Apprentices and Masters in Arts, Trades and Disciplines, a classical view of learning and teaching
December 28th, 2007
In many arts, trades and disciplines, the apprentices learn to follow and
apply rules and patterns, steps and methods, practices given or
demonstrated by masters, and to do so with sufficient care to obtain
repeatable, reproducible and verifiable results. The apprentice in the
first instance follows the customs and conventions of the master.
In this education, rules and patterns, steps and methods or practices may
be learnt with or without explanation of why they work or why are they
are followed. But over time, the apprentice may see or the master
may demonstrate how to combine rules and patterns, steps and methods, or
practices to compound them to form further ones in a repeatable,
reproducible and hence verifiable manner. That process of combining
or compounding lends or creates a hierarchical structure to the learning
and mastery of the rules and patterns, steps and methods, or practices.
The extent to which the apprentice may meet and obtain an
operational command of art, trade or discipline may be subjective - some
apprentices will develop abilities beyond that of their master, while
others will equal or develop lesser skills. Masters and apprentices alone
and in groups may accumulate rules and patterns, steps and methods, or
practices to share and extend in a repeatable, reproducible and therefore
verifiable manner. Moreover some rules and patterns will fall into disuse
or be forgotten while newer ones arise. Each participant in the art,
trade or discipline will see practices come and go, and may in time, see
why.
Intelligence within an art, trade or discipline appears and is used when
or while apprentices and masters are carefully to apply their practices,
carefully, while learning about the benefits, flexibility, limitations
and origins of elementary or compounded (combined) practices. In this,
there may some be approximations or some uncertainty known to the master,
if not the apprentice, through trial and error, and/or stories of what is
feasible or not. The master of an art, trade or discipline in
meeting situations that have been handled before or not, will look for
practices that work, and try to duplicate or refine them, and if need-be
and if-possible, invent new practices to handle new situations.
Operational command of a discipline may be enhanced and advanced by
stories or theories to explain why rules and patterns work. On the
other hand, the latter may also unnecessarily inhibit and limit the
operational command. Whence not all is certain.
Over years and decades, the customs and conventions of an art, trade or
discipline in being refined may become more and more contrived and cease
to be immediately obvious to the apprentice. Whence the apprentice
needs a guide or a master to show what is possible, and self-instruction
is impeded. The operational command of an art, discipline and
trade with a history of custom and convention including a hierarchical
organization in which some skills and concepts depend on earlier ones in
ways that took time and effort to discover and perfect requires guidance
from masters of the art, discipline or trade. The apprentice is
well-advised to seek that guidance and stand on the knowledge and wisdom
of others, including practical and theoretical knowledge of the benefits,
limits and origins of steps and methods, to avoid an ad hoc,
incomplete and most likely slow, construction or reconstruction of the
latter skills and concepts.
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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:
-
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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