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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 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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-/[]\- 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. |
Foreword (Area Introduction)
Logic, that is a mastery of rule- and pattern-based reason is needed in all disciplines. In particular, it may lead to precision reading and writing. If you cannot read precisely, how will you understand and how will you see errors in your own work or that of others. The first chapter on logic or rule-based reason shows the difference between one- and two-ways implication rules. Not seeing this difference is a source of confusion. Seeing the difference is a first step towards the better understanding of the implications, suggestions, rules or information met in daily life, at work and in school or college. The initial chapters on reason talk about chains of reason, about islands and divisions of knowledge and about longer chains of reason. The last chapters on logic connect the ideas of a rule being true or not with the common ideas of a rule being obeyed, disobeyed and/or not disobeyed. (In retrospect, there should also be a discussion of when a rule applies or not. In the latter case, the rule is vacuously true -holds vacuously.)
Three Skills for algebra are as follows.
The first skill, talking about numbers and quantities, use words to describe them, gives a unique comprehension of numbers and quantities apart from but parallel to the the shorthand role of letters and symbols in mathematics. The separation here is needed for a clearer, more precise understanding of the shorthand, symbolic, way of writing and reasoning that we call algebra. Canadian Cataloguing in Publication Data
Selby, Alan M,
Understanding and Explaining reason and math Contents: v. 1. Elements of Reason - v. 2. Three Skills for algebra - v.3. Why Slopes and more math. ISBN 0-9697564-4-5 (set) - ISBN 0-9697564-1-0 (v. 1) - ISBN 0-9697564-2-9 (v. 2) - ISBN 0-9697564-3-7 (v. 3) - 1. Mathematics–Philosophy. 2. Reason. 3. Algebra. 4. Calculus. I. Title. II. Title: Elements of reason. III.Three Skills for algebra. IV. Title: Why Slopes and more math. QA8.4.S44 1995 510’.1 C95-900945-0 Reprinting may lead to new ISBN numbers A Postscript: While we may understand on sight, the meaning of word as a unit, most words can be read aloud. In contrast, while mathematical expression can also be interpreted on sight by people at ease with such expressions, most expressions are hard to read aloud or hard to digest when read aloud (spelled) letter by letter and symbol by symbol. So formulas and expressions are better seen and mastered silently. The first skill for algebra in explicitly recognizing our ability to talk about numbers and quantities apart from arithmetic and algebraic expressions adds a new verbal view of mathematics which compensates and facilitates the silent visually comprehension of most formulas and expression in mathematics. The first skill puts words before symbols. |
Foreword, Chapters and Appendices follow.
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www.whyslopes.com
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