Original Site Title: Appetizers and Lessons for Mathematics and Reason, June 1995 to April 2012. New site title:
Logic and Mathematics Skill & Concept Development How-TOs Site Map || Français: 26 pages
for college students, gifted teens, home-tutoring and K1-12 schooling; and for avid readers not in school

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 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:   8 Unifying Theme For Algebra/
  6.    wt: 1:   7 Axioms Logic and Equivalent Equations/

Web Page Search

55 matches:

  1.    wt: 1:   K LAMP Musings Science Education
  2.    wt: 1:   C LAMP Introduction Culture in Mathematics Education
  3.    wt: 1:   Skills Chapter 4 Logic
  4.    wt: 1:   7 logic review and decimals an odd combination
  5.    wt: 1:   Math Ed if it must be short make it lean effective
  6.    wt: 1:   links Education Resources online
  7.    wt: 1:   Mathematics Education Professors
  8.    wt: 1:   teacher certification
  9.    wt: 1:   modern education
  10.    wt: 1:   Education Reform Inconsistencies
  11.    wt: 1:   five decades make a difference
  12.    wt: 1:   three difficulties
  13.    wt: 1:   mathematics curriculum shifts
  14.    wt: 1:   geometric implications for algebra
  15.    wt: 1:   Lessening Algebra Difficulties
  16.    wt: 1:   three goals for Mathematics Education
  17.    wt: 1:   02 20 mathematics education references
  18.    wt: 1:   Education in mathematics science and technology
  19.    wt: 1:   Different Kinds of Reasoning in maths
  20.    wt: 1:   Four ways to improve education reform
  21.    wt: 1:   education an empirical art
  22.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  23.    wt: 1:   11 Help and Defend Your Child or Teens Education
  24.    wt: 1:   4 quadratics difference of two squares
  25.    wt: 1:   2 Square Root Simplification a prequel
  26.    wt: 1:   24 tangent Angle Difference Formula
  27.    wt: 1:   13 Naming Identifying Formulas with Words
  28.    wt: 1:   6 Simplification of Fractions with Units
  29.    wt: 1:   11 Simplification an Algebraic View
  30.    wt: 1:   10 Simplification of Fractions and Mixed Numerals
  31.    wt: 1:   17 Identify and Count Factors using Primes
  32.    wt: 1:   6 Sieve of Eratosthenes and Square Rule
  33.    wt: 1:   8 Differentiation of polynomials
  34.    wt: 1:   7 Animated Differentiation Examples
  35.    wt: 1:   2 Algebraic codification
  36.    wt: 1:   G.3 Constant Difference Theorem Proof
  37.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  38.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  39.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  40.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  41.    wt: 1:   Postscript Unifying Theme A Fourth Skill For Algebra
  42.    wt: 1:   Postscript B Mathematics Education References
  43.    wt: 1:   Chapter 3 Algebra Difficulties
  44.    wt: 1:   Chapter 22 Contrapositive and Vacuously True Implications
  45.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  46.    wt: 1:   Q How Logic and Proofs extend Show Work Practices
  47.    wt: 1:   I. Logic and language skills
  48.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  49.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  50.    wt: 1:   2 Identifying Size and Position Place and Spatial Sense
  51.    wt: 1:   Helping the Blind in Logic and Mathematics
  52.    wt: 1:   Mathematics Education References
  53.    wt: 1:   Mathematics Education References
  54.    wt: 1:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  55.    wt: 1:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years

Extended Search

144 matches:

  1.    wt: 5:   Math Ed if it must be short make it lean effective
  2.    wt: 5:   links Education Resources online
  3.    wt: 5:   Mathematics Education Professors
  4.    wt: 5:   teacher certification
  5.    wt: 5:   modern education
  6.    wt: 5:   Education Reform Inconsistencies
  7.    wt: 5:   five decades make a difference
  8.    wt: 5:   three difficulties
  9.    wt: 5:   mathematics curriculum shifts
  10.    wt: 5:   geometric implications for algebra
  11.    wt: 5:   Lessening Algebra Difficulties
  12.    wt: 5:   three goals for Mathematics Education
  13.    wt: 5:   02 20 mathematics education references
  14.    wt: 5:   Education in mathematics science and technology
  15.    wt: 5:   Different Kinds of Reasoning in maths
  16.    wt: 5:   Four ways to improve education reform
  17.    wt: 5:   education an empirical art
  18.    wt: 4:   why bother
  19.    wt: 4:   which way to go
  20.    wt: 4:   website reviews
  21.    wt: 4:   three goals to set for students
  22.    wt: 4:   Teach the teachers plus goals
  23.    wt: 4:   permissions for teachers
  24.    wt: 4:   Applied Maths Program14092009 POMME variant
  25.    wt: 4:   activities for students
  26.    wt: 4:   site origins
  27.    wt: 4:   site eurekas
  28.    wt: 4:   About site lesson plans
  29.    wt: 4:   key notes and themes
  30.    wt: 4:   learning takes time
  31.    wt: 4:   grouping students according to ability
  32.    wt: 4:   what should be learnt and When
  33.    wt: 4:   mathematics in context
  34.    wt: 4:   Postscript 2007 01 10
  35.    wt: 4:   Maps Plans Drawings
  36.    wt: 4:   how letters appear
  37.    wt: 4:   Secondary Three Mathematics
  38.    wt: 4:   Secondary Two Mathematics
  39.    wt: 4:   Secondary One Mathematics
  40.    wt: 4:   talk the algebra talk
  41.    wt: 4:   teaching tips
  42.    wt: 4:   What to Tell Students
  43.    wt: 4:   teaching tutoring algebraic reason
  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:   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:   7 logic review and decimals an odd combination
  65.    wt: 2:   K LAMP Musings Science Education
  66.    wt: 2:   C LAMP Introduction Culture in Mathematics Education
  67.    wt: 2:   Skills Chapter 4 Logic
  68.    wt: 2:   11 pure mathematics
  69.    wt: 2:   10 statistics
  70.    wt: 2:   9 combinatorics probability sets
  71.    wt: 2:   8 analytic geometry etc
  72.    wt: 2:   6 polynomials etc
  73.    wt: 2:   5 logarithms and exponentials etc
  74.    wt: 2:   4 algebra
  75.    wt: 2:   3 Euclidean Geometry Leanly
  76.    wt: 2:   2 arithmetic with signed numbers
  77.    wt: 2:   1 arithmetic with unsigned numbers
  78.    wt: 2:   What is POMME
  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:   Ramblings Extrinsic numbers theory
  91.    wt: 1:   Ramblings Introduction Algebra Essay
  92.    wt: 1:   Skills Chapter 3 Algebra
  93.    wt: 1:   Skills Chapter 2 Geometry
  94.    wt: 1:   Skills Chapter 1 Arithmetic
  95.    wt: 1:   Skills Chapter 0 Introduction
  96.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  97.    wt: 1:   11 Help and Defend Your Child or Teens Education
  98.    wt: 1:   4 quadratics difference of two squares
  99.    wt: 1:   2 Square Root Simplification a prequel
  100.    wt: 1:   24 tangent Angle Difference Formula
  101.    wt: 1:   9 Circle Area and Perimeter Formula Backwards Forwards
  102.    wt: 1:   8 Pythagorean Relation Forwards Backwards
  103.    wt: 1:   7 Pythagorean Theorem Chinese Square Proof
  104.    wt: 1:   6 Compound Interest Forward and Backwards
  105.    wt: 1:   5 Triangle Area Formula Backwards
  106.    wt: 1:   4 Rectangle Area and Like Formulas Backwards
  107.    wt: 1:   3 Linear Equation Literal Solution More
  108.    wt: 1:   2 Linear Equation Literal Solution
  109.    wt: 1:   1 Changing Calculations
  110.    wt: 1:   6 Equations and Systems Equivalent or Implied
  111.    wt: 1:   5 Equality in Algebra
  112.    wt: 1:   4 Subtraction and Division Axioms
  113.    wt: 1:   3 Product Axioms Two Forms
  114.    wt: 1:   2 Addition and Multiplication Axioms
  115.    wt: 1:   1 Equivalent Computation Rules
  116.    wt: 1:   13 Naming Identifying Formulas with Words
  117.    wt: 1:   6 Simplification of Fractions with Units
  118.    wt: 1:   11 Simplification an Algebraic View
  119.    wt: 1:   10 Simplification of Fractions and Mixed Numerals
  120.    wt: 1:   17 Identify and Count Factors using Primes
  121.    wt: 1:   6 Sieve of Eratosthenes and Square Rule
  122.    wt: 1:   8 Differentiation of polynomials
  123.    wt: 1:   7 Animated Differentiation Examples
  124.    wt: 1:   2 Algebraic codification
  125.    wt: 1:   G.3 Constant Difference Theorem Proof
  126.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  127.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  128.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  129.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  130.    wt: 1:   Postscript Unifying Theme A Fourth Skill For Algebra
  131.    wt: 1:   Postscript B Mathematics Education References
  132.    wt: 1:   Chapter 3 Algebra Difficulties
  133.    wt: 1:   Chapter 22 Contrapositive and Vacuously True Implications
  134.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  135.    wt: 1:   Q How Logic and Proofs extend Show Work Practices
  136.    wt: 1:   I. Logic and language skills
  137.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  138.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  139.    wt: 1:   2 Identifying Size and Position Place and Spatial Sense
  140.    wt: 1:   Helping the Blind in Logic and Mathematics
  141.    wt: 1:   Mathematics Education References
  142.    wt: 1:   Mathematics Education References
  143.    wt: 1:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  144.    wt: 1:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
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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