Original Site Title: Appetizers and Lessons for Mathematics and Reason, June 1995 to April 2012. New site title:
Logic and Mathematics Skill & Concept Development with How-TOs Français: 26 pages
for college students, gifted teens, home-tutoring and K1-12 schooling. Avid readers in school and out may like Site Volumes.

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

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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  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 2 Three Skills For Algebra/

Web Page Search

42 matches:

  1.    wt: 2:   three goals for Mathematics Education
  2.    wt: 2:   Postscript A Three Remarks
  3.    wt: 2:   Three Remarks
  4.    wt: 1:   K LAMP Musings Science Education
  5.    wt: 1:   C LAMP Introduction Culture in Mathematics Education
  6.    wt: 1:   three goals to set for students
  7.    wt: 1:   links Education Resources online
  8.    wt: 1:   Mathematics Education Professors
  9.    wt: 1:   modern education
  10.    wt: 1:   Education Reform Inconsistencies
  11.    wt: 1:   Secondary Three Mathematics
  12.    wt: 1:   three difficulties
  13.    wt: 1:   02 20 mathematics education references
  14.    wt: 1:   three aims for mathematics students
  15.    wt: 1:   Education in mathematics science and technology
  16.    wt: 1:   three kinds of reason in mathematics
  17.    wt: 1:   Four ways to improve education reform
  18.    wt: 1:   education an empirical art
  19.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  20.    wt: 1:   11 Help and Defend Your Child or Teens Education
  21.    wt: 1:   8 The Effect of Negative Remarks
  22.    wt: 1:   4 Equations for lines three forms
  23.    wt: 1:   C Three Decimal Subtraction Methods
  24.    wt: 1:   2 Essentially one exercises three with solution
  25.    wt: 1:   2 Three Examples
  26.    wt: 1:   9 Three Examples
  27.    wt: 1:   6 Three Examples
  28.    wt: 1:   5 Three Examples
  29.    wt: 1:   2 Three Examples
  30.    wt: 1:   6 Three Notions of What is a Variable
  31.    wt: 1:   1 Three Skills For Algebra
  32.    wt: 1:   D Three Term Ratios
  33.    wt: 1:   4 Two and Three Digit Multipliers
  34.    wt: 1:   Appendix 2 Three Decimal Subtraction Methods
  35.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  36.    wt: 1:   1 Place Value in Three Digit Whole Numbers
  37.    wt: 1:   11 Limits at infinity Three Examples
  38.    wt: 1:   10 Three one sided limits with infinite values
  39.    wt: 1:   Chapter 8 Three Skills For Algebra
  40.    wt: 1:   Postscript B Mathematics Education References
  41.    wt: 1:   Mathematics Education References
  42.    wt: 1:   Mathematics Education References

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174 matches:

  1.    wt: 6:   three goals for Mathematics Education
  2.    wt: 5:   three goals to set for students
  3.    wt: 5:   links Education Resources online
  4.    wt: 5:   Mathematics Education Professors
  5.    wt: 5:   modern education
  6.    wt: 5:   Education Reform Inconsistencies
  7.    wt: 5:   Secondary Three Mathematics
  8.    wt: 5:   three difficulties
  9.    wt: 5:   02 20 mathematics education references
  10.    wt: 5:   three aims for mathematics students
  11.    wt: 5:   Education in mathematics science and technology
  12.    wt: 5:   three kinds of reason in mathematics
  13.    wt: 5:   Four ways to improve education reform
  14.    wt: 5:   education an empirical art
  15.    wt: 4:   why bother
  16.    wt: 4:   which way to go
  17.    wt: 4:   website reviews
  18.    wt: 4:   Teach the teachers plus goals
  19.    wt: 4:   permissions for teachers
  20.    wt: 4:   Math Ed if it must be short make it lean effective
  21.    wt: 4:   Applied Maths Program14092009 POMME variant
  22.    wt: 4:   activities for students
  23.    wt: 4:   site origins
  24.    wt: 4:   site eurekas
  25.    wt: 4:   About site lesson plans
  26.    wt: 4:   key notes and themes
  27.    wt: 4:   teacher certification
  28.    wt: 4:   learning takes time
  29.    wt: 4:   grouping students according to ability
  30.    wt: 4:   what should be learnt and When
  31.    wt: 4:   mathematics in context
  32.    wt: 4:   Postscript 2007 01 10
  33.    wt: 4:   five decades make a difference
  34.    wt: 4:   Maps Plans Drawings
  35.    wt: 4:   how letters appear
  36.    wt: 4:   Secondary Two Mathematics
  37.    wt: 4:   Secondary One Mathematics
  38.    wt: 4:   talk the algebra talk
  39.    wt: 4:   teaching tips
  40.    wt: 4:   What to Tell Students
  41.    wt: 4:   mathematics curriculum shifts
  42.    wt: 4:   geometric implications for algebra
  43.    wt: 4:   teaching tutoring algebraic reason
  44.    wt: 4:   Lessening Algebra Difficulties
  45.    wt: 4:   the trouble with algebra
  46.    wt: 4:   05 13 OldSiteEntrancePage
  47.    wt: 4:   04 29 New Mathematics Curriculum
  48.    wt: 4:   04 25 when to stop or suspend mathemat
  49.    wt: 4:   02 21 words for teachers
  50.    wt: 4:   standards for course material
  51.    wt: 4:   Operational Viewpoint to Value
  52.    wt: 4:   formal or informal peer review
  53.    wt: 4:   Theory of Knowledge
  54.    wt: 4:   mathematics instruction in general
  55.    wt: 4:   Different Kinds of Reasoning in maths
  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:   Chapter 8 Three Skills For Algebra
  79.    wt: 2:   Chapter 3 Chains of Reason
  80.    wt: 2:   Postscript A Three Remarks
  81.    wt: 2:   Three Remarks
  82.    wt: 1:   Appendix 2 primary school Arithmetic 01
  83.    wt: 1:   Appendix 1 primary and preschool mathematic
  84.    wt: 1:   J LAMP Introduction Extrinsic Origins
  85.    wt: 1:   I LAMP Introduction Study Habits
  86.    wt: 1:   H LAMP Introduction Instructional Concepts
  87.    wt: 1:   G LAMP Introduction Problem Solving Skills
  88.    wt: 1:   F LAMP Introduction Prerequisites
  89.    wt: 1:   E LAMP Introduction Modern Mathematics
  90.    wt: 1:   B LAMP Introduction Curriculum Development Standards
  91.    wt: 1:   A Introduction Objectives
  92.    wt: 1:   Skills Chapter 5 Calculus
  93.    wt: 1:   Skills Chapter 4 Logic
  94.    wt: 1:   Ramblings Extrinsic numbers theory
  95.    wt: 1:   Ramblings Introduction Algebra Essay
  96.    wt: 1:   Skills Chapter 3 Algebra
  97.    wt: 1:   Skills Chapter 2 Geometry
  98.    wt: 1:   Skills Chapter 1 Arithmetic
  99.    wt: 1:   Skills Chapter 0 Introduction
  100.    wt: 1:   B Electromotive force conventional current01
  101.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  102.    wt: 1:   11 Help and Defend Your Child or Teens Education
  103.    wt: 1:   8 The Effect of Negative Remarks
  104.    wt: 1:   3 Formula or function graphing exercise
  105.    wt: 1:   3 Natural Logarithms and Exponentials Basic Properties
  106.    wt: 1:   9 Straight Lines through Origin Equations
  107.    wt: 1:   4 Equations for lines three forms
  108.    wt: 1:   26 More Less Greater Than Comparison
  109.    wt: 1:   25 Mid way Convergence to Axiomatic Approach
  110.    wt: 1:   24 Signed Numbers Arithmmetic Properties
  111.    wt: 1:   23 Distributive Law Two Derivations
  112.    wt: 1:   22 Multiplication of Signed Numbers
  113.    wt: 1:   C Three Decimal Subtraction Methods
  114.    wt: 1:   2 Essentially one exercises three with solution
  115.    wt: 1:   2 Three Examples
  116.    wt: 1:   9 Three Examples
  117.    wt: 1:   6 Three Examples
  118.    wt: 1:   5 Three Examples
  119.    wt: 1:   2 Three Examples
  120.    wt: 1:   6 Three Notions of What is a Variable
  121.    wt: 1:   1 Three Skills For Algebra
  122.    wt: 1:   D Three Term Ratios
  123.    wt: 1:   6 Remainder Arithmetic Modulo 5 Propertie
  124.    wt: 1:   4 Two and Three Digit Multipliers
  125.    wt: 1:   Appendix 2 Three Decimal Subtraction Methods
  126.    wt: 1:   3 More on Groups of 3 Multi Digit Place Value
  127.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  128.    wt: 1:   1 Place Value in Three Digit Whole Numbers
  129.    wt: 1:   11 Limits at infinity Three Examples
  130.    wt: 1:   10 Three one sided limits with infinite values
  131.    wt: 1:   4 Numerical properties
  132.    wt: 1:   Postscript More on Better Performance
  133.    wt: 1:   Postscript For Better Performance
  134.    wt: 1:   Appendix E. How To Study Mathematics and Why
  135.    wt: 1:   Appendix D. What to do in School and Why
  136.    wt: 1:   Appendix C. How to Read
  137.    wt: 1:   Appendix B. How To Learn
  138.    wt: 1:   Appendix A. Reading Guide For Next Appendices
  139.    wt: 1:   Chapter 31 Direct and Indirect Reason
  140.    wt: 1:   Chapter 30 Truth Tables
  141.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  142.    wt: 1:   Chapter 28 Occurrence Tables
  143.    wt: 1:   Chapter 27 Shorthand Symbols as Pronouns
  144.    wt: 1:   Chapter 26 What is in chapters 27 to 31
  145.    wt: 1:   Chapter 25. Mathematical Induction Examples
  146.    wt: 1:   Chapter 24. Personal Investment and Pension EGS
  147.    wt: 1:   Chapter 23. Notation For Sums
  148.    wt: 1:   Chapter 22. Geometric Sums and Sequences
  149.    wt: 1:   Chapter 21. Third Reading Guide
  150.    wt: 1:   Chapter 20. Degrees and Radians
  151.    wt: 1:   Chapter 19. Functions and Sets
  152.    wt: 1:   Chapter 18. Rules for Algebra
  153.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  154.    wt: 1:   Chapter 16. Painless Theorem Proving
  155.    wt: 1:   Chapter 15. Solving Linear Equations
  156.    wt: 1:   Chapter 14. Forward and Backward Use of a Formula
  157.    wt: 1:   Postscript Unifying Theme A Fourth Skill For Algebra
  158.    wt: 1:   Chapter 13. Second Reading Guide
  159.    wt: 1:   Chapter 12. Shorthand Usage Guide
  160.    wt: 1:   Chapter 11. Why Shorthand
  161.    wt: 1:   Chapter 10 Describing and Changing Calculations
  162.    wt: 1:   Postscript What is a Variable
  163.    wt: 1:   Chapter 9 Talking about Numbers or Quantities
  164.    wt: 1:   Solutions For Arithmetic Exercises
  165.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  166.    wt: 1:   Chapter 6 Change of Language
  167.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  168.    wt: 1:   Chapter 4 Longer Chains of Reason
  169.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  170.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  171.    wt: 1:   Foreword
  172.    wt: 1:   Postscript B Mathematics Education References
  173.    wt: 1:   Mathematics Education References
  174.    wt: 1:   Mathematics Education References

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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