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Volume 2, Three Skills for Algebra
Previous: B How to
Learn
To find the ideas new to you in a book (or a course), you need to
understand each word and each example fully. Each word, example or
sentence not understood, may hide an idea new to you. So look carefully.
Search everywhere and begin at a place suitable for you. New ideas, or
ideas worth repeating, are the rewards for reading.
Try to begin at a place where everything makes sense. After this, if you
meet a hard-to-understand word, phrase or paragraph, do the following:
-
- First, make a note of where it is. A question mark penciled in the
margin is fine, if the book in question is yours. A bookmark or note of
the page number can be used as well - especially if the book is borrowed.
Your notes or marks identify or list the pages to revisit.
- Second, skip the hard or awkward words and read the words that
follow. The ideas which follow may help explain the skipped words and
place them in context. The words that came before might also explain the
omitted material. So instead of skipping the material, consider returning
to a previous part. What is best here depends on the passage being read
and how often awkward passages occur.
Return to awkward words, phrases and sections later. If you do this as
you read and reread, you should see the number of items to revisit get
smaller(decrease).
You may then uncover most and perhaps all the ideas new to you in the book.
Remember that in the search for ideas new to you, your aim in reading
should be to understand the meaning of every word, every sentence and every
example. Details are important. Every meaning not mastered hides an idea
new to you.3
3These
words represent the fear inspiring approach to education.
Your ability to understand ideas or master skills depends on your mood
and perhaps the hour. So skip the hard passages. Relax and take a small
break. Afterwards return to the omitted passages in a different and
fresher mood. A second view or expression of the ideas in question may
unlock their meaning and make them easier to understand. Seeing two
viewpoints, or two presentations of the same material, in different
orders, may help you understand what is meant.
When and where words are still hard to follow, another book or person
gives a second view, easier perhaps to understand. When there is
difficulty with what is written, talk about the words in question with
others. What is hard for you to follow may be easier for another, and
vice-versa. Finally, a page of a novel or a work of fiction may take a
few minutes to read while one textbook page can take several minutes or
even hours to be fully understood. Understanding takes time.
The meaning of a word or phrase may depend on how it is used or who is
speaking. So look for the most appropriate or intended meaning. Several
possible meanings are given in a dictionary because the everyday usage
may differ from place to place and from time to time.
To be precise each word, heard or spoken, should have one and only one
meaning in a particular context. To be precise, a single meaning for the
usage of a word or term is given or described by a sentence or two. The
sentences form a definition and a reference for later use.
In reading textbooks (and regulations), watch for definitions. They may
be hidden, buried in the text, and hard to spot. Alternatively, they can
be stated boldly, apart from other material. All is a matter of style,
the taste of the author and the expected audience.
Definitions select or give a single meaning to words and terms and so
should avoid ambiguity, in the context they are used. Definitions are
written in the statement of laws and regulations, to limit and define the
effects of rules in question. Definitions may be changed to tighten or
loosen the effects of the rules. To some people, that may be important.
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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