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HIP,
HIP, HIP, Hooray
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
liinear2007 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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Logic Objectives
A Skill and Concept Check List
For answers, see Volume 1A, Pattern
Based Reason, and Volume 2, Three
Skills for Algebra.
-
How
to use implication rules, one at a time, and one after another, to
arrive at conclusions, one at a time or one after another. NB. the
route, how it is covered, may be of more interest than the conclusion.
-
How
two-way implication rules say more than one-way implications.
-
How
to read precisely what is written.
-
How the ability to climb a ladder or not is related to mathematical
induction.
-
How
different starting points may make a subject easier or harder to
explore.
-
How
to justify entries in truth tables for one-way implications starting
from the common notions of a rule being obeyed, disobeyed or not disobeyed.
-
How
to use the contrapositive of a one-way implication to arrive at a
conclusion (indirect reason I)
-
How
proof by contradiction may be recast as using the contra-positive of a
one-way implication.
Skill and confidence in logic (rule-based
thought) comes from precisely applying implication rules, one at a time and
one after another, to arrive at conclusions, one at a time and one after
another, with the knowledge that any other thinking starting with the same
circumstances and using same implication rules, may follow your chain of
reasoning with the same result. This makes logic (how to argue you must)
repeatable and reproducible, independent of the thinker or initial discover of
a chain of reason. But an a mistake in one step of a chain of reason makes all
the rest suspect
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Reason -Indirect
Reason More
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