Primary Skill Development
The question of what abilities to develop, why and how why is of interest
to students, parents and teachers. Each year of primary, secondary and
college level instruction covers more and more logic, language and
mathematics skills and practices. Later abilities depend on earlier ones.
Primary school lessons in reading, writing and arithmetic usually give
and leave a good impression because they provide know-how with value
clear to parents, teachers and students. The first least controversial
aim of primary level instruction is provide mastery of common skills and
know-how. The second more controversial aim is to introduce parental or
community concepts of citizenship - there views may widely differ.
The What and the Why
At home, before and in primary level lessons one may or should learn
about counting, figuring and measuring in several application areas.
- Time, date and calendar matters for daily, family and community
events
- Counting and Handling money for saving, buying and selling
- Using maps and plans for seeing where you and for measuring or
calculating distances and areas indirectly
- Chance or likelihood or odds for deciding what risks to take or avoid
in games and daily life
- Units of time, distance, mass, weight alone and multiplied by numbers
for describing and figuring.
- Solving logic puzzles for sharpening or developing thinking skills
through playful to serious exercises and activities. Learning can be fun
and serious. Cooking, building, making, buying and selling provides
chances to develop and strengthen counting, figuring and measuring
abilities. In cooking, building and figuring, the domino effect of errors
may be learnt. Avoiding that domino effect becomes an end, value and tool
for skill development. Experience counts. The above application areas
should be included in primary instruction because of their currrent or
possible future value for life at home, at work and in the street. Most
of who can, may remember strongly and then more dimly primary school days
as time to play and time to learn skills and things needed for adulthood.
In the foregoing, learning to measure and draw with rulers,
tape-measures, protractors and compasses directly or with the aid of
maps, plans and diagrams drawn to scale provides an introduction to
geometry. In that students may be shown how to draw triangles,
rectangles and regular polygons and plans using given data, and then be
asked to find missing angles, lengths and areas. Maps and plans drawn
to scale may be used to not only to find missing measures, but also to
plan and plot routes and detemine location. All that may give a playful
to practical geometric command of measurement and estimation with maps
and plans drawn to scale before any mention of trigonometry.
Quantitative skills may be further extended through activites and
instruments to measure and estimate mass, wieght and volume in a
repeatable and reproducible manner. In that basic principles may be
introduce and illustated with devices - balances included - whose
mechanism are visible and not hidden before the introduction of
electronic scales or mechanical boxes whose inner operations is hidden.
Calculation methods for volumes, areas and lengths - perimeters
included - may be introduced as alternatives to counting or measuring
them. Methods to determine measures directly or not should be seen as
consistent alternatives, subject to measurement or figuring
errors/approximations
The How
Children in the presence of adult or family members who value their skill
development will have teachers at home before school and teachers at home
and in school who deliberately help or encourage children master common
language, logic and mathematics skills and practices. Those children will
have a head-start. On the other hand, apart from questions of ability,
children who do not have adult or family members near-be to help and
encourage learning will have a greater dependence on their primary school
teachers for skill development. Those children may need greater
attention.
For the application areas above, the mastery of methods - that is,
learning to do for the sake of skill and practice mastery has more
current or future value for life at home, at work and in the street than
fully understanding why methods work. In that, some students require less
explanation or less comprehension of why methods work because for them
learning to do quickly is their objective. In contrast, some students
immediately or eventually need and ask for greater explanation. In the
case of counting and figuring with decimals, place value comprehension is
a must - cannot be avoided. But in figuring, the addition, subtraction,
multiplication and division of decimals may be learnt in all or part by
rote in accordance with the abilities and wants of learners and teachers.
In that, some students will find it easier to learn to do without
explanation while other students find it it easier to do with some
explanation.
In my earlier thoughts about developing arithmetic skills, I was
advocate of making and even giving a full-explanation of how and why
arithmetic methods work due to my then aversion to rote learning.
However, the full explanation would likely overwhelm students, most
parents and teachers too. So I now I believe full explanations should
be available but not imposed. In daily life, we eat, sleep and work
with the help of skills or abilities in a practice first, theory
unavailable or optional manner. That being said, in mathematics unlike
many other disciplines includes a nearly complete explanations for
immediate or later comprehension in accordance with the individual
wants and abilities. Mathematics skill development may be put practice
first and offer more and more explanation as required by the wants of
learners or their hoped for work and academic destinations.
Primary school skills in counting, figuring and measuring may be
introduced through activities and exercises. First in decimal
arithmetic, and then in the evaluation of arithmetic expressions and
simple formulas, students should be shown how to do and record work or
reasoning in steps that can be seen as done or later for the sake of
confirmation or correction. With steps written and recorded, the domino
effects of care and of error will be observable.
In the initial introduction and development of mathematics, learning to
use methods is far important than learning in full why methods work.
Children may expect their formal and informal instructors to give them
reliable methods. In that, avoidance of the domino effects of errors may
be emphasized as a must for repeatablea and reproducible results not only
in arithmetic, but also in all arts and disciplines where skills and
practices are multi-step. Avoidance of this domino effect of errors, or
being careful to do each step of a skill or practice provides an end,
value and tool for skill mastery in general. Figuring well with its
avoidance of this domino effect of errors is a sign of wit or
intelligence of the practical kind. Adults, teachers and trainers
included, need to emphasize for skill development at home, in school and
work.
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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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