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Volume 2, Three Skills for Algebra
Here are five more suggestions for learning well.
A Look for New Ideas
First, learning will be the most rapid when you look for ideas new to
you. They make your studying a subject for the first or last time,
worthwhile. Meeting familiar ideas may refresh your memory but you only
learn from new ideas. The familiar ones will take care of themselves.
When you can find no more ideas new to you, your study or review of a
subject is done - or you are tired and you need a rest before starting
again.
B Look for Names
Second, look for the names of ideas, places and people. Coin or invent
names if need be. An idea, object or person once named or identified is
yours to speak or write about. Names may banish the vague or unclear use
of the words it and they from your speech and
writings.1
1In old and possibly some present-day
religions, people thought that another's knowledge of their names made
them vulnerable to spells and curses. Today knowledge of your name,
address or various identification numbers make you more vulnerable to a
loss of privacy, junk mail, and legal proceedings - a kind of spell different from that previously envisioned or
anticipated yesterday.
C Proceed (Go) Step by Step
Third, find a step by step explanation or description of the skills you
need. Then begin your study of a subject at a step where everything is
understood. Starting elsewhere leads to confusion. It may cause you to
turn away from the subject. In particular, if you try to master a subject
too quickly, you will find some skills are too hard. Then you will need
to start again with the simpler ones before them. You may further need to
ask someone about which skills you will need to know to master the ones
hard for you. Lessons taught by others, or self-taught, must build new
skills on those previously mastered.
D Be Persistent
(Be Stubborn)
Fourth, understanding whatever you have to do or read takes time. If you
have ever done a crossword or jigsaw puzzle, then you know you can work
on one part of the puzzle and then another. Each part you do, manage to
solve or understand, may help with the rest of the puzzle. The same is
true of a book or class notes. Read them in order if you can. But do not
be afraid to look ahead, or behind, for clues to what the current passage
or word means. So read with patience. Be prepared to puzzle or think.
Further, do not hesitate to get a second opinion or view from another
person or book. The words of others may provide a path to follow but the
understanding of any subject is an individual effort. No one else can do
this for you. So be persistent and look for the ideas new to you.
E Ask Why
Fifth, ask your teachers why each course or lesson is given, or what they
hope to show you. Reasons for learning this or that can be requested.
Sometimes we teachers cannot give a full answer - our
employees (School boards) may have told us to teach you a topic based
on great or little wisdom. In education, too many cooks spoil the
broth.
Appendices with (repetitive) advice for Students: [ B How to Learn ]
[ C. How to Read ]
[ D. What to do in School ]
[ PS. Study Tips ]
[ PS: Time and Effort ]
[ E. How to Study Math and Why ]
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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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