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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25 matches:

  1.    wt: 6:   Volume 1B Mathematics Curriculum Notes/
  2.    wt: 2:   Volume 1 Elements of Reason/
  3.    wt: 1:   LAMP Lean Applied Mathematics Program/
  4.    wt: 1:   Progressive Observable Motivated Mathematics Education/
  5.    wt: 1:   Mathematics Education Essays/
  6.    wt: 1:   Volume 1A Regles et modeles/
  7.    wt: 1:   Mathematics Skills Year by Year/
  8.    wt: 1:   A Origins of Counting and Figuring Methods/
  9.    wt: 1:   10 Examples of Algebraic Reasoning/
  10.    wt: 1:   12 Comparison of Unsigned and Signed Numbers/
  11.    wt: 1:   6 Fractions and Ratios/
  12.    wt: 1:   D Decimal Long Division Methods/
  13.    wt: 1:   C Decimal Multiplication Methods/
  14.    wt: 1:   B Decimal Comparing and Subtracting Methods/
  15.    wt: 1:   A Decimal Counting and Adding Methods/
  16.    wt: 1:   2 Arithmetic with Decimals/
  17.    wt: 1:   12 Webvideo Lessons on Area and Volume Calculation/
  18.    wt: 1:   Advanced Calculus Volume 3 Appendices/
  19.    wt: 1:   Volume 3 Why Slopes A Calculus Intro Etc/
  20.    wt: 1:   Volume 2 Three Skills For Algebra/
  21.    wt: 1:   Volume 1A Pattern Based Reason/
  22.    wt: 1:   Mathematics 506 Lessons/
  23.    wt: 1:   Secondary Mathematics A Practical Approach/
  24.    wt: 1:   PreSchool and Primary Mathematics or Quantitative Skills/
  25.    wt: 1:   Mathematics Skill Development Framework/

Web Page Search

241 matches:

  1.    wt: 2:   Mathematics Education Professors
  2.    wt: 2:   mathematics curriculum shifts
  3.    wt: 2:   04 29 New Mathematics Curriculum
  4.    wt: 2:   three kinds of reason in mathematics
  5.    wt: 2:   need for a mixed mathematics curriculum
  6.    wt: 2:   Leaner mathematics curriculum
  7.    wt: 2:   19 Extending the Oral Dimension of Mathematics
  8.    wt: 2:   4 Resultant of a Sum of Movements
  9.    wt: 2:   27 Logarithmic use of products of sines and cosines
  10.    wt: 2:   5 An Easy Proof of the Distributive Law
  11.    wt: 2:   2 Similar Triangles Equality of Corresponding Side Ratios
  12.    wt: 2:   10 Similarity of Triangles Equivalent of Two Criteria
  13.    wt: 2:   21 Addition of Multiples of a Single Vector
  14.    wt: 2:   11 Volume of Sphere
  15.    wt: 2:   10 Volume of Pyramid
  16.    wt: 2:   9 Volume of Cone
  17.    wt: 2:   2 Groups of Three Place Value for Multidigit Decimals
  18.    wt: 2:   Example 2 volume of a cone
  19.    wt: 2:   Example 1 volume of a pyramid
  20.    wt: 2:   Volume of Solid by Cross Sections Lesson
  21.    wt: 2:   17 Derivatives of quotients of sine and cosine
  22.    wt: 2:   16 Derivatives of reciprocals of sine and cosine
  23.    wt: 2:   Chapter 14 Deductive and Empirical Views of Mathematics
  24.    wt: 1:   E LAMP Introduction Modern Mathematics
  25.    wt: 1:   C LAMP Introduction Culture in Mathematics Education
  26.    wt: 1:   B LAMP Introduction Curriculum Development Standards
  27.    wt: 1:   11 pure mathematics
  28.    wt: 1:   7 logic review and decimals an odd combination
  29.    wt: 1:   key notes and themes
  30.    wt: 1:   mathematics in context
  31.    wt: 1:   Secondary Three Mathematics
  32.    wt: 1:   Secondary Two Mathematics
  33.    wt: 1:   Secondary One Mathematics
  34.    wt: 1:   three goals for Mathematics Education
  35.    wt: 1:   02 20 mathematics education references
  36.    wt: 1:   three aims for mathematics students
  37.    wt: 1:   Theory of Knowledge
  38.    wt: 1:   mathematics instruction in general
  39.    wt: 1:   Education in mathematics science and technology
  40.    wt: 1:   Different Kinds of Reasoning in maths
  41.    wt: 1:   words for mathematics instructor
  42.    wt: 1:   E Kirchoffs Second Law
  43.    wt: 1:   D Kirchoff First Law
  44.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  45.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  46.    wt: 1:   22 Student Centered Highschool Mathematics
  47.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  48.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  49.    wt: 1:   18 Primary School Mathematics
  50.    wt: 1:   16 Secondary Mathematics Tips
  51.    wt: 1:   12 Goals and Objectives For Mathematics
  52.    wt: 1:   8 The Effect of Negative Remarks
  53.    wt: 1:   21 Graphs of functions given by Horizontal Line Method
  54.    wt: 1:   15 Sign analysis of functions
  55.    wt: 1:   8 Set view of relations and functions
  56.    wt: 1:   4 Function notation in and beyond mathematics
  57.    wt: 1:   2 Algebraic use of function notation
  58.    wt: 1:   1 Geometric Introduction of Function Notation
  59.    wt: 1:   8 quadratics backward use of various formulas
  60.    wt: 1:   4 quadratics difference of two squares
  61.    wt: 1:   8 Notes for instructors or tutors
  62.    wt: 1:   11 arctan left inverse of tangent Graph
  63.    wt: 1:   10 arctan left inverse of tangent Definition
  64.    wt: 1:   8 arcsin left inverse of sine Graph
  65.    wt: 1:   7 arcsin left inverse of sine Definition
  66.    wt: 1:   6 Graph of arccos function
  67.    wt: 1:   3 Left Inverse of cosine arccos definition
  68.    wt: 1:   8 Radian Measures of Common Angles
  69.    wt: 1:   2 Radian Measure Numerical Value of one degree
  70.    wt: 1:   12 From Applied To Pure Mathematics
  71.    wt: 1:   Proportionality of Line Segments From Parallel Transversals
  72.    wt: 1:   Analytic View of Triangle Construction or Line Instersection More
  73.    wt: 1:   Straight Lines Intersection of
  74.    wt: 1:   3 Straight Lines Slope as Tangent of Inclination Angle
  75.    wt: 1:   35 sines and cosines of 2A 3A 4A 5A
  76.    wt: 1:   34 sines and cosines of 2A 3A 4A 5A
  77.    wt: 1:   33 sines and cosines of 2A 3A 4A 5A
  78.    wt: 1:   32 seven rows of pascals triangle
  79.    wt: 1:   30 unit circle calculation of six trigonometric functions
  80.    wt: 1:   28 Expressing products of sines cosines as sums
  81.    wt: 1:   26 Formulas for products of sines and cosines
  82.    wt: 1:   23 sine and cosine of 180 plus 22.5 degrees
  83.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  84.    wt: 1:   18 sum of sinusoidal waves as a single wave
  85.    wt: 1:   17F Law of cosines
  86.    wt: 1:   13 Graph of tangent function many periods
  87.    wt: 1:   12 Graph of tangent function for one period
  88.    wt: 1:   10 Graphs of sines and cosines many periods
  89.    wt: 1:   9 Graphs of sine and cosine over one period
  90.    wt: 1:   8 period of tangent function
  91.    wt: 1:   7 period of sine and cosine
  92.    wt: 1:   Unit Circle Development of Trigonometry
  93.    wt: 1:   20 N th Roots of Complex Numbers
  94.    wt: 1:   19 N th Roots of Unity
  95.    wt: 1:   18 Sixth Roots of Unity
  96.    wt: 1:   17 Cube Roots of unity
  97.    wt: 1:   14 Law of cosines
  98.    wt: 1:   8 Unit Circle Development of Trigonometry
  99.    wt: 1:   6 Field Properties of Complex Number
  100.    wt: 1:   7 Trignometric Ratios Unit Circle
  101.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  102.    wt: 1:   5 Trigonometric Ratios For Tangent and Special Triangles
  103.    wt: 1:   4 Trigonometric Ratios For Two Special Triangles
  104.    wt: 1:   3 Trigonometric Ratios sine and cosine
  105.    wt: 1:   9 Similarity of Triangles Usual Criteria
  106.    wt: 1:   8 Similarity of Triangles and Polygons
  107.    wt: 1:   5 Similarity of Circles Squares and Rectangles
  108.    wt: 1:   1 Early Concept of Like or Similar Shapes
  109.    wt: 1:   10 Midpoint of [a b] and [b a]
  110.    wt: 1:   6 Intersection of lines by solving linear systems
  111.    wt: 1:   5 Algebraic View of Slopes
  112.    wt: 1:   1 Numerical view of lines and their equations
  113.    wt: 1:   9 Pythagorean Theorem Chinese Square Proof
  114.    wt: 1:   17 Right Bisectors of Triangle Sides
  115.    wt: 1:   9 Construction of a right bisector
  116.    wt: 1:   3 Isometry of Triangles Congruence
  117.    wt: 1:   8 More Use of Maps Not Drawn to Scale
  118.    wt: 1:   22 Multiplication of Signed Numbers
  119.    wt: 1:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  120.    wt: 1:   19 Signed Multiples of Vectors
  121.    wt: 1:   8 Division and Mulplication of Compound Fractions
  122.    wt: 1:   6 Infinite Decimals Ending in 9 repeating
  123.    wt: 1:   4 Location of Point in Decimal Addition
  124.    wt: 1:   3 Location of Point in Decimal Multiplication
  125.    wt: 1:   7 Decimals Multiplication Methods Examples
  126.    wt: 1:   1 The Counting Origins of Numbers
  127.    wt: 1:   5 Areas of Rectangles Revisited
  128.    wt: 1:   1 Decimals Modular and Remainder Arithmetic
  129.    wt: 1:   4 Rates Ratios and Proporitionality
  130.    wt: 1:   7 Pythagorean Theorem Chinese Square Proof
  131.    wt: 1:   4 Comparison of Negative Numbers
  132.    wt: 1:   Skill Development Notes
  133.    wt: 1:   5 Box Volume Formula Example
  134.    wt: 1:   10 Set View of Wordy Extensions To Arithmetic
  135.    wt: 1:   8 Sets of Numbers
  136.    wt: 1:   6 Three Notions of What is a Variable
  137.    wt: 1:   4 A Brief Story of numbers and algebra
  138.    wt: 1:   3 Comparison of Negative Numbers
  139.    wt: 1:   3 Properties of Square Roots with example
  140.    wt: 1:   17 GCD LCM of 85 and 60 via Prime
  141.    wt: 1:   16 GCD and LCM of 650 225 via Prime
  142.    wt: 1:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  143.    wt: 1:   14 GCD of 650 110 via Primes LCM via Product Rule
  144.    wt: 1:   9 GCD of 360 110 via Primes and Euclid Algorithm
  145.    wt: 1:   4 LCM of 8 and 10 via Prime
  146.    wt: 1:   5 lengths and signs of numbers
  147.    wt: 1:   6 Simplification of Fractions with Units
  148.    wt: 1:   D Three Term Ratios
  149.    wt: 1:   C Equality for Fractions and Two Term Ratios and Fractions
  150.    wt: 1:   B Fractions and Two Term Ratios
  151.    wt: 1:   A Similarities between Fractions and Two Term Ratios
  152.    wt: 1:   10 Simplification of Fractions and Mixed Numerals
  153.    wt: 1:   6 Multiplication of Mixed Numbers
  154.    wt: 1:   3 Unit fraction of a fraction
  155.    wt: 1:   2 Integers Multiplies of a Unit Moverment
  156.    wt: 1:   A Decimals Modular and Remainder Arithmetic
  157.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  158.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  159.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  160.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  161.    wt: 1:   20 Uniqueness of Prime Factorization
  162.    wt: 1:   16 video Factors of 980 using prime
  163.    wt: 1:   15 video Factors of 20 using Prime Factorization
  164.    wt: 1:   14 video Factors of 24 Take II
  165.    wt: 1:   13 video Factors of 24 using prime
  166.    wt: 1:   7 Calculator Usage Notes and Cautions
  167.    wt: 1:   6 Sieve of Eratosthenes and Square Rule
  168.    wt: 1:   C Counting Areas with Powers of Ten
  169.    wt: 1:   B Powers of Ten
  170.    wt: 1:   Appendix 1 Decimals Comparison Method Take II
  171.    wt: 1:   8 Subtraction with Units of Measure
  172.    wt: 1:   5. How to add decimals C. Examples
  173.    wt: 1:   4. How to add with decimals B with conversions
  174.    wt: 1:   3. How to add with decimals A sans conversions
  175.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  176.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  177.    wt: 1:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  178.    wt: 1:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  179.    wt: 1:   5 More on Groups of 3 Place Value in Decimal Fractions
  180.    wt: 1:   4 Groups of 3 Place Value in Decimal Fractions
  181.    wt: 1:   3 More on Groups of 3 Multi Digit Place Value
  182.    wt: 1:   Quick history of numbers and algebra
  183.    wt: 1:   012 Division of Time Intervals by Time Intervals
  184.    wt: 1:   011 Division of Time Intervals By Numbers
  185.    wt: 1:   010 Repeated Addition of Time Intervals
  186.    wt: 1:   9 Comparison and Subtraction of Time Intervals
  187.    wt: 1:   8 Addition of Time Intervals via subtotaling
  188.    wt: 1:   7 Addition of Time Intervals
  189.    wt: 1:   4 Mixing and Changing Units of Time
  190.    wt: 1:   3 Units and Lengths of Time
  191.    wt: 1:   1 Intro of Kids To Time Date Skills
  192.    wt: 1:   Example 4 with x function of y
  193.    wt: 1:   A Related Material in Volume 3
  194.    wt: 1:   A Related lessons in Volume 3
  195.    wt: 1:   34 Derivative of exponential function
  196.    wt: 1:   31 Derivatives of inverse functions
  197.    wt: 1:   30Chain Rule A Proof
  198.    wt: 1:   28 Chain Rule Preparation for a Proof
  199.    wt: 1:   8 Differentiation of polynomials
  200.    wt: 1:   5 Jumps and absence of unlimited error control
  201.    wt: 1:   G.1 First Fundamental Theorem of Calculus
  202.    wt: 1:   G.3 Constant Difference Theorem Proof
  203.    wt: 1:   E2 Algebraic Properties of Limits
  204.    wt: 1:   D2 Limits of Monotone Sequences
  205.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  206.    wt: 1:   Postscript Pythagorean Theorem yet another proof
  207.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  208.    wt: 1:   Chapter 14 Limits and Continuity with and sans Decimals
  209.    wt: 1:   Appendix E. How To Study Mathematics and Why
  210.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  211.    wt: 1:   Chapter 14. Forward and Backward Use of a Formula
  212.    wt: 1:   Chapter 6 Change of Language
  213.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  214.    wt: 1:   Chapter 4 Longer Chains of Reason
  215.    wt: 1:   Chapter 3 Chains of Reason
  216.    wt: 1:   Postscript B Mathematics Education References
  217.    wt: 1:   Chapter 7 Two Treatments of Geometry
  218.    wt: 1:   Chapter 6 Rule Based Reason in Mathematics
  219.    wt: 1:   Chapter 2 For and Against Mathematics
  220.    wt: 1:   Postscript D Reflections on Law of the Excluded Middle
  221.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  222.    wt: 1:   Chapter 12 Islands and Divisions of Knowledge
  223.    wt: 1:   Chapter 8 Change of Language
  224.    wt: 1:   Chapter 7 Longer Chains of Reason
  225.    wt: 1:   Chapter 6 Chains of Reason
  226.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  227.    wt: 1:   R Why Learn Mathematics Skills
  228.    wt: 1:   Q How Logic and Proofs extend Show Work Practices
  229.    wt: 1:   O On Learning Mathematics and Science
  230.    wt: 1:   N Mathematics Prepare for College Studies
  231.    wt: 1:   C. Domino effect of being careful
  232.    wt: 1:   B. Domino effect of errors
  233.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  234.    wt: 1:   6 Measuring via counting or arithmetic the role of fractions
  235.    wt: 1:   Helping the Blind in Logic and Mathematics
  236.    wt: 1:   Mathematics Education References
  237.    wt: 1:   Mathematics Education References
  238.    wt: 1:   Multiple Ways to Improve Mathematics Skill Development
  239.    wt: 1:   Implementation Notes
  240.    wt: 1:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  241.    wt: 1:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years

Extended Search

579 matches:

  1.    wt: 7:   Postscript B Mathematics Education References
  2.    wt: 7:   Chapter 7 Two Treatments of Geometry
  3.    wt: 7:   Chapter 6 Rule Based Reason in Mathematics
  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 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 Education Professors
  18.    wt: 3:   mathematics curriculum shifts
  19.    wt: 3:   04 29 New Mathematics Curriculum
  20.    wt: 3:   three kinds of reason in mathematics
  21.    wt: 3:   need for a mixed mathematics curriculum
  22.    wt: 3:   Leaner mathematics curriculum
  23.    wt: 3:   Example 2 volume of a cone
  24.    wt: 3:   Example 1 volume of a pyramid
  25.    wt: 3:   Volume of Solid by Cross Sections Lesson
  26.    wt: 3:   Chapter 14 Deductive and Empirical Views of Mathematics
  27.    wt: 2:   E LAMP Introduction Modern Mathematics
  28.    wt: 2:   C LAMP Introduction Culture in Mathematics Education
  29.    wt: 2:   B LAMP Introduction Curriculum Development Standards
  30.    wt: 2:   11 pure mathematics
  31.    wt: 2:   7 logic review and decimals an odd combination
  32.    wt: 2:   key notes and themes
  33.    wt: 2:   mathematics in context
  34.    wt: 2:   Secondary Three Mathematics
  35.    wt: 2:   Secondary Two Mathematics
  36.    wt: 2:   Secondary One Mathematics
  37.    wt: 2:   three goals for Mathematics Education
  38.    wt: 2:   02 20 mathematics education references
  39.    wt: 2:   three aims for mathematics students
  40.    wt: 2:   Theory of Knowledge
  41.    wt: 2:   mathematics instruction in general
  42.    wt: 2:   Education in mathematics science and technology
  43.    wt: 2:   Different Kinds of Reasoning in maths
  44.    wt: 2:   words for mathematics instructor
  45.    wt: 2:   19 Extending the Oral Dimension of Mathematics
  46.    wt: 2:   4 Resultant of a Sum of Movements
  47.    wt: 2:   27 Logarithmic use of products of sines and cosines
  48.    wt: 2:   5 An Easy Proof of the Distributive Law
  49.    wt: 2:   2 Similar Triangles Equality of Corresponding Side Ratios
  50.    wt: 2:   10 Similarity of Triangles Equivalent of Two Criteria
  51.    wt: 2:   21 Addition of Multiples of a Single Vector
  52.    wt: 2:   7 Decimals Multiplication Methods Examples
  53.    wt: 2:   1 The Counting Origins of Numbers
  54.    wt: 2:   5 Areas of Rectangles Revisited
  55.    wt: 2:   1 Decimals Modular and Remainder Arithmetic
  56.    wt: 2:   11 Volume of Sphere
  57.    wt: 2:   10 Volume of Pyramid
  58.    wt: 2:   9 Volume of Cone
  59.    wt: 2:   3 Comparison of Negative Numbers
  60.    wt: 2:   D Three Term Ratios
  61.    wt: 2:   C Equality for Fractions and Two Term Ratios and Fractions
  62.    wt: 2:   B Fractions and Two Term Ratios
  63.    wt: 2:   A Similarities between Fractions and Two Term Ratios
  64.    wt: 2:   10 Simplification of Fractions and Mixed Numerals
  65.    wt: 2:   6 Multiplication of Mixed Numbers
  66.    wt: 2:   3 Unit fraction of a fraction
  67.    wt: 2:   C Counting Areas with Powers of Ten
  68.    wt: 2:   B Powers of Ten
  69.    wt: 2:   Appendix 1 Decimals Comparison Method Take II
  70.    wt: 2:   8 Subtraction with Units of Measure
  71.    wt: 2:   5. How to add decimals C. Examples
  72.    wt: 2:   4. How to add with decimals B with conversions
  73.    wt: 2:   3. How to add with decimals A sans conversions
  74.    wt: 2:   2 Groups of Three Place Value for Multidigit Decimals
  75.    wt: 2:   Example 4 with x function of y
  76.    wt: 2:   17 Derivatives of quotients of sine and cosine
  77.    wt: 2:   16 Derivatives of reciprocals of sine and cosine
  78.    wt: 2:   G.1 First Fundamental Theorem of Calculus
  79.    wt: 2:   G.3 Constant Difference Theorem Proof
  80.    wt: 2:   E2 Algebraic Properties of Limits
  81.    wt: 2:   D2 Limits of Monotone Sequences
  82.    wt: 2:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  83.    wt: 2:   Postscript Pythagorean Theorem yet another proof
  84.    wt: 2:   Chapter 15. Algebraic Evaluation of Limits
  85.    wt: 2:   Chapter 14 Limits and Continuity with and sans Decimals
  86.    wt: 2:   Appendix E. How To Study Mathematics and Why
  87.    wt: 2:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  88.    wt: 2:   Chapter 14. Forward and Backward Use of a Formula
  89.    wt: 2:   Chapter 6 Change of Language
  90.    wt: 2:   Chapter 5 Islands and Divisions of Knowledge
  91.    wt: 2:   Chapter 4 Longer Chains of Reason
  92.    wt: 2:   Chapter 3 Chains of Reason
  93.    wt: 2:   Postscript D Reflections on Law of the Excluded Middle
  94.    wt: 2:   Chapter 16 Origins and Limitations of Rules and Patterns
  95.    wt: 2:   Chapter 12 Islands and Divisions of Knowledge
  96.    wt: 2:   Chapter 8 Change of Language
  97.    wt: 2:   Chapter 7 Longer Chains of Reason
  98.    wt: 2:   Chapter 6 Chains of Reason
  99.    wt: 2:   Appendix A Calculus with Proofs for Keen or Gifted
  100.    wt: 2:   6 Measuring via counting or arithmetic the role of fractions
  101.    wt: 2:   Helping the Blind in Logic and Mathematics
  102.    wt: 2:   Mathematics Education References
  103.    wt: 2:   Mathematics Education References
  104.    wt: 2:   Multiple Ways to Improve Mathematics Skill Development
  105.    wt: 2:   Implementation Notes
  106.    wt: 2:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  107.    wt: 2:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  108.    wt: 1:   Appendix 2 primary school Arithmetic 01
  109.    wt: 1:   Appendix 1 primary and preschool mathematic
  110.    wt: 1:   K LAMP Musings Science Education
  111.    wt: 1:   J LAMP Introduction Extrinsic Origins
  112.    wt: 1:   I LAMP Introduction Study Habits
  113.    wt: 1:   H LAMP Introduction Instructional Concepts
  114.    wt: 1:   G LAMP Introduction Problem Solving Skills
  115.    wt: 1:   F LAMP Introduction Prerequisites
  116.    wt: 1:   A Introduction Objectives
  117.    wt: 1:   Skills Chapter 5 Calculus
  118.    wt: 1:   Skills Chapter 4 Logic
  119.    wt: 1:   Ramblings Extrinsic numbers theory
  120.    wt: 1:   Ramblings Introduction Algebra Essay
  121.    wt: 1:   Skills Chapter 3 Algebra
  122.    wt: 1:   Skills Chapter 2 Geometry
  123.    wt: 1:   Skills Chapter 1 Arithmetic
  124.    wt: 1:   Skills Chapter 0 Introduction
  125.    wt: 1:   10 statistics
  126.    wt: 1:   9 combinatorics probability sets
  127.    wt: 1:   8 analytic geometry etc
  128.    wt: 1:   6 polynomials etc
  129.    wt: 1:   5 logarithms and exponentials etc
  130.    wt: 1:   4 algebra
  131.    wt: 1:   3 Euclidean Geometry Leanly
  132.    wt: 1:   2 arithmetic with signed numbers
  133.    wt: 1:   1 arithmetic with unsigned numbers
  134.    wt: 1:   What is POMME
  135.    wt: 1:   why bother
  136.    wt: 1:   which way to go
  137.    wt: 1:   website reviews
  138.    wt: 1:   three goals to set for students
  139.    wt: 1:   Teach the teachers plus goals
  140.    wt: 1:   permissions for teachers
  141.    wt: 1:   Math Ed if it must be short make it lean effective
  142.    wt: 1:   Applied Maths Program14092009 POMME variant
  143.    wt: 1:   activities for students
  144.    wt: 1:   links Education Resources online
  145.    wt: 1:   site origins
  146.    wt: 1:   site eurekas
  147.    wt: 1:   About site lesson plans
  148.    wt: 1:   teacher certification
  149.    wt: 1:   modern education
  150.    wt: 1:   learning takes time
  151.    wt: 1:   grouping students according to ability
  152.    wt: 1:   what should be learnt and When
  153.    wt: 1:   Postscript 2007 01 10
  154.    wt: 1:   Education Reform Inconsistencies
  155.    wt: 1:   five decades make a difference
  156.    wt: 1:   Maps Plans Drawings
  157.    wt: 1:   how letters appear
  158.    wt: 1:   talk the algebra talk
  159.    wt: 1:   three difficulties
  160.    wt: 1:   teaching tips
  161.    wt: 1:   What to Tell Students
  162.    wt: 1:   geometric implications for algebra
  163.    wt: 1:   teaching tutoring algebraic reason
  164.    wt: 1:   Lessening Algebra Difficulties
  165.    wt: 1:   the trouble with algebra
  166.    wt: 1:   05 13 OldSiteEntrancePage
  167.    wt: 1:   04 25 when to stop or suspend mathemat
  168.    wt: 1:   02 21 words for teachers
  169.    wt: 1:   standards for course material
  170.    wt: 1:   Operational Viewpoint to Value
  171.    wt: 1:   formal or informal peer review
  172.    wt: 1:   cultivating intelligence
  173.    wt: 1:   Four ways to improve education reform
  174.    wt: 1:   How to be a better instructor
  175.    wt: 1:   Motivation and Context Problem
  176.    wt: 1:   Prequel In For A Penny In For A Pound
  177.    wt: 1:   education an empirical art
  178.    wt: 1:   fairness and inductive principles for instruction
  179.    wt: 1:   chapitre 12 00 les iles et division
  180.    wt: 1:   chapitre 07 01 principle D induction mathematique
  181.    wt: 1:   chapitre 07 00 Des chaines plus longues de la raison
  182.    wt: 1:   chapitre 06 00 Chaines de la raison
  183.    wt: 1:   chapitre 05 00 Deception
  184.    wt: 1:   chapitre 04 10 Etapes pour une meilleur raison
  185.    wt: 1:   chapitre 04 09 Regles accidentelles
  186.    wt: 1:   chapitre 04 08 Limitations et benefices
  187.    wt: 1:   chapitre 04 07 RepetablesEtReproductibles
  188.    wt: 1:   chapitre 04 06 engagements
  189.    wt: 1:   chapitre 04 05 Implication versus suggestion
  190.    wt: 1:   chapitre 04 04 Parlons de la logique
  191.    wt: 1:   chapitre 04 03 Unidirectionnel versus bidirectionnel
  192.    wt: 1:   chapitre 04 02 Deuxieme enigme
  193.    wt: 1:   chapitre 04 01 Premiere enigme
  194.    wt: 1:   chapitre 04 00 Les regles d implication
  195.    wt: 1:   chapitre 03 A Propos Des Prochains Chapitre
  196.    wt: 1:   chapitre 02 00 La Communication des idees
  197.    wt: 1:   chapitre 01 00 Introduction
  198.    wt: 1:   E Kirchoffs Second Law
  199.    wt: 1:   D Kirchoff First Law
  200.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  201.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  202.    wt: 1:   22 Student Centered Highschool Mathematics
  203.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  204.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  205.    wt: 1:   18 Primary School Mathematics
  206.    wt: 1:   16 Secondary Mathematics Tips
  207.    wt: 1:   12 Goals and Objectives For Mathematics
  208.    wt: 1:   8 The Effect of Negative Remarks
  209.    wt: 1:   Ages 12 to 14 Skills with take home value
  210.    wt: 1:   Ages 12 to 14 Geometry
  211.    wt: 1:   Ages 12 to 14 Arithmetic
  212.    wt: 1:   Ages 10 to 12 Geometry
  213.    wt: 1:   Ages 10 to 12 Arithmetic
  214.    wt: 1:   Ages 9 to 10
  215.    wt: 1:   Ages 8 to 9
  216.    wt: 1:   Ages 7 to 8
  217.    wt: 1:   Ages 6 to 7
  218.    wt: 1:   Ages 4 plus to 5 plus
  219.    wt: 1:   Ages 3 plus to 4 plus
  220.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  221.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  222.    wt: 1:   21 Graphs of functions given by Horizontal Line Method
  223.    wt: 1:   15 Sign analysis of functions
  224.    wt: 1:   8 Set view of relations and functions
  225.    wt: 1:   4 Function notation in and beyond mathematics
  226.    wt: 1:   2 Algebraic use of function notation
  227.    wt: 1:   1 Geometric Introduction of Function Notation
  228.    wt: 1:   8 quadratics backward use of various formulas
  229.    wt: 1:   4 quadratics difference of two squares
  230.    wt: 1:   8 Notes for instructors or tutors
  231.    wt: 1:   11 arctan left inverse of tangent Graph
  232.    wt: 1:   10 arctan left inverse of tangent Definition
  233.    wt: 1:   8 arcsin left inverse of sine Graph
  234.    wt: 1:   7 arcsin left inverse of sine Definition
  235.    wt: 1:   6 Graph of arccos function
  236.    wt: 1:   3 Left Inverse of cosine arccos definition
  237.    wt: 1:   8 Radian Measures of Common Angles
  238.    wt: 1:   2 Radian Measure Numerical Value of one degree
  239.    wt: 1:   12 From Applied To Pure Mathematics
  240.    wt: 1:   Proportionality of Line Segments From Parallel Transversals
  241.    wt: 1:   Analytic View of Triangle Construction or Line Instersection More
  242.    wt: 1:   Straight Lines Intersection of
  243.    wt: 1:   3 Straight Lines Slope as Tangent of Inclination Angle
  244.    wt: 1:   35 sines and cosines of 2A 3A 4A 5A
  245.    wt: 1:   34 sines and cosines of 2A 3A 4A 5A
  246.    wt: 1:   33 sines and cosines of 2A 3A 4A 5A
  247.    wt: 1:   32 seven rows of pascals triangle
  248.    wt: 1:   30 unit circle calculation of six trigonometric functions
  249.    wt: 1:   28 Expressing products of sines cosines as sums
  250.    wt: 1:   26 Formulas for products of sines and cosines
  251.    wt: 1:   23 sine and cosine of 180 plus 22.5 degrees
  252.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  253.    wt: 1:   18 sum of sinusoidal waves as a single wave
  254.    wt: 1:   17F Law of cosines
  255.    wt: 1:   13 Graph of tangent function many periods
  256.    wt: 1:   12 Graph of tangent function for one period
  257.    wt: 1:   10 Graphs of sines and cosines many periods
  258.    wt: 1:   9 Graphs of sine and cosine over one period
  259.    wt: 1:   8 period of tangent function
  260.    wt: 1:   7 period of sine and cosine
  261.    wt: 1:   Unit Circle Development of Trigonometry
  262.    wt: 1:   20 N th Roots of Complex Numbers
  263.    wt: 1:   19 N th Roots of Unity
  264.    wt: 1:   18 Sixth Roots of Unity
  265.    wt: 1:   17 Cube Roots of unity
  266.    wt: 1:   14 Law of cosines
  267.    wt: 1:   8 Unit Circle Development of Trigonometry
  268.    wt: 1:   6 Field Properties of Complex Number
  269.    wt: 1:   7 Trignometric Ratios Unit Circle
  270.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  271.    wt: 1:   5 Trigonometric Ratios For Tangent and Special Triangles
  272.    wt: 1:   4 Trigonometric Ratios For Two Special Triangles
  273.    wt: 1:   3 Trigonometric Ratios sine and cosine
  274.    wt: 1:   9 Similarity of Triangles Usual Criteria
  275.    wt: 1:   8 Similarity of Triangles and Polygons
  276.    wt: 1:   5 Similarity of Circles Squares and Rectangles
  277.    wt: 1:   1 Early Concept of Like or Similar Shapes
  278.    wt: 1:   10 Midpoint of [a b] and [b a]
  279.    wt: 1:   6 Intersection of lines by solving linear systems
  280.    wt: 1:   5 Algebraic View of Slopes
  281.    wt: 1:   1 Numerical view of lines and their equations
  282.    wt: 1:   9 Pythagorean Theorem Chinese Square Proof
  283.    wt: 1:   17 Right Bisectors of Triangle Sides
  284.    wt: 1:   9 Construction of a right bisector
  285.    wt: 1:   3 Isometry of Triangles Congruence
  286.    wt: 1:   8 More Use of Maps Not Drawn to Scale
  287.    wt: 1:   22 Multiplication of Signed Numbers
  288.    wt: 1:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  289.    wt: 1:   19 Signed Multiples of Vectors
  290.    wt: 1:   8 Division and Mulplication of Compound Fractions
  291.    wt: 1:   6 Infinite Decimals Ending in 9 repeating
  292.    wt: 1:   4 Location of Point in Decimal Addition
  293.    wt: 1:   3 Location of Point in Decimal Multiplication
  294.    wt: 1:   E Long Division Methods more
  295.    wt: 1:   D Long Division Methods
  296.    wt: 1:   C Three Decimal Subtraction Methods
  297.    wt: 1:   B Decimal Comparison and Subtraction
  298.    wt: 1:   A Decimal Addition Columm Methods
  299.    wt: 1:   8 Column Multiplication Methods in General
  300.    wt: 1:   6 Column Methods for Decimal Multiplication
  301.    wt: 1:   5 Distributive Law for Whole Numbers
  302.    wt: 1:   4 Commutative Law Groups Counting Form
  303.    wt: 1:   3 Multiplicative Counting Skills Principles
  304.    wt: 1:   2 Combing Counts Addition Skills and Principles
  305.    wt: 1:   4 Fraction Operations Axiomatic Development
  306.    wt: 1:   3 Inequalities Algebraically
  307.    wt: 1:   2 Fraction Operations Physical Development
  308.    wt: 1:   4 Rates Ratios and Proporitionality
  309.    wt: 1:   7 Pythagorean Theorem Chinese Square Proof
  310.    wt: 1:   4 Comparison of Negative Numbers
  311.    wt: 1:   Skill Development Notes
  312.    wt: 1:   5 Box Volume Formula Example
  313.    wt: 1:   10 Set View of Wordy Extensions To Arithmetic
  314.    wt: 1:   8 Sets of Numbers
  315.    wt: 1:   6 Three Notions of What is a Variable
  316.    wt: 1:   4 A Brief Story of numbers and algebra
  317.    wt: 1:   4 Greater More Less Than Signs in General
  318.    wt: 1:   2 More and Less Than with Unlike Signs
  319.    wt: 1:   1 More and Less Than for Counts and Measures
  320.    wt: 1:   3 Properties of Square Roots with example
  321.    wt: 1:   17 GCD LCM of 85 and 60 via Prime
  322.    wt: 1:   16 GCD and LCM of 650 225 via Prime
  323.    wt: 1:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  324.    wt: 1:   14 GCD of 650 110 via Primes LCM via Product Rule
  325.    wt: 1:   9 GCD of 360 110 via Primes and Euclid Algorithm
  326.    wt: 1:   4 LCM of 8 and 10 via Prime
  327.    wt: 1:   5 lengths and signs of numbers
  328.    wt: 1:   6 Simplification of Fractions with Units
  329.    wt: 1:   22 Complex Compound Fractions
  330.    wt: 1:   21 Working With Signs
  331.    wt: 1:   21 Reciprocals for Fractions and Wholes
  332.    wt: 1:   20 Dividing Fractions the Why
  333.    wt: 1:   19 Dividing Fractions How TO
  334.    wt: 1:   18 Efficient Ways to Multiply
  335.    wt: 1:   17 Efficient Ways to Add and Subtract
  336.    wt: 1:   16 Addition Subtraction Comparision Compared
  337.    wt: 1:   15 Adding and Subtracting with Unlike Denominators
  338.    wt: 1:   14 Adding and Subtracting with Like Denominators
  339.    wt: 1:   13 Fraction Comparison Algebraic View
  340.    wt: 1:   12 Fraction Comparison
  341.    wt: 1:   11 Simplification an Algebraic View
  342.    wt: 1:   9 Improper Fractions and Mixed Numbers
  343.    wt: 1:   8 Numerals Fractionals Quantals Take II
  344.    wt: 1:   7 Numerals Fractionals Quantals
  345.    wt: 1:   6 Multiplication Algebraically Take II
  346.    wt: 1:   5 Equivalent Fractions
  347.    wt: 1:   4 Fraction Multiplication
  348.    wt: 1:   2 Unit Fraction Multiplication
  349.    wt: 1:   1 What is a fraction Take II
  350.    wt: 1:   1 What is a fraction
  351.    wt: 1:   Fraction Operations by Raising Terms A Simple Innovation
  352.    wt: 1:   2 Integers Multiplies of a Unit Moverment
  353.    wt: 1:   A Decimals Modular and Remainder Arithmetic
  354.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  355.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  356.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  357.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  358.    wt: 1:   20 Uniqueness of Prime Factorization
  359.    wt: 1:   16 video Factors of 980 using prime
  360.    wt: 1:   15 video Factors of 20 using Prime Factorization
  361.    wt: 1:   14 video Factors of 24 Take II
  362.    wt: 1:   13 video Factors of 24 using prime
  363.    wt: 1:   7 Calculator Usage Notes and Cautions
  364.    wt: 1:   6 Sieve of Eratosthenes and Square Rule
  365.    wt: 1:   Long Division Backwards more
  366.    wt: 1:   Long Division Backward
  367.    wt: 1:   Division with Counts and Length
  368.    wt: 1:   Long Division forwards and backwards Example 3
  369.    wt: 1:   Long Division forwards and backwards Example 2
  370.    wt: 1:   Long Division forwards and backwards Example 1
  371.    wt: 1:   12 Why Long Division Works Take III
  372.    wt: 1:   11 Another Single Digit Divisor Example
  373.    wt: 1:   10 Division by Five Long and Short Ways
  374.    wt: 1:   9 Why Long Division Works Take II
  375.    wt: 1:   8 Correcting the Mistake
  376.    wt: 1:   7 Long Divison Mistake Catching
  377.    wt: 1:   6 Why Decimal Long Division Methods Works Take I
  378.    wt: 1:   5 Long Division Include Zeroes or not
  379.    wt: 1:   4 Division with 2 Digit Divsors
  380.    wt: 1:   3 Division Single Digit Divisor Example
  381.    wt: 1:   2 Division with Single Digit Divisors
  382.    wt: 1:   1 Divsion Physical Examples
  383.    wt: 1:   D Decimal Multiplication Methods Derived
  384.    wt: 1:   A Elementary Basis for Multiplication Methods
  385.    wt: 1:   6 Multiplication Commutes Order Not Important
  386.    wt: 1:   5 Decimal Fraction Multiplication
  387.    wt: 1:   4 Two and Three Digit Multipliers
  388.    wt: 1:   3 More One Digit Multipliers
  389.    wt: 1:   2 One Digit Multipliers
  390.    wt: 1:   Video Decimal Multiplication Geometric View Example 2
  391.    wt: 1:   Video Decimal Multiplication Geometric View Example 2
  392.    wt: 1:   Video Power Notation in Decimal Expansion
  393.    wt: 1:   1 Why 3 times 5 gives 15
  394.    wt: 1:   Appendix 2 Three Decimal Subtraction Methods
  395.    wt: 1:   Subtraction with J Conversions Example
  396.    wt: 1:   Subtraction Another Video Lesson
  397.    wt: 1:   9 22 Minute Subtraction Review Video
  398.    wt: 1:   7 Subtraction for Decimal Fractions with Exercises
  399.    wt: 1:   6 Subtraction with Conversion Example with Exercises
  400.    wt: 1:   5 A Tip for Efficent Subtraction
  401.    wt: 1:   4 Subtraction with Conversions Borrows and Letter J
  402.    wt: 1:   3 Harder Cases Convert to Compare and Subtract
  403.    wt: 1:   2 Subtraction Easy Case Examples
  404.    wt: 1:   1 Comparison and Subtraction Easy Direct Cases
  405.    wt: 1:   Appendix 1 Counting Revisited 15 minute video
  406.    wt: 1:   8 What skills and work habits to require
  407.    wt: 1:   7 Adding decimal fractions using decimal point
  408.    wt: 1:   6. Counting and adding units and mixed units
  409.    wt: 1:   2 Decimal Counting Practices
  410.    wt: 1:   1. Explaining Addition Table
  411.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  412.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  413.    wt: 1:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  414.    wt: 1:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  415.    wt: 1:   5 More on Groups of 3 Place Value in Decimal Fractions
  416.    wt: 1:   4 Groups of 3 Place Value in Decimal Fractions
  417.    wt: 1:   3 More on Groups of 3 Multi Digit Place Value
  418.    wt: 1:   Quick history of numbers and algebra
  419.    wt: 1:   012 Division of Time Intervals by Time Intervals
  420.    wt: 1:   011 Division of Time Intervals By Numbers
  421.    wt: 1:   010 Repeated Addition of Time Intervals
  422.    wt: 1:   9 Comparison and Subtraction of Time Intervals
  423.    wt: 1:   8 Addition of Time Intervals via subtotaling
  424.    wt: 1:   7 Addition of Time Intervals
  425.    wt: 1:   4 Mixing and Changing Units of Time
  426.    wt: 1:   3 Units and Lengths of Time
  427.    wt: 1:   1 Intro of Kids To Time Date Skills
  428.    wt: 1:   Example 1. Area Between x and x squared
  429.    wt: 1:   Area Between Crossing Curves Lesson Take 2
  430.    wt: 1:   Area Between Crossing Curves Lesson Take 1
  431.    wt: 1:   Example 3
  432.    wt: 1:   Example 2
  433.    wt: 1:   Example 1
  434.    wt: 1:   Area Between Curves Lesson Take 2
  435.    wt: 1:   Area Between Curves Lesson Take 1
  436.    wt: 1:   Summary
  437.    wt: 1:   A Related Material in Volume 3
  438.    wt: 1:   A Related lessons in Volume 3
  439.    wt: 1:   34 Derivative of exponential function
  440.    wt: 1:   31 Derivatives of inverse functions
  441.    wt: 1:   30Chain Rule A Proof
  442.    wt: 1:   28 Chain Rule Preparation for a Proof
  443.    wt: 1:   8 Differentiation of polynomials
  444.    wt: 1:   5 Jumps and absence of unlimited error control
  445.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  446.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  447.    wt: 1:   G.6 Bounded Derivatives implies Lipshitz Continuity
  448.    wt: 1:   G.5 Motions With Bounded Velocities
  449.    wt: 1:   G.4 Lipschitz Continuity implies EquiContinuity
  450.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  451.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  452.    wt: 1:   F.5b Extreme Value Theorem
  453.    wt: 1:   F.5a Equicontinuity Theorems
  454.    wt: 1:   F.4 Finite Covering Theorem
  455.    wt: 1:   F.3 Intermediate Value Theorem
  456.    wt: 1:   F.2 Closed Range Theorem
  457.    wt: 1:   F.1 What Functions are Continuous
  458.    wt: 1:   E1 Error Control Inequalities
  459.    wt: 1:   D1 Sets and Sequences GLBs and LGBs
  460.    wt: 1:   C Triangle Inequalities
  461.    wt: 1:   B3 Bolzano Weierstrass Theorem
  462.    wt: 1:   B1 Pigeon Hole Principles from combinatorics
  463.    wt: 1:   PostScript For and Against Decimal Perspectives
  464.    wt: 1:   A1. Introduction
  465.    wt: 1:   Chapter 24 Logarithms Powers and Exponentials
  466.    wt: 1:   Chapter 23 Links To Trigonometry
  467.    wt: 1:   Chapter 22 Complex Numbers
  468.    wt: 1:   Chapter 21 Arrow Addition
  469.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  470.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  471.    wt: 1:   Chapter 18. Slopes Areas Integration
  472.    wt: 1:   Chapter 17. Area Approximation
  473.    wt: 1:   Chapter 16. Velocity Approximation
  474.    wt: 1:   Chapter 15. Slope Approximation
  475.    wt: 1:   Chapter 13. Acceleration
  476.    wt: 1:   Chapter 12. Units and Slopes
  477.    wt: 1:   Chapter 11. Graphing Slope versus Position
  478.    wt: 1:   Chapter 10 Slopes and Units
  479.    wt: 1:   Chapter 9 About First Courses in Calculus
  480.    wt: 1:   Chapter 8. Slope Interpretation
  481.    wt: 1:   Chapter 7 Slopes and Velocity
  482.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  483.    wt: 1:   Chapter 5. Slope Sign Tests
  484.    wt: 1:   Chapter 4. More Slope Sign Analysis
  485.    wt: 1:   Chapter 3. Slope Sign Analysis
  486.    wt: 1:   Chapter 2. Slopes and Ski Trails
  487.    wt: 1:   Chapter 1.Introduction
  488.    wt: 1:   Fall 1983 Calculus Appetizer
  489.    wt: 1:   Foreword
  490.    wt: 1:   Postscript More on Better Performance
  491.    wt: 1:   Postscript For Better Performance
  492.    wt: 1:   Appendix D. What to do in School and Why
  493.    wt: 1:   Appendix C. How to Read
  494.    wt: 1:   Appendix B. How To Learn
  495.    wt: 1:   Appendix A. Reading Guide For Next Appendices
  496.    wt: 1:   Chapter 31 Direct and Indirect Reason
  497.    wt: 1:   Chapter 30 Truth Tables
  498.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  499.    wt: 1:   Chapter 28 Occurrence Tables
  500.    wt: 1:   Chapter 27 Shorthand Symbols as Pronouns
  501.    wt: 1:   Chapter 26 What is in chapters 27 to 31
  502.    wt: 1:   Chapter 25. Mathematical Induction Examples
  503.    wt: 1:   Chapter 24. Personal Investment and Pension EGS
  504.    wt: 1:   Chapter 23. Notation For Sums
  505.    wt: 1:   Chapter 22. Geometric Sums and Sequences
  506.    wt: 1:   Chapter 21. Third Reading Guide
  507.    wt: 1:   Chapter 20. Degrees and Radians
  508.    wt: 1:   Chapter 19. Functions and Sets
  509.    wt: 1:   Chapter 18. Rules for Algebra
  510.    wt: 1:   Chapter 16. Painless Theorem Proving
  511.    wt: 1:   Chapter 15. Solving Linear Equations
  512.    wt: 1:   Postscript Unifying Theme A Fourth Skill For Algebra
  513.    wt: 1:   Chapter 13. Second Reading Guide
  514.    wt: 1:   Chapter 12. Shorthand Usage Guide
  515.    wt: 1:   Chapter 11. Why Shorthand
  516.    wt: 1:   Chapter 10 Describing and Changing Calculations
  517.    wt: 1:   Postscript What is a Variable
  518.    wt: 1:   Chapter 9 Talking about Numbers or Quantities
  519.    wt: 1:   Chapter 8 Three Skills For Algebra
  520.    wt: 1:   Solutions For Arithmetic Exercises
  521.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  522.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  523.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  524.    wt: 1:   Foreword
  525.    wt: 1:   Postscript C Consistency as a Tool for Reason
  526.    wt: 1:   Postscript B More on Story Telling and Reason
  527.    wt: 1:   Postscript A Story Telling
  528.    wt: 1:   Chapter 24 Direct and Indirect Reason
  529.    wt: 1:   Chapter 23 Truth Tables
  530.    wt: 1:   Chapter 22 Contrapositive and Vacuously True Implications
  531.    wt: 1:   Chapter 21 Occurrence Tables
  532.    wt: 1:   Chapter 20 Shorthand Symbols as Pronouns
  533.    wt: 1:   Chapter 19 What is in chapters 20 to 24
  534.    wt: 1:   Chapter 18 Sense and Knowledge
  535.    wt: 1:   Chapter 17 Objective Ways Trial and Error Discovery
  536.    wt: 1:   Chapter 15 Objective Processes
  537.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  538.    wt: 1:   Chapter 11 Accidental Patterns
  539.    wt: 1:   Chapter 10 Responsibility
  540.    wt: 1:   Chapter 9 What is in Chapters 10 to 18
  541.    wt: 1:   Chapter 5 Deception
  542.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  543.    wt: 1:   Chapter 3 What is in chapters 4 to 8
  544.    wt: 1:   Chapter 2 Skill Development
  545.    wt: 1:   Chapter 1 Introduction
  546.    wt: 1:   Three Remarks
  547.    wt: 1:   Foreword
  548.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  549.    wt: 1:   R Why Learn Mathematics Skills
  550.    wt: 1:   Q How Logic and Proofs extend Show Work Practices
  551.    wt: 1:   O On Learning Mathematics and Science
  552.    wt: 1:   N Mathematics Prepare for College Studies
  553.    wt: 1:   C. Domino effect of being careful
  554.    wt: 1:   B. Domino effect of errors
  555.    wt: 1:   Chapter 8 Skipped Topics and Why
  556.    wt: 1:   Chapter 7 Calculus Previews and Calculus Lightly
  557.    wt: 1:   Chapter 6 More Algebra and Geometry
  558.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  559.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  560.    wt: 1:   Chapter 3 Algebra Starter Lessons
  561.    wt: 1:   Chapter 2 Why Sets
  562.    wt: 1:   Chapter 1 Arithmetic
  563.    wt: 1:   Primary and Secondary Skills and Practices with Take Home Value
  564.    wt: 1:   7 Games and Activities for Instruction
  565.    wt: 1:   5 Interpreting and Drawing Maps and Plans.
  566.    wt: 1:   4 Money Matters Saving Earning Buying Selling and Budgets
  567.    wt: 1:   3 Telling Tracking Time Temporal and More Place Sense
  568.    wt: 1:   2 Identifying Size and Position Place and Spatial Sense
  569.    wt: 1:   1 From Number Recognition and Counting to Arithmetic B
  570.    wt: 1:   1 From Number Recognition and Counting to Arithmetic A
  571.    wt: 1:   Ends Values Methods For Skill Development Framework Prequel
  572.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  573.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  574.    wt: 1:   More Algebra and Slope based Calculus Preview
  575.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  576.    wt: 1:   Systematic Algebra Skill Development Missing Links
  577.    wt: 1:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  578.    wt: 1:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  579.    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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