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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  5.    wt: 1:   Mathematics Skills Year by Year/
  6.    wt: 1:   B Real Numbers Extrinsic Development/
  7.    wt: 1:   A Origins of Counting and Figuring Methods/
  8.    wt: 1:   Volume 1B Mathematics Curriculum Notes/
  9.    wt: 1:   Mathematics 506 Lessons/
  10.    wt: 1:   Mathematics Skill Development Framework/

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  1.    wt: 4:   J LAMP Introduction Extrinsic Origins
  2.    wt: 3:   E LAMP Introduction Modern Mathematics
  3.    wt: 3:   C LAMP Introduction Culture in Mathematics Education
  4.    wt: 2:   I LAMP Introduction Study Habits
  5.    wt: 2:   H LAMP Introduction Instructional Concepts
  6.    wt: 2:   G LAMP Introduction Problem Solving Skills
  7.    wt: 2:   F LAMP Introduction Prerequisites
  8.    wt: 2:   B LAMP Introduction Curriculum Development Standards
  9.    wt: 2:   Applied Maths Program14092009 POMME variant
  10.    wt: 2:   Leaner mathematics curriculum
  11.    wt: 2:   12 From Applied To Pure Mathematics
  12.    wt: 1:   K LAMP Musings Science Education
  13.    wt: 1:   A Introduction Objectives
  14.    wt: 1:   Ramblings Extrinsic numbers theory
  15.    wt: 1:   Ramblings Introduction Algebra Essay
  16.    wt: 1:   Skills Chapter 0 Introduction
  17.    wt: 1:   11 pure mathematics
  18.    wt: 1:   3 Euclidean Geometry Leanly
  19.    wt: 1:   Math Ed if it must be short make it lean effective
  20.    wt: 1:   site origins
  21.    wt: 1:   Mathematics Education Professors
  22.    wt: 1:   mathematics in context
  23.    wt: 1:   Secondary Three Mathematics
  24.    wt: 1:   Secondary Two Mathematics
  25.    wt: 1:   Secondary One Mathematics
  26.    wt: 1:   mathematics curriculum shifts
  27.    wt: 1:   three goals for Mathematics Education
  28.    wt: 1:   04 29 New Mathematics Curriculum
  29.    wt: 1:   02 20 mathematics education references
  30.    wt: 1:   three aims for mathematics students
  31.    wt: 1:   mathematics instruction in general
  32.    wt: 1:   Education in mathematics science and technology
  33.    wt: 1:   three kinds of reason in mathematics
  34.    wt: 1:   need for a mixed mathematics curriculum
  35.    wt: 1:   words for mathematics instructor
  36.    wt: 1:   chapitre 01 00 Introduction
  37.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  38.    wt: 1:   22 Student Centered Highschool Mathematics
  39.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  40.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  41.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  42.    wt: 1:   18 Primary School Mathematics
  43.    wt: 1:   16 Secondary Mathematics Tips
  44.    wt: 1:   12 Goals and Objectives For Mathematics
  45.    wt: 1:   Objectives for Mathematics and Logic Language Skill Development
  46.    wt: 1:   9 Set theory term relation possible origins
  47.    wt: 1:   4 Function notation in and beyond mathematics
  48.    wt: 1:   1 Geometric Introduction of Function Notation
  49.    wt: 1:   Introduction Reading Guide
  50.    wt: 1:   1 Degrees and Radians Introduction
  51.    wt: 1:   1 The Counting Origins of Numbers
  52.    wt: 1:   5 Algebraic Solutions Introduction
  53.    wt: 1:   7 Compound Interest Formula Introduction
  54.    wt: 1:   1 Squares and Square Roots Introduction
  55.    wt: 1:   1 Least Common Multiples LCM Introduction
  56.    wt: 1:   4 video Prime Factorization Introduction
  57.    wt: 1:   18 Chain Rule Introduction
  58.    wt: 1:   1 Numerical introduction
  59.    wt: 1:   A1. Introduction
  60.    wt: 1:   Chapter 1.Introduction
  61.    wt: 1:   Appendix E. How To Study Mathematics and Why
  62.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  63.    wt: 1:   Postscript B Mathematics Education References
  64.    wt: 1:   Chapter 6 Rule Based Reason in Mathematics
  65.    wt: 1:   Chapter 2 For and Against Mathematics
  66.    wt: 1:   Chapter 1 Introduction
  67.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  68.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  69.    wt: 1:   Chapter 1 Introduction
  70.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  71.    wt: 1:   R Why Learn Mathematics Skills
  72.    wt: 1:   O On Learning Mathematics and Science
  73.    wt: 1:   N Mathematics Prepare for College Studies
  74.    wt: 1:   Helping the Blind in Logic and Mathematics
  75.    wt: 1:   Multiple Ways to Improve Mathematics Skill Development
  76.    wt: 1:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  77.    wt: 1:   Montreal Basic and Advanced Mathematics Tutoring

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215 matches:

  1.    wt: 9:   E LAMP Introduction Modern Mathematics
  2.    wt: 9:   C LAMP Introduction Culture in Mathematics Education
  3.    wt: 8:   I LAMP Introduction Study Habits
  4.    wt: 8:   H LAMP Introduction Instructional Concepts
  5.    wt: 8:   G LAMP Introduction Problem Solving Skills
  6.    wt: 8:   F LAMP Introduction Prerequisites
  7.    wt: 8:   B LAMP Introduction Curriculum Development Standards
  8.    wt: 7:   K LAMP Musings Science Education
  9.    wt: 7:   A Introduction Objectives
  10.    wt: 7:   Ramblings Extrinsic numbers theory
  11.    wt: 7:   Ramblings Introduction Algebra Essay
  12.    wt: 7:   Skills Chapter 0 Introduction
  13.    wt: 6:   Appendix 2 primary school Arithmetic 01
  14.    wt: 6:   Appendix 1 primary and preschool mathematic
  15.    wt: 6:   Skills Chapter 5 Calculus
  16.    wt: 6:   Skills Chapter 4 Logic
  17.    wt: 6:   Skills Chapter 3 Algebra
  18.    wt: 6:   Skills Chapter 2 Geometry
  19.    wt: 6:   Skills Chapter 1 Arithmetic
  20.    wt: 4:   Applied Maths Program14092009 POMME variant
  21.    wt: 4:   Leaner mathematics curriculum
  22.    wt: 3:   11 pure mathematics
  23.    wt: 3:   3 Euclidean Geometry Leanly
  24.    wt: 3:   Math Ed if it must be short make it lean effective
  25.    wt: 3:   site origins
  26.    wt: 3:   Mathematics Education Professors
  27.    wt: 3:   mathematics in context
  28.    wt: 3:   Secondary Three Mathematics
  29.    wt: 3:   Secondary Two Mathematics
  30.    wt: 3:   Secondary One Mathematics
  31.    wt: 3:   mathematics curriculum shifts
  32.    wt: 3:   three goals for Mathematics Education
  33.    wt: 3:   04 29 New Mathematics Curriculum
  34.    wt: 3:   02 20 mathematics education references
  35.    wt: 3:   three aims for mathematics students
  36.    wt: 3:   mathematics instruction in general
  37.    wt: 3:   Education in mathematics science and technology
  38.    wt: 3:   three kinds of reason in mathematics
  39.    wt: 3:   need for a mixed mathematics curriculum
  40.    wt: 3:   words for mathematics instructor
  41.    wt: 2:   10 statistics
  42.    wt: 2:   9 combinatorics probability sets
  43.    wt: 2:   8 analytic geometry etc
  44.    wt: 2:   7 logic review and decimals an odd combination
  45.    wt: 2:   6 polynomials etc
  46.    wt: 2:   5 logarithms and exponentials etc
  47.    wt: 2:   4 algebra
  48.    wt: 2:   2 arithmetic with signed numbers
  49.    wt: 2:   1 arithmetic with unsigned numbers
  50.    wt: 2:   What is POMME
  51.    wt: 2:   why bother
  52.    wt: 2:   which way to go
  53.    wt: 2:   website reviews
  54.    wt: 2:   three goals to set for students
  55.    wt: 2:   Teach the teachers plus goals
  56.    wt: 2:   permissions for teachers
  57.    wt: 2:   activities for students
  58.    wt: 2:   links Education Resources online
  59.    wt: 2:   site eurekas
  60.    wt: 2:   About site lesson plans
  61.    wt: 2:   key notes and themes
  62.    wt: 2:   teacher certification
  63.    wt: 2:   modern education
  64.    wt: 2:   learning takes time
  65.    wt: 2:   grouping students according to ability
  66.    wt: 2:   what should be learnt and When
  67.    wt: 2:   Postscript 2007 01 10
  68.    wt: 2:   Education Reform Inconsistencies
  69.    wt: 2:   five decades make a difference
  70.    wt: 2:   Maps Plans Drawings
  71.    wt: 2:   how letters appear
  72.    wt: 2:   talk the algebra talk
  73.    wt: 2:   three difficulties
  74.    wt: 2:   teaching tips
  75.    wt: 2:   What to Tell Students
  76.    wt: 2:   geometric implications for algebra
  77.    wt: 2:   teaching tutoring algebraic reason
  78.    wt: 2:   Lessening Algebra Difficulties
  79.    wt: 2:   the trouble with algebra
  80.    wt: 2:   05 13 OldSiteEntrancePage
  81.    wt: 2:   04 25 when to stop or suspend mathemat
  82.    wt: 2:   02 21 words for teachers
  83.    wt: 2:   standards for course material
  84.    wt: 2:   Operational Viewpoint to Value
  85.    wt: 2:   formal or informal peer review
  86.    wt: 2:   Theory of Knowledge
  87.    wt: 2:   Different Kinds of Reasoning in maths
  88.    wt: 2:   cultivating intelligence
  89.    wt: 2:   Four ways to improve education reform
  90.    wt: 2:   How to be a better instructor
  91.    wt: 2:   Motivation and Context Problem
  92.    wt: 2:   Prequel In For A Penny In For A Pound
  93.    wt: 2:   education an empirical art
  94.    wt: 2:   fairness and inductive principles for instruction
  95.    wt: 2:   Objectives for Mathematics and Logic Language Skill Development
  96.    wt: 2:   12 From Applied To Pure Mathematics
  97.    wt: 2:   1 The Counting Origins of Numbers
  98.    wt: 2:   Postscript B Mathematics Education References
  99.    wt: 2:   Chapter 6 Rule Based Reason in Mathematics
  100.    wt: 2:   Chapter 2 For and Against Mathematics
  101.    wt: 2:   Chapter 1 Introduction
  102.    wt: 2:   Helping the Blind in Logic and Mathematics
  103.    wt: 2:   Multiple Ways to Improve Mathematics Skill Development
  104.    wt: 2:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  105.    wt: 1:   chapitre 01 00 Introduction
  106.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  107.    wt: 1:   22 Student Centered Highschool Mathematics
  108.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  109.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  110.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  111.    wt: 1:   18 Primary School Mathematics
  112.    wt: 1:   16 Secondary Mathematics Tips
  113.    wt: 1:   12 Goals and Objectives For Mathematics
  114.    wt: 1:   Ages 12 to 14 Skills with take home value
  115.    wt: 1:   Ages 12 to 14 Geometry
  116.    wt: 1:   Ages 12 to 14 Arithmetic
  117.    wt: 1:   Ages 10 to 12 Geometry
  118.    wt: 1:   Ages 10 to 12 Arithmetic
  119.    wt: 1:   Ages 9 to 10
  120.    wt: 1:   Ages 8 to 9
  121.    wt: 1:   Ages 7 to 8
  122.    wt: 1:   Ages 6 to 7
  123.    wt: 1:   Ages 4 plus to 5 plus
  124.    wt: 1:   Ages 3 plus to 4 plus
  125.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  126.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  127.    wt: 1:   9 Set theory term relation possible origins
  128.    wt: 1:   4 Function notation in and beyond mathematics
  129.    wt: 1:   1 Geometric Introduction of Function Notation
  130.    wt: 1:   Introduction Reading Guide
  131.    wt: 1:   1 Degrees and Radians Introduction
  132.    wt: 1:   musings do not puiblish real numbers
  133.    wt: 1:   A Modular and Remainder Arithmetic
  134.    wt: 1:   A Signed Number Arithmetic Review
  135.    wt: 1:   26 More Less Greater Than Comparison
  136.    wt: 1:   25 Mid way Convergence to Axiomatic Approach
  137.    wt: 1:   24 Signed Numbers Arithmmetic Properties
  138.    wt: 1:   23 Distributive Law Two Derivations
  139.    wt: 1:   22 Multiplication of Signed Numbers
  140.    wt: 1:   21 Addition of Multiples of a Single Vector
  141.    wt: 1:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  142.    wt: 1:   19 Signed Multiples of Vectors
  143.    wt: 1:   18 Geometrically Why Vector Addition Commutes
  144.    wt: 1:   17 Arrows Rotate to Reverse with Length Unchanged
  145.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  146.    wt: 1:   15 Head to Tails in place Addition Associative
  147.    wt: 1:   14 Vector Head to Tail Sums and Resultants
  148.    wt: 1:   13 Arrows and Vectors in a Plane
  149.    wt: 1:   12 Real Numbers Line Signed Coordinates
  150.    wt: 1:   11 Signed Number Addition and Addition Properties
  151.    wt: 1:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  152.    wt: 1:   9 Division with Digits after Decimal Point
  153.    wt: 1:   8 Division and Mulplication of Compound Fractions
  154.    wt: 1:   7 Arithmetic with Infinite Decimal Expansions
  155.    wt: 1:   6 Infinite Decimals Ending in 9 repeating
  156.    wt: 1:   5 Fractions with Infinite Decimal Expansions
  157.    wt: 1:   4 Location of Point in Decimal Addition
  158.    wt: 1:   3 Location of Point in Decimal Multiplication
  159.    wt: 1:   2 Counting Digits in Decimal Multiplication
  160.    wt: 1:   1 Fractions with Finite Decimal Expansions
  161.    wt: 1:   E Long Division Methods more
  162.    wt: 1:   D Long Division Methods
  163.    wt: 1:   C Three Decimal Subtraction Methods
  164.    wt: 1:   B Decimal Comparison and Subtraction
  165.    wt: 1:   A Decimal Addition Columm Methods
  166.    wt: 1:   8 Column Multiplication Methods in General
  167.    wt: 1:   7 Decimals Multiplication Methods Examples
  168.    wt: 1:   6 Column Methods for Decimal Multiplication
  169.    wt: 1:   5 Distributive Law for Whole Numbers
  170.    wt: 1:   4 Commutative Law Groups Counting Form
  171.    wt: 1:   3 Multiplicative Counting Skills Principles
  172.    wt: 1:   2 Combing Counts Addition Skills and Principles
  173.    wt: 1:   5 Algebraic Solutions Introduction
  174.    wt: 1:   7 Compound Interest Formula Introduction
  175.    wt: 1:   1 Squares and Square Roots Introduction
  176.    wt: 1:   1 Least Common Multiples LCM Introduction
  177.    wt: 1:   4 video Prime Factorization Introduction
  178.    wt: 1:   18 Chain Rule Introduction
  179.    wt: 1:   1 Numerical introduction
  180.    wt: 1:   A1. Introduction
  181.    wt: 1:   Chapter 1.Introduction
  182.    wt: 1:   Appendix E. How To Study Mathematics and Why
  183.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  184.    wt: 1:   Annotated Links to Material Elsehwere
  185.    wt: 1:   Postscript A Three Remarks
  186.    wt: 1:   Chapter 12 Four Phases
  187.    wt: 1:   Chapter 11 Elementary Instruction
  188.    wt: 1:   Chapter 10 Transition
  189.    wt: 1:   Chapter 9 The Two Ends
  190.    wt: 1:   Chapter 8 Modern Instruction
  191.    wt: 1:   Chapter 7 Two Treatments of Geometry
  192.    wt: 1:   Chapter 5 Four References
  193.    wt: 1:   Chapter 4 Complex Numbers and Why Slopes
  194.    wt: 1:   Chapter 3 Algebra Difficulties
  195.    wt: 1:   Foreword
  196.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  197.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  198.    wt: 1:   Chapter 1 Introduction
  199.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  200.    wt: 1:   R Why Learn Mathematics Skills
  201.    wt: 1:   O On Learning Mathematics and Science
  202.    wt: 1:   N Mathematics Prepare for College Studies
  203.    wt: 1:   Ends Values Methods For Skill Development Framework Prequel
  204.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  205.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  206.    wt: 1:   Implementation Notes
  207.    wt: 1:   More Algebra and Slope based Calculus Preview
  208.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  209.    wt: 1:   Systematic Algebra Skill Development Missing Links
  210.    wt: 1:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  211.    wt: 1:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  212.    wt: 1:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  213.    wt: 1:   Which Way To Go
  214.    wt: 1:   Montreal Basic and Advanced Mathematics Tutoring
  215.    wt: 10:   J LAMP Introduction Extrinsic Origins

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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.

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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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