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

Logic 5 Chapters Arithmetic 10 Steps Algebra 12 Starter Steps & 5 Advanced Steps
Work & Study 23 Tips Geometry 15 Steps Calculus 70 Lessons

Ages 15+: Why study slopes Polynomials Quadratics Why factor polynomials Logarithms Functions
What is similarity Euclidean geometry leanly Coordinates + complex no.s Vectors DC Electric Circuits

Ages 12+: Prime factorization Written work formats Decimal place value Extend arithmetic skills orally
What is a variable 5. Fraction Operations by Raising Terms Solving Linear Equations: Take I Take II


Online Volumes: 1 - Elements of Reason, 2 - 3 Skills For Algebra, 3 - Why Slopes and
More Math
, 1A - Pattern Based Reason, 1B - Skill Development Principles + Troubles

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

Teachers & Tutors: This December 2011, 5-phase framework offers a context for mathematics & logic education. Phases 1 to 3 focus on skills with actual or potential local value for adult & daily life. College-oriented phases 5 & 4 focus on calculus & preparation for it. Phases 1 to 4 may also serve trades & professions not dependent on calculus.

Site Review: Math resources ... span ... arithmetic, logic, algebra, calculus, complex numbers, and Euclidean geometry. Lessons and how-tos .... provide a good foundation for high school and college ... mathematics. Read more.

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  1.    wt: 4:   Mathematics Education Essays/
  2.    wt: 2:   Progressive Observable Motivated Mathematics Education/
  3.    wt: 1:   LAMP Lean Applied Mathematics Program/
  4.    wt: 1:   Archives/
  5.    wt: 1:   Volume 3 Why Slopes A Calculus Intro Etc/

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27 matches:

  1.    wt: 1:   K LAMP Musings Science Education
  2.    wt: 1:   C LAMP Introduction Culture in Mathematics Education
  3.    wt: 1:   8 analytic geometry etc
  4.    wt: 1:   6 polynomials etc
  5.    wt: 1:   5 logarithms and exponentials etc
  6.    wt: 1:   links Education Resources online
  7.    wt: 1:   Mathematics Education Professors
  8.    wt: 1:   modern education
  9.    wt: 1:   Education Reform Inconsistencies
  10.    wt: 1:   three goals for Mathematics Education
  11.    wt: 1:   02 20 mathematics education references
  12.    wt: 1:   Education in mathematics science and technology
  13.    wt: 1:   Four ways to improve education reform
  14.    wt: 1:   education an empirical art
  15.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  16.    wt: 1:   11 Help and Defend Your Child or Teens Education
  17.    wt: 1:   3 Counting with Sets etc
  18.    wt: 1:   1 Two cubic sketching exercises with 1st derivative
  19.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  20.    wt: 1:   Foreword
  21.    wt: 1:   Foreword
  22.    wt: 1:   Postscript B Mathematics Education References
  23.    wt: 1:   Foreword
  24.    wt: 1:   Foreword
  25.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  26.    wt: 1:   Mathematics Education References
  27.    wt: 1:   Mathematics Education References

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  1.    wt: 5:   links Education Resources online
  2.    wt: 5:   Mathematics Education Professors
  3.    wt: 5:   modern education
  4.    wt: 5:   Education Reform Inconsistencies
  5.    wt: 5:   three goals for Mathematics Education
  6.    wt: 5:   02 20 mathematics education references
  7.    wt: 5:   Education in mathematics science and technology
  8.    wt: 5:   Four ways to improve education reform
  9.    wt: 5:   education an empirical art
  10.    wt: 4:   why bother
  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
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  24.    wt: 4:   learning takes time
  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: 3:   8 analytic geometry etc
  65.    wt: 3:   6 polynomials etc
  66.    wt: 3:   5 logarithms and exponentials etc
  67.    wt: 2:   K LAMP Musings Science Education
  68.    wt: 2:   C LAMP Introduction Culture in Mathematics Education
  69.    wt: 2:   11 pure mathematics
  70.    wt: 2:   10 statistics
  71.    wt: 2:   9 combinatorics probability sets
  72.    wt: 2:   7 logic review and decimals an odd combination
  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:   Foreword
  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:   3 Counting with Sets etc
  100.    wt: 1:   1 Two cubic sketching exercises with 1st derivative
  101.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  102.    wt: 1:   Postscript Pythagorean Theorem yet another proof
  103.    wt: 1:   Chapter 24 Logarithms Powers and Exponentials
  104.    wt: 1:   Chapter 23 Links To Trigonometry
  105.    wt: 1:   Chapter 22 Complex Numbers
  106.    wt: 1:   Chapter 21 Arrow Addition
  107.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  108.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  109.    wt: 1:   Chapter 18. Slopes Areas Integration
  110.    wt: 1:   Chapter 17. Area Approximation
  111.    wt: 1:   Chapter 16. Velocity Approximation
  112.    wt: 1:   Chapter 15. Slope Approximation
  113.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  114.    wt: 1:   Chapter 14 Limits and Continuity with and sans Decimals
  115.    wt: 1:   Chapter 13. Acceleration
  116.    wt: 1:   Chapter 12. Units and Slopes
  117.    wt: 1:   Chapter 11. Graphing Slope versus Position
  118.    wt: 1:   Chapter 10 Slopes and Units
  119.    wt: 1:   Chapter 9 About First Courses in Calculus
  120.    wt: 1:   Chapter 8. Slope Interpretation
  121.    wt: 1:   Chapter 7 Slopes and Velocity
  122.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  123.    wt: 1:   Chapter 5. Slope Sign Tests
  124.    wt: 1:   Chapter 4. More Slope Sign Analysis
  125.    wt: 1:   Chapter 3. Slope Sign Analysis
  126.    wt: 1:   Chapter 2. Slopes and Ski Trails
  127.    wt: 1:   Chapter 1.Introduction
  128.    wt: 1:   Fall 1983 Calculus Appetizer
  129.    wt: 1:   Foreword
  130.    wt: 1:   Postscript B Mathematics Education References
  131.    wt: 1:   Foreword
  132.    wt: 1:   Foreword
  133.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  134.    wt: 1:   Mathematics Education References
  135.    wt: 1:   Mathematics Education References
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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The Rest © 1995-2011, by site author, Alan Selby, Ph. D., Montreal,
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