomials
  450.    wt: 1:   21 Chain Rule for powers
  451.    wt: 1:   20 Chain Rule for Pulley Systems
  452.    wt: 1:   19 Chain Rule for linear functions
  453.    wt: 1:   10 Power rule for negative integers
  454.    wt: 1:   3 Motivation for Limit Definition Take 2
  455.    wt: 1:   2 Motivation for Limit Definition Take 1
  456.    wt: 1:   3 Decimal insights for limits continuity convergence
  457.    wt: 1:   2 Algebraic codification
  458.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  459.    wt: 1:   E2 Algebraic Properties of Limits
  460.    wt: 1:   PostScript For and Against Decimal Perspectives
  461.    wt: 1:   Postscript Pythagorean Theorem yet another proof
  462.    wt: 1:   Chapter 24 Logarithms Powers and Exponentials
  463.    wt: 1:   Chapter 23 Links To Trigonometry
  464.    wt: 1:   Chapter 22 Complex Numbers
  465.    wt: 1:   Chapter 21 Arrow Addition
  466.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  467.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  468.    wt: 1:   Chapter 18. Slopes Areas Integration
  469.    wt: 1:   Chapter 17. Area Approximation
  470.    wt: 1:   Chapter 16. Velocity Approximation
  471.    wt: 1:   Chapter 15. Slope Approximation
  472.    wt: 1:   Chapter 14 Limits and Continuity with and sans Decimals
  473.    wt: 1:   Chapter 13. Acceleration
  474.    wt: 1:   Chapter 12. Units and Slopes
  475.    wt: 1:   Chapter 11. Graphing Slope versus Position
  476.    wt: 1:   Chapter 10 Slopes and Units
  477.    wt: 1:   Chapter 9 About First Courses in Calculus
  478.    wt: 1:   Chapter 8. Slope Interpretation
  479.    wt: 1:   Chapter 7 Slopes and Velocity
  480.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  481.    wt: 1:   Chapter 5. Slope Sign Tests
  482.    wt: 1:   Chapter 4. More Slope Sign Analysis
  483.    wt: 1:   Chapter 3. Slope Sign Analysis
  484.    wt: 1:   Chapter 2. Slopes and Ski Trails
  485.    wt: 1:   Chapter 1.Introduction
  486.    wt: 1:   Fall 1983 Calculus Appetizer
  487.    wt: 1:   Postscript B Mathematics Education References
  488.    wt: 1:   Chapter 3 Algebra Difficulties
  489.    wt: 1:   Chapter 2 For and Against Mathematics
  490.    wt: 1:   Foreword
  491.    wt: 1:   Postscript C Consistency as a Tool for Reason
  492.    wt: 1:   Chapter 22 Contrapositive and Vacuously True Implications
  493.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  494.    wt: 1:   Foreword
  495.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  496.    wt: 1:   S Adding words to algebra
  497.    wt: 1:   N Mathematics Prepare for College Studies
  498.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  499.    wt: 1:   Chapter 6 More Algebra and Geometry
  500.    wt: 1:   Chapter 3 Algebra Starter Lessons
  501.    wt: 1:   7 Games and Activities for Instruction
  502.    wt: 1:   Mathematics Education References
  503.    wt: 1:   Mathematics Education References
  504.    wt: 1:   Ends Values Methods For Skill Development Framework Prequel
  505.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  506.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  507.    wt: 1:   More Algebra and Slope based Calculus Preview
  508.    wt: 1:   Systematic Algebra Skill Development Missing Links
  509.    wt: 1:   Talking pdf files for online lessons a webvideo alternative
  510.    wt: 1:   The Math Forum and Site Content
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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