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The White Rabbit put on his spectacles. "Where
shall I begin, please your Majesty?" he asked. "Begin at the
beginning," the King said gravely, "and go on till you come to
the end: then stop." (Alice's Adventures in Wonderland,
Chapter
12)
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The full programs above for primary and junior high school quantitative
skill development describe the start and a possible middle for
mathematics education. Now the question becomes how to how end
mathematics education. Many stop due to failure and thus a poor
view of mathematics or their own skills in it. Governments may want
to train engineers, scientist and mathematicians and even commerce
students in some or many elements of advanced mathematics. But before any
focus on formal or advanced knowledge of mathematics in school,
mathematics teaching needs to development skills and concepts in
mathematics and logic likely to have take-home value for students, so
that students are prepared to solve routine problems. For that methods
may be learnt and taught without or with full explanation of why they
work. The aim is observable and verifiable skill development so that
students are equipped to face common needs in reading, writing and
arithmetic. In that, the careful evaluation of formulas is
considered to be part of arithmetic.
In mathematics education, the take-home value of skills and concepts
should be explicitly identified - obvious or not; and long-term reasons
and context for skill development should be explicitly
identified as a guide for instruction and studies for the sake of
transparency for better or worse. Mathematics education should stop
(or go into maintenance and refinement mode) when further skill
development is seen to be too hard for a student or for the available
teaching corp. In the latter case, it better to stop instruction
and say the subject cannot be taught in place of misleading
students. Or, in place of misleading students , instructors should
describe what they know and do not know, carefully and precisely, so that
students understand the instruction given is honestly done. While
mathematics education may continue indefinitely in the face of
success, some how we need to find a way to stop mathematics
instruction at a point where students have developed observable and
verifiable abilities.
Schooling may develop skills and concepts with take-home
value. Reading, writing and arithmetic provide examples. That
kind of education is very positive. Schooling in competitive arts
and disciplines may provide students with an chance to succeed, but not
guarantee it. That kind of education is positive for students who want
to compete and are able to do. The third kind of schooling
is not to my liking. It is bureaucratic. It appears when topics are
covered in class without any comprehension of why they covered, except
that a final examination will require them, while long-term reasons for
them are unclear or absent. While it appears certain that primary
and junior high school mathematics should provide skills and concepts
likely to serve common needs of students and their families, sooner or
later. That should include mastery of logic and arithmetic
because one or both are needed to develop or improve work and studies
skills, and because there is need for self-interest, self-defense
included, to understand the words and arithmetic present in agreements
involving work, property and money matters. Beyond that ends and
values for mathematics education needed to be clarified. Site pages
do not that fully.
While many schools give mathematics education, that education becomes
bullshit when and when or where skill mastery becomes a bureaucratic
formality with ends and values unclear to parents, students and teachers.
Learning and teaching mathematics should continue or resume when or
if skill development and maintenance is justified by clear ends and
values. That being said, there is bullshit in education when students in
need of remedial instruction in basic mathematics are placed in courses
covering topics unrelated to their likely academic and work
destinations. Invest instead in a review of primary school and
junior school mathematics with the aim of showing how to develop and
perfect skills and concepts at their level, so that when or if they
become parents, they may set the stage for their children to do well in
mathematics. With that, fewer students may be seen to school by
parents whose last image of mathematics was failure.
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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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