Three Remarks
1. Society and Pattern Based Reason
Rules and patterns need to be read and written with precision.
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If you do not read precisely what is meant, how will you
understand?
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If you do not write precisely what you mean, who will
understand you?
Volume 1A, Pattern Based Reason,
read slowly, will test and develop precision reading and writing while
pointing to the benefits, origins and limits of rule and pattern-based methods
in thought and deed. Not all is certain. The question of what rules and patterns
are reliable remains open. But in daily life we do assume or rely upon
many rules and patterns. There is no escape.&
2. Science and Pattern Based Reason
In science and technology, rules and patterns range from being reliable to
speculative. Engineers and scientists need to know the benefits, origins
and limits of their rules and patterns, that is, when they may be applied&
or not.&
Mathematics offers the most certain area of rule-based
thought. Physics, chemistry and biology include rules and patterns that can be
tried and tested in lab work (experiments). Biological descriptions of
anatomy can be verified in the lab via dissection - direct verification. . In
contrast, quantum physic and cosmology offers speculations on the origins and
evolution of the universe at the subatomic and macroscopic level- these
speculations provide& calculations that sometime work regardless of
justification. Finally, evolution theory in biology is based on or the
fits the clues that come from geology, the dating of fossil layers and
fossils, and the similarity of organisms, adult or embryonic, at the
anatomical and microscopic level. If you accept the dating methods or
how they were established, you will come to a conclusion that the earth is old
and that life did not appear quickly.
There was a dream that empirically discovered rules and patterns would
provide answers. But such rules and patterns have their limitations.&&
In society, religion, commerce and science, the follower of rule- and
pattern-based thought and methods needs to the know the origins, benefits and
limitations of those rules and patterns, and so see when to apply them and to
when further thought is required.&
3. Scale Factors in Science and Society - Ecology and Pattern&
Based Reason
Questions of scale appear in society, science and technology. Processes
that appear beneficial and harmless on a small scale may on a larger scale bring
ill-effects. Think of towns on a river. Untreated sewage may leave
river waters drinkable when the towns are small. But the growth of towns and
population may pollute the waters and require remedies. City planners and
designers of industrial processes need to consider the effects of scale.
The unchallenged right to pursue methods or processes that do no harm to
others and yourself, may need to be revisited when a method or process is
practiced on a larger and larger scale, as side effects initially considered
harmless accumulate. Ouch
Rule and pattern based methods with results that appear to be repeatable and
reproducible on a small scale may be rotten on a larger scale due to accumulated
side effects.
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Teachers & Tutors: Site pages offer better or best practices for providing skills -
simpler than expected & comprehensive but for exercises. For your charges, your duty is to study them alone or in
groups and develop skill building exercises & activities to share. Start now. The effort here is the best I can do.
Others are welcome to refine or exceed it. Please do.
Secondary
Mathematics for Ages 11+, A Practical Approach for home-tutoring or -schooling, or for schools & colleges
with local curriculum control. Study how to include site content - its skill development how-TOs and innovations
into present or future lesson plans - some reading required.
Road
Safety Messages and Questions: When and why should you face
traffic when walking along a road or cycle path? Is it a good
idea to hang limbs outside of cars etc? What gives more
protection in a crash: a car, motorbike or bicycle?
See too, the BBC-Belgium story Texting and
Driving - texting & the impossible test - the article links to a gruesome utube video on the subject
The Logic of Injustice:
How Texas sent
an innocent man to his death - The wrong Carlos. Some judgments are irreversible. Procescution: Where and when prosectors play to win rather than for
justice, guilt beyond a reasonable doubt goes unrespected due to prosecutors who putting winning
first, those innocence before the law may be convicted. Some procescutors offices in continuing to accuse after a pardon
due to reasonable doubt or innocent being shown, may sucessfully oppose compensaton for false convictions
by asserting a pardon individual is still under suspicion. Then the pardoned individual or the latter's estate
is not compensation for years or decade
of improper or false imprisonment, or for execution. Site chapters on Logic
and some in Pattern
Based Reason may slowly lead to greater precision in reading, applying and
writing laws.
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:
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How to Ace Calculus: Street Wise Guide - Mostly
Text.
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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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