Written Work and Observable Skill Development
In mathematics and science, with methods can be followed, done and
recorded step by step on paper, the follower or doer and others may see
and check what is done as it is done or later. The ability to do and
record steps so that the doer or another may see makes skill and know-how
development observable and verifiable.
Watch for this ideal situation in mathematics and science
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Courses employ and emphasize skill development, usually on paper, in
an observable and mechanical manner that can be easily seen, checked
and corrected by the doer - the student; by others - say fellow
students; or by teachers, parents or tutors. In this development,
observable skills (movements on paper) should be taught in small
steps, not too large. Moreover, when difficulties are seen, students
alone or in groups may be taken back by a parent, tutor or teacher
before the likely source to rebuild skills and confidence, and to
address the likely source of the difficulty.
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Final examinations and in-class tests are based on yours skills and
your skills alone. But in exercises and assignments, there is no harm
in having another correct your work to identify flaws or shorter
routes for solutions and answers, provided that you rewrite your work
by yourself after the correction. Having some one identify errors in
your work may be regarded as part of your skill mastery process. If
you cannot solve a problem or question by yourself, ask some one else
to show you the key to the answer, or even to show you how to answer
with the same or different problem. In that and in the earlier
corrections, you should not become dependent on others to do the work
for you. If you do become dependent on others to provide answers or
solutions, the questions on final examinations should keep you
honest. While marks may be given for homework, those marks should
given for motivation, and home work conditions should encourage skill
development, not prevent or slow it. The main point of submitted
homework is or should be the submission of written work for step by
step skill checking and correcton.
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In each course, there is a list of observable skills to master, or at
least a clear list of problems to solve in an show-work manner, so
that someone, possibly yourself, may follow and check the work, step
by step. Ideally, a teacher or someone else reviews your written work
for errors in format. Skill needs to be practiced, seen and corrected
to be credible, reliable and well-done.
If there is a list of observable skills, you or your teacher, may chart
or track your level of mastery in each skill. Then when you given
optional exercises of the type whose solution is well-remembered and
well-mastered, you may decide to do other exercises or study another
subject, your time and energy being limited. One day perhaps teachers
will chart or track what skills you have likely mastered and only give
your exercises for skills that you have yet to master. That kind of
instruction may require more tracking but less repetitive correction for
instructors. That situation may occur in self-paced, modular type,
instruction at home or in school. Good luck.
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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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