The Motivation Problem:
By the end of primary schools students and their parents may not see
great value in mastering more mathematics. But arithmetic is needed for
buying and selling goods and services (consumer & merchant math).
Formulas are used directly & indirectly in business, science,
engineering & technology. Measurement & Geometry appears in map
and plan reading & making. Arithmetic & further mathematics
demands and practices the ability to follow steps, one at a time, and one
after another, carefully, patiently and precisely. Parents &
teachers have a responsibility to emphasize that ability and its value in
all tasks, at home and at work, where steps will have to be followed with
care.
While I would like to see a leaner math curriculum focused on practical
ends and an efficient preparation for calculus, the mathematical key to
college studies in business, science and engineering, and while the
practical ends need to be identified clearly - a to do for site content -
site content and advice serve the needs of calculus, what it requires
from primary and secondary school mathematics. The question of how to
provide a clearer context and path for primary & secondary school
mathematics from counting to calculus remains open.
Cultures with weights, measure, counting, commerce and
clocks in common use and appreciated provide a firmer base for
primary school mathematics. First Nation & Aboriginal
Societies: Cultures now meeting fast lane, modern, pollution
age civilizations will have to help themselves, no one else will
do that for them, in adopting notation and adopting or coining
words and concepts to preserve, extend and refine existing
elements of mathematics in their societies. For better or worse, do not
ask what is right, old ways may be lost - so record them. Good
luck.
The importance and extent of numerical and quantitative
skills and concepts may depend on society needs or their development.
Today many societies work by the clock instead of the sun or sundial.
So time telling and using for appointments and duration of activities
appears in homes, schools and business. Everything is schedule
according time during and over hours, days, weeks and months. Whence
time telling and using is a quantitative skills that appears in school
and even before, as parents try to schedule the day of their charges
and say how long to wait. The concepts of counting and division,
fair shares and fractions, may appear in home when eating and when
dealing with money matters. Primary school mathematics has to build on
skills and concepts familiar to students from local culture or home
environments. Cultures which depend on numerical and quantitative
skills and concepts will develop words and/or written methods for
communicating those key skills and concepts. Local languages will
reflect key numerical and quantitative skills and concepts. However
some societies and languages are more quantitative and numerical than
others in the home and in the occupations of parents. The city child,
the farmland child and the hunting society child will all see different
ways of measuring and discussing amounts, time and distance. There can
be great variation within a single society between such ways and even
greater variation between societies. If a society does not employ or
did not a skill or concept in the past that society may lack the
words, oral and written, to discuss the skill and concept. Whence some
invention or adoption of terms may be needed.
Further Readings: See the current or forthcoming site discussion
of inductive principles for instruction, of critical paths for
course design, of ends, means and values for mathematics education,
and of theme based instruction. The themes may develop application
areas (time, maps and plans, money matters, game playing, ...
) or technical elements of mathematics in parallel, but as
independently as possible, to minimize the barriers to comprehension in
anyone theme or thread of skill and concept development.
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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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