Three Skills For Algebra
The following logic and algebra chapters may make the hard
easier. Chapter 7 will test and enrich arithmetic skills - catch a few errors.
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Foreword
Volume 2, Three Skills for Algebra
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.)
Altogether, the logic chapters provide a unique mathematics-free
introduction to the direct and indirect definition and rule-based
thinking that appeared in Euclid's work a long time ago (2300 years
ago)
Three Skills
For
Algebra
understanding and explaining
reason and math
Volume 2
by
Alan M. Selby
Ph. D.
Printed in Canada
ISBN 0-9697564-2-9
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Three Skills for algebra are as follows.
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We can talk about numbers and quantities. The words or
adjectives used here may be used in mathematics after arithmetic.
There is more to mathematics than just doing arithmetic.
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We can describe calculations that might be done (or
postponed) with words alone or with an (algebraic) shorthand
notation. The description of calculations that might be done is also
part of mathematics after arithmetic. There is more to mathematics
than just doing arithmetic.
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We can change the way a number or quantity is
computed. Some rule-based reason is required here. There
is more to mathematics than just doing arithmetic.
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.
Alan Selby
Montreal, 1995
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
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