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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
correct, for some circumstances, not all. That leaves room for thought |
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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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PS: How To Improve Learning
Previous: How to Study Math and Why
-
Adopt some goals or aims for your learning. Seek and find a
reason, approximately correct, for studying a subject. Reasons may be
as crude as improving marks, or more fundamental. Ask your instructors
for reason approximately correct for studying a subject, or topics in
it. That may provide a context and motivation for learning. That being
said, a teacher saying a topic is required because of the final
examinations or course requirement could be giving a full and honest answer.
But in general we hope you and your teachers can find reasons and a context
approximately correct for most topics in a course.
-
Mathematics mastery is best checked and proven on paper. As
in English, apart from a few mistakes, if we do not write exactly what
we mean, we do not understand what we are writing and most likely what we
are reading. Precision reading and writing, are musts for better study
skills in all subjects, mathematics included.
-
If one explanation here or elsewhere is not to your liking,
hard or nonsensical, try again and try another here or elsewhere, alone or
with help
Variety in the presentation and development of ideas means if one
explanation here or elsewhere is not to your liking, another might be.
Different people have different likes and dislikes. Another
explanation, written or in person, could be clearer. Different
authors and different teachers all provide different ways to learn or
introduce ideas and skills. So again, if one explanation here or
elsewhere is not to your liking, try another. May will,
stubbornness and patience be with you.
- Know-how without know-why is incomplete in
mathematics. Mastery of fraction sense and operations, mastery of logic,
mastery of algebra and mastery of geometry may help at home and work in
money problems and in construction or maintenance problems. The know-why
part of mathematics provides stories or theories to follow, one
at a time and one after another, some independently, to provide a
greater context for know-how not only in mathematics but also in other
quantitative disciplines.
-
For skill and knowledge perfection, ask your teachers
or tutors to encourage you, say what you are doing right, but also ask
that all errors in your written work, concept and notation, be caught
and corrected. Errors need to be corrected. Otherwise, they
return to slow or stop instruction.
-
In each subject, you may further focus your studies
with the question: how can I transfer or teach to others the skills and
concepts I am learning? A subject is not fully understood until you can
explain it clearly and directly.
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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