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LAMP Prequel - Previous Instruction
In the first years of education, primary school and even before,
children in well-protected environments may be enthused, initial
reluctant aside, about going to school to learn and growing up to
follow in the footsteps of their parents or guardians. For
students with sight, learning to read, write and do arithmetic is
based on our ability to recognize shapes as different or similar,
and to draw or write those shapes on paper. Elementary or
primary education may or should introduce students to decimal
notation; to associated place-value methods for the arithmetic
operations of addition, subtraction, multiplication and short &
long division; to the meaning of fractions and arithmetic
operations with them; to measures and calculations - more addition,
subtraction, multiplication and division - with whole and
fractional units of time, length, area, volume, money and mass (or
weight) present in our cultures. As time permits, parents and
teachers of children may expose students to planning and making
meals; to following daily, weekly and longer schedules; to buying
and selling goods and services in many situations - travel, work
and restaurants.
Applications: Book that teaches another language, say
French, may describe people or a family in situations at home, at
work, in town, on the land, at seas or in air, course
designs and materials and in that description introduce to
associated vocabulary. Likewise, course materials in
mathematics may describe the calculation present in common place
situations and activities with simplest ones first. Examples
in primary and secondary school years could place students in the
mathematical shoes of buyers and sellers, carpenters, painters,
construction workers, health workers, taxpayers, wage earners,
business operators, investors, bankers, planners, navigators,
surveyors, and so on. The description of mathematical
reasoning would provide a context and motivation for
mathematics learning and teaching whose extent depends on local
culture and conditions. The mathematics of activities that
are not in local favour - a favor that depends on time, place and
culture - should be presented so that students can recognize
what to avoid.
Operation viewpoint of arithmetic
operations: Whole numbers and fractions may describe
how many units or objects are present. They may also describe
position in terms of placement (1st, 2nd, 3rd, etc) or in terms
of coordinates ( 10, 0, -10.5). Whole numbers and fractions
may be classified as numerical adjectives. Then physical
addition, subtraction, multiplication and division may be
described in terms of and imply corresponding operations on whole
numbers and fractions. That implies our numerical
adjectives are closed under these numerical operations when the
corresponding physical operations are feasible. Before the
introduction of signs, a larger quantities cannot be subtracted
from smaller ones. Division by a whole number (answer to
the question how many whole times one count goes into another and
what is the remainder, if any) may lead to a quotient and
remainder calculations. But also, division by a whole
number or fraction (how many times a shorter length goes into
another length) may also be described by a whole number
plus a fraction.
Signed Numbers: That being said, if signs are
introduced as prefixes on whole numbers and fractions, and these
signed numbers are used as coordinates along a line and to
describe displacement, arithmetic operations on signed numbers
can be implied and thus defined by physical operation on
displacements. Displacements to the left or right are easily
added in a head to tail many. Unsigned or positive multiples of a
displacement are easily defined through repeated addition, While
negative multiples are defined by a change of direction.
The latter and the adjectival description of displacements as
signed multiplies of a unit displacement (vector) implies the
definition of products of signed numbers. Whence signed numbers
are adjectives on which arithmetic operations are implied by
their roles as adjectives.
Put Performance First. That is to say or suggest, skills and
confidence in arithmetic may follow in the first instance from a
rote or near rote mastery of calculation methods, so that results
are obtained in a repeatable, reproducible and hence verifiable
manner. While thought based development and comprehension of
operations on whole numbers and fractions, including place value
methods for operations on decimals, is preferable. It may aid
mastery of arithmetic operations and should be emphasized for that,
but any further comprehension of why operations work need not be
required. In the first instance, skill and confidence may be
produced by emphasizing drill and practices, so that students
figuring skills becomes automatic. However, for students who
refuse to apply methods before understanding the origins or
justifications, the course materials should provide explanations in
an appendix for the sake of completeness.
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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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