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YOU are better than YOU think. Show
yourself how:
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Logic
chapters 1 to 5 re- appear not in sequence, as is or longer,
in Volume 1A, Pattern Based
Reason, Bon Appetite.
Logic
Mastery
Amazing, Amusing, Amorous, Delicious, Delightful, Edifying,
Strengthening Elixir.
It eases work & learning difficulties Makes the hard easier. Opens eyes.
Leads to greater precision.
in reading and
writing
Logic
mastery makes the hard, easier. Logic
mastery leads to better, stronger and richer comprehension. Logic
mastery improves reading and writing. Logic
mastery ease learning difficulties. Logic
mastery gives a headstart. In sum, logic
mastery will develops critical thinking, improve reading and writing,
and give a firmer base for work and studies at many levels. Good luck.
After logic,
(a) continue reading Three
Skills for Algebra, chapters 8 to 14 and do so alongside site area on solving
liinear Equations ; or (b) see this calculus
starter lesson and Volume 3, Why
Slopes & More Math, chapters 2 to 6;
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Caution: Site advice is approximately
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What may be learnt and when depends on how skills
and concepts are developed. Making the hard easier and clearer will allow
earlier & richer development of skills and concepts.
Try the Twiddla
Whiteboard. In principle, it allows
to people to draw and chat together online on a copy of this webpage or a clean
sheet. The chat may be via text or audio. Visit www.twiddla.com
to set up whiteboards to work with the webpage of your choice.
For online automated help in senior high school maths & calculus,
visit quickmath.com For Automatic
Calculus and Algebra Help with derivatives, integrals, graphs, linear equations,
matrix algebra, visit calc101.com
With overlap, each site quickmath
& calc101offers a different range of
services, some free, some not, all based on webmathematica. Good luck.
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Previous: B How to Learn
To find the ideas new to you in a book (or a course), you need to understand
each word and each example fully. Each word, example or sentence not understood,
may hide an idea new to you. So look carefully. Search everywhere and begin at a
place suitable for you. New ideas, or ideas worth repeating, are the rewards for
reading.
Try to begin at a place where everything makes sense. After this, if you meet
a hard-to-understand word, phrase or paragraph, do the following:
- First, make a note of where it is. A question mark penciled in the margin
is fine, if the book in question is yours. A bookmark or note of the page
number can be used as well - especially if the book is borrowed. Your notes
or marks identify or list the pages to revisit.
- Second, skip the hard or awkward words and read the words that follow. The
ideas which follow may help explain the skipped words and place them in
context. The words that came before might also explain the omitted material.
So instead of skipping the material, consider returning to a previous part.
What is best here depends on the passage being read and how often awkward
passages occur.
Return to awkward words, phrases and sections later. If you do this as you read
and reread, you should see the number of items to revisit get smaller
(decrease). You may then uncover most and perhaps all the ideas new to
you in the book. Remember that in the search for ideas new to you, your aim in
reading should be to understand the meaning of every word, every sentence and
every example. Details are important. Every meaning not mastered hides an idea
new to you.3
3These words
represent the fear inspiring approach to education.
Your ability to understand ideas or master skills depends on your mood and
perhaps the hour. So skip the hard passages. Relax and take a small break.
Afterwards return to the omitted passages in a different and fresher mood. A
second view or expression of the ideas in question may unlock their meaning and
make them easier to understand. Seeing two viewpoints, or two presentations of
the same material, in different orders, may help you understand what is meant.
When and where words are still hard to follow, another book or person gives a
second view, easier perhaps to understand. When there is difficulty with what is
written, talk about the words in question with others. What is hard for you to
follow may be easier for another, and vice-versa. Finally, a page of a novel or
a work of fiction may take a few minutes to read while one textbook page can
take several minutes or even hours to be fully understood. Understanding takes
time.
The meaning of a word or phrase may depend on how it is used or who is
speaking. So look for the most appropriate or intended meaning. Several possible
meanings are given in a dictionary because the everyday usage may differ from
place to place and from time to time.
To be precise each word, heard or spoken, should have one and only one
meaning in a particular context. To be precise, a single meaning for the usage
of a word or term is given or described by a sentence or two. The sentences form
a definition and a reference for later use.
In reading textbooks (and regulations), watch for definitions. They may be
hidden, buried in the text, and hard to spot. Alternatively, they can be stated
boldly, apart from other material. All is a matter of style, the taste of the
author and the expected audience.
Definitions select or give a single meaning to words and terms and so should
avoid ambiguity, in the context they are used. Definitions are written in the
statement of laws and regulations, to limit and define the effects of rules in
question. Definitions may be changed to tighten or loosen the effects of the
rules. To some people, that may be important.
Appendices with (repetitive) advice for Students: [ B How to Learn ] [ C. How to Read ] [ D. What to do in School ] [ PS. Study Tips ] [ PS: Time and Effort ] [ E. How to Study Math and Why ]
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www.whyslopes.com
Volume 2, Three Skills for Algebra -
Preview, starter & further lessons for logic and algebra
to (i) improve work & study skills; (ii) to to ease or avoid
algebra (math) fears & difficulties; and (iii) to fill gaps in the
exposition of mathematics.
Foreword, Chapters and Appendices follow.
Foreword
1. Introduction
2. Implication Rules
3. Chains of Reason
4. Romeo and Juliet
4. Induction Mathematical
5 Knowledge Islands
6 Old Language
7 Arith Skill Check
7. The Next Chapters
8 The Three Skills
8 VNR-Concise-Encyclopedia
PS. What is a Variable
9. Algebra Talk
10 Two More Skills
11 Why Shorthand
12 Shorthand Usage
13 What's Next
14 Compound Interest
15 Linear Equations
PS I. Distributive Law
PS II. Polynomials
16 Painless Proofs
17 Pythagoras
18 Rules of Algebra
19 Functions & Sets
20 Degrees & Radians
21 What's Next
22. Arith & Geometric Sums
23 Summation Notation
24 Your Money
25 Induction & Recursion
26 What's Next
27 Pronouns in Logic
28 Occurrence Tables
29 Contrapositive
30 Truth Tables
31 Indirect Reason
A. Advice For Learning
Words Before Symbols:
What is a Variable?
Introduction
Variation between Examples
Variation of Letters
A letter denotes a variable
Cases of Double Variation
Three Notions of a Variable
Constants, Parameters
& Variables
Talking about numbers
Dependent
or Independent
Variable, a Matter of Choice
Complex number: starter lesson
Solving Linear Equations:
A. Letters and Lengths
B. & C. Solving Linear Eq'ns
with stick diagrams.
(i) x + 20 = 29
(ii) 2x + 5 = 20
(iii) 3x + 10 = 32
(iv) 5a + 16 = 3a+ 24
(v) (½)x + 8 = 24½
(vI) (¾)a + 16 = (¼)a+ 24
(vii) (¾)q + 17 = 32
(viii) 13 =[2/3]x +7 twice
(x) Animated Examples
(i) Integral Coefficients (A)
(ii) Integral Coefficients (B)
(iii) Fractional Coefficients
(iv) With
Parameters
Problem Solving with Linear
Equations in one or many
unknowns, and in essentially
one unknown - Symbols before
words.
C. Solving Linear Eq'ns
without
Stick Diagrams
D.
Problems in
essentially one unknown
E: 2D Systems - Sub Methods.
F. Larger Systems
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