Appendix A. Story Telling
Key Talent
The ability to tell, invent and follow stories is transformed in
education and research into the ability to tell, invent and follow
explanations and instructions as a means to enrich, advance and provide a
context for observable skill development, and a means to share what is
the mind. In essence telling stories, one step at a time, and one step
after another (in order perhaps) is the key to knowledge of folklore,
culture and technical knowledge. We may judge stories as fictional or
not, to greater or lessor extent. We judge the consistency of stories in
accordance with our knowledge or view of what is possible or allowable.
So a good alibi allows a detective to ease or remove suspicions about who
committed a action. In writing or inventing a story, an author will
attempt to avoid immediate or implied inconsistencies. What Louis
Carroll's Alice sees in Wonderland or Through the Looking Glass provides
an story to follow, one that is not realistic. Shakespeare and Moliere
through their writing create pieces of fiction for us to follow on paper
or even to act out. We may judge the characters and plots in stories and
plays by our own ideas on what is not possible. But in telling stories,
the tellers provide us with a imaginary world to follow and judge.
Likewise in telling theories or providing instructions for the operation
of a machine or the creation of a product, researchers and teachers are
telling us stories, ones that may correspond to and be useful in
practice. The composers of a story may adhere to rules and criteria for
consistency, rules and criteria that say what is or should be possible or
not, in order to decide or conclude what may be in the story or not.
Chains of reason may be employed to find what a story implies or
requires. The composer may include or not, those implications or
requirements in the telling and extension of a story or theory.
The developers of empirical theories in science and technology tell many
small technical stories which individually work and are practice in
special cases, but not necessarily in all cases. High school and college
chemistry for example include alternative theories for the identification
of acids, salts and bases. The oxymoron acid-salt reflects the idea that
what is an salt in one theory is an acid according to another (a litmus
paper test say).
reality, imagination and fiction - exploring ideas, continued
The author of a story in a book or a play creates an imaginary world for
us to visit in our minds. The story may or not be consistent with our
knowledge of real life. More and less can be suggested in a story than
occurs in real-life. Stories can be fictional, half-fictional,
approximately true to life or true.
Stories may explain or describe how things came to be. Stories may
provide lessons a for reader directly or through the words and
interpretations of another. Stories may give us ideas of what to do or
not. Stories have plots and chains of events or reasons to follow, real
or not. Stories presented on stage as plays may include not only words
but also actors and props to make the plot or reenactment easier to
follow. Actors have scripts to follow. Actors are defined by their names,
costumes and actions.
Most of us, many of us, have the ability to follow a story, its sequence
of scenes with words and events, and to recognize what is real or
pretend. We can learn stories, invent them and tell them to others via
spoken and written words. Stories can be told and retold in ways that are
almost repeatable and reproducible. Our knowledge of a culture may come
from its stories and myths.
In cooking and construction, plans and recipes give or suggest sequences
of steps or actions to take to arrive at results. The steps and the
results should be repeatable and reproducible. Technical know-how is
based on rules and patterns to follow plus some judgment as to when they
can be applied. Trying to apply rules and patterns when items they
require are missing usually leads to bad results.
In mathematics, science and technology, as in daily life, there are
stories to follow. These stories, normally called theories, describe a
situation (say what is what is assumed) and describe as a well assume
methods for arriving at results or conclusions in a step by step way. The
authors of these stories or theories would like their consistency with
reality. A theory is inconsistent with reality if it says two exclusive
events occur at the same time or if predictions based on it fail.
Unfortunately, the author of theory to say what should happen may capture
a pattern in theory that works in some circumstances, but not all. So a
theory may be applicable and sufficiently consistent with reality to be
useful in some circumstances - those it reflects - while failing in
others.
Knowledge in mathematics and science and technology is based on theory
and practice. A method or procedure describe in a lab or controlled
circumstances how following certain steps will give a result. Those steps
and the results, done carefully enough, appear to give repeatable and
reproducible independent of the doer. Methods that work in practice may
be described and accumulated, and used one at a time and one after
another to follow steps and arrive at results, one at a time and one
after another. A skilled practitioner may recognize when one method can
replace another because it gives the same result or a more convenient
result.
Geometry was codified in the works of Euclid, about 300 B. C. The
codification consisted of assumptions or definitions about points,
straight lines, circles, triangles and the geometric figures composed
from the latter. The resulting theory or theories was presented not on
stage, but on paper (a prop) with the aid of rulers and compass (more
props) to provide construction methods and to suggest and describe
results and conclusions one at a time and one after another. Students and
teachers and philosophers could follow explanations one at a time and one
after another in way that follow some or all of the strands of thought in
Euclid's work. The codification provides a mechanical knowledge of
geometry because each of us in following the steps should verify that the
steps are valid, that the implication rules used in each step are justly
applied.
The foregoing gives rule- and pattern-based chain of reasons independent
of the followers and authors. All that provides a model for making and
arriving at conclusions with rules and patterns not only in geometry, but
also in other disciplines where rules and patterns are valued as guides.
But this model for reason has its limitations.
Rules and patterns describing what we have observed, drawn from
experience, are not absolute. We do not know if they are fully reliable,
or we may not precisely when they apply, if at all. When rules and
patterns are not reliable, a risk appears. What they suggest, one at a
time and one after another, may not be consistent with reality. None the
less, recognizing rules and patterns in a subject provides a means for
accumulating know-how for arriving at results, and a limited know-why.
The latter is given by the chain of reason or suggestion with rules and
patterns, reliable or not, that led to a result. (Implication rules and
suggestions in a theory may themselves rely on the need for a theory to
be consistent. See above).
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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:
-
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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