Volume 1A Pattern Based Reason
Foreword
Three Remarks
Chapter 1 Introduction
Chapter 2 Skill Development
Chapter 3 What is in chapters 4 to 8
Chapter 4 Implication Rules - Forwards and Backwards
Chapter 5 Deception
Chapter 6 Chains of Reason
Chapter 7 Longer Chains of Reason
Chapter 8 Change of Language
Chapter 9 What-is-in-Chapters-10-to-18
Chapter 10 Responsibility
Chapter 11 Accidental Patterns
Chapter 12 Islands-and-Divisions-of-Knowledge
Chapter 13 Geometric-Thinking-Euclidean-Model-For-Reason
Chapter 14 Deductive-and-Empirical-Views-of-Mathematics
Chapter 15 Objective-Processes
Chapter 16 Origins-and-Limitations-of-Rules-and-Patterns
Chapter 17 Objective-Ways Trial and Error Discovery
Chapter 18 Sense-and-Knowledge
Chapter 19 What-is-in-chapters-20-to-24
Chapter 20 Shorthand-Symbols-as-Pronouns
Chapter 21 Occurrence-Tables
Chapter 22 Contrapositive and Vacuously True Implications
Chapter 23 Truth Tables
Chapter 24 Direct-and-Indirect-Reason
Postscript A Story-Telling
Postscript B More-on-Story-Telling-and-Reason
Postscript C Consistency-as-a-Tool-for-Reason
Postscript D Reflections-on-Law-of-the-Excluded-Middle
Foreword
This work Pattern Based Reason surveys rule and pattern based
thought in daily life, society, science and technology. There are simple
ideas which should be more widely known.
The first chapters below show how reliable implication rules can be
employed one at a time or one after another to arrive at conclusions.
These chapters are very simple. Mastery of their ideas will serve well
all students of logic.
Pattern
Based
Reason
understanding and explaining
reason and math
Volume 1A
by
Alan M. Selby
Ph. D.
Printed in Canada
ISBN 0-9697564-5-3
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The middle chapters describe or survey the origins, discovery and
applications of rules and patterns. Not all is certain. Further data to
use with them may be missing or not available. In the middle chapters,
the problem of identifying reliable knowledge is described, but not
solved, except for an explanation of the empirical method of coping. The
identification problem touches many subjects. Students of critical
thinking, persuasion, philosophy, mathematics, science and technology
should find its discussion helpful.
The last chapters in this book show how the common concepts of a rule
being obeyed, disobeyed or not disobeyed may justify or explain or
provide a context for the entries in truth tables for material
implication. Some symbols appear in the discussion of logic. All may be
regarded as substitutes for the pronoun IT. The last chapter describes
indirect methods for using implication rules to arrive at conclusions - a
subject of interest to mathematics students and perhaps readers of
detective mysteries.
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
Note: Volume 1 consists of Volumes 1A and 1B bound together
with a foreword to introduce both and volumes 2 and 3.
Selby A, Volume 1A, Pattern Based Reason, 1996.
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For home-tutoring or -schooling, or for schools or colleges
with course content control: Secondary
Mathematics for Ages 11+, A Practical Approach.
May 2012, Composition Starting:
Pre-School and Primary Mathematics - Quantitative Skills, An
Intellectual View, Feedback Welcome:
The 8 Most Popular Site Inlinks
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
Geometry
- maps plans trigonometry vectors
More
Algebra
70
Calculus Starter Lessons
Calculus Lessons Elsewhere:
-
How to Ace Calculus: Street Wise Guide - Mostly
Text.
-
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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