Education, An Empirical Art
In empirical arts, practices with repeatable and reproducible results
come first, tested via trial and error. Then theories and principles
come later to summarize, to codify, to refine and even enlighten the
practices. While practices or sequences of them in some empirical or
hands-on arts in science, technology and business, assembly lines
included, may comply with principles and standards, even be
connected and organized and designed around said principles and
standards, the forerunner to such organization or optimization
should consists of methods that are tried and tested, methods that work
in a plug and play manner, methods whose benefits, origins and
limitations are described..
Education is an empirical art. We may not read a student's mind, how a
student thinks or links together skills and patterns, yet we can
observe and test student performance, skill by skill, concept by concept,
and encourage, but not guarantee, mastery of standard calculations and
standard arguments or chains of reason in algebra, geometry and beyond.
In some disciplines, not all, there are right and wrong answers due to
methods that lead to repeatable and reproducible, and thus verifiable
results independent of whom-ever applies the method. Learning how to
apply and combine methods carefully to obtain reproducible and thus
verifiable results is an old sign of intelligence in many old arts and
disciplines in business, trades, science, engineering, technology
and bureaucracy. The latter is subject to the limitations of rule and
pattern based thought and practices, and the critical knowledge that not
all is certain in empirical based thought and practice.
Critical thinking in science and technology begins with an awareness that
what we hope for, dream of or construct in our minds remains speculation
or faith IF or WHILE it or its consequence cannot be observe or tested
directly to be corroborated if not confirmed. The foregoing is a rebuttal
to the constructivist theory of learning, the part which opposes testing,
the existence of questions with right or wrong answers, and which says
student knowledge, if individually constructed, should not be
contradicted. Empirically sound education must oppose wishful
thinking. That being said, constructivist methods for engaging,
authentic, genuine material and the development of critical thinking
could be incorporated into education as an empirical art.
More on Testing. Knowledge empirically found or
tested is relative and not absolute. Instruction which relies on
testing skills and concepts can only identify errors in the mastery of
the latter while correct responses only confirm, but do not guarantee
mastery. But the level of student competence in a discipline defined by
skills and concept mastery can be estimated from the degree of
difficulty, the unlikelihood of correct responses if skills and
concepts have not been mastered, and comprehensive of a test or
series of test. Here individualized testing may be informative that
mass testing. Empirical soundness of instruction and testing, the issue
of lessons and associated tests with repeatable and reproducible
results locally and beyond, should not be scrutinized in an absolute
manner. Cognitive theory should look at education as an empirical
art.
While a teacher can not read the mind of a student, a teacher may see and
correct mistakes, minor to major, in the content and style of student
writings and further endeavors or products, so that the student may
learn from his or her mistakes, and possibly learn how to make fewer
mistakes. In the short span of education, several years or more, the
student will meet subjects in which individual construction or
organization of skills and concepts cannot in the first instance replace
the early collective and refined products of many minds.
Instruction is an empirical art with value judgments and decision
dependent on the subject at hand and what students produce -
observable behaviors or products only. Any else is subjective - not
repeatable and reproducible. In particular, the constructivist
approach to instruction, despite fine calls for authentic, realistic and
engaging material and practices in the classroom, calls that should be
heeded and empirically supported as much as possible, in its opposition
to the testing and measurement of skills and performance provide vacuous
standards for instruction and undermines the sequential nature of
learning in which skills and concepts at one level need to be learnt and
verified before the next level begins.
|
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.
|
|