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.

Location: Site Entrance << Work and Study Tips


Work and Study Tips

     How to Build Skills and Confidence
     A. Skill has to be seen to believed
     B. Domino effect of errors
     C. Domino effect of being careful
     D. Check work - a must with a caution
     E. When and how to correct errors
     F. The student teacher tutor feedback loop
     G. Written work formats for developing and showing skill
     H Jigsaw puzzles and problem solving
     H more - Routine to non-routine problem solving
     I. Logic and language skills
     J. More on written work and showing skill
     N Improving Marks on Tests and Finals
     L Skills with take home value
     M Words to extend arithmetic
     N Mathematics - Prepare for College Studies
     O On Learning Mathematics and Science
     P Exact Arithmetic With Whole Numbers and Fractions
     Q How Logic and Proofs extend Show Work Practices
     R Why Learn Mathematics Skills
     S Adding words to algebra
     V Reasons and Motivations for Logic and Mathematics
     1 Links to Online Resources Elsewhere Take 1

The tips above reflect ends and values for work and studies. Site material covers elements of logic and of high school and college mathematics from arithmetic to advance calculus. Site material may help in learning, review or revision just before tests or final examinations - the time when most are the most keen to learn. If you cannot find a topic you need, try a site keyword search.

Food for thought

In many high schools, the question of why this or that is in a mathematics course has the answer: Preparation for final examinations. This answer turns students and teachers alike into bureaucrats: Ours is but to learn or teach without understanding why.

"Would you tell me, please, which way I ought to go from here?"
"That depends a good deal on where you want to get to," said the Cat.
"I don't much care where--" said Alice.
"Then it doesn't matter which way you go," said the Cat.
"--so long as I get SOMEWHERE," Alice added as an explanation.
"Oh, you're sure to do that," said the Cat, "if you only walk long enough."
(Alice's Adventures in Wonderland, Chapter 6

If you do not care where you are going, if you do not have ends and values, then any path will do. In instruction, I have had to teach mathematical topics because questions on them might appear on forthcoming final examinations. I would have preferred to teach skills and topics to fill gaps in their know-how of mathematics with take-home value.

Mathematics may be taught to give skills and concepts useful for life in the street. For that, see existing cnline chapters on logic and future site pages on application areas: time and date matters, on money matters, on counting, measuring and figuring, on on maps and plans and on decision-making (chance) when not all is certain. Study of the foregoing areas will take time and effort.

In primary school, you may have met mathematics with take-home value for daily and adult life. And in many primary schools, there is no guarantee that basic reading, writing and figuring skills are taught. I have met primary school graduates who cannot figure with fractions because they were not taught how, and because their teachers and parents did not know better. Central planning and central control can lead to substandard practices in education. Central planning and central control needs to do better. Otherwise, home schooling becomes a better and stronger choice. If you become a parent, watch for substandard practices or substandard skill development and try to remedy or avoid that in the education of your child - good luck.

But in secondary school and the first years of college, mathematics courses mostly cover skills and concepts required for college programs in business, commerce, banking, insurance, science, engineering and technology. Each requires mathematics, some more than others. High school and college mathematics topics apart from the in above application areas has long-term value for the practice and theory in college programs, or for student or employer selection by college programs. With regrets, most mathematics coursed after primary school does not have take-home value. They are college oriented with courses that are not being reserved for weaker students not heading for college.

Site content may help secondary and college course designers recognize and include (i) skill which serves actual or potential common needs; and (ii) skills and concepts which are needed by college programs. Then the full coverage of (i) by age 14 may provide motivation, context and even an end for mathematics instruction while preparing for and overlapping (ii). Food for thought: all students should meet (i) with observable and verifiable skill mastery vital apart from full comprehension, because of actual or likely take-home value. After that, the college oriented mathematics in (ii) is optional.

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Road Safety Messages. First Question: When and why should you face traffic?

More Site Folders and Pages

Parents: Help your child or teen learn:

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.

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


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Location: Site Entrance << Work and Study Tips


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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