Appetizers and Lessons for Mathematics & Reason Français: 26 pages
A 1100+ page site with math-free logic chapters and wordy algebra chapters.
For comprehension, study site chapters and steps. Go beyond rote learning.

Logic mastery strengthens comprehension and so improves home, work & study abilities .
 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 14+: 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
Forewords + leading chapters give original reasons, still valid, for site content & growth.

Site Review: Mathphobics, this site may ease your fears of the subject, perhaps even help you njoy it. ... unintimidating, sometimes funny and very clear. ... . Read all. Continue with Volume 2, Three Skill for Algebra.

Site Review. Math resources ... span ... arithmetic, logic, algebra, calculus, complex numbers, and Euclidean geometry. Lessons and how-tos .... provide a good foundation ... Read all. See site books as well.

Teachers & Tutors: Site material uniquely explains common troubles in terms of steps too large or missing. Plus, this December 2011, 5-phase framework offers a context for mathematics & logic education. Phases 1 to 3 may 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.

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  1.    wt: 4:   Mathematics Education Essays/
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  5.    wt: 1:   Volume 3 Why Slopes A Calculus Intro Etc/

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  1.    wt: 2:   why bother
  2.    wt: 2:   Why Trigonometry the whyslopes view
  3.    wt: 1:   K LAMP Musings Science Education
  4.    wt: 1:   C LAMP Introduction Culture in Mathematics Education
  5.    wt: 1:   links Education Resources online
  6.    wt: 1:   Mathematics Education Professors
  7.    wt: 1:   modern education
  8.    wt: 1:   Education Reform Inconsistencies
  9.    wt: 1:   three goals for Mathematics Education
  10.    wt: 1:   02 20 mathematics education references
  11.    wt: 1:   Education in mathematics science and technology
  12.    wt: 1:   Four ways to improve education reform
  13.    wt: 1:   education an empirical art
  14.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  15.    wt: 1:   11 Help and Defend Your Child or Teens Education
  16.    wt: 1:   14 Why Scalar Multiplication Distributes Physical Argument
  17.    wt: 1:   18 Geometrically Why Vector Addition Commutes
  18.    wt: 1:   20 Dividing Fractions the Why
  19.    wt: 1:   12 Why Long Division Works Take III
  20.    wt: 1:   9 Why Long Division Works Take II
  21.    wt: 1:   6 Why Decimal Long Division Methods Works Take I
  22.    wt: 1:   1 Why 3 times 5 gives 15
  23.    wt: 1:   1 Fall 1983 Why Slopes Appetizer
  24.    wt: 1:   Appendix E. How To Study Mathematics and Why
  25.    wt: 1:   Appendix D. What to do in School and Why
  26.    wt: 1:   Chapter 11. Why Shorthand
  27.    wt: 1:   Postscript B Mathematics Education References
  28.    wt: 1:   Chapter 4 Complex Numbers and Why Slopes
  29.    wt: 1:   R Why Learn Mathematics Skills

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  1.    wt: 6:   why bother
  2.    wt: 5:   links Education Resources online
  3.    wt: 5:   Mathematics Education Professors
  4.    wt: 5:   modern education
  5.    wt: 5:   Education Reform Inconsistencies
  6.    wt: 5:   three goals for Mathematics Education
  7.    wt: 5:   02 20 mathematics education references
  8.    wt: 5:   Education in mathematics science and technology
  9.    wt: 5:   Four ways to improve education reform
  10.    wt: 5:   education an empirical art
  11.    wt: 4:   which way to go
  12.    wt: 4:   website reviews
  13.    wt: 4:   three goals to set for students
  14.    wt: 4:   Teach the teachers plus goals
  15.    wt: 4:   permissions for teachers
  16.    wt: 4:   Math Ed if it must be short make it lean effective
  17.    wt: 4:   Applied Maths Program14092009 POMME variant
  18.    wt: 4:   activities for students
  19.    wt: 4:   site origins
  20.    wt: 4:   site eurekas
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  22.    wt: 4:   key notes and themes
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  25.    wt: 4:   grouping students according to ability
  26.    wt: 4:   what should be learnt and When
  27.    wt: 4:   mathematics in context
  28.    wt: 4:   Postscript 2007 01 10
  29.    wt: 4:   five decades make a difference
  30.    wt: 4:   Maps Plans Drawings
  31.    wt: 4:   how letters appear
  32.    wt: 4:   Secondary Three Mathematics
  33.    wt: 4:   Secondary Two Mathematics
  34.    wt: 4:   Secondary One Mathematics
  35.    wt: 4:   talk the algebra talk
  36.    wt: 4:   three difficulties
  37.    wt: 4:   teaching tips
  38.    wt: 4:   What to Tell Students
  39.    wt: 4:   mathematics curriculum shifts
  40.    wt: 4:   geometric implications for algebra
  41.    wt: 4:   teaching tutoring algebraic reason
  42.    wt: 4:   Lessening Algebra Difficulties
  43.    wt: 4:   the trouble with algebra
  44.    wt: 4:   05 13 OldSiteEntrancePage
  45.    wt: 4:   04 29 New Mathematics Curriculum
  46.    wt: 4:   04 25 when to stop or suspend mathemat
  47.    wt: 4:   02 21 words for teachers
  48.    wt: 4:   three aims for mathematics students
  49.    wt: 4:   standards for course material
  50.    wt: 4:   Operational Viewpoint to Value
  51.    wt: 4:   formal or informal peer review
  52.    wt: 4:   Theory of Knowledge
  53.    wt: 4:   mathematics instruction in general
  54.    wt: 4:   Different Kinds of Reasoning in maths
  55.    wt: 4:   three kinds of reason in mathematics
  56.    wt: 4:   cultivating intelligence
  57.    wt: 4:   How to be a better instructor
  58.    wt: 4:   Motivation and Context Problem
  59.    wt: 4:   need for a mixed mathematics curriculum
  60.    wt: 4:   Leaner mathematics curriculum
  61.    wt: 4:   Prequel In For A Penny In For A Pound
  62.    wt: 4:   fairness and inductive principles for instruction
  63.    wt: 4:   words for mathematics instructor
  64.    wt: 2:   K LAMP Musings Science Education
  65.    wt: 2:   C LAMP Introduction Culture in Mathematics Education
  66.    wt: 2:   11 pure mathematics
  67.    wt: 2:   10 statistics
  68.    wt: 2:   9 combinatorics probability sets
  69.    wt: 2:   8 analytic geometry etc
  70.    wt: 2:   7 logic review and decimals an odd combination
  71.    wt: 2:   6 polynomials etc
  72.    wt: 2:   5 logarithms and exponentials etc
  73.    wt: 2:   4 algebra
  74.    wt: 2:   3 Euclidean Geometry Leanly
  75.    wt: 2:   2 arithmetic with signed numbers
  76.    wt: 2:   1 arithmetic with unsigned numbers
  77.    wt: 2:   What is POMME
  78.    wt: 2:   Why Trigonometry the whyslopes view
  79.    wt: 1:   Appendix 2 primary school Arithmetic 01
  80.    wt: 1:   Appendix 1 primary and preschool mathematic
  81.    wt: 1:   J LAMP Introduction Extrinsic Origins
  82.    wt: 1:   I LAMP Introduction Study Habits
  83.    wt: 1:   H LAMP Introduction Instructional Concepts
  84.    wt: 1:   G LAMP Introduction Problem Solving Skills
  85.    wt: 1:   F LAMP Introduction Prerequisites
  86.    wt: 1:   E LAMP Introduction Modern Mathematics
  87.    wt: 1:   B LAMP Introduction Curriculum Development Standards
  88.    wt: 1:   A Introduction Objectives
  89.    wt: 1:   Skills Chapter 5 Calculus
  90.    wt: 1:   Skills Chapter 4 Logic
  91.    wt: 1:   Ramblings Extrinsic numbers theory
  92.    wt: 1:   Ramblings Introduction Algebra Essay
  93.    wt: 1:   Skills Chapter 3 Algebra
  94.    wt: 1:   Skills Chapter 2 Geometry
  95.    wt: 1:   Skills Chapter 1 Arithmetic
  96.    wt: 1:   Skills Chapter 0 Introduction
  97.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  98.    wt: 1:   11 Help and Defend Your Child or Teens Education
  99.    wt: 1:   14 Why Scalar Multiplication Distributes Physical Argument
  100.    wt: 1:   18 Geometrically Why Vector Addition Commutes
  101.    wt: 1:   20 Dividing Fractions the Why
  102.    wt: 1:   12 Why Long Division Works Take III
  103.    wt: 1:   9 Why Long Division Works Take II
  104.    wt: 1:   6 Why Decimal Long Division Methods Works Take I
  105.    wt: 1:   1 Why 3 times 5 gives 15
  106.    wt: 1:   1 Fall 1983 Why Slopes Appetizer
  107.    wt: 1:   Postscript Pythagorean Theorem yet another proof
  108.    wt: 1:   Chapter 24 Logarithms Powers and Exponentials
  109.    wt: 1:   Chapter 23 Links To Trigonometry
  110.    wt: 1:   Chapter 22 Complex Numbers
  111.    wt: 1:   Chapter 21 Arrow Addition
  112.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  113.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  114.    wt: 1:   Chapter 18. Slopes Areas Integration
  115.    wt: 1:   Chapter 17. Area Approximation
  116.    wt: 1:   Chapter 16. Velocity Approximation
  117.    wt: 1:   Chapter 15. Slope Approximation
  118.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  119.    wt: 1:   Chapter 14 Limits and Continuity with and sans Decimals
  120.    wt: 1:   Chapter 13. Acceleration
  121.    wt: 1:   Chapter 12. Units and Slopes
  122.    wt: 1:   Chapter 11. Graphing Slope versus Position
  123.    wt: 1:   Chapter 10 Slopes and Units
  124.    wt: 1:   Chapter 9 About First Courses in Calculus
  125.    wt: 1:   Chapter 8. Slope Interpretation
  126.    wt: 1:   Chapter 7 Slopes and Velocity
  127.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  128.    wt: 1:   Chapter 5. Slope Sign Tests
  129.    wt: 1:   Chapter 4. More Slope Sign Analysis
  130.    wt: 1:   Chapter 3. Slope Sign Analysis
  131.    wt: 1:   Chapter 2. Slopes and Ski Trails
  132.    wt: 1:   Chapter 1.Introduction
  133.    wt: 1:   Fall 1983 Calculus Appetizer
  134.    wt: 1:   Foreword
  135.    wt: 1:   Appendix E. How To Study Mathematics and Why
  136.    wt: 1:   Appendix D. What to do in School and Why
  137.    wt: 1:   Chapter 11. Why Shorthand
  138.    wt: 1:   Postscript B Mathematics Education References
  139.    wt: 1:   Chapter 4 Complex Numbers and Why Slopes
  140.    wt: 1:   R Why Learn Mathematics Skills

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More Site Folders and Pages

Parents: Help your child or teen learn:

Parent-friendly Work Booklets for ages 3+ to 13 Use these or others to check or build skills.

Mathematics Skills For Ages 3 to 14

Skills with take home value

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

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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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