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/
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  5.    wt: 1:   4 Computation Rules and Function Notation/
  6.    wt: 1:   Volume 1B Mathematics Curriculum Notes/

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54 matches:

  1.    wt: 1:   K LAMP Musings Science Education
  2.    wt: 1:   C LAMP Introduction Culture in Mathematics Education
  3.    wt: 1:   links Education Resources online
  4.    wt: 1:   key notes and themes
  5.    wt: 1:   Mathematics Education Professors
  6.    wt: 1:   modern education
  7.    wt: 1:   Education Reform Inconsistencies
  8.    wt: 1:   three goals for Mathematics Education
  9.    wt: 1:   02 20 mathematics education references
  10.    wt: 1:   Education in mathematics science and technology
  11.    wt: 1:   Four ways to improve education reform
  12.    wt: 1:   education an empirical art
  13.    wt: 1:   Trois Notions qui menent a algebre
  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:   sign monoticity analysis example 4
  17.    wt: 1:   sign monoticity analysis example 3
  18.    wt: 1:   sign monoticity analysis example 2
  19.    wt: 1:   sign monoticity analysis example 1
  20.    wt: 1:   24 Monotoncity Injectivity and Inverse Functions
  21.    wt: 1:   10 Interval Notation
  22.    wt: 1:   6 Set Existence Formation and Notation
  23.    wt: 1:   5 Function notation for geometric transformations
  24.    wt: 1:   4 Function notation in and beyond mathematics
  25.    wt: 1:   2 Algebraic use of function notation
  26.    wt: 1:   1 Geometric Introduction of Function Notation
  27.    wt: 1:   8 Notes for instructors or tutors
  28.    wt: 1:   What is and is not here
  29.    wt: 1:   8 More Use of Maps Not Drawn to Scale
  30.    wt: 1:   6 Figuring with Maps Not to Scale
  31.    wt: 1:   musings do not puiblish real numbers
  32.    wt: 1:   3 Geometric Formulas and Function Notation
  33.    wt: 1:   1 Formulas Dependence and Function Notation
  34.    wt: 1:   Skill Development Notes
  35.    wt: 1:   2 Another Rectangle Area Formula Example
  36.    wt: 1:   6 Power Set Notation
  37.    wt: 1:   5 Product Builder Notation
  38.    wt: 1:   4 Subset Builder Notation
  39.    wt: 1:   6 Three Notions of What is a Variable
  40.    wt: 1:   A Associative Law Theorectical Note
  41.    wt: 1:   7 Calculator Usage Notes and Cautions
  42.    wt: 1:   11 Another Single Digit Divisor Example
  43.    wt: 1:   5 Long Division Include Zeroes or not
  44.    wt: 1:   6 Multiplication Commutes Order Not Important
  45.    wt: 1:   Video Power Notation in Decimal Expansion
  46.    wt: 1:   Subtraction Another Video Lesson
  47.    wt: 1:   D2 Limits of Monotone Sequences
  48.    wt: 1:   Postscript Pythagorean Theorem yet another proof
  49.    wt: 1:   Chapter 23. Notation For Sums
  50.    wt: 1:   Annotated Links to Material Elsehwere
  51.    wt: 1:   Postscript B Mathematics Education References
  52.    wt: 1:   Mathematics Education References
  53.    wt: 1:   Mathematics Education References
  54.    wt: 1:   Implementation Notes

Extended Search

157 matches:

  1.    wt: 5:   links Education Resources online
  2.    wt: 5:   key notes and themes
  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:   Prequel In For A Penny In For A Pound
  11.    wt: 5:   education an empirical art
  12.    wt: 4:   why bother
  13.    wt: 4:   which way to go
  14.    wt: 4:   website reviews
  15.    wt: 4:   three goals to set for students
  16.    wt: 4:   Teach the teachers plus goals
  17.    wt: 4:   permissions for teachers
  18.    wt: 4:   Math Ed if it must be short make it lean effective
  19.    wt: 4:   Applied Maths Program14092009 POMME variant
  20.    wt: 4:   activities for students
  21.    wt: 4:   site origins
  22.    wt: 4:   site eurekas
  23.    wt: 4:   About site lesson plans
  24.    wt: 4:   teacher certification
  25.    wt: 4:   learning takes time
  26.    wt: 4:   grouping students according to ability
  27.    wt: 4:   what should be learnt and When
  28.    wt: 4:   mathematics in context
  29.    wt: 4:   Postscript 2007 01 10
  30.    wt: 4:   five decades make a difference
  31.    wt: 4:   Maps Plans Drawings
  32.    wt: 4:   how letters appear
  33.    wt: 4:   Secondary Three Mathematics
  34.    wt: 4:   Secondary Two Mathematics
  35.    wt: 4:   Secondary One Mathematics
  36.    wt: 4:   talk the algebra talk
  37.    wt: 4:   three difficulties
  38.    wt: 4:   teaching tips
  39.    wt: 4:   What to Tell Students
  40.    wt: 4:   mathematics curriculum shifts
  41.    wt: 4:   geometric implications for algebra
  42.    wt: 4:   teaching tutoring algebraic reason
  43.    wt: 4:   Lessening Algebra Difficulties
  44.    wt: 4:   the trouble with algebra
  45.    wt: 4:   05 13 OldSiteEntrancePage
  46.    wt: 4:   04 29 New Mathematics Curriculum
  47.    wt: 4:   04 25 when to stop or suspend mathemat
  48.    wt: 4:   02 21 words for teachers
  49.    wt: 4:   three aims for mathematics students
  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:   three kinds of reason in mathematics
  57.    wt: 4:   cultivating intelligence
  58.    wt: 4:   How to be a better instructor
  59.    wt: 4:   Motivation and Context Problem
  60.    wt: 4:   need for a mixed mathematics curriculum
  61.    wt: 4:   Leaner mathematics curriculum
  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:   3 Geometric Formulas and Function Notation
  79.    wt: 2:   1 Formulas Dependence and Function Notation
  80.    wt: 2:   Annotated Links to Material Elsehwere
  81.    wt: 2:   Postscript B Mathematics Education References
  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:   Trois Notions qui menent a algebre
  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:   sign monoticity analysis example 4
  104.    wt: 1:   sign monoticity analysis example 3
  105.    wt: 1:   sign monoticity analysis example 2
  106.    wt: 1:   sign monoticity analysis example 1
  107.    wt: 1:   24 Monotoncity Injectivity and Inverse Functions
  108.    wt: 1:   10 Interval Notation
  109.    wt: 1:   6 Set Existence Formation and Notation
  110.    wt: 1:   5 Function notation for geometric transformations
  111.    wt: 1:   4 Function notation in and beyond mathematics
  112.    wt: 1:   2 Algebraic use of function notation
  113.    wt: 1:   1 Geometric Introduction of Function Notation
  114.    wt: 1:   8 Notes for instructors or tutors
  115.    wt: 1:   7 Tangent Function is odd on this domain
  116.    wt: 1:   What is and is not here
  117.    wt: 1:   8 More Use of Maps Not Drawn to Scale
  118.    wt: 1:   6 Figuring with Maps Not to Scale
  119.    wt: 1:   musings do not puiblish real numbers
  120.    wt: 1:   5 Independent versus Dependent Variables
  121.    wt: 1:   4 Changing Letters
  122.    wt: 1:   2 Computation Rules Evaluation
  123.    wt: 1:   Skill Development Notes
  124.    wt: 1:   2 Another Rectangle Area Formula Example
  125.    wt: 1:   6 Power Set Notation
  126.    wt: 1:   5 Product Builder Notation
  127.    wt: 1:   4 Subset Builder Notation
  128.    wt: 1:   6 Three Notions of What is a Variable
  129.    wt: 1:   A Associative Law Theorectical Note
  130.    wt: 1:   4 Remainder Arithmetic Modulo 10 in general
  131.    wt: 1:   7 Calculator Usage Notes and Cautions
  132.    wt: 1:   11 Another Single Digit Divisor Example
  133.    wt: 1:   5 Long Division Include Zeroes or not
  134.    wt: 1:   6 Multiplication Commutes Order Not Important
  135.    wt: 1:   Video Power Notation in Decimal Expansion
  136.    wt: 1:   Subtraction Another Video Lesson
  137.    wt: 1:   28 Chain Rule Preparation for a Proof
  138.    wt: 1:   D2 Limits of Monotone Sequences
  139.    wt: 1:   Postscript Pythagorean Theorem yet another proof
  140.    wt: 1:   Chapter 23. Notation For Sums
  141.    wt: 1:   Postscript A Three Remarks
  142.    wt: 1:   Chapter 12 Four Phases
  143.    wt: 1:   Chapter 11 Elementary Instruction
  144.    wt: 1:   Chapter 10 Transition
  145.    wt: 1:   Chapter 9 The Two Ends
  146.    wt: 1:   Chapter 8 Modern Instruction
  147.    wt: 1:   Chapter 7 Two Treatments of Geometry
  148.    wt: 1:   Chapter 6 Rule Based Reason in Mathematics
  149.    wt: 1:   Chapter 5 Four References
  150.    wt: 1:   Chapter 4 Complex Numbers and Why Slopes
  151.    wt: 1:   Chapter 3 Algebra Difficulties
  152.    wt: 1:   Chapter 2 For and Against Mathematics
  153.    wt: 1:   Chapter 1 Introduction
  154.    wt: 1:   Foreword
  155.    wt: 1:   Mathematics Education References
  156.    wt: 1:   Mathematics Education References
  157.    wt: 1:   Implementation Notes

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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